343

WEDNESDAY MORNING SESSION

November 6 , 1963

The sess ion convened at n ine-f ive o*clock, Doctor

James V. Nee1 presiding.

NEEL: We seem t o have a quorum, so we will begin.

T h i s morning, we come t o a discussion of the problems tha t

a r i s e from in t e rp re t ing da t a of the type we have been consider-

ing in the pas t two days, and I th ink it is fair to say tha t

these problems of interpretati .cn have provoked about as much

l i v e l y comment as any other issue in contemporary genetics.

' The Chairman would l i k e t o nake two reques ts w i t h r e s p e c t t o .

t oday ' s d i scuss ion : F i r s t l y , i n a good many of the exchanges,

i t seems tha t problems of d e f i n i t i o n have loomed r a t h e r l a r g e .

It would be a valuable contr ibut ion, I think, if we could dis-

t inguish between problems of semantics and problems of sub-

stance, and, i n t h i s vein, please, would everyone who has

something to say define h i s terms before he begins t o use them?

The second request is much simpler. Please don't

a11 t a lk a t once .

The discussion will be opened by. Jim Crow.

CROW: T h i s i s going t o be gross ly overs impl i f ied , ~

a s several people will probably-point out eventual ly , but I

want to sharpen t h e ques t ion a s f a r a s possible , by so doing,

and c l a s s i f y gene loc i as be ing of two kinds. I will c a l l

them M, if they are what I call mutation, which means t h a t

the mutant a l l e l e s have this frequency determined by-well, 1

don't think I need t o w r i t e t h i s out--some r e l a t i o n s h i p be-

tween the muta t ion ra te and the se lec t ive ac t ion on these

a l l e l e s ; and, secondly, segregational, by which I mean tha t t b e

a l l e l e s a t t h i s l o c u s have their frequency determined by some

kind of balance among se l ec t ive fo rces .

1 would l ike to exc lude in te rdemlc se lec t ion and ,

miotic dr ive from selection because, perhaps, they can be

brought i n l a t e r , but I'm i n t e r e s t e d h e r e i n any kind of f r e -

quency other than mutat ion that is maintaining the frequency

of these a l le les . The most obvious, of course, is s e l e c t i o n

f o r a heterozygote, but t h i s i s 'by no means t h e only possi-

b i l i t y .

I will irse the word, t f segrega t iona l , t l in p refer -

snce t o D r . DoSzhansky*s ttbalance,'t for the same reason I ,

always have, but I would l i k e t o g i v e i t once; that is , these

a r e a l l b a l a n c e d and i n one case you're balancing selection

against nutat ion, and i n t h i s case you're balancing selection

against se lect ion and, to ne, segregat ion seem to say it a

l i t t l e b e t t e r .

DOBZHANSKY: May i en te r a comment a t t h i s point?

I prefer ttbalanced,tf because balancing describes what a c t u a l l y

happens in the populat ion. There are different kinds of

balance; heterotic balance, where t h e thing is maintained by

an advantage of heterozygotes, and, a s Professor Crow says,

t he re a r e many other kinds of balances, due t o t h e v a r i e t y of

environments and a l l o t h e r t h i n g s , so t h e word, ttbalance,lt I

think, i s descr ibing t h e s i t u a t i o n more log ica l ly than "segre-

gation."

'CROW: Well, may I suggest t h a t t h i s is a semantic

or def in i t i on ques t ion and doesn r t r e a l l y concern the issue?

DOBZHANSKY: R i g h t . CROW: However, t h e r e s t of my d i scuss ion will be

framed in connect ion w i t h using t h e l e t t e r , S, r a the r t han

t h e l e t t e r , B, so I will continue using that . If somebody

wants to say t rSf f stands for t tbalance, t f I have no object ion.

Now, the ques t ions tha t I would l i ke t o a sk a r e -

t h e f a c t t h a t my terminology and aaproach here a r e l a r g e l y

those of Dr. Wright is no coincidence. It has to do w i t h

proximity and reading of papers.

The f i r s t quest ion is, are t h e majority, o r a t

l e a s t a subs tan t ia l minor i ty , o f new mutants of class S?

The second question is--I would l i k e t o s t a t e t h e

four questions and then, perhaps, have d i scuss ion , if necessary,

a s to whether these are real ly the r i g h t way t o ask these

34 5

questions. Secondly, do the majority o f l o c i i n a population--

LEWONTIN: Or a substant ia l rninorl ty , again?

CROW : Yes. I th ink I can always add "or R sub-

s tant ia l minori ty ," because i t hinges on t h a t . Do the ma-

j o r i t y o r a subs tan t ia l minor l ty of l o c i i n a population have

two o r more a l l e l e s o f c l a s s S?

WALLACE: When you say t f loci in the populat ion,"

do you aean a f t e r t h e e f f e c t s of s e l e c t i o n and a l l t h a t ?

CROW: Yes, blaybe, i n an equilibrium population.

Let me add tha t here .

Thirdly, is t h e concealed or inbred load--or I

don't care whether we speak in terms o f variances. If we

speak in terms of loads, 1'11 speak of the load, and if we

t a l k i n t e r m s of var iances , 1'11 speak of the variance--or

var iab i l i ty , main ly S?

Fourth, i s i t expressed load o r ex i s t ing l oad?

GLASS: I n the third one, Jim, by fl lnbred,t l do

you mean the load that would become apparent upon inbreeding?

CROW: Right ; i n p a r t i c u l a r , t h a t would become

apgarent on inbreeding without intervening selection during

the process, which i s quite important here and, I think, one

of the sources of the confusion which has taken place here.

Is expressed load or var i ab i l i t y ma in ly S? Tha t i s the fou r th

question.

DOBZHANSKY: May I a-sk a quest ion? Does t h a t

equate load with t h e v a r i a b i l i t y ?

CROW: No. One i s t h e mean change, and the o ther

i s t h e variance change. But, in an important sense, yes .

"LLER: The genetic variance changes.

CROW: Yes. I should say l tgenetictt here, very much;

so we have "genetic" in f r o n t o f f l va r i ab i l i t y f f bo th times.

ROBINSON: Are you implying that you are thinking

always of components of f l t n e s s ?

CROW: I t h i n k , f o r t h e moment, y e s , Alan; compon-

e n t s of f i t n e s s .

346

DEMPSTER: Can I ask what you mean by the inbred

v a r i a b i l i t y , s i n c e you donr t l ike- - I mean, more than one

thing.?.

CROW: I have i n mind the d i f fe rence between one

inbred l ine and another inbred l ine.

FALCONER: What do -you mean by Itnew mutantstt

i n t h e f i r s t ques t ion? Wtan t s t ha t have never occurred be-

fo re?

CROW: No, t h a t a r e new i n t h i s population. May-

be, I should say Itnewly ar is ing.I t They may be recurrences of

Previous mutations, fox all I care . Are there any other ques-

t ions of de f i n l t i on?

LEWONTIN: Would i t be f a i r t o pa raphrase 1 and

say, what IS the nature of the recurrent mutational element

t h a t i s being brought i n a l l t he t ime?

CROW : Ye s . LEWONTIN: That's what it r e a l l y is.

WRIGHT: It sort of narrows i t a l i t t l e ; t h a t is ,

a r e a l l y new mutation could be considered there, too. I don ' t

see the necessi ty f o r r e s t r i c t i n g i t to recurrent , even

though that i s 99.9 per cent of them.

CROW: All r i g h t ; t h i s i s new, whether or not re-

cur ren t .

DICKERSON: What i s new, anyway?

CROW: A l l I mean by it i s t h a t t h i s a l l e l e was

not a l ready in t h i s population at the t ime the mutation oc-

curred. Now, what I want to suggest i s t ha t t he re a r e f i ve

in t e rna l ly cons i s t en t pos i t i ons - -

WRIGHT: I n t h e l a s t , i t could be in the popula-

t i on . You j u s t mean ac tua l muta t ions tha t have been observed

t o occur, say, in an x-ray experiment, that these are the mu-

t a t ions tha t occur in the x-ray experiment, whether o r not they

a re i n the population?

CROW: That 's r i g h t ; I apologize. It i s new

whether i t i s o r i s not a l ready in the popula t ion .

347

MULLER: DO you mean s u b s t a n t i a l l y mutations which

have not yet come into balance w i t h s e l ec t ion?

WRIGHT : After the occurrence

DISKERSON : Nos a l l mutat ions

MULUR: They have not yet cone into balance?

WRIGHT: But they a re t h e kind t h a t will come i n t o

balance by the M o r t h e S.

CROW: Some a re and some a r e not. We ' r e r e a l l y

asking, what f r a c t i o n of t h i s kind.

DOBZHANSKY: I'm s t i l l worried about point 4, a s t o whether t h i s does not introduce t h i s shadow of optimal

genotype'. Does i t ?

CROW: Well, I don't know. To what e x t e n t ? Is

t h a t r e l e v a n t t o t h i s discussion?

DOBZHANSKY: I s n t i t ?

LEVENE: It might be when you're talking about ex-

pressed load. If you ' re t a lk ing about expressed var iab i l i ty ,

then, I th ink , t he re ' s no argument.

LEWOMTIN: That ' s r i g h t ; t h e r e ' s c e r t a i n l y no argu-

ment.

SLATIS: If it i s a questionable point, then, i t

is r e l a t i v e t o the discussion.

DOBZHANSKY: The Chairman asked us t o de f ine our

terns, so what is an "expressed load"?

CROW: 1'11 s t a t e iE as t h e f rac t ion , no t t h e abso-

l u t e amount but the fraction, by which t h e genotype average

dev ia t e s from t h e best genotype.

DOBZHANSKY: So you do introduce an optimal geno-

t y p e i n t h i s ?

CROW: Oh, yes.

WRIGHT: I th ink what Dr. Dobzhansky means is t h a t

"load1' i s a loaded word. [Laughter]

CRO'd: Well, 1'11 be happy t o s u b s t i t u t e some o the r

word t h a t means the same thing. [Laughter]

!IIIRICHT: T h a t ' s a l l r i g h t , b u t i t r a i s e s a quest ion

as t o how t o neasure it .

CROW: Yes. There a r e many questions as t o how

to aeasure i t . .

WRIGHT: But the quest ion asks what t o do about i t .

NEZL: Let 's accept the question f o r the c?oment I

and come back to the problem of -measurement.

LEWONTIN: Perhaps, I could s t i l l c l a r i f y t h e

quest ion a l i t t l e , o r perhaps not. T h i s i s l i ke t he ques t ion

one asks in any ana lys i s of var iance. Om asks, what a re the

components whfch are the major ones making u p the mean? I n

one sense , th i s i s a nonsense question. The aean is the re ,

and t h e r e i s n ' t much you can do- about i t . But we s t i l l ask

the biological quest ion, which fac tors a re mos t ly respons ib le

for height , and what we r e a l l y mean is, which f a c t o r s a r e

mostly responsible for the var ia t ion In he ight , bu t , in soae

sense, we a l so mean which a re t he f ac to r s t ha t a r e most r e -

sponsible f o r creating the average value of the characters *

you can see? It has t h i s same meaning, exact ly .

CROW: Yes. Let me say one ,other thing. The answer

t o t h i s quest ion would be exact ly the sane, I think, whatever

my reference point , which migh t as wel l be the nean a s well a s

the extreme genotype . DOBZHANSKY: Let * s reserve this for fur ther d i scus-

s ion.

CROW: Because I;m per fec t ly w i l l i ng , fo r t he pur-

pose of asking t h i s quest ion, t o sag tha t the amount by which

the mean of any population deviates from any point you want t o

talk about, which could be the mean of soxe other populatlon,

f o r that matter-

DCBZHANSKY: It i s the deviat ion of mean from the

man .

CROW: Well, i t doesn't have much meaning. It would

be zero over zero, and I don ' t t h ink t ha t ' s it. [Laughter]

This is one o f the reasons why I prefer no t to def ine it t h i s

way, a s you suggested.

.

349

DICKERSON: What would be wrong w i t h s imply ca l l -

ing it "genet ic var iabi l l ty , l l in point 4?

CROW: It does seem t o me t h a t one i s sometimes

i n t e r e s t e d i n t h e mean by which two circumstances differ , as

well a s the amount of variance created by t h i s . T h i s i s

cer ta in ly go ing to be r e l a t e d i n t h i s t h i n g .

DICISRSON: But i s n ' t t h a t s t i l l a question? To

what extent i s t h i s responsible for observed genet ic var ia-

b i l i t y ?

CROW: Perhaps.

LENONTIN: Between populations.

WRIGHT: But you've got tha t somewhere e l s e .

DICKERSON: No, i t ' s r i g h t t he re . He says lfor.f t

. CROW: Let me read i t f o r you, This says-

DOBZHANSKY: I s t h i s t h e law f o r an expressed

gene t i c mean d i f f e r e n t from the population nean? Vould t h a t

be a possible question?

CROW: If we don' t how what questicn we're ask-

ing, we can' t very well ask i t .

NEEL: Jim, is there any o t h e r term which you

could use for lfload,ff because I think it is obvious that

llloadw does ca r ry t he c l ea r imp l i ca t ion of an optimum--

CROW: I think what. Dick said makes sense to me.

NEEL: Ekit i s there any other term you could use -

i n framing the question?

ElORTON: ffLoadtf i s an old Engl ish word which means

the SZLA thing as a L a t i n word which comes from a wagon, o r

I f to bear"; in other words, i t i s t h e same as cfcargo. 'f Cargo

i s something that is ca r r i ed . No shipowner could consider

an unloaded s h i p t h e i d e a l s h i p . It has no i m p l i c a t i o n a t a l l

of good o r bad, It is something tkat is carr ied a long in the

pop~la t ion . [Laughter ]

NEEL: Before you entered the room, Dr. Morton,

[ l augh te r ] t he re was an e f f o r t made t o frame the questions i n

t h e most neut ra l t e ras poss ib le , and i t has become apparent

3 50

that the term, ' l load,l t does have connota t ions for Some peo-

ple. Now, mine is an honest question.

DOBZHANSKY: ! ; J e l l , l e t me t r y t o compromise.

W 3 L : Is there 'any other way to phrase i t ?

DOBLHAKSKY: Vould question 4 be acceptable to

you, fo rau la t ed a s follows: Is the expressed genet ic var ia-

b i l i t y due mainly to S? That avoids any implication as to--

CRO':!: Except that I t m i n t e r e s t e d i n means a s w e l l

as var iances .

LEWONTIN: . Let me aake a suggestion, again. The

means have a mcaning on ly from population to population, Or

a s a dev ia t ion from some absolute , so youl re rea l ly ask ing

the following two quest ions: Is the expressed gene t ic var i -

ance within a population nain1.y due t o S? And the load ques-

t i o n i s r e a l l y a question, i s the difference between any popu-

l a t i o n and any o the r g iven popu la t ion e i the r r ea l o r hypothet i -

cal , a lso mainly Cue t o S? You see, you are always express-

ing the load, the mean, w i t h respect t o some X point and, if

you l i k e , you can express it a s t h e d i f f e r e n c e i n means among

nany po pula t ions.

CROW: Well, t h i s i s p re t ty c lose , and I th ink i t

helps the discussion to keep t h i s noticn, yes.

WLLE3: If wet re wi l l ing to accept in 3 t h a t t h e

load i s in the inbred , then , why aren' t , we wi l l ing t o accep t

i t i n 4, a s imilar load in the ordinar i ly nated populat ion as

compared w i t h the most fit genotype?--if we wish t o def ine i t

so. A f t e r a l l , lzle cannot dodge questions of f i t n e s s . The

question of f i t n e s s i s the ch ie f one we are concerned w i t h

here. There i s no use using a neutral term that dodges f i t -

ness when we are concerned w i t h f i t n e s s .

DOBZHAXXY: Well, Professor Muller, yuestior, 3 clpn

be f o m u l a t e d l o g i c a l l y by saying, " the deviat ion from mean

f i t n e s s of a random-mating population." question 4 cannot be

so s t a t e d .

>iULU,R: No, i t means t h e d e c l i n e i n r e l a t i o n t o

3 51

nean f i t n e s s . You don' t get i t , usua l ly , at, a s u p e r i o r i t y

i n t h a t r e s p e c t from inbreeding.. You may on a ra re occas ion ,

yes .

DGRZHA13SKY: EUt it is Zefined from mean.

NJLLE,?: Cafined fyom mean f i t n e s s . The inbreed-

i n g , you don't eet i t from. _.

DOEZHAXSKY: Not from optiaal genotype.

XU~LLER: I would use optinal genotype sgnoaymously

with t h e h ighes t f i t nes s ob ta inab le , o r t heo re t i ca l ly conce iv -

able , under t h e circumstances.

. DOBZUANSKY: Well, l e t 's post pone t h a t .

MULLER: You c a n ' t postpone i t i f you r a i s e t h e s e

questions here.

3EEL : !?lell, now, I wonder, fo r t hose of u s i n

the group who migh t like to equate load with genet ic var ia-

b i l i t y a t t h i s p i n t , is t h a t f o r u s a gera iss ib le p rocedure?

CROW: Well, for the _ourposes of the discussion,

yes, but mean and var iance, to me, have two d i f f e r e n t mean-

ings, and I don ' t s8e how one can equate them.

DEMPSTZR : T hat s T ig h t . GLASS': Wouldr,:t ' b a r i a b i l i t y " be a broader term,

that includes both nlean and var iance?

CROW: C e r t a i n l y n o t . V a r i a b i l i t y i s v a r i a b i l -

i t y , and neans are neans.

DEXPSTER: I thin!<- t h a t vould be avoiding one of

t he most important issues.

CIIOW: I do, too.

NECL: I ' m t r y i n g t o f i n d a n e u t r a l expression

so we can get on with the issues.

C R O X : I think, Jim, i f you t h i n k there is no

such thing as an optimal geno%ype, if you th ink there is rc

such thing as a de f in i t i on t ha t measwes t h e devia t ions from

t h a t , I'm pe r fec t ly w i l l i ng t o s ay t ha t t h e devia t ion froa

point X t h a t you would make is j u s t a s sood a s t h e optimal

genotype that I would make, but i t s t i l l has t o be a mean

4

I

3 52

di f fe rence and not a var iance difference.

KEEL: l:!eli, then, as a f i f t h q u e s t i o n , a ques-

t i o n which we may never get to today, i s there an opt imal

genotgae? T h i s i s a basic question, as basic a s any of the

o t h e r four

DOBZHAK3KY: That is hidden in quest ion 4 .

CRO'$!: The answer is no, but that doesn ' t prevent

ne from discussing the existence of a perfect vacuu.rll.

DEMFSTER: Suppose one measures the f i tness of

an individual; suppose one takes a d e f i n i t i o n like t h i s ,

which measures the f i t n e s s o f an i nd iv idua l i n a l l t he env i r -

onments i n which the population i s . Mow, a t each locus, we

make every possible substi tution of the genes in the popula-

t i on . We try every possible combination. The combination

which we put i n t h i s popu la t ion t ha t g ives t he h ighes t f i t nes s

is the optimum. T h i s i s a d e f i n i t i o n which you can ' t ca r ry

o u t , a c t u a l l y , i n

i s an empir ica l ly

on t h i s b a s i s , i f

CEOW :

that wasn ' t c leas

person, so to speak, but i t s e e m t o me i t

poss ib l e de f in i t i on and one can discuss i t

one wishes.

That Is exac t ly what I 'm thinking , and if

to everybody, maybe, you should s t a t e i t

again, because that is my d e f i n i t i o n f o r t h i s purpose.

DOBZEIANSKY: I would cer ta in ly t ake except ion t o

t h a t d e f i n i t i o n . Maybe, we should postpone i t f o r t h e discus-

s ion .

ROBINSON: bkl.1, now, there is another question on

def in i t ion . ques t ions 3 and 4 a r e n o t c l e a r t o me . It seems

t o ne t h a t t h e key words are t tconcealedlt and tfexpressed.l l

What do you mean by tfconcealedll?

CROW: By 'konc.ealed,lt I mean what one would f i n d

i n an individual who is homozygous.

ROBIKSON: Eut t h a t i s o n l y i n terms of a mornmt

in space , i sn ' t tha t r igh t?- -because you ' re going t o move now

from concealed to expressed ra ther f ree ly .

ROBEIITSOK: ftConcealedll i s inbreeding depression.

,

'3 53

DILXERSON: Tha t ' s what I was wondering. Couldn't

you say "inbreeding depression'"?

CROW: Yes, t h a t ' s why I put the word, t t inbred, l f

here.

NEEL: Then, a re la ted ques t ion is, if you l r w p '

the concept o f opt iaal genotype, do you agree that the o p t i n a i

genotype a t t h i s par t icu lar po in t i n time and space may not be

the optimal genotype a g e n e r a t i o n l a t e r ?

CROW: O f course; t h i s seems se l f -ev ident to me.

NEEL: But i f you would accept , then, that the

optimal genotype may change ra ther in the geneologica l sense ,

rapidly--

CROW: O f course , th i s is the whole s t o r y of evo-

l u t i o n , a s f a r a s I'm concerned.

NE%: T h i s is part of the quest ion. Dr. Wright

j u s t made a statement. Would you Like to repea t i t ?

WXGHT: I t h i n k i t i s not merely a t d i f f e r e n t

times. There can be several d i f ferent concept ions of the

o p t i m m genotype a t t h e same' time.

CROW: Oh, sure. I donrt see any question about

t h i s .

ROmRTSON: Could I aake a po in t , t ha t i n 4, there

a r e two things, one r e f e r r i n e t o means, which is not an ope-

ra tLonal ly obvious concept , that i s to say, i t doesn' t say

"do something and you ' l l get a measurement,t1 The v a r i a b i l i t y

i s immediately subject to doing something and g e t t i n g a meas-

urement.

CROW: That is t rue, yes .

DICKERSON: And v a r i a b i l i t y implies a mean t h a t

is suboptimum. If you have va r i ab i l i t y , obv ious ly - -

CROtd: I guess so, yes . 9ICERSCN: --that means i t is suboptimum.

MULLER: But only on t h e genera l p r inc ip le of the

natural cussedness of things, that most v a r i a t i o n s - - - i t * s down-

h i l l .

3 54

DICKERSON: There is no q u a l i f i c a t i o n on i t a t a l l .

CROW: I think t h a t even Professor Dobzhansky

will admit there a re some genotypes in the population that

are bet ter than average.

DOBZHANSKY: And I hope Professor Crow -dill ac'...nit

t ha t soae are better than the average.

CROW: That's what I said, exact ly . [Laughter]

NEEL: Jim, could you now quickly move on? Mow

is the t ine to proceed. [Laughter]

CROW: I would like 'to say one thing, Professor

Dobzhansky. I would l ike to para9b.rase "uurton Eussell*s

s ta tement that 'T go to Edinburgh," and IIEdinburgh comes t o

!ne," are the sane s ta teaent . I would Like to s ay t ha t t he

s ta tement that some genotype i s bet ter than the average i s

the equivalent of saying that the average is l e s s t h a n some

genotype. Agreed?

DOBZHANSKY: O.K., f ine . [Laughter]

CROb!: I think nuch of the quibbling is over the

assumption that these are different s ta tements .

LEVEN?l: Jim, before you go on--

DOBZHANSKY: That i s not quibbl ing a t a l l . I take

except ion to t h e cha rac t e r i za t ion of t h i s d i s c u s s i o n a s

quibbling. [Laughter ]

L3VENZ: Jim, I th ink t ha t if you use t h e red

and yellow chalk up there, i t would be m c h more v i s i b l e .

LEWONTIM: Can we discuss that? [Laughter]

CROt!: ,Well , I t h i n k we have discussed t h e ques-

t i on . Whether o r n o t t h i s i s v i s i b l e , it i s apparent. Now,

if I may go on--I thought t h i s par t would be noncontroversial .

[Laughter]

LEVENE : It was re la t ive ly noncont rovers ia l .

CROW: I would l i k e to say t he re a r e f i v e i n t e rn -

a l l y c o n s i s t e n t p o s i t i o n s t h a t one would occupy w i t h respect

to these questions. I will c a l l t h e ? pos i t i ons A through 3.

Pos i t ion A would be that the answer t o t h e f i r s t q u e s t i o n

e

a, rn s a, Y

C' U n

c a,

P a,

v) CrJ L

0 w 4 v)

rl rl 4 3 v)

k 0 M

4J 0

a, c 0

h m a

0 *

+J 4 2

0 a, 3

0 m c 0 n

a') c 4

v1 0 f5

r: 0 c CAJ

- 4 X

c

4

k a 3 UJ

0 0

3 c 0

cd c. v)

+J

a, CJ

v, c a V) Q) h - c

a, SI a,

v) a -d

U

4.J

ii 4 v) d

4

4 ta k 0

d H

P Q, .

a 3 v)

N

d 6,

d 0

U

a, E! 0 0

a x! E-c

5 c n: 0

k a, * .

a. .. a, h -

.. a c H

2 0 2

a, tu

.. 2 d

u)

M

+i 4

.. 5 0 lx u

P Q) 9-l

0

v) v)

cd ri 0

a 42u

tJ-4

8 w 0

rl 4. 4

v) a

a 4 k c +J m UJ H V )

a, 2 3 c Q)

I,

SLATIS: I th ink you wrote i t in 1.958.

CROW: Well , that doesn' t say I understand i t i n

1963, but go ahead. [Laughter1

SLATIS: I'm point ing out that you could have

almost a l l t h e genes of t h e S type, but a s you went toward

inbreeding, they m i g h t b a l a x e o u t and c o n t r i b u t e v e r y l i t t l e

t o t h e v a r i a b i l i t y t h a t you ge t ,on inbreeding , o r t o the

s h i f t s t h a t you g e t on inbreeding.

CROW: Well, i n .other words, you are saying that

t he re i s such a thing a s "no, no, y e s , yes," and I'm going

to ge t t o t h a t i n a minute.

SLATIS : "No, yes, yes, no. It

LEVENE: I th ink what Herman i s g e t t i n g a t is

that If the major i ty of new mutants are S, but w i t h very,

very smal l se lec t ive coef f ic ien ts , and the re a r e a number o f

other mutants that a r e not S, t h a t a re M bu t a r e l e tha l s ,

then, on inbreeding, thesa Tare le thals migh t Sroduce more

depress ion than a l l the S genes t h t t have v e r y s l i g h t l y r e -

duced f i tness.

LI3:JONTIX : Oh, dear !

CRCW: Kow, l e t * s see ; I * m not sure I understood

t h a t .

CROW: That 's ali r i g h t , but--

SLATIS: A cou?2e 0,' genes, a very small proportion

of a l l the genes, might be tke ones tha t cont r ibu te to t h e

inbreeding depression.

XRIGHT: I t h i n k he 's r i g h t there , tha t t h e S

genes, and there a re on ly t w G of them, c a n ' t g e t mors than a

cloubledepyession f r o n t h e hetsrozygote, w h i l e your :I genes,

you see, could get a hundredfold depression from the equi-

l i b r ium cond i t ion i n r e l a t ion t o t h e optimum, t h e best . I

think fIerman is p e r f e c t l y c o r r e c t t h e r e , t h a t you could have

a recessive. It would ruin your population.'

CROW: Well-, l e t me s t a t e i t , a n o t h e r way round,

o r nay I wri te my o the r pos i t i ons h2i.e f i r s t and then coae

3 57

back t o t h i s ?

WALLACE : May I a slr a que s t lon before you do

t h a t ?

CXX.': I'm saving up quest ions t o answer, but go

aheac! e

!./ALLACE: 'dhen you . t a l k about S, nov thinkirg

i n t erm of S in the sense o f deviat ion, 1 - S , 1 - T-- SliC!..:' : ?To , no , S . YALL.4CE: Yes, I know tha t , bu t a re you thinking

i n t e r a s of l a r g e e f f e c t or s n a l l e f f e c t o r d o e s n ' t it make

any d i f fe rence to you?

CROV: If11 t e l l you what I was thinking. I was

th inking , in o rder t o frame up the issue, I would l i k e t o as-

sume that both kinds of loci have about the same kinds of e f -

f e c t , and, i n e f f e c t , t h i s i s what is being chalLenged, and,

I th ink , appropr ia te ly , an6 t h a t i s why I would l ike- - the

magnitude of S i s about the sane in bo th .

FALCON%: I just rea l ized tha t ques t ions 1 and 2

a re frarned i n t e rns of number o f Zocl, and 3 and 4 a re framed

i n terms of magnitude o f e f f e c t of the gene.

CROri': Yes, purposely.

FATCO?JER: J e have to keep t h a t c l e a r , 1 think.

SLATIS: But t h i s was your arguinent f ive years ago,

that the large number of l o c i t h a t might con t r ibu te t o normal

v a r i a t i o n might be coapletely overruled by just a couple of

l o c i t h a t had enormous e f f e c t s , but they were r a r e and the

e f f ec t s t u rned up on ly on in t ens ive i nb reedhg .

CROK: No, no.

DEPIPSTER: !dhat he sa id was t h a t t h e r e migh t be

two o r t h ree s eg rega t iona l l oc i t ha t con t r ibu ted ve ry g rea t ly

t o t he va r i ab i l i t y , bu t t ha t , OR inbreeding, the aavinum. irl-

bred load that one loclx can possibly cont r ibu te i s , I t h i n k ,

t h e c lue t o the nutat ion. If you have a l e t h a l Locus w i t h a

cer ta in mutat ion ra te , the f requency of the gene i n t h e ?

equi l ibr ium populat ion i s 1/S. If you let S equal. 1 and

358

n u l t i p l y it by S, you get the sp i r i t of the thing. If you

got a n u t a t i o n r a t e of 1 i n 10,000, it would be very h i g h .

The absolute maxiaum inbred load would be 1 per cent, whereas

s e g r e g a t i o n a l l o c i have t o have very small Ss and Ps i n o r d e r

to Cont r ibu te tha t small load. Almost any segregational locus

will cont r ibu te more load on inbreeding than a nu ta t iona l

gene. I t h i n k t h a t ' s i t .

CFOW: Thank you, Everet t . Yes, t h i s i s what I

would have sa id had I thought o f i t .

IJRIGXT: But, i n your 1 there , there i s nothing

said about t h e e f f e c t of these genes; nerely t h e majority.

That i s the po in t there ; to be cans is ten t :qith your ttyestt

f o r 1, if t h i s major i ty of t he he t e ro t i c l oc i have exceedingly

smal l e f f ec t s ,wh l l e t he re a r e a few nnrtational ones which,

when expressed uneer inbreeding, had ve ry devas t a t ing e f f ec t s ,

t he he t e ro t i c e f f ec t s , o r the deviation fron t h e optimum,

would be rnerely doubled under inbreeding, and the expressed

e f f ec t - -

CROW: I think you're r i g h t , Dr. W r i g h t .

WRIGHT: The main point is t ha t you have sa id

nothing about effect in the f iyst , so th i s major i ty , the

he t e ro t i c , may have n e g l i g i b l e e f f e c t s , Then, you jump t o

e f fec ts wi th inbreeding .

MORTON: Your "yes, yes, no, yes," i s a t e n a b l e

posf+ion with cer ta in other assumptions.

CROW: Yes, I th ink I have to say tha t , and the

assumptions are that the magnitude of i n d i v i d u a l e f f e c t is f a r

d i f f e r e n t f o r one c l a s s of locus than i t is for the o ther c lass

of locus.

WXGHT: There i s nothing sa id i n 1 about that .

XORTON: Or i t could be tenable in another way,

t h a t you are not measuring f i tr ,ess w i t h some component. There

a r e l o t s o f ways of making i t--

CliOTrJ: Nonetheless, I- said I was going to simplify

i t , and I would l i k e t o c o n t i n u e t h i s way. It seems to me,

4

3 59

without bringing in this kind of assumption, which may or

nay not be r e a l i s t i c - - w d l l , l e t me go ahead w i t h ny discus-

s ion, anyhow.

Another possible position is, we may have to say

t h a t these Ityesestt on 3 and 4, and 1 and 2 are apples and

oranges, and there i s not much r e l a t i o n s h i p between them, but

I Can't th ink t h i s i s true, because I'm no t w i l l i ng t o make

the_& assumpt ion tha t these a re to ta l ly d i f fe ren t c lasses

of nutants in t e r a s of t h e i r e f f e c t o n t h e organisa .

If the answer to 2 is ttno,tt then 3 can c l ea r ly

s t i l l be 'tyes,'t for the reasons that have been brought ou t ,

and if 3 i s then 4 is I tyes"; t ha t is, because of t h e '

t endency for he te ro t ic nu tan ts to pers i s t and c lass ica l nu tan ts

t o be l o s t , i t i s poss ib le tha t th i s [ques t ion 2 ) i s tfyestt

and this [ques. t ion 11 is ltno'.tt Then, 2 can be ltno," 3 and.

4 can continue to be ttyes,lt f o r the same reason , t ha t he t e ro t i c

I .oci contribute more to inbyeeding depression than c l a s s i c a l

l o c i do, per locus ; t he re fo re , t h i s 2 can be tfnott and 3 can

be ttyes.tt The he te ro t i c l ocus is l i k e l y t o be a t a higher

frwquency i n the population than a c l a s s i c l o c u s , and t h e r e f o r e ,

on the average, i t will cont r ibu te more to t h e inbreeding

e f f e c t s .

ROBZRTSON: Will you say t ha t again?

LE1JONTIrJ: Given an equal effect , the numbers of

h e t e r o t i c l o c i n i g h t be very smli., but the total var iance

associated with then might be ve ry l a rge .

ROEERTSOPT: Oh, y e s , t h a t ' s r i g h t .

WRIGHT: But you have to add a comparable e f f e c t

under 1, if you're going to xake these def ini te answers . *

CROlI: If the t h i rd and fourth answers go w i t h

ansvers 1 anG 2, I have to say !:of comparable e f fec tOtf Perhaps ,

I should. j u s t s ay i t up here. Should I put itcomparable effecttt

i n t h e s t a t e a e n t t;p here?

X X G H T : I t h i n k i t r a t h e r s p o i l s the ques t ion t o

put it in , though.

CROW: Well, maybe, i t p i n t s up the issue, Dr.

W i g h t . 4

WRIGHT: Unless you put i t i n , I th ink , fo r ex-

ample, in the f i r s t one, 3 can be just anything.

DEMPSTER: I don ' t th ink tha t i s q u i t e t r u e ,

Professor 'Aright. I xean, you speak of the naxinum e f f e c t i n

one case being 50 per cent and in the o ther case a very much

largsr per cent . .I think we have to think i n terms o f the de-

gree of effect ra ther than the percentage. You're comparing

the percentage a t randon mating w i t h the percentage under in-

breeding. If you have the maxiwrn p o s s i b l e e f f e c t t h a t you can

have w i t h a mutat ional locus equi l ibr ium, unless you a r e meas-

u r ing some o the r component, it is 1 per cent, and t h a t i s w i t h

the enooraous mutation frequency of 1 i n 10,000. To have tha t

smal l an e f fec t o f segrega t iona l loc i , you have to have the

S and T i n t h e neighborhood of 2 per cent, and I would submit

t h a t i t i s un l ike ly t ha t yourve go t s eg rega t ion l oc i t ha t a r e

held i n the populat ion, le t ' s say, by something l i k e .l per

cent, because mutation then begins to be important.

I t seems to me, t he re fo re , t ha t , subs t an t i a l ly

speaking , f lu don ' t rea l ly have to say much about the degrees

of e f fec t of these two c l a s ses . of loc i , because there i s ha rd ly

any range there, where their re la t ive degrees could be so d i f - fe rn t tha t tha t s ta te lnent wouldn* t be t rue in the o rder in

which he has put those "yesestt and ltnoes.lt

WRIGHT: I woul6 be i nc l ined t o answer him under 3,

I think, under just t h e o rd ina ry s i t ua t ion .

CROW: That 's a l l r i g h t , but you probably would--

WRIGHT: llYestl f o r 1' and l tnolt for 3, i n t h e f i rs t

column.

NEEL: Why don' t we l e t Jim put down t h e f i v e a l -

t a rna t ive formula t ions he wishes t o pose, and then see how

heavy the pressure is t o put on other formulat ions? We may end

up exhausting a l l t h e combina t ions and permutations.

CROlJ: That 's what I- 'a going to do. Pos i t i on D i s

4

363-

a l l "noes" and E is all "noes."

. DICKERSOM: If you have a quest ion on the f i r s t

case, under 30- cno!!: I was mere ly t ry ing to wr i te these in a

probable hierarchy.

VRIGHT: Your l i n e between Y and R i s j u s t a diag-

onal .

CRO1J: Right. Well, I ' m inclined to agree with

what Dr. Jknpster says, that unless you assune a qu i t e d i f -

f e r en t o rde r of magnitude of the mutants involving the two

kinds of e f f e c t s , this i s t h e logical system.. MOW, I can con-

t r ive systems where i t i s not t rue.

MORTON: I don ' t th ink that is true, because the

f i r s t two questions can be formulated i n a way which is con-

pletely unreasonable , that is , in terms of e f f e c t s t h a t you

c a n ' t measure. They can talk about i so le les , we '11 say, as

. always aaintained.

CROW: Well, I f!id have one th ing in m y notes tha t

I thought I would bring il?, but I was going to say I would

omi t f ron d i scuss ion , se lec t ive1 .y neut ra l i so le les a s being

p r e t t y much beyond the pale of invest igat ion, by population

methods, a t l e a s t .

Ns'i: But do !.de know t h a t i s o l e l e s a r e s e l e c t i v e -

ly neutral? I

CRO!.i: I would say t h a t s e l e c t i v e l y n e u t r a l i s o - .I i

#

l e l e s do no t ex i s t .

of the gene

I t seems t o

DEXPSTER: There a re muta t iona l loc i , a ren ' t there?

LEWUNTIN: Alle les .mst be de f ined a s t hose s t a t e s

which are d i s t ingu i shab le t o na tu ra l s e l ec t ion .

me tha t every th ing e l se- -

[Cries of "No, no!"]

LSWONTIN: Well , within t h e popula t ion a t a given

t i a e . BODIIER:. They may not be d is t inguishable a t one t ime

an6 they may be expressed la te r in i n t e r a c t i o n w i t h some o t h e r

l o c i .

NEEL : Actually o r po ten t i a l ly .

BODMER : Yes

LEWONTIN: Actually, the questionswe do ask about

a population ane .?leasure about a populat ion are w i t h respec t

to the current select ive forces . I f we ' re going to ask,

What is the potent ia l of this populat ion for future evolu-

t ion?" then, I ag ree en t i r e ly t ha t t he whole range of possible

changes of s t a t e of DNA is important. But you don ' t ask those

quest ions in experimental pract ice . When you say, "1s t h e

expressed load o r expressed gene t ic var iab i l i ty main ly S?"

you can t a lk on ly abou t t he a l l e l e s which have been and a r e a t

the present t ime dist inguished by na tu ra l s e l ec t ion . If no

se l ec t ion has a r i s en ye t which will dist inguish between two

i sopro te ins o r isoenzymes, then, as f a r a s n a t u r a l s e l e c t i o n

is concerned, they are both the same.

NEEL: But, Dick, they aay have been se lec ted in

the past .

LEWONTIX: Indeed., they may. All Jim is saying i s

that if there is no selective difference between them,you

count them a s one.

BOD3ER: Byt, in exper inen , ta l p rac t ice , you' have

a s o r t of uncertainty pr inciple . There i s a limit--

LEWONTIN: T h i s is unfortuna te.

BODMER: - - to t he s e l ec t ive d i f f e rence which you

can de t ec t , and there may be a very l a rge number of a l l e l e s

which will be below the l i a i t o f . t h e s e l e c t i v e d i f f e r e n c e which

you can detect and which are , nevertheless , important .

CROW: Then, one t r i e s t o invent techniques t o do

t h i s .

LEWONTIN: A l l Jim i s t r y i n g t o e l imina te is--

CROW: Those t lhich are neutral .

LEWONTIN: --those which by d e f i n i t i o n a r e i n d i s -

t inguishable to na tura l se lec t ion . If there a re some 6is-

t inguishable t o na tu ra l s e l ec t ion bu t which a re unfor tuna te

enough to be unab le t o d i s t i ngu i sh , this c r e a t e s a kink in the

363

e x t e r n a l problem. All hers t rying to do is f ind a way out of

t h i s d l f f l cu l ty .

WRIGHT: In questions 1 and 3, if you say ttcom-

parable e f fec t , " do you mean cornparable e f f e c t i n the hetero-

zygste, or what? If you mean in the heterozygote, then, you

could have a grea t many Efs t ha t have s l i g h t e f f e c t s , and,

perhaps, a major i ty of Ss, i f you're going to answer ttyes,"

tha t have the same s l i g h t e f f e c t , The l a t t e r will go up i n

the other homozygote, while t h i s M, we will say, is d e v a s t a t -

ing tha t homozygote. It's alrllost a r eces s ive l e tha l , or

something o f t h a t s o r t . But it has comparable e f f e c t s when

they ,occur a s heterozygotes.

I n the inbreeding e f fec t , the ?.I, of course, will

bring out the devastat ing homozygotes, and be a tremendous

depression. In the Ss, the depression can' t be more than

twice the depression of the homozygotes with respect t o the

heterozygotes , or I'm thinking of e x a c t l y a gene frequency o f

50 per cent, but i t will be about two t i ae s , so t h a t i t will

not produce very much inbreeeing depTession if t h e e f f e c t s on

the heterozygotes are about the same. The o t h e r will produce

a very g rea t depress ion in inbreds .

CROW: Measured on ly a s a f r a c t i o n of what i t was

doing . in the outbred population, but not in absolute terms,

. Dr. ':{right. It depends on the gene frequency.

DICKERSON: Yes, t h a t ' s i t .

CROW: You see, your mutat ional a l le les are going

t o be low gene frequency and your s e g r e g a t i o n a l a l l e l e s a r e

not.

WRIGHT: But, on your own principle , the inbred

depression can be a hundred times the difference between-

CROW: It will be a hundred times the effect of

t h a t same locus on the hybrid population, yes, but i f t ha t is

v e r y m a l l , t h e hundred times i s a ve ry s aa l l quan t i ty . It i s

no t necessa r i ly two t imes larger than the large quant i ty .

Tt,r31GHT: But we're assuming that the others have

364

a cornparable e f f e c t .

CROW: No, no! The comparable e f f e c t of the gene,

but the locus will accumulate--

!!.%IGIiT: I t depends w,hether you nean in the he te ro-

zygote o r in the homozygote. If you're talking about the

heterozygote, then, this would be I1not1; i f you ' re ta lking

about the homozygote, then it will be a different answer.

CRObi: No, the difference has to do w i t h t h e f a c t

t h a t one kind of locus will accumulate to a h i g h f requency in

the population and the o ther will not.

Iv1ORTOIIU': But, Jim, l e t ' s t a k s a hypothesis that

a l l genes are heterotic, but soue are more he te ro t ic than

o the r s . Then, a gene that, is b t h a l i n the homozygote has a

s l i g h t advantage, an advantage, we will say, which i s not

measurable in t h e heterozygote. These aye r aCica l ly c ' i f f e ren t

e f f e c t s . I'm not sure that; t h Q f i r s t two p r i n c i p l e s a r e formu-

l a ted in such a way tha t I would know whether ycu're counting

tha t as a segrega t iona l o r nu ta t iona l load.. "Jhenever the

heterozygote i s so small that rnuta t ion must a l s o be invoked

to keep t h e gene in the pogulakion, you a re i n an a r ea t ha t

isn ' t investigatable, but these benes, presumably, unless you

def ine then out , will cont r ibu te to your f i r s t two proposi t ions.

LZVIh l : I would l i k e to ask another question.

Are we assuming that there are two aLlc?les t h a t a re a locus?--

because Dr. Xright has been saying t h z t segregat ion can only

depress by a f a c t o r of 2. T h i s i s t x e onLy if you have these

two a l l e l e s . .

WRIGW: Yes, t h a t 1s r i g h t .

CROW: . Yes. I'm not assuming t h i s . I th ink i t ' s

c l e a r enough t h a t one can in5ent s i tuat ions i n which this

hierarchy i s not necessary . Wel l , l e t ' s go on with the d i s -

cvssion from hei-e. . Ifhat I wanted to do was to ask two o the r

ki!lds of questions. \!by ~7.0 we want to know the answers to

these four points? Seconi!, what kind of experinents have been

done o r are proposed to be done, t l h i c5 , a t l ea s t i n p r inc ip l e ,

could answer some of these questions, and which of the ques-

. t i ons do the experiments bear on?--because, once again, I

think, whether thls is s t r i c t l y r i g h t o r i s not-and I agree

i t is n o t s t r i c t l y r i g h t , but I th ink i t is probably r i g h t

f o r most s i t u a t i o n s t h a t one thinks are rc!al is t ic-- i t i s s t i l l

possible that some people are talking about t h i s [quest ion 11

and other people are ta lking about this [quest ion 41, and don ' t

r ea l i ze t ha t t hey ' r e t a lk ing abou t d i f f e ren t t h ings , o r a t

l e a s t t h e r e is a poss ib l e sh i f t i ng of grounds.

NOV, excuse me for being personal f o r j u s t a

moment, but I would l i k e t o i d e n t i f y what, my own view has been

at various t imes in the past an& what i t i s a t p re sen t . When

I express a view, t h i s doesn ' t mean tha t i t is a 6ogaa o r t h a t

i t i sn ' t capable of being changed. I am simply saying what I

th ink i s the most l i ke ly p i c tuye of n a t u r e a t t h e p a r t i c u l a r

t i n e .

I n 1948 anc! in 1952, I wrote papers tha t arguee

e s s e n t i a l l y f o r viet.1 "Dtt here. The a r p m e n t was primari ly

that hySrid corn was $nough be t te r than the average of ranclom-

nqting corn that removal of concealed classicai mutar, ts was

hard ly suf f ic ien t to account for t h i s . There, have been two

f a c t o r s s i n c e 1948 t h a t have roitigsted that statement sonewhat.

One was my l ack of r ea l i za t ion , o r anybody ' s , n re t ty much a t

t ha t t ime , t ha t pa r t i a l dominance was a ubiquitous thing, and

t h a t changes by a f a c t o r of 2 were the kind of estimate that I

was using.

The other one is t h a t , w i t h more s tudy of ,nutation

rates--I th ink, I was choosing too low a value f o r the mutation

r a t e t o mild u s e a s opposed to drastic changes, so, if the

muta t ion ra te , as I took. i t then, was too low, and i f the amount

a? cioninance o r complete r e c e s s i v i t y was not so much t h e r u l e ,

v l c h of th2 f o r c s of that argun?ent clisappeared, and my pos i t ion ,

i f I can c a l l i t t h a t , s h i f t e c ? t o one of uncertainty between

these two a l t e r n a t i v e s , and t h a t i s where i t s t i l l i s [D and E].

I apologize f o r being personal, but I want i t c l e a r

367

tha t I have never argued f o r a view like t h e one t h a t t h i s

view [Z J was co r rec t .

LE?ONTIl!: At the present time, you think, the

choice is betveen D and X ; is that; r i g h t ?

CROW : Ye s . WXLER: That i s where you anC! I differ, t o Some

exten t .

CROC.!: I th ink Dr. Yhller might take view E . Am

I r i g h t ?

NULLEp\: Yes.

CROW: I , think, i f anybody e l s e would l i k e t o ex-

press a.n opinion a s to where he stards on t h i s , I would gather

from ,the d iscuss ions w i t h Dr. Wright-but he i s perfect ly cap-

a b l e , a s you how, o f speaking for himself--that probably he

would be here or here [D and E ] o r soqewhere in between.

LIICICXSON : Tha t woulC: be the democrat lc way to

decii2e i t , woulcln't i t ? [Laughter]

CRO'J : Ye s . LTrJO1+!TIK : I would l i k e to point out t h a t i f ne

use t he s t a t i s t i ca l p r inc ip l e of Ignorance, the answer t o ques-

t i on 4 i s clearly t tyes,l t the answer t o question 3 i s probably

'Iyes,'I the answer to question 2 is pTobably Itno,ll and the answer

to quest ion 1 i s c e r t a i n l y %o. It

CROV: Based purely on t hese s t a t i s t i c s?

LEWMTIN: Yes. [Laughter]

LEVENE: As a s t a t i s t i c i a n , you would take No. 3? LEWONTIN : Ye s . DOBZHANSKY: Well, now, i f I may add my voice, I

would put myself i n t he category of C, with the r e s e r v a t i o n t h a t

quest ion 4 is formulated i n a way which I f ind d i f f i cu1 . t t o

ar,sver. 0 thertt ise, ,I woult! favor C.

CRO% !.Jell, this i s Dr. !fuller an? this i s D, so

yo& can take whichever you l i k e . I think everybody is pre jug

d i c e d i n t h i s 5y saying, if sonebody knew the answer to A , we

woull?n * t have any argurnen t .

SLATIS: I s someone wi l l ing to a rgue for A ?

CROW: That s Bruce.

WALLACE: Yes. No, 1 i s the one I'm trying to

g e t a t , personally. I don t care where my personal views

f a l l . I feel t ha t is unimportant. The in t e re s t ing t h ing is

the experiment, and I i n t e r g r e t my experiment a s saying "yes"

t o Mo. 1.

I

CROW: T h a t ' s r i g h t . How, l e t me proceed from

here, because-.

'A~ALLACE: Given that one a d d i t i o n a l f a c t o r , t h a t

the a l le les involved in the experiment a re those taken from

the population ko begin with and.mt: f rog some labora tory

s toc4.

CRO1.r: I woulc! l i k e t o a s k why we war,t t o knof:I the

ansvers to these fou r ques t ions , i n add i t ion t o j u s t t he f ac t

t ha t we want to know anything wc c a n f i n d o u t , f o r i t s o w

i n t e r e s t . The relevance o f question 1 has t o d.o w i t h the

assessment of the impact of nutation on the populakion, a s , I

think, everybody has c lear ly real ized.

Question 4 i s p r e t t y largely i r r e l evan t t o t h a t

par t icular point , but i s very re levant to the ques t ion of the

choice o f breeding system f o r f u t u r e s e l e c t i o n i n l i v e s t o c k

populations or plants , o r short-range evoiut ion in any species ,

I would say.

quest ions 2 and 3 seen t o rlle t o be of considerably

l e s s i n t r i n s i c i n t e r e s t .than e i t h e r I o r 4. I t seems to me

tha t 2 is most useful because, with. one answer t o 2, i t

p r e t t y c l e a r l y i n p l i e s t h e a n w e r t o 1.

Juest ion 3 is useful bacause the answer t o 3

p r e t t y c l e a r l y i m p l i e s the answer to question 4.

I had a l i t t l e b i t of r e se rva t ion t ha t has cone ou t

f m nore strongly here, a s to the poss ib le fac t tha t there is a

l o g i c a l gap between thase two things an2 these two things

[quest ions L and 2, ane 3 and 41, but , to a l a rge ex ten t , I

think, i t i s f a i r t o s a y we a r e i n t e r e s t e d i n 2 because of i t s

369

bearing on 1, and we a re i n t e re s t ed i n ques t ion 3 becaus

of i t s bearing on 4 ; a t l eas t , t o my own way of thinking,

t h i s is to a la rge ex ten t t rue .

LEWONTIN: Excuse me, Jim, but if I n a y s t a t e a

pos i t ion which, 1 think, Dr. t u l l e r s t a t e d , i t is that ques-

t i o n 1 has another inportance, in addl t ion tc i t s bearing on

2; t h a t i s , i t would be the inmediate question of the damage

done to the population by mutagenic agents.

CROV: I think, Dick, I said the opposite of what

you said. I sa id I am no t e spec ia l ly i n t e re s t ed i n 2 SO f a r

a s i t bears on 1.

LEWOYTIN: Oh, sorry! Eut one night ask quest ion

1 qui te hdependent ly of 2.

CRCiJ: Oh, sure, but t h i s i s what I'm saying,

t ha t i is in te res t , ing In i t s own r i g h t , because that is 'the

quest ion that will t e l l u s the most about t h e e f f e c t of a

change in muta t ion ra te on the fu tureppula t ion , i t seems t o

me. Question 2, by i t s e l f , w o u l d n f t r e a l l y ' t e l l us very much

about that . But: 2 would help us answer 1, i f i t had a cer-

t a i n answer.

DOBZHAMSKY: Excuse ne, but there i s one word

which nay cause t rouble , if I may point t h i s ou t ; t l aa in ly , t l

in ques t ion 3. You say ltmainly.tt Yould you agree to change

i t t o "substant ia l ly , t l subs tant ia l f ract iont t? I1Xainlyt t may

be misuneerstoot a s meaning 99 per cent .

CROK: By %ain ly , t l I mean more than h a l f .

D03ZHANSXY: I t i s subs t an t i a l ly .

CROV: Mainly i s ' subs t an t i a l ly . I would r a the r

say ttrnore than h a l f , " i f t h a t % whal; you wish, but i t is un-

ambiguous.

DO:-XANSXY: Cculd we say 40 to 60 per cen t?

CR31V': Is Itnore than halfi1 a l l r i g h t ?

LEWGNTiN: Thatcs not 40 t o 6C per cent;.

DOBZHANSXY: Fo. I would be in doubt .

h'EEL: BLt a t l e a s t i t makes the question less

ambiguous.

370

CROW: More than 25 per cent, or something?

DOBZHANSKY: Why not say t tsubstan, t ia l lyt t?

[Laughter] It means a l l s o r t s of--50 per cent i s not a

sacred percentage, i s i t ?

CROW: I don't favor i t , p a r t i c u l a r l y . Let's s ay

l1substantia1ly. It

GLASS: I th ink l t subs t an t i a l ly t t is j u s t a s vague

a s Itma in ly . It

:,3ZL : Ani! t o ?u t an exac t f igure in g ives us

some thlng to shoot a t , so Let s say Itmore than half . +' L13:40T.!TIW: Ffy only ob jec t ion to t ha t , Jin, is t h a t ,

p r e c i s e l y by giving you s o w t h i n g to shoot, a t , i t may be g i v -

ing you a fa l se t a rge t . People may s t a r t t o a r g u e w h e t h e r i t

is 40 o r 50 per cent , which may not be worth arguing about.

NEEL: Is t h a t any worse than arguing about what

"na i n ly t t o r t t subs t an t i a l l y t f aean?

L%'JONTIM: The r ea l ques t ion i s not whether i t is

40 o r 60 per cent, but whether i t is 1 per cent a s opposed to

sose th ing la rger , 25 o r 30 per cent . It i s an order-of-

magnitude ques t ion ra ther than- -

BODNR: You could frame i t t h i s way: You could

say, ''1s there a d i f f e rence of order o f magnituee between

1 per cent and 2C o r 30 per cent?"

DOBZHANSKY: But 30 per cent f o r some purposes i s

a subs tan t ia l aercentage .

CRG'3: Yes, but i f tha corn breeder learned i t

was 20 per cent , he would fallow one breeding proceeure, and

if he learned i t was 50 per cent, he would follow another.

b.IALLACE : I'm a l i t t l e confused by your reqarks

on category 1, and why i t i s important. Would you repeat

them?

CROW: I d o n ? t t h i n k I said anything that hasn ' t

been sa id a g r e a t many tines, t h a t i f the majori ty of mutants

a r e M, then, the impact of the mutation on the population i s

proport ional t o t he mutat ion ra te . If the major i ty are S--

WALLACE: But you say Ita subs tan t ia l minor i ty ."

Does tha t l eave a subs tan t ia l major i ty of M? As long a s the

argument runs tha t nu ta t ion of any magnitude i s important,

how will the argument be changed i f there i s a s u b s t a n t i a l

minority of mutants that are S? Tha t ' s my question.

CROW: 1.4e11, could I say i t t h i s way, t h a t if S

i s 50 per cent, then, the Haldane pr inciple appl ies to the ex-

t en t of 40 per cent of m t a n t s , and i t does no t in o thers .

There i s 50 per cent uncertainty introduced b y t h i s e f f e c t .

EOEIRTSON: You should. pu.t in t h e condition here

tha t this statement i s a large-po2ulation statement. The

noment you get down into the small thousands, i t ceases to be

t rue.

CXOV!: That s t rue , though, Clai?, f o r g r a c t i c a l l y I

anything e lse we could say, it s e e m to no. Agreed, but--

WALLACE: But i s n : t i t t rue tha t t h e cor rec t ion

is a r e l a t i v e l y s i n p l e and s t ra ightforward o m ? It depends

upon the proportions themselves.

CROW : Ye s . WALLACE: I don't lcnow what a substantial minority

is, but l e t ' s say i t ' s 10 per cent; then, we know t h a t 9 C pe7

cent of the o r i g i n a l argument h o l d s , and, a s long a s we sa id

t h a t i r r a d i a t i o n a t any l e v e l was in;portant, then 90 per cent

of t h a t i s presumably s t i l l inpor t an t .

CROi!: I would say even xore than tha t , tha t the

e r r o r i s inherent on the e:;sQaption of tha inpact on the human

gopulation of e r r o r s f a r i n e x c e s s of 1C per cen t for o ther

causes, so I wouldn't worry i n t h e l e a s t ab0u.t t h i s .

PfOI?TGN: Jimn, yo9 mace a statement that wasn't

chalienged by any of the y x n t i t a t i v e g e n e t i c i s t s , I assumed

we wzre ta lk ing here about f i tness ; is t h a t r i g h t ? Or a re we

kz2king aboct any character?

CEv%NE : Fi tness .

MORTON: Then, yau s a i d that the corn breeder would

do something different if the segregation load wGre 20 per cent

372

t han i f i t were 50 per cent of the inbred load. But, sure ly ,

the corn breeder is i n t e r e s t e d i n y i e l d , i s n * t he?

C30W: A t l e a s t , what X would like t o s a y i s , t h a t

f i t n e s s arguments are not total ly i r re levant to yield, because

i t has been subject to selection.

MORTON: But wourd t h a t , i n f a c t , t h a t k i n d of

q u a n t i t y , t e l l you anything? Tli-is is an in te res t ing po in t .

If a corner breeder found that, measuring fitness, i f he could

do t h i s i n some way, would he aake a d i f fe ren t b reeding p lan

i f he knew that the inbred load was mostly segregational?

You see, he i s dealing always in corn w i t h hybrids, but the

inbred load i s mostly ssgzegational and mostly mutational. 1

th ink it would be i r r e l evan t .

CROW: I:m talking about t he random load , for one

thing . IIORTON : Po I.n t 3 . CROW: No, I:m sorry ; I meant 4. SLATIS : I think he meant poin t 4.

LEVEN%: The point is t h a t when you're dealing

w i t h corn, y ie ld and f i t n e s s a r e e x a c t i y t h e same thing.

Whether a part icular seed has lots of descondants depends on

y i e l d and nothing e lse .

CROW: Well, a t l e a s t , thepe i s a co r re l a t ion .

LEVENE: V i a b i l l t y is part of y ie ld .

LEWONTIN: You never grew corn.

DOBZHANSKY: I never grew a co rn p l an t , e i t he r ,

but, D r . R o b k s m , l e t me ask you a quest ion, Would i t be

f a i r , f o r p u r p o s e s of pogulation genetics, t o d e f i n e f i ' t n e s s

of domesticated animals and p l a n t s a s f i t n e s s f o r the purposes

f o r which they are raiscli.?

ROBINSON: For the pixrpose f o r which they a r e r a i sed?

DGZHANSKY: Yes . _.

ROBINSON: Mot necessar i ly .

DOBZHAKSKY: Or usefulness to nan.

EIOBINSON: No, not necessarily, because, I think,

373

this changes. Man changes h i s requirements for these plants

and animals.

DOBZHAMSKY: Znvironment changes of f i t n e s s of

wi ld animals and p lan ts a l s o occur, but, at any given moment,

s h a l l we say, f i t f iess of corn or of poul t ry i s def ined as

the yield, the number of do l l a r s .

ROBINSON: Well, l e t ne speak to t h i s . You see,

e a r l i e r , we t r i e d t o equate yielC! t o f i tness In oorn , bu t , on

the other hand, you can argue the point , and effect ively so,

t h a t t h i s i s not t rue , for t h i s reason: Without man, a n e a r

of corn that has a r e l a t i v e l y small number of seeds may be

more f i t I n t h a t , If i t were dropped a t t h e s i t e of the plant

and a small number of seeds were here, then, these might grow

and reproduce better. On the other hang, a very l a rge ear ,

with a h i g h number of seeds, nay be so competit ive fo r t ha t

p a r t i c u l a r s i t e t h a t t h i s would be de t r i aen ta l t o t he p l an t .

NOW, that i s without man in t he p i c tu re , T h i s i s j u s t n a t u r a l

reproduction.

With man, ant! i f you make cer tah other assumptions

here, then, I think, the higher number of seed expressed in

y i e l d would be a component of f i t n e s s h e r e .

DEMPS'IER: The quest ion of whether o r not some

kind of equilibrium has been reached under man's se lec t ion has

been going on long enough.

CROk!: Well, may .I go t o $ome experiments now? 1

would l i k e t o ment ion severa l exper iments tha t a re fami l ia r t o

everyone in the room, and say then, to me, the quest ion they

bear on, and a l so the poss ib le answer they could give to t h i s

i f there were no ques t ions about exper inenta l de ta i l s ani!

things l i k e t h a t .

I will l i s t the exper iment , the ques t ion tha t i t

s e e m t o me i t bears on, and l i s t the possible answer that i t

could g ive ; t h a t i s , t he re a r e two kinds of experiment, those

t h a t can answer the question i f i t is Ityes,lt and those tha t

can answer the question i f i t i s "no," and those that are

374

meaningful in only one d i r e c t i o n ,

I will l i s t , f i r s t , the Gallace experiment, con-

s i s t i n g o f comgaring a f l y t h a t i s homozygous f o r two chromo-

sones, one of which has a h i s t o r y of i r r a d i a t i o n and the other

of which does not, w i t h the f l y )1 homozygous f o r t h e same two

chronosomes when one does not hzve a h i s t o r y of i r r a d i a t i o n .

That bears clearly on question 1, and it could answer i t

o i t h e r way, i t seems to me, yes or no.

A second kitld of experiment i s the one tha t

Comstock, Robinson, Gardner and o t h e r s have done a t North

Carolina and other places , where they answer a ques t ion r e l a t ed

t o yield or some o t h e r c h a r a c t e r i n t h e c o r n i t s e l f . I ' m

talking about what I th ink you called your plan 3; i s t h a t

r igh t , Cot ton?

ROBIF?SOM: Crossing back and f o r t h .

CRO!J: Where you double-cross and. put these back

together a g a i n and permit randoQization of l i n k e d combinations

a t a predictable ra te over a period of t i n e .

ROBIMSGN : T ha t ' s rig h.t . CROLJ': T h i s seems to ?le to bear qui te unambiguously

on question 4, and I think i t , too, can provi6.e e i ther k ind of

an answer; that is, i f corn yieZd i s pr imari ly due t o h e t e r o t i c

genes, a t l ea s t , t he l i nkage equ i l ib r ium will not disappear ,

The linkage bias, perhaps, I should say, will not disappear.

If t h e apparent overdominance i s pr imari ly due to l inkage, i t

will d i s a p a e a r a t a t l e a s t a somewhat pred ic tab le ra te ; so i t

seems t o me t h a t i s a meaningful experiment, a t l e a s t , and,

whichever way i t goes, i t bears on t h e quest ion.

LEVOUTIN: Do you agree that that answers question 4

o n l y i n t h e case where you are dea l ing w i t h th ings t aken ou t

of ai1 equilibrium of a pollinated variety?--because, i f you take

zust two long-tine inbreds, these two long-time inbreds are,

a f t e r a l l , .s small sample of t h e kin& of gene act ion which

ex i s t ed in the population. You will ge t a var ie ty , an a r ray ,

of answers, if you do t h i s w i t h many d i f f e r e n t s e t s of inbreds.

37 5

CROW: Yes, to the extent t h a t the inbred l ines

you s t a r t w i t h and put together can be regarded as reconst i -

t u t i n g a random population.

LEWONTIN: Yes, t h a t 's important

NEEI.: I ' m so r ry t o i n t e r rup t t h i s t ra in o f thought ,

Jim, but I'm doing a "delayed take" here. Isn't there a

f i f t h q u e s t i o n which l i e s behind a good dea l of the disagree-

ment? T h i s i s the question of the proper frame of reference

in answering a11 four of these questions. Is i t the population

mean, o r i s i t the best genotype? If i t i s the best genotype,

do you s h i f t s tandards a s you -go from segregat ional t o .nutation-

a l systems? Before we can jus t d i scuss any of these, what i s

your frame of re ference in t ry ing to answer these questions?

DOBLHANSRY: I very much agree w i t h our Chairman.

T h i s is what I t r i e d t o say. Rut I take i t tha t we have post-

poned t h i s c ruc i a l ques t ion fo r d i scuss ion l a t e r . I s tha t

co r rec t ?

NEEL: T h i s is ce r t a in ly t he ques t ion o r the i s s u e

about which more blood is be ing sp i l led r i g h t now, i n a sense,

than any other.

CROW: Wefli get t o i t .

ROBINSON: Yes, t h a t is the question.

CROW: Let ne sax tha t ne i ther of these two ex-

periments i s t h e l a s t b i t i n j u r e d by any amount of d i scuss ion

on the subject. Cornst.ock*s measurements a r e e n t i r e l y on

var iance, an2 'j,raLlace's on scale . I can ' t see anything am-

biguous about Wallace 's neasurement s c

E4ORTON: It would answer the question if i t in-

volved a whole possible spectrua of variances, but, since i t

doesn ' t , i t can% I submit that one could not reasonably

answer the f irst two quest ions if they were expressed in a

genera l way, by any experiment that we could now perform, under

any circumstances. You don* t have anytay of get t ing informa-

t i o n on the f i r s t two points, There is a b ias there .

LEWOHTIN: What i s the bias in the argunent of

NOZTON: A t l e a s t w i t h respec t t o c e r t a i n r a t h e r

gross types of mutation.

MULLER: Yes, and you ' re aeasur ing f i tness as

defined under certaln particul-ar conditions, of course, which

you always have to do.

LEWONTIN: Doesn't the strength of your argument,

Newt, depend on t h i s d i f f e r e n c e between chromosomal and locus

e f f e c t s , if you gave a gent le enough t r e a t a e n t so you could

assume that near ly every chromosome t r e a t e d had a t most one

nu.tant?--because, in fact , the mean nunber of mutations induced

?;r t h i s l e v e l of r a d i a t i o n i s probably l ess than one per

ckromosome.

LEVENE: But we don ' t know what t h e n u t a t i o n r a t e

is for , l e t ' s say , po lygenes , and you may have a l o t of those

ineuced.

Wallace * s experinent? I * m sorry.

MORTON: You would have t o be able t o enumerate

every mutation without regard t o i t s e f f e c t , and then de te r -

nine i ts e f fec t in hoaozygotes and in heterozygotes , and t h i s

doesn' t seem t o be f e a s i b l e ,

DZXPSTER: Neither of those experiaents g i v e s an

unambiguous answer, but i t gives some information on i t .

XORTON: No, I would th ink not; unless you couid

imagine an experiment that would b e a r d i r e c t l y on that ques-

tion. It doesn't glve any information on i t .

FlLJLLER: l4hy can ' t an experiment bear on that in .

which you don ' t t ry to ident i fy the mutants bu t jus t apply

mutagenic agents , so you know that .the mutations have been

producec?, and then compare what happens when those chromosomes

are used w i t h what happens when the-"

MORTON: Operat ional ly , you ' re looking a t chromo-

somes that are heterozygous and homozygous. It t e l l s you

no'thing very much about the mutants.

MULLER: Y e s , it does, because you're applying

r a d i a t i o n a t a l e v e l a t which the effects , f o r the ma t pa r t ,

a r e i nd iv idua l ,

377

LEWOMTIN: But t h i s i s n ' t t h e quest ion that was

raised. I'm t r y i n g t o f i n d o u t what the ques t ion is.

DOBZHANSKY: I'm s w p r i s e d t h a t Dr. Wallace doesn't

say anyth ing about i t , bu t i sn ' t i t t rue tha t h i s exper iments

bear on quest ion I, under cer ta in spec ia l c i rcuxs tances?

CROlr: I s n ' t t h a t - t r u e of any experiment a t any

time?

GOSZXAITSKY: I th ink Dr. Norton is p e r f e c t l y r i g h t . I

FIGRTOM: T h e mutat icns that are induced are tes ted

only in he te rozygotes . They a r e never observed i n hoaozygotes,

so I don ' t th ink one car, t a lk about a h e t e r o t i c gene unless

you see i t in a homozygote.

. CROW: I'll accept that .

b,fALIJACE: If I say that; the mean goes up, though--

ivDRTOM: You're cozparing a homozygote with a

heterozygote. You're not comparing o r s a y i n g a n y t h i n g a b u t

the other homozygote . LEWOMTIN: Do yot.1 bel ieve these mu ta ' t ions he has

incluced will, i n f ac:, cause an increase i n the other homozy-

gote? That seems unl ike ly . The reason he dicln't bother to do

i t is because, I think, i f there i s one thing that everybody

i n t h i s room accepts , i t i s t h a t newly a r i s ing muta t ions , when

maze homozygous, will be lousy.

MORTON: I'm not sur.e t h i s i s so.

LE!JONTIk Do you thinlc that t h e frequency of newly

ar i s ing muta t ions which a r e b e t t e r t h a n t h e o l d ones in the

homozygous condi t ion will throw t h i s out?

VALLACE: Then, we can throw cu,t the idea that ?

equals the square root of S, and so on.

MORTON: But, yuu a r e assuming i n t h i s argument

that genes have a vezy small e f f e c t ; % h a t a l t h o u g h t h e i r r a t a -

tion :late has nev.rer been measured, i n f a c t , the mutat ion r a t e

i s no t app rec i ab ly g rea t e r t han t he l e tha l r a t e , f o r oxarngle.

Is t h a t r i c h t ? If i t were t rue that there were a very high

probabi l i ty but inf ' in i tes inal xuta tions, so-called, If these

were what was being measured, you don't know how they would

behave i n homozygotes.

DEMPSTER: That i s always true. You are always

making some kind of assumption when you i n t e r p r e t a n e x p e r i -

aerrt. These assumptions may be. wrong, but they are reasonable

f i r s t assumptions to make . I f we can si y t h a t xutc.';lons of

small effect are not very f requent , then, we can give a

probable answer, yes or no, perhaps; I mean, i t doesn' t pive

an absolute answer, but you'l l never f ind an experiment that

g i v e s an absolute answer to anything.

MULLER: If you take Jinn's or iginal assumption,

t h a t t h e r e is a s i m i l a r i t y in the amount of e f f e c t of these

d i f f e ren t c l a s ses , t hen you can do i t ,

MORTOH: I submit that the question, in general

terms, i s not meaningful. It, will be made meaningful only by

introducing an arbi t rary assuapt ion. Perhaps, the quest ion

is n o t r e a l l y u s e f u l .

DEMPSTER: The assurnptions are not completely

arbitrary. For example, the f i r s t suggestion you made, t h a t

you want to know what hapaens in the homozygo te--if you make

the assumption that most new auta t ions wi th small e f f e c t s

when introduced by r a e i a t i o n a r e favorable i n t h e homozygote

cond i t ion , t h i s Leads you to an untenable assumption.

MORTON: If you don ' t know how many mutations have

been induced by 500 r , how do you know how many a r e l e t h a l ?

Since you can't count mutations, i t has no bearing on t h i s .

MULLER: You can count them u p t o a c e r t a i n limit

of s i zab le e f f ec t .

MORTON: You have t o assume an awful lot .

DEMPSTER: I agree. If you say t he re a r e a l a r g e

nmber of nu ta t ions produced that are , say, completely re -

cessive' and have an e f f e c t of about one pa r t i n a mil l ion,

you can ' t answer this quest ion, but you can say--

NORTON: And tha t shows t he supe r io r i ty of the

3'7 3

t h i r d and fourth quest ions, and you migh t get some informa-

t ion.

NEEL: Walt u n t i l we g e t t o t he t h i rd and fou r th

quest ions.

3EE.IPSmR: You can say e i tker there is a t r e -

meadous nunber of mSa t ions produced. t ha t have very small

e f f e c t s , r e c e s s i v e l y , o r you give an answer, yes o r no.

There are a few other assumptions. I ax grea t ly s impl i fy ing

i t , but you've gotter, sone information that bears on the

question. I t h i n k t h a t : s a l l J i n is t ry ing to say.

3ODNZR: I s n ' t t h e mre important quostion, i n a ,

way, the fact that the rsuta,t ior,s you induce will not give you

a spectrum of m . t a$ ion type which I s a t a l l coaporable t o

what o c c ~ r s spontaneously?

. PULLER: Except that we have evidence that i t is

s pon t aneous . BODN3R: Mot fron microorpanisas.

74ULLZR: I : n thinkiilg of Dros9phi la .

CROU: i t bears on quest ion 1, as f a r a s mutation-

induced e f f e c t s are concerned, which i s a l l you!re reaily

trying to say.

EOBIiWOnT: Befors you i e a m Eo. 2, on the corn,

you brought i t u p in 1948 ani! 1952, and, where you a r e askir,g

for other information, you may bring i t up, but, you remeaber,

i n terms of the 1948 and 1952 papers, tke question about corn

in t he opcn po l l i na t ed va r i e t i e s , and then the randcrn s e t of

l i n e s - - t h i s i s one reason we prociuced this mater ia l , to make

then in terms of a11 possibie c?osses and see wkat the maxi-

mu9 performance of t hes s ms , i n terms cf mean performance,

Plost hybrids might come ou t o f that population, because, you

rcmmbcr,in t s x s of you: hy;othssis--.I d m f t know whether

~ ~ ~ . - 3 vi11 f i t iii h r e , >ut tha t has bee;? done. I;ie hare an .A. 'n 7 c)

ail 'ay of hybrids, and i t seems t o ma tha t bears on the ques-

t i o n of whether you a r s i n D or E. I s n ' t t h a t r i g h t ?

CliO!.!': I think i t does, yes. I have overlooket! i t ,

a s a matter of f a c t .

MORTON: So i t would be acceptable to everyone

to modify the f i r s t one and say that the majority o r a t

l e a s t a subs tan t ia l minor i ty , a s suming that !nos t rm ta t ions

which have not been measured and, i n f a c t , cannot be measured

t h i s procechre, I can imagige, do not , in f a c t , e x i s t . The quest ion i s meaningful when so phrased. [Laughter]

CROV: I th ink tha t i s a fa i r s ta tement , bu t you

could say the same thing, . real ly , about a whole v a r i e t y of

experiments.

MJLLE3: No, assuning tha t they can , for p rac t i -

ca l purposes , a t this point , be a f fec ted , you can say.

ROBINSON: I suggest we go ahead.

CROW: There i s not going to turn out t o be any

fur ther experiment in t h i s fu r the r d i scuss ion .

Let me mention, GS the t h i r d point , one of my own,

but I would suggest deferr ing discussion of i t , because I'm

sure i t will lead to some. I would l i k e to say where I th ink

i t bears on what Newt 'and I have ca l l ed the B plus A over A

r a t i o of Mor ton, ?fuller an6 myself.

T h i s bears on quest lor , 3 and not on 4, o r a t l e a s t

i t would have to take some r a the r unusua l va lues t o t e l l you

very much about 4. T h i s i s what I would ra ther say . It can

answer the question only one way, which, it seems t o me, is,

important ,to say. I t can give you an M answer, but i t canf t

g ive you an S answer, except under what seems to me--well, i t

can give only a %ott answer, unless the typical number of

a l l e l e s i s quite high.

LEWOMTIN: Jim, I would like t o defer that , except

t h a t I want t o say something now. I b e l i e v e , i n f a c t , if you look c a r e f u l l y a t q u e s t i o n 3, i t can give both a "yes"and a

I::1of1 answer. What it can give a l'nolt answer to i s e s s e n t i a l l y

quest ion 2, on ,the number of l o c i . But, I bel ieve, if you t a l k

about the genetic variance or t h e a v e r a g e e f f e c t , i t r e a l l y .

turns out to be pret ty symmetr ical i n tha t resgec t .

381

CROW: I t h i n k we are agreed, but l e t me see if

we are saying the same thing. If the value here is h i g h ,

it po in t s i n one d i r e c t i o n ; i f the value here i s low, i t

may be t h a t A i s in f l a t ed , by causes tha t a re unre la ted to

g e n e t i c f a c t o r s t h a t you are trying to study. If you have

some way of removing the environmental part of A , then, I

think, a low value is meaningful.

LE!:!ONTIN: So I say , under the idea l s i tua t ion ,

a s i tua t ion unde r which the B/A r a t i o c a n , i n f a c t , be a two-

s i d e d t e s t o f hypothesis 3 but not of hypothesis 2.-

ROBERTSON: Will you s p e c i f y f o r u s e x a c t l y what,

A and B a r e ?

CROW: Well, A i s the measuremen.t of whatever you

are 'measuring on the inbred coeff ic ient , and B i s the other

end of the constant regression equat ion.

NEEL: DO you now o r l a t e r want t o say ttha t you

nean by "high"? You say, i f i t is h i g h , thisanswers the

question.

CROW: Ch, 1.0 07 soae th ing l ike tha t . I would

say, if i t i s 10 o r more, i t a rgues in favor of Y. If i t i s

2 o r 3 o r l e s s , ani! A as an environmental component of A i s not the

l e t t e r ,

l a t ion,

reason, I would argue that i t argues f o r the o ther

and i t bears more on 4 than on 3. NEEL: I would cha l lenge tha t from your own form-

t ha t 10 j u s t g i v e s you a c r i t i c a l r a t i o .

CROW: All r i g h t

NEEL: That 10 would be a c r i t i c a l r a t i o , and

dividing point of re la t ive importance.

CROW: Well, make i t 6, you Itlean?

LEWONTIN: Or 20.

WALLACE: I'm a l i t t l e b i t confused. Did you say

i t would. answer 10 to 3 o r t o 4? You've switched questions.

CROIJ: I've f o r g o t t e n what N and Y means; t h a t ' s

the t rouble . I think I wrote i t backwards. If t h i s can o f f e r

evidence against S, which means "no," yes to ques t ion 3. If

382

it can o f f e r evidence in favor of Y, i t i s primarily "not' to

question 4. I haven't thought t h i s through.

L%L!OMTIN: I would l i k e to say some thing about

t h i s l a t e r . CROW: Let me take t h i s p a r t ou t for the moment.

In any event, a h i g h value of t h i s a rgues t ha t the answer t o

question 3 is N, Perhaps, a very high value argues that the

answer to ques t ion 4 is a l s o N, but more s t r o n g l y f o r 3 than

f o r 4. Now, experimsnt No. b--and some of these are

classical experiments , but I woul.8 l i k e to l i s t then, anpayo-

E4ULLER: You will take up l a t e r whether A i s d i s -

cernible?

CROY: Yes. I think t h i s i s something we \do want

t o d i scuss , bu t i t cou ld l ead t o qu i t e a long discussion. A t

l e a s t , i f the discussion i s proportional to the nuaber of

words that have been wri t ten about i t , i t might; r u n f o r qai te

a while.

Let ne l i s t the por, ple vho d i d the experiment.

I ' m thinking of t h e d i r e c t e f f e c t of heterozygous effect of

newly'arislng mutations done 5y S te rn and Wovitslcy and t h e i r

group, on the one hand, and by !fuller and Campbell, on the

o the r .

DOBZHANSKY: Nobody else? [Laughter]

;JIITLLER: He was too modest to go i n t o it.

CROW: Whoa em I missing? CJi te se r ious ly , for

new mutations--

WALLACE: !Jell, tSe other day, Wallace was men-

tioned. [Laughter]

CROW: Yes. Excuse me. I was thinking of acldi-

t i o n a l experiments. I was distinguishing between heterozygous

e" fec t s ar.d new mutations.

!:IALLACE: Are yo! r e s t e c t i n g t h i s t o new ones?

CRO\?: I:m r e s t r i c t i n g ,myself t o the following

experiaer,t: where you ir.duco a m t a t i o a , clissx-er tha't i t i s

,

353

t r u l y l e t h a l , and t e s t t ha t i n t he h t e rozygous s t a t e .

'JALLACE: We shoulddt forget the Sterr is , on the

spontaneous, because that i s inportan,t .

ROBIFSON: Where would Sprague and Schuler go?

CRO*:!: :%!as tha t t he same kind of thing?

LTdONTIN: No, double haplo id , i n o the r words,

with the chromatic mutant.

ROBIKSON: I t wasn' t a11 double haploid, was it?

DSMPSTER: Schuler ' s experiments have touched on

t h a t .

MULLER: You a l so have .the James expe r i aen t s i n

yeast

CROW: I don* t have the Schuler experiment well

enough i n nind to discuss i t , so someone e l s e will have to do

i t . , Eut i s there anyone fron Dr. abzhansky!s Laboratory

vho has done this experiment? T really didn't think I was

overlooking anybody i n t h i s r e s p e c t , who has induced the

l e t h a l s o r founc'; them f i r s t , and then put them in the hetero-

zygous s t a t e an8 t e s t e 6 them. .

L3WOKTIM : Corde i r o ,

CROW: Are they net!ly induced?

LE!.:'ONTIM: No, they were po?uia t ion le tha ls . I'm

sorry.

CFIOV: I th ink I was r i g h t i n the f i rs t place.

I ' m not trying to be a l l - i m i u s i v e , anyway, so if somebody's

p r i o r i t y is hur t , tha t ' s no t the main purpose of t h i s d i s c u s -

s ion. T h i s bears on quest ion 1 f o r l e t h a l s o n l y . Most of

Stern's were probably spontaneous, and most of I . h l l e r*s .

MULLER: Excuse me, but James also a p p l i e s t o

nonlethals .

CIlOW: Stern Is experiments were n o s t l y spontaneous,

a l . k k u g h they nay have inclu3ed a few radiation-induced.

NuuLler's and Caapbell 's were all radiation-induced, but UV

3ore than x-ray.

DOBLHAFSKY: Yas that published?

384

iK??LXt: Not & extenso-, but; I gave t h e conclu-

s i o m i n my 1956 ?aper.

DOEZHBNSKY: Could one sea the data?

IULLZ 3 : Ce r t a i n l y . DOBZXNXKY: I t would be good t o have them pub -

i i shed .

CROW: % e l l , t hey a r e ava i l ab le i n some kine of

mimeographed form, aren ' t ' they, f o r people who want them?

IKJLLER: They a re ava i l ab le , I'm not sure tha t

i t ' s mimeographed, but I have some carbon copies.

CEOW: The f i f t h experinent is of the kind that

Cordeiro, Kiraizumi and I d i d , and sone other experiments

from South America, and seve ra l o the r s . These have t o do

w i t h doing the same kind of experiment , ident i fying the

l e t h a ; f i r s t , ani! t h e n d i r e c t l y t e s t i n g i t s haterozygous e f -

f e c t . Thsse bear on quest ions 2 and 3, i t s e e m t o ne,

with a possible l lyesf l or rrno.ll

LEWONTIN : Don't you think they bear on No . 4?

If we discover tha t l e tha ls a re sen idoz inant , f o r example,

they have nothing to say about the expressed load.

CZOW: I*Jel l , I guess, they bear on 4 in t h e f a c t 8

that the r ight answer to 3 will ' t e l l . you something about 4. They bear one way on 4, i t s e e m t o me.

DOBZHANSKY: Wallace's experiments have no t con t r i -

buted anything t o t h a t ?

CIIOW: I've already taiked about 'dallace.

DOBZHAESKY: I mean, experimect 5 , WALLACE: '.Jetre being modest. He put my narne up

first, and we're not putt ing it up every time i t appears.

CROE: I'm not t rying to l i s t every person who d i d

t h i s kind of experiment. It* would take me t h e r e s t of Lhe +-y.

DOBZHANSKY: Is that not somewhat s e l e c t i v e ?

LEdOiJTIN: I t h i n k i , t i s an fmportafit point. It; i s important for us t o decide on whether ':!allacets experiment

bears on any other experiment.

385

'JALLACE: !.Jait a minute! Xhat experiment are you

talking about?

PCEZEIAMSKY: I mean . the experiments publ ished in

1961 and 1952, which were tes t ing for he te rozygous e f fec ts

of lethals, sub le tha l s , and s e n i v i t a l s , and so on.

WALLACE: I don ' t c am whether I'm on there o r

not . I know what you ' re ta iking about , and I'm pe r fec t ly

happy.

MULLER: We have t o remember Falk, a lso, i n con-

nect ion w i t h t h i s . Iie i s a v e r y f i n s worker. He i s the

b e t t e r worker i n t h e f i e l d .

\!ALLACE: Yes, p,ut F a i k up i n 30. l.

C R U i : I ' m sor ry , br;t I'm t ry ing t o i d e n t i f y t h e

kind of experiment, not c r e d i t the intell igence behind i t .

On f!o. 6, I have the kind of experiment tha. t , as

f a r a s I know, was f i r s t done by Dobzhanslcy and '&r igh t , but

since has been Zone by a g rea t many peogle, which i s the com-

parison of frequency of a l i e l i s m , m t a t i o n r a t e , and frequency

It seems t o me tha t t h i s bears p r i a a r i l y on 2 and

3. I r e a l i z e t h a t you can ' t ar.swer 3 without i t t e l l i n g you

something about 4, but i t s e e m t o me t h a t the iamediate bear-

ing o f t h i s p a r t i c u l a r e x p e r i x n t is on 3. What I'm t a lk ing

about "ow is an experiment in which you obtair , t h e following

da ta : You make chromosomes hcaozggous fros natural popula-

t ions , you measure the frecluerxy of l e t h a l s among such, which

aeans tha t you are aeasuriflg the gene frequemy i n t h e

equilibrium population rather than the phenotype frequency. i: ou l ea rn t he mu ta t ion r a t e e i t he r i n the same experiment or

froa some other source. You a l s o masure the frequency o f

a l l e l i sm, and you compare the f requency of l e t h a l mutants i n

the population with what would be expected on the basis of the

Iccurrence of the mutat ion ra te and t h e r a t e a t which these

0

386

have been eliminated. I th ink X r i g h t and Dobzhansky were

the f i r s t to argue th i s , paybe; I shoule! say to suggest , i t .

DCBZFAiiSKY: I t m sorry, but that bears on No. 1,

not on 2 or 3. LEWOMTIW : 110 t newly a r i s ing rnutant s,

CROW: These a re i n equilibrium.

DOBZH.INSKY: Sorry, mutat ion ra te . You determine

it by newly arising mutants, obviously.

CROK: Right, but, t h a t doesn't mean tha t the ex-

periment bears on that .

DOBZHA?!SKY: '.&ll, then, you compare i t with t h e

gossibZe r a t e of e l imina t ion due t o hoxozygosis, not f o r

newly a r i s ing nu tan t s bu t of nu tan ts which a re i n t he popu-

l a t i o n ; so what you ' re deal ing with is quest ion 1.

CROW: I have to dissgree. It seem to me t h a t

i t bears on question 3.

DOBZBAXSKY: I have to d isagree , very c lear ly .

WALLACE: I would l i k e t o a s k a ques t ion i n con-

nect ion with quest ion 2. Suppose you f i n d t h a b y o u a r e com-

puting an average H .out of thess chta, r i g h t ? Suppose you

find t h a t i t i s s l i g h t l y n e g a t i v e , which means t h e l e t h a l s

a r e s l i g h t l y h e t e r o t i c . Let s assume + h a t is what one f i n d s ,

although no one has done i t , apparent ly . Does , that say the

majori ty of l o c i i n e q u i l i b r i u n p o p u l s t i o n s have two o r more

a l l e l e s i n c l a s s S?

CROW: Only i f ose equates the s ize of mutant

e f f e c t i n t h e t?do systems, a s we have sa id . It bears more

directly on this one . WALLACE: I th ink t ha t ' s t he ques t ion . I sn ' t i t

poss ib le tha t the H you g e t , l e t ' s s a y , which i s a negative

v d u e on the average, is due to- a small number of l o c i ?

CROW: Yes, w i t h a b i g effect averaged over a

much l a rge r number' with a m a l l e f f e c t . ? e r h a p s , I shoul t

Put parentheses around both 2 and 3 here.

DOBZHANSKY: I th ink we should be able to agree

3 87

a t l e a s t w i t h t h i s . You are coapar ing nu ta t ion ra tes , obvi-

ous ly , f o r t h e newly ar i s ing .nu ta t ions ; cor rec t? w i t h the

computed e l i m i n a t i m r a t e or. mutiitions which you are f ind ing

i n the natural population. R i g h t ?

CROW : Yes . DOBZ€iA?iSKY: Doe sn 't that bear on quest ion l?

CROW: [Laughter] t!o. Yaybe, somebody e l s e

could ex?la in i t .

DOiXHAtlJEY: Suppose half of the mutations tqhlch

a r i s e are de le t e r ious and quick2.y e l in lna t ed , and the other

half are re ta ined in the populat ion. The r a t e of hoflozygosis

of t h i s second half and the rate of mutations pxducing them

would not be the en t i re nu ta t ior , ra te , bu t 0~1y par t o f i t .

LE1!OKTIN: 2xcusa me, but , i n your experiment, d i d

you t e s t t h e ililryterozygous e f f e c t of new2y a r i s ing nu tan t s ,

o r d i d you jus t use the rnu ta t lon ra te as a paraneter f o r the

res t?

DOBZHANSKY: That i s prec ise ly what you do. You

must use t h e muta t ion r a t e .

. LENONTIN: But you do not a s k the ques t ion d i r ec t -

l y , what i s the average heterozygous effect of the new lnutants

i n your experiment?

DOBLHA3SK.Y: Consequently, ycu ge t t h e average \

heterozygous effects of n u t a n t s which a r i s 9 , not of t h e

mutants which a re ir, the pogulation.

CRG:..!: KO, :'ou g e t the heterozygous effect of the

mutants t h a t are i n the populstion. Look, ycuweere the f i rs t

person to do this kind of exper iaent , o r you and AProfessor

?!right. Maybe, he d i d the al.gebra.

ROBINSON: Maybe, t h i s i s put t ing the quest ion

?!:other way, bu't I s t a r t e d t o ask t h i s ques t ion o r ig ina l ly ,

ani I th ink t h i s i s the argument. !/,!here does t h e experiment

tha t Sears on mutation rate f i t i n t o t h i s ?

CRO:!: I d o n r t want to ge t involved i n EI l o t of

a lgebra, and i t nay not be possible--

388

3OBINSON: I mean, which one of these four? I

t h i n k t h a t i s the argument here.

CRC'.J: \.'ell, Ilve just about exhausted m y a b i l -

i t y to s z y t h i s , b c t let me t r y i t a g a i n . The i t e m o f da ta

t h a t one uses he:e a re the f r e q u e x f a s of l e t h a l s i n t h e

naturai goyL,at ions, and the frequency cf alLr;l isn amoagst

these Lethals in a natural populat ion. Then, one brings i n

a s another necessary parameter, the .nutation rate a s measured

from some independent experiment, almost always. ru'ow, on2

can predict , thinking of a single locus, th3 avesage domi-

nance of t h f s pa r t i cu la r l ocus , Sut t h e pa r t i cu la r gene

whcse dominance you are measuring i s a gsne t h a t i s in t he

population.

LEWOXTIN: But, Zim, I th ink , I 've jus t rea l ized

what DT. Dobzhansky is saying. €:e is saying that , neverthe-

less, the difference between the standing nunber of l e t h a l s i n 1

the population and what you get by mutation must be due t o

e i i a i n a t i o n o f mutants, o r t o an accumla t ion of mutants,

whichever way the difference hagpens t o go, and therefore i t

is evidence, ir, f a c t , of the way ir. which these mutants are

a c t i n g when they a r i s e .

CROII: Yes, through t k a otker qusst ion.

LE:dOETIN: SuFpose newly a r i s i n g mutafits, on t h e

average, are heterot ic . r'!len, you wlil. f i n6 a vast number of

l e t h a l s i n t h e population a s comparec! with t he r a t e o f muta-

t i on . If they are semidomfcanf, you will have a f i l t e r i n g out

of them. It can, in fact , theyefore, bear on quest lon 1.

CROW: O.K. , i n t h e s a m e t h a t an answer to ques-

t i o n 2 i s always bearing on I. .

DOBZHANSKY: KO, I don't think i t bears on 2

3i:d 3 a t a l l .

LE~,s~Cl13NTIN: In the sense t h a t t h s comparison of

t he r a t e of arising u i t h the standi,rg nunber must be a r e s u l t

of the selection process between t h e ,time t h e mutant a r i s e s

and the equ i l ib r ium s i t ua t ion .

389

cR01.4: Yes, Dick, but there is another point t h a t

you haven't mentioned, that cones i n t o t h i s . If you are do-

ing t h i s for a single mutant, t h a t ' s f i n e , but now, wh&t

you're eoing is averaging second chroaosoxes in the popula-

tion. )!ow are these weighted? They m e weighted by the f r e -

quency of the occurrence of let5-a1.s i n that population. That

mear,s they are g0ir.g to be most heavily wsighted i n t e r m of

those mutants which have pers is ted in the gopulat ion. There-

f o r e , you are measuring the average dominance of those mutants

which have p e r s i s t e d i n t h e population long enough f o r you

t o ? ick them out .

LEWOI?TIN : That s t rue .

CROW: SO, then, you a r e measuring the average

dominance of a group of mutants t h a t have pe r s i s t ed i n t he

populat ion ra ther than the averaze dominance of' a group of

mutants a t t h e time of a r r i v a l . T h i s i s d i f f e7en t .

NZL: Coffee is waiting.

CEIOK: This is a p o d . point to d i scuss over

coffee, but I ' n p r e t t y s u r e 1'3 r igh t abou t t h i s .

LZVEW: You:re both r i g h t .

[Recess]

X?EL,: 2 t h ink i t would be qu i te noncont rovers ia l

if I were to wr i t e a l e t t e r t o the Ifacy Foundation, express-

ing our apprec ia t ion for the ia s.t th ree dr::.ys. [Applause]

DICKERSON: It may be too e a r l y to say. [Laughter]

CROW: The one surviving person is empowered t o

w r i t e t h e l e t t e r . Well, l e t me ra ther qu ick ly pu t down my re-

maining points. I am conscious o f having taken un too much

time already.

?IULLE3: I th ink most of us would agree tha t we and

not you took up the time. [Laughter]

CR01J: There a r e sone kinds of exgeriments that

have been used a t va r ious t imes by corn b reeders tha t , i t seems

to me, may have some bearing on the quest ion, a l though they have

not been wicely discussed. Dickerson has done a l i t t l e b i t of

389a

t h i s kind of work. I have i n nind some of the ideas growine

o u t of t h e suggstions of Hull on constant Pair regress ion

techniques, that bear on question 4, i t Seems to 1119. It would

be aore probable to be d e f i n i t i v e If the afiswer were "Y~s"

instead of f lno, l f that is, t h i s t a i l i n g o f f a t the top of the

regression, i f i t were sharp, would argue f o r overdominance..

In the absence of t ha t , I think, i t is cons is ten t w i t h sev-

e ra i hypotheses . Xowever, t h i s has ro t been widely used, and

I'm putt ing i t in here aainly because of t h e f a c t t h a t it

has played such a l a r g e h i s t o r i c a l p a r t i n t h e discussions

among corr , breeders in this cour , t ry .

I also think that experiments such as--I don't

know what t o c a l l them, but t he kind t h a t R i t c h i e and Sprague

and o thers have done, of recurrent conversion improvement--

ROBINSON : C a l l them "conversion inprovement , '' I

guess . CRCW: In f a c t , some of the s t rongest evidence

ex is t ing t en years ago , i t seems t o ne, fo r pa r t i a l doa inance

o r h t Least not overdomirance of corn y ie ld came out of t h i s

kind of experiment, and I was the nost shaken in 1948 by

Ritchie and Sprague's papers, more than by any other data ex-

i s t i n g a t t h a t tine, i n arguir,g f o r ovesdoninance a s an argu-

aen t i n co rn y i e ld . Anyhow, i t bears on question 4 , on posi-

t ive regression. Regression argues s t rongly for llno.ff I

think no s l o p e a t a l l is uninterpretable on t h i s , and t h i s is

par t of the problem, too. . "

LEWO?JTIN: For t k benefit of the Drosophi l is ts ,

I take i t , t he Sprague and Ritchie experimerts are e s s e n t i a l l y

the same a s r e g r e s s i v e homozygous on heterozygous?

CROW: I n p r i n c i p l e , y e s , b u t t h i s i s the e f f ec t

of seeing the s e l e c t i o n for combhining of one type, if it

.:lakes i t improved i n a b i l i t y t G combine w i t h o t h e r types.

LEYONTIN: Yould you include ' th is regression of

honozygous on heterozygous?

CRO'd: I was coming t o t h a t . I was going t o

, make t h i s the next one.

LE?.IN'~IK: Because tha t is always one-sided.

CEIG;.:.Y':. Yes , regression of homozygote on hetero-

ZYCOtCI.

XIBINSON: What 1.s the difference te tween that

and No. 7?

. CEO::;: What Hu11'2id was t o do regress ion of

homozygote on heterozygote, holding the one parent COB t a n t

through a whole series , whereas, not:, these a re genera l re -

gressions of homozygote on heterozygote, done mainly by

Yallace and Ijobzhansky in T)roso?hila. T h i s bears on question

No. 4.

It s e e m t o me tha t . th i s can p rovide a %ott answer

i f the regzession i s strong and pos i t ive , bu t tha t a ''no"

slope i s unin te rpre tab le i n t e r n s of these kinds of quest ions.

This may be debatable, because Itm not sure whether Bruce

would agree with t h i s statement. 4s a mat'ter of f a c t , I'm

p r e t t y s u r e he wouldn't. Let me leave this one out, because

i t i s in t he fu tu re r a the r t han t he pas t , bu t I would l i k e t o

mention i t , nonetheless; that one asproach to the question i s

t h a t if we know the nature of l e t h a l s i n th,e popula t ion , tha t

is, i f we can assume t h a t t h e t y p i c a l l e t h a l i s p a r t i a l l y domi-

nant, and l e t ' s j u s t assuine fcr the mo3ent t h a t we do know that--

if we know tha t , then , we can a s k the question about whether

the typ ica l de t r imenta l i s a l s o pa r t i a l ly don inan t by t h e r s l a -

t i v e r a t e of accumulation of detr i3entaI .s in the populat ion,

and comparison with lethals in .the population.

The information I need t o know t o answer t h i s i s

t h e r a t i o of the load due to de t r imen ta l s t o t h a t due t o lethals

f o r two populations, on new croups of mutants and an equ i l ib r iun

group of nutants .

brow, I have been s tynied i n t h i s Irinc? of exyt-im-t

because of the d i f f icu l ty o f ge ' t t ing a measurement of t h i s

quantity for new mutants. It ought to be done fo r spontaneous

mutants if you're going to aalce the gopc la t ion compzLson f o r

b

There are two i:Iportant points--

WALLACE : What symbol a r e ;ro1: going to put down

t h e r e ?

load, and L

Uiil.

CROSJ: Let's say D/L, and D s tands f o r de t r imen ta l

s t a2ds fo r l e tha l l oad , i n new v e r s u s e q u i i i b r i -

LEWONTIN: What question does t h i s answer, Jim?

CROV: It answers question No. 2, I think.

LJ3WCXJ'TIN : I th ink , in the same way t h a t S l r igh t

and Dobzhansky answer question 1; r i g h t ?

CROW: I t arswers question 1 i n an ayerage sort

o f way, ani! i f one kind of l ocas i s o ~ C i n a ~ i l y having a big

effect and another kind of l ocus is havi2g a s 9 a l l e f f e c t ,

t h i s average can be n i s l eae ing , a s has been abundantly pointed

ou t t h i s morning.

Final.ly, or next to f i n a L y , tt:ere is t he d i r ec t

measurement of t h e segregat ion load, r.ain2y by Morton, f o r

s p e c i f i c human t r a i t s . Tho idea here i s primarfly Xortonts.

I had it all a l g e b r a i c a l l y ar.d did.n1t knov what it, meant. He

saw what i t meant. The idea is t h a t i f t h e population is a t

equilibrium, and i f you def ine segregat ion load a s I have d e -

f i ned i t , then, you can estimate t h i s from a surpr i s ing ly min i -

mal piece of information; namely, .the frequency of the t r a i t

under consideration, i f i t i s due t o a homozygous recessive,

and the d e l e t e r i o u s e f f e c t of t h a t p a r t i c u l a r t r a i t i n t h e

hmozyzote. From this information, you can e s t i aa t e t h e ssgre-

,al.icm l o a d , i r r e s p c t i v e of t h e nmber o f alleles involved ir,

the locus o r i r r e s p e c t i v e of the mechaniss t h a t .mir, tains then,

a s long a s i t i s a t e q u i l i b r f K a , under s e l e c t i v e balance.

I t seeus t o r,~e l i k e a very powerful p r inc ip l e .

392

T h i s i s a minium est imate . It is an i nequa l i ty r a the r t han

an equa l i ty . But t h i s does mean, given the facts , say, that

phenylketonuria is l e t h a l i n a natural populat ion, then, you

can estimate the segregation load that would be required t o .

maintain phenylketonuria, if i t were at equi l ibr ium under t h i s

mechanism.

I t seems t o me t h a t t h i s bears on question 2, i n

one s e n s e a t l e a s t , t h a t t,he're nust be--although I don*t have

any bet ter idea than anybody e l s e e x a c t l y how to def ine i t--

an upper limit somehow on the total . amount of v a r i a b i l i t y o r

the total load that a population can have, and, t h e more seg-

r e g a t i o n l o c i t h e r e a r e , a s Dr. ';!right has frequently pointed

out, the less se lec t ion can be brought t o bear on any one of

them. The more rar,dom d r i f t becomes important, the more d i f f i -

c u l t i t is t o exp la in t he popu la t ion s t ruc tu re w i t h too many

polymorphisms i n i t . But I don't know how t o se t a meaningful

limit on t h i s . Perhaps, we could discuss what approaches we

have tothat quest ion. T h i s i s what I would r a t h e r like t o do,

a t l e a s t f o r t h e r e m a i n d e r o f the day.

In any event , tha t bears on ques t ion No. 2, i t

seems t o me, and we can answer i t i n on ly one d i r ec t ion ; t ha t

is, i f i t looks a s if t he re is too rnuch o f the segregation

load, then, some of these must be maintained by other mechnnisms,

and so no answer i s the "yestf answer

KEEL: But, Jim, I think, there i s one problem.

In one o f your papers, you have r e f e r r e d t o t h e t r a i t s t h a t

have been worked with,as muscular dystrophy and so on, as

having been selected because they have t h e f requency a t which

they could be maintained by rscurrfng mutat ion, and I would

say t ha t your arguments extrapolated f rom such t r a i t s have no

value, because you a l r eady have a ve ry spec ia l s e l ec t ed c l a s s .

If you can show that muscular dystrophy i s not being mahtained

by segregat ional load, I don ' t know-

CT(Ci!: Does i t show i t very much? T h i s may be

r i g h t .

393

NEEL: I don't know the conditions that you're

ta lking about here .

CROW: i f one i s wi l l ing to say t h a t one simply

shows what i s already obvious by t h i s mechanism, I have no

object ion.

;\EEL: Eiut i n one of your other papers, you have

s a i d these were solecteC because they hae about the f re-

quency \!here they would be xatnts ined by mutation, so you

end up showinq they have the frequency about where they should

be maintained by mutation. .-.

C R O ~ And, if t h i s i sn l t t rue , t he re i s a meas-.

u rab le segrega t ion load , which seeins too la?p? . Therefore,

I s imply re inforce what a l r eady seemed comparable. T h i s is

not c i rcular reasoning, though. I want t o make a d i s t i l l c t i on .

I sa r e in fo rc ing a conclus ion tha t a l ready seemed probable, SO

i t is n o t c i r c u l a r .

WEL: That t h i s v e r y s p c i a l c l a s s is probably

maintained by mutation, which nobody would ever have disputed.

CROW: All r i g h t , but I t h i n k human gene t i c s i s

not so wel l es tab l i shed bu t tha t soae b!eU-established con-

c lusions can s t i l l be checked.

DZXPSTER: I qu?stion t h a t rsrnark, because I'm

s i t t i n g v e r y c l o s e t o a person wko, on occasion, told me he

thought i t was not improbable that the f i tness of the popula-

t i o n was due t o a number of these r a the r d ra s t i c genes . They

have r a t h e r d r a s t i c d e l e t e r i o u s e f f e c t s on homozygotes. He

d i d n l t s a y this was t rue , but he put i t a s a very plausible

hypothesis. Wouldn't you agree w i t h t h a t , Dr. Dobzhansky,

t h a t you have en te r t a ined qu i t e seriously the hypothesis that

t h e wellbeing of man is dependent, or migh t be dependent, to

2 very considerable extent , on heterozygosis for a number 3.f

genes which a re q u i t e d e l e t e r i o u s t o homozygotes?

DOBZHANSKY: Only af ter severai cocktai ls . [Lsl~g: i te?!

WLLER: Isnrt t ha t when peo7lefs t rue na ture

comes out? [Laughter 3

394

DOBZYANSKY: Professor ? h l l e r , you have scored a

point. [Laughter 1 CRCW: Well, if there is nobody here t o defend the

p o s s i b i i i t y t h a t most ordinary recessive genes are segrega-

t i o n a l , w e ' l l d rop i t . I think t h i s means that ' the people in

this room are honor bound no t t o r a i se t h i s a s a hypothesis

in the future , or a t leest not without disclaiming what they

sa it here.

YZZL: Tha t most r a re recessives a r e .

CROiJ: That 's r i g h t . To me, i t i s not t h a t se l f -

evident , Jim. I don ' t want t o be a segregationist, but--

[ laughter ]

MULLER: You want t o be an i n t e g r a t i o n i s t ?

CROW: Yes. Well, t he twe l f th poss ib i l i t y , I want

t o say, too, i s n o t t o t a l l y i r r e l e v a n t .

WALLACE: What i s tha t?

C8015': Minimum segregat ion loae. It sgems t o me

t h a t there i s a place f o r a l i t t l e b i t of t h e o r e t i c a l work

t h a t E4ot0, Klmura alrd I have done recently, bearing on the

question i n this fashion: Suppose we ask how mch se lec t ior i

i t takes to maintain a polymorphism, l o a d i n g t h e d i f f i c u l t i e s

i n every way we can t o minimize the mount of s e l ec t ion . Vhat

can a population do, if It would l i k e , a s i t were, to maintain

the maximum nuaber of polymorphism? One thing i t can do is t o

have a s many a l l e l e s a s p o s s i b l e , assuming t h a t all mutually

heteratzygous combinations are beneficial , and, i f i t turns out

tha t there i s a l o c u s o r t h e r e a r e s e v e r a l l o c i which Rave

th i s p rope r ty , t ha t t he re are multiple alleles, any combinatlon

of which Is b e n e f i c i a l and any honozygous combination of which

i s de le te r ious , then , the l a rger the nuaber o f s u c h a l l e l e s

Ln peneral , the s n a l l e r will be the seEregation load , just be-

c . v s e the more a l l e l e s t h e r e a r e , t h e l a r g e r t h e r a t i o of homo-

zygotes t o heterozygotes.

The limit placed on t h i s process is random d r i f t ,

I think, because the tendency for a l le les to be l o s t from the

395

population by randon d r i f t is not very l a r g e b;hen the number

of aLleles i s small, but, when the;. ge t to be l a r g e , t h i s be-

coaes very large, because the random-drift effect , a s Dr.

':.!right, Ilinurn o r somebod.y has ShOtJR, i s proport ional to the

square of the number of alleles involved in t he mu i t i a l l e3 . i~

locus ; SO, once you get; up to twenty o r t h i r t y a l l e l e s , random

d r i f t becomes very important even in the large population 'and

even w i t h f a i r l y s t r o n g s e l s c t i o n .

Therefore, one could ask f o r a g iven se lec t ive ad-

vantage of homozygotes, and l e t t he po2u la t ion have a t fts

disposa l a l l t h e a l l e l e s a r i s i n g by mutat ion that i t can

make use o f . What, i n f a c t , will i t do? There will be an

equilibrium reached by most of the randon d r i f t and, again,

of new a l l e l e s giver, nutation. One can ask what the segrsga-

t ion load would be i n such a system. You see , c l ea r ly , t he re

i s going t o be a segrecation loa3. If you increase the number

of a l l e l e s , t hey t end t o be l o s t by random d r i f t , so these

will come t o e q u i l i b r i m a t a ce r t a in po in t and, a t t h a t p o i n t ,

tke segregat ion load will be rrinimized.

IiIALSAC3: Yon't there a l s o be the load which will

be l / I i , the nunber of alleLes which we mak ta ined t imes t he

se l ec t ion you put in?

CROW: That is e k a c t l y i t .

WALLACE: That i s a ckance load ; i n o ther words,

you can think of a.loae. iaposed by chance. The chance loss of

t h e s e a l l e l e s must impose a ce r t a in l oad . i t i s the frequency

of homozygotes ' t i xes t he de l e t e r ious e f f ec t of the homozygotes,

because if a l l the alleles have been kept-.

CROG: T h i s is purely vhat I am def i r , ing as the

load .

YALLACE: Eut tha t i s char,ce.

CXOW: Call i t chance, i f p u want t o .

'..!ALLACE: Because t h e d l e l e s a r e n ' t t h e r e , be-

cause they are lost by chance.

CROZ: Yel l , 112 t a lk ing sbout an ex is t ing

396

popula t ion re la t ive to a pQpuiation nade up o n l y of honozy-

gotes .

WALLACE: T h a t f s e r i g h t , but since you said thesg

a l l e l e s c r e Lost b;t random d r i f t - , t k i s i s a chance l o a d .

CRCti : I donl t care %hat you c a l l i t , b u t 1 th ink

we 'agree a s t o what we are .xasur ing . The aaenitude o f t h i s

can be qu i t e small. Let me see i f I can f ind m y notes , to

give you j u s t one i ! . lustrat ion. Suppose I ' t a k e t h e S value

t o be .C1. By t h a t , I mean t h a t t h e homozygotes a re 1 per

c e n t l e s s f i t t h a n h e t e r o z y g o t e s . The nininurn segregat ion

load for such a locus in a populatlon--I took a population of

e f f e c t i v e s i z e , lC,OOO--excuse ne a minute. I ' m not sc re

about that and I would l i k e t o check i t .

Y e s , I too!: an e f fec t ive aopu la t ion number of

10,000, with selected disadvantsge of I. per cent . If we say

tha t a subs t an t i a l minor i ty i s 50 per cent of a l l l o c i , i n

o ther wcr ds, say, 5000 l o c i , t h m 3 f o r 5003 l o c i , t k segrega-

t i o n Load is about 6. The l c a d per locus under t h i s assump-

t i o n is 1.2 x 10-3.

WAL'sAC3: How aany a l l e l e s a r e ob ta ined t he re?

CROW: I 've forgot ten, but I t i s q u i t e a la rge

nunber, 20 o r 30 o r s o m e t h i q l i k e t h a t .

LZWOIiTIN: I n such a large popuia t ion?

CROY: Yes, t h l s is a large populat ion and i t car,

maintain a l a rge number o f a l l e l e s . I!11 look u p i n a minute

what the nLzmber of a l l e l e s i s . Bnyvag, the load imposed by

maintaining t h i s number of alleles, whatever i t is, i s 1000.

Therefore , i f I have 5000 i o c i , i f khey are independent of

each o ther a t I -eas t , t h i s woul-C: be TOGO tLmes t h i s , o r , roughly:

e - 6 , which is .002.

This i s the kind of argumant I am. t ry ing t o mske,

thzk t h i s s e e m to be l i k e a n irnFzobably l a rge load f o s a

populatior, t o bear. This would mean that the average of t h e

population has a f i t n e s s o f .552 r e l a t ive t o t he i nd iv idua l

who i s h e t e r o z y g o u s a t a l l the loci.

397

L2IIIOI:TIN :

o f individuals .

CR0i.I : BU t

LE'.dO!!T I N :

It i s n ' t t h e load; i t i s t h e proport ion

the load i s .998.

The proportion of individuals?

c8O';I: Yes, so s l l I have t o s ay is t h a t if t h i s

is true--now, remember, we're assurnir,g indecendence o f act lor ,

of these genes. The effect of synergism or t h e e f f e c t Of ePi-

s t a s i s depends a l i t t l e o n t h e d i rec t io r , of i t . Eut i t seems

t o me, a s a q u a i i t a t i v e argument, t h i s has some weight ; that

is t o s a y , i f t h e r e a r e . t h i s many segrega t ing loc i , then , if

I could obtain an individual heterozygous for every loci , i t

would be 500 times a s v iab le a s the pmsent average of t h e POPU-

l a t i o n . To ae, i t is inconceivable t o think of a f l y with 500

times the f i t n e s s of t he ex i s t ing nean; ergo, I: would r u l e o u t

t h i s kind of hypothesis on t h i s !rind of ground.

LJC:O??TIX: But l e t * s en?t;asize t h i s i n answer t o

question 2, which is the number of l o c i and not the r e l a t i v e

con. t r ibut ion to the t o t a l load .

CROW : That * s r i g h t . LZWONTIIJ: T h s t p o i n t has bsen missed too fre-

quently, I think, not t o r e a m t i t .

33OW: Thnt*s 711' 1 hr,-~z :c ~ q y by way of i n t r o -

duction. [Laughter] Now, I t i l s t a r t n:.' nain t a l k .

30BZHANSKY: Frof essor Crow, wowld 1 t be possible

to introduce p i n t 13-which i s an unlucky nu.?ber--but has

the coaparative study of gene t ic loads i n 3 i f f e r e n t p o p u l a t i o n s

of a species and d i f f e ren t spec ie s , l i v ing ir, a i f f e ren t eco -

logical condi t ions, anythigg of i n t e r e s t t o cont r ibu te t o this

general problem?

trio!!!: Well, it i s not obvious to me how i t c o n t r i -

3Lte.s to these par t icu lar ques t ions , Dr. DobzhanskJr. It nay

heve trernen2ous inter&, but fcr other reasons.

KORTOK: There 1s one case I can think of ea s i ly , ?

and t h a t isbk?1mickrts s t u d i e s on two types of bees, those

where there i s a balanced lethal sex determining system and

those where there is not. The loads seem to be qui te cons is ten t

398

w i t h the mutat ioml hypothesis .

ETJLLER: In stuciies on bees by whom?

b1ORTC.K: Uerniker. k t leas$ t h a t is hov he i n t e r -

prets then. I wouldn’t agree with him.

CRO’;:: These a r e simply the things I can th ink of .

I’m sure other people will have other experiments .

BODMER: I would l i k e to br ing up , t en ta t ive ly ,

some inforaat ion in biochemical genet ics , a l i t t l e b i t aore

de ta Fled knowledge of t h e way the genes work t h a t we have now,

and what Sear ing that might have on t h i s . It i s d i f f i c u l t t o

f o r a u l a t 9 somathing s p e c i f i c , b u t , I t h i n k , c e r t a i n l y , t o my

mind, i n tu i t i ve ly , , i t argues strongl:? against 1, what knowledge

we have nowadays in , t e rns of the way .penes work. To my mind,

i t .?lakes i t ve ry ua l ike ly , fo r example, t h a t 1 Zs a p o s s i b i l -

i t y ; so i t seeas t o me t h a t one should r e a l l y add to t h i s l i s t

something t o i n d i c a t e t h a t w2 do know a l i t t l e b i t about how

genes work nowasays.

DICKERSCN: P r i a a r i l y o r s e c o n d a r i l y ?

CROW: We have known qu i t e a b i t about how genes

work f o r qu i t e a while. I have l a i 6 . down f o r inyself a s e t of

ru les , tha t I was t r y i n g to specify here experiments of a popula-

t ion gene t ic type . It is p e r f e c t l y c h a r t o me t h a t once one

knows enough about DNA and proteins, the answer to question 1

should be known. Maybe, we should. simpLy s h u t u p u n t i l t h a t

time comes.

BODFBR: I don’t think that is so.

LE!.JOfL”=Il<: I d i sag ree en t i r e ly . You may not know

what the primary products, protein products, of a h e t e x q g o t e

nap be, but t o ask what e f f e c t t h i s heterozygote may have on

f i t n e s s i s not a quest ion of knowing a l l about DNA, si r . I t i s

a c u e s t i o n of knowing a l l about development i n physioLogy, i n

dffferent environments. That is a much d i f f e ren t ques t ion .

BODXER: You would have t o consine the two s o r t s of

s t u d i e s .

CROW: I agree. Anyhow, ques t ion 2, I can conceive

e

399

of answering by biochenical methods. YOU s i n p l y ask whether

an ex is t ing popula t ion is polymorphic.

LZ. TONTIN : T h a t s r i g h t . PEEL:: Z i m , tlould you accept anot,her line of e v i -

dence here? T h a t i s , the study of t he s t r u c t u r e of na' iural

popul.ations, For instance, you have put down t h a t lj equal led

10,000 w i t h respec t to man, ana N probably equalled 50 f o r

Eost of h i s time on earth. Y 3 t , we see these extreme poly-

morphisms. This is t r u e f o r many of the small mamsals we have

been talking about. Contt you g e t sone valuable c i rcuastan-

t i a l evidence out of definiri ing the s t r u c t u r e of populations?

CROK: I t i s c e r t a i n l y worth pointicg out that if

N were changed from 10,000 t o 100, t h i s q u a n t i t y would change

t o e - 600.

3GBZHANSKY: Nr. Chairman, t h i s i s iden t i ca ; t o

what I have suggested, and which was re jec ted .

FEEL: I'm sorry not t o havs had t h e perspicr:cZty

to recognize a t the moner-t th r t t we were on t he same s i b .

CRChr: Let me go. f i rg t t o Kim, who said soaething

I d idn ' t hea r j u s t now.

ATWOOD: I donZt %no:.] what '1. said, 5ut I o b j e c t t o

t he cava l i e r a t t i t ude w i th which the remark about t h e nolecu-

l a r age has been rejected. , The g o i n t i s t h a t i f No.1were

t r u e , you would have to say t h a t , i n given individuals , the

population of protein nolecules of a given species is poly-

morphic. This is j u s t no t the case,

CROW: I agree.

NEEL: So i t is pe-lfectly obvious that 1 i s f a l s e .

If the answer is %ott t o i t , and we can j u s t say, 2 p r i o y i ,

it i s fino,it because the reason i'; I s ?!hott is pushed f a r in

tb-e background, we don? even know where it or ig ina ted .

ROBINSOM: Jim, when you weye d iscuss ing the 191:O-

1952 work, yau remember, in t e rms of whether , on r b . 4, you

put a Y and N in terms of corn, t h e hypothesis which I'OU put

f o r t h t h e n involved t h i s quest ion of popula t ion s t ruc ture .

4oc The best ?ossible hybrid which night be developed from lir.es

out of an equilibrium pogulation, you remernber, is t h a t 5 per

c e n t f i g w e . Now, i n the first, place, you've change2 this--

CROI: : 'Ve1.1, I changed it only by saying I didnl t . forget paTtial dominance. I r e e l l y d o n ' t kr,ow about the

gar t i a l doninance.

R O B I F k O N : All r i g h t . 'dhere does t h i s bring you

w i t h r ega rd t o this 5 per cent value?

CROW: I made i t 5 per ser.t instead o f 20 per cent .

ROBINSON: All rights. We've gone at-,ead w i t h these

random l i n e s I was ta lk ing about , and r e c e n t l y have done ex-

tens ive s tud ies on making the i n t e rc ross between these l i n e s .

Tha t i s a type of e-Ji2.ence which b e a r s v e r y d i r e c t i y o n t h i s .

C R W : Good! Can you descr ibe i t b r i e f l y ?

ROBINSON: I n Dr. 3 o s s f s discuss ion o n his 1?4c!

and 1952 !.Jerk, when he v i s i t e d u s , t h a t was one o f t h e reasons

we went in to !nnaking these random l i n e s , because o f h i s hypothe-

s i s and his theory tha t he had cone oGt s r i t h , of the best pos-

s i5ie combinat ion, .!f ve can assums that th3se are equilibrium

populations, of course, which he inc'icated we could do . Well,

t hen , i n a recent s tudy fro% l i n e s v i t h these populations, from

a very high number of i n f e r c r c s s i q s w i t h t h e s e l i n e s , we were

looking t o see what would be tke ra,rg:e of the y ie ld , t he d i s t r i -

but ion of t h e y i e l d , when you intarcrossed these random l i n e s

of seven or t en genera t ions o f inbFeedinp.

All we came u p w i t h was on the high s ide. Some were

32 to 33 per cent above . the average of t h e o?en po l l i na t ion

or this equiLibrium po2uLation i t s e l f , which i s f a r beyond.

even your aejusted f igure here, which seems t o me ano t h S r l i n e

of evidence, and a very impor tan t l ine .

CX'f!: In favor of t h e hypothesis, say, D instesc?

o f B?

RGBIXSON: Right. In b o t h cases, w i t h the var ious

i i l t e r l i ae c ros ses ar,d wi th the Indian Chief , they are running

f r o n 30 t o 35 per c e n t ; t h a t i s , the bast possible coabinat ion

of l i n e s , a g a i n , j u s t a cyclic productior. of a whole series

of in te rcrosses arllong these random l i n e s . The o b j e c t i o n t o

i t i s the fact that there has been some se l ec t ion . >le went

i n t o t h i s on Monday.

CROSS: Yes. I f m stlll caught between what you

sre saying ar.d whzt Kim was saying, !!hat I r e a l l y wanted t o

say, or should have said, was not to dismiss the suggestion

of the molecular gene t ic i s t s a s irrelevant, because i t obvi-

ous ly is relevant , but to say, on my own views, the physio-

logic genes, which I thought were pre t ty un iversa l ly accepted

views, are 0y8s11 a s the answer to quest ion 1. T h i s was p r e t t y

much 5 p r i o r i before anyone d i d any experinent. It was only

the fac t tha t the ques t ion was r a i s e ? by some p e o p l e t ha t I I

thought i t worth discussing. -1 th ink the genera l rehc tance

to accept Bruce's results has nothing to do w i t h the goodness

o r baeness of t h e expe r inen t ; i n f ac t , I t h i n k i t i s p r e t t y

good. I ts 5 p i o r l p l a u s i b i l i t y o r 1ikeLikooC of r e s u l t s i n

terns of the conveat ional no t ion an8 h a s of gene act ion-

VALLACE: Yourre talking about a c l a s s of genes

charged w i t h r e s p o n s i b i l i t y f o r making tke proteins , and i t

seems to me tha t you ' re forge t t ing the cont ro l l ing e le rnents

and l o t s of o ther th ings o f the genoze.

LE.WC!NTIN: You' see, the poin t K i m has made, per fec t -

l y co r rec t ly , is t h a t i f we could find ou t t ha t t he re was very

l i t t l e t i i f f e r e n c e i n p r o t e i n , t h e n we would know t k e s t r u c t u r a l

genes, a t l eas t , a re no t very hs te rozygous i n the populations.

That would be a d i r e c t answer to quest ion 2, but, i t i s not an

ansver to question I, f o r t h i s reeso3, which I d iC n o t d i s a i s s

cava l i e r ly ; namely, that the quest ion of t he poss ib i l i t y of

he t e ro t i c nu ta t ions ani! whether new mutations can be h e t e r o t i c

2nd i n what propor tior, i s a quest ion of a t e rmina l po in t i n

the developmental sequence, not an i n i t i a l point.

BOWER: But i f every new mutant were he te ro t i c ,

then, every locus would. be polymorphic, and the species would

l o se i t s iden t i ty .

402

LEWONTIN: That is not t rue , as Jim has pointed

ou t . I n a f in i te popula t ion , even i f zos t new mutants were

he t e ro t i c , you ' s t i l l cou ld no t ma in ta in an awfu l l o t of them,

because of the fact that the populat ior , i s f i n i t e .

30DMZR: BL:t ysu n o & X have up to tventy o r t n l r t y

rllales polpmorghic i n e v e r y s i n g l e locus.

LWONTIX: In a populat ion s ize of iC,OOO?

FIs.T,Sr? : Ycu would have two o r Lhree, anyway,

wouldn't you, very commonly?

BODMER: Yes, and, eTten i f i t is o x , i t would be

inconsis tent .

LEVONTIN: This i s another way t o -knowing the

answer t o 2 may givo you tke answer to I, bt;lt knowing the

answer to 1 doesn't necessa2i;y give you an answwto 2. That%

a11 wetze saying. A prior i information about t h e InutatLons

and the nature of deve lopnanta l p rocesses can te l l you some-

thing about whether mutations can be h e t e r o t i c . That i s abso-

l u t e ly t rue ,bu t t hey a?e two d i f fe ren t ques t ions .

GLASS: It seems t o me there is one other b i t of

evidence on t h e biochemical side t h a t makes the considera-

tions t h a t have been mentionec! a l i t t l e i e s s c e r t a i n ; t h a t is ,

the inceas ing ev idence tha t nos t e:??yjr'lles, o r a t l e a s t a g r e a t

many, ex is t in the form o f v a r i e t i e s , which have been c a l l e d

isozymes, and t h a t i n a t l e a s t the best analyzed case, these

are varLous combinations, a l l pcs s ib l e t e t r amer i c conb ina t ions

of two essent ia l polypept ide coapcnents ; so we don't know

what the genetic background of thesa i s .

We h o w f a i r l y well. what t h e r e l a t i o n o f c e r t a i n

genes t o c e r t a i n polypspti .de structures is , but we don't 'mow

as y e t , o r we don't have very .mv.ch knowledge, how thsse poly-

:%;=.bides are CGil i ; rolhd genet ical ly in t h e i r cssemblage into

7 ~ ? h r z s te t7armric o r other kinds of coak:na~',icns, which a r e

of ten the funct ional developaental uilits.

C3OW: I wonder if I coul-d suggest procedure for

a mqment? There are two or three geople who have s p e c i f i c a l l y

403

said they would l i k e t o have t h e f l o o r b r i e f l y t h i s mOrniRg,

and I think, perhaps, I should c a l l on them f i r s t , and then

have a general d iscussion. Dr. Li has w i t t e n t h r e e a r t i c l e s

c r i t i c a l of the t h i r d concept here and t ~ o u l d l i k e t o d i s c u s s

t h i s . Let me say something about i t i n advance: that if if;

tu rns ou t tha t 3 is an idea which may or may not be good, but

on which the Cata a r e l i k e l y t o be so poor t ha t we czn* t u se

them, t h i s rnear,s, perhaps, there i s not too much p o i n t i n d i s -

cussing it. However, t h i s is a s Dr. L i ant! the rest of the ,

group wish. I'm p e r f e c t l y w i l l i n g t o go on with i t .

L I : The d i scuss io r , i n t he l a s t few minutes has .

spoi led my wish, because t h i s meeting has reminded me of the

genetic meetings I used to a t tend twenty years ago, when we

just ta lked about crosses and o f f sp r ing and no DNA i n t h e mole-

cule and so f o r t h . I was saying that t h i s i s the kind of

genetic meeting I havent t a t tended for years . But, i n t h e

l a s t few minutes, DNA has come up. [Laughter ]

Before I ta lk about the nain t o p i c of load o r i s sue

and. so f o r t h , I have sevepal other unrelated points , which I

wanted to s t a t e bu t d idn ' t have a chance. I was s i t t i n g be-

hind the projector a l l t h e time.

T h i s is Dr. Sewall '2Jr ight ' s correlat ion coeff ic ient--

well, there a re two approaches t o t h i s problem. One i s the

classical approach. T h i s i s the thing I l e a r n e d e a r l y i n t h e

t h i r t i e s . Now, we have the probabi l i ty approach. I personal ly

h a v e , u s e d t h i s c o r r e l a t i o n a l l t h e t i m e . I admit it is not

t h e simplest. Sometimes, t h i s probabi l i ty approach i s simpler.

But I s t i c k w i t h t h e c o r r e l a t i o n method. I have heard two

explana t ions for i t . Both of them a r e t r u e . One i s , I'm old-

fashioned. That is ve ry t rue . The second explanation is t h a t

I don't saeak French, but I d i d g e t an Eng l i sh t r ans l a t ion

from Jim, ten years ago, when you made a rough t r ans l a t ion snd

I got hold of a copy. A recent addi t ion t o t h i s i s t h e reason

Dr. Wrigh t brought up yesterday. But I have a personal reason,

a s t o why I trould r a t h e r us2 correlat ion than probabi l i tzr .

. 404

In developing a genet ic method, you have two ac id

t e s t s . One is to genera l ize the mul t ip le a l le les and. see

how it works, and the o ther ac id test is t o general ize i t

with sex-l.ir.keC genes. With respect to sex-linked genes, I

cculd get the r i g h t co r re ln t ion cc2 f f i c i en t s imp ly by a proba-

b i l i t ; ? argument, because, conceptualiy, these are really two

d i f fe ren t th ings . Corre la t ion o rd inar i ly has no d i rec t phps i -

cal aeaning. It is an index of associat ions. For sex-l inked,

we have a c o r r e l a t i o n like t h i s [ i cd i ca t lng on board]. You. see,

I can obtain t h i s c o r r e l a t i o n c o e f f i c i e n t v e r y e a s i l y by t h e

c o r r e l a t i o n method, but i couldni t reech ? robabi l i ty w i t h this.

Another exanple is t h i s [2 over t h e square of 23. ?

When you read Nonteil 's book, therefore , whai; i s i n t h e r e i s

excel lent , but what i s not in there is a l s o s i g n i f i c a n t . He

never mentions t h i s business of bringing it to sex-l inked

genes, you see. I th ink I'm going to s tay old-fashioned.

CROW: %hat i s t h i s 2 over the square of 2 the

co r re l a t i o n o f ?

LEWONTII!: For sex-1 in!ted genes.

LI: Y e s , sex-linked genes, s i m p l y because we don' t

have a symmetr ical correlat ion table . For autosomal genes,

it works so well because i t i s always on 3 x 3 o r 6 x 5, but

f o r a c o r r e l a t i o n t a b l e of t h i s kin<, on a 2 x 3--well, we

have no trouble i n ca lcu la t ing the cor re la t ion , bu t I couldn ' t

argue on the bas i s of p robabi l i ty any more. But l e t me go on.

CROW: IS i t f a i r t o i n t s r p o s e a remark? I t h i n k

i t i s proper to say that i f you a r e computing a c o r r e l a t i o n co-1

e f f i c i e n t , t h e c o r r e l a t i o n is t he d i r ec t way t o do i t . If t h e

quest ion is one of inbreeding, i t seems t o me tha t to a rgue

tha t one is bet te r than the o ther , when the re a r e two ways o f

s c l v i n g problems, d o e s n f t really arswer i t .

LI: No, I ha te to use the word f15e t te r11 or %!orse. It

CRCW: I *a sure you could a r r ive a t a lnros t any

mswer e i t h e r way, so t h i s is a matter of personal preference.

L I : If you d m r t t a l k about any par t icular case,

.

4

405-6

i f p u review t h e e n t i r e f i e l d of population genetics, you will

f ind t he co r re l a t ion method i s more v e r s a t i l e . You can use

it from the beginning to the very end. But t he p robab i l i t y

method is very powerful w i t h respec t t o one p a r t i c u l a r problem.

For the second point, i t i s more i n t e r e s t i n g , It

is t h i s : I used to see Jim Crow every year but f o r t h e l a s t

three years , I haven't seen him. The very f i rs t day, when we

saw each o ther , as long- los t f r iends , he sa id , We should

have seen each other more o f t en t han we did." While t h i s i s

a so r t o f i so l a t ion , I sa id , "Coodlt--you know, Dr. Crow and

I, both of us t oge the r , have managed t o prove one of t he bas i c

t heo r i e s i n evo lu t ion ; t ha t i s , evolu t ion by i s o l a t i o n . When

you a r e i s o l a t e d from each other , you a re bound t o d i v e r t .

That i s a law of nature. [Laughter ] At l e a s t , I th ink , Jim

and I have proved this. If no th ing e l se , t ha t one point i s

already worth while. I n view of t h i s , I th ink tha t the Macy

Foundation probably should promote more i s o l a t i o n r a t h e r t h a n

more conferences. [Laughter 1 SLATIS: But t h i s gives us the chance for competi-

t i on , so you can g e t s e l e c t i o n and su rv iva l of the f i t t e s t .

L I : The next point i s to argue about an issue,

I made a s ta tement l ike this : [Writing on board, "The l i t e

is g r e e n o f f ] Or you ask me about the co lo r of t he L i g h t , and

I say, "The l i t e is green." You immediately say,I1You d idn ' t

spel l It r igh t . " From now on, the discussion i s a l l about

spe l l i ng , how i t i s spel led in Webster , how i t was s p e l l e d i n

the s ix teenth cen tury , and nobody bothers about t h e o r i g i n a l

statement any more. [Laughter] This bothers me quite a l o t .

My o r i g i m l statement i s about the inbreeding

method, t o d i s t i n g u i s h two types of equi l ibr ium. This was my

original s ta tement , and Jim and I agreed not to bring up any

publ i shed resu l t s , to which I agreed.

CROW: Inc iden ta l ly , I don ' t o b j e c t t o this.

LI: Yes, I th ink it's a good rule; o therwise, we

could go on to next week. I wouldn't want to mention old things,

but I do want t o mention a f e ' w th ings . These are t h e points

and. then we t r y t o d i s t i n g u i s n them. In o rde r t o d i s t i n g u i s h

them, we apply a k h d of t e s t . You tail ta!ce any kind of t e s t

you can think o f , but the purpose is t o dfst icgcish between

the two types of eqai i ibr ium. This i s thz main purpose. I

prsonal ly thought tha t tk i s very p remise i s mt s a t i s f y i n g t o

me, from t h s very beginfling, becausa this i s like going to

a f r u i t s t a n d . You will see a hunc!rcii k inds o f f ru i t s there ,

407

t h a t I would L i k e to l i s t , in the fashion of Dr. Crow, 1,2,

3,4,5 and 6. O f t h e s i x p i n t s , I will probably ta lk o n l y

about No. 5 , and j u s t mention the t i t l e of No. 6.

No. 1 is the c l a s s i f i ca t ion o f t ypes of e q u i l i b r i -

um. T h i s i s d i f f aTen t from t . h t Cr. CTOW has on t h e other

s i d e o f t h i s board. He i s ta lkLng about the a l le les , the e f -

f e c t on the heterozygous, and so f o r t h . I talking about

the type of equilibrium.

I

Usually, we c l a s s i f y t h e s e as the mutational type,

and you t r y t o c i a s s i f y t h e n . Bcfore ~ C ' J see t h e f r u i t , you

have a l r eady ag reed t o c l a s s r fy them i n t o two types. One i s an

app le and one i s a banana. There a x o ~ l y two !cines of f r u i t ,

to begin with. In yaur own mind, then, you pick U P a pear.

Then, I couldnl t c a l l i t a peal b3cause, on the blackboard,

there a re on ly two t y 2 e s of equ i l lb r iun . When 1 see the ?ear,

then, I am forced to c a l l i t an a p p l e . From the very beginning,

t h e r e a r e two types of equilibrium snecif ied, and, from then on,

I an go ing to c lass i fy th!.s- h t o t h i s o r t h a t ,

This point i s no t ve ry s a t i s fy ing t o me, because I

thought t h i s i s t h e a t t i t u s e of a lawyar zather than a n a t u r a l -

ist. You see, a lawyer has a - pTinted book, If you do some-

th ing wrong, he has to f i t you i n t o one of the charges in the

bo&. He cannot charge you w i t h something which i s no t i n t he

1 . a ~ bo3k.s. The n a t u r a l i s t is dcing t k 9 oppasi ta . Ere gaac cff

Lo n;ltwe an& t r i e s t o f i n d DUC, what th9;.2 i s , and then c o m s

beck and c l a s s i f i e s i t . I thought of the concept of c lass i fy-

iiIg eqGilib?iun into two types; get, th i s very approach i s

son9how not satiss'yizg eaoGgh f o r cs.

The basic reason i s t h a t 1 must say there a re

hundreds of kinds of equilibrium i n nature. 'de don ' t know

them, sirnply because of our own ignorance, not because of the

d i v e r s i t y o f nature . Ne have no r i g h t t o c l a s s i f y them i n t o

apple and banana and r,othing else . T h i s i s the f i r s t point .

The second. point i s to describe a d i f f e rence . In ,

descr ibing 2 d i f f e rence , t he re a r e many :days, but t h i s i s the

quest ion dim Neel kept on asking, an6 Dr. Crow ti idn' t have a

chance t o answer. There are so many other quest ions involve0.

What C r . Neel a c t u a l l y was asking was t h i s : Suppose I have a

. t h i s 11oigLt ami ' tE.5 si?,.?; c rd ina r i ly , I would compare these

two. I would s a y t h i s i s f i v e i n c h e s t a l l e r , o r I can take t h e

r a t i o and say t h i s is 100 per cent higher than t h i s , and t h a t ' s

a l l . The load r a t io , he has defingd now, a s being l ike t h i s :

'Je don't measure th ings from the bot ton. We mzasure the

h e i g h t f rom the cei l ing down. We assume t h a t t h e r e is a c e i l -

i ng and we measure t h i s space betwsen the ceiling and t h e

height , Here, we assume a ce i l ing an2 we measurs t h i s , and

then we compare the two. This, e s s e c t i a l l g , is the l oad - ra t io

met hod

If you i c k n t i f y t h i s with t h e man, then, t h i s i s

the deviat ion of the m8an from the h l g h s s t psss ib le po in t .

The ce i i i r ,gs a re no t a t t h e same l e v e l . I can inodify the load

r a t i o n i n a nwnber of wzys such a s t h i s [ lowering ceil ing]. .

Then, these two r a t i o s would be enormous. If I ax not s a t i s -

f ied wi th t h i s , I trill piit th i s ce i l i ng up he re , and then t h e

l oad would be even more tremeneous. Actually, t h i s [ c e i l i n g

height] i s unknown. There i s no way to determine the maximum

f i t n e s s of an unknown genotype, That is the second point.

These p o i n t s a r e a l l c o n t r o v e r s i a l , b u t I will eo

over them vezy quickly.

The t h i r d aoint i s iilbreeding is a dii;gnos't!.c t o n l .

Well, since we don't know which type of equi l ibr ium i t is,

t h i s i s j u s t like t he i n t e r2 re t a t ion of u r i n e sugar o r blood

count. We apply a t e s t he re . We subject the ponulation to

inbreeding without determining gene frsquency. By t h a t

method, we hope we compare the d i f fe rence between the two

types. Then,. essent ia i ly , the cont roversy is, somebody says

we can, and somebody else says MS cannot. I P m not going t o

go ir.to t h a t c o c t r o v a r s y again, ?xt t h i s Is the mafn point

of my theory. I say, when you sub:ect G population to inbreed-

i n g , there aka a l o t of hic?.?den recess ives t o g e t o c t , and t h i s

would be t rue regai*dless of the tyne of equilibrium. Whether

i t i s one type of equi l ibr ium or another, upon Inbreeding,

you get the saEe segregat ion phenomana. But t h e y do have a

very strong argument i n favo? of this method. By the way,

t h i s is the only na jo r .m int here in the whoLe thing.

No. 4 I s the r ror ta l i ty da t a . One of the strong-

e s t arguments of the LoaC-ratio people is t h a t we don' t

claim -1ery much. We admit that load r a t i o doesn ' t work a l l the

time. But, screly, i t carr be epp ' l ied in a very s tFa ight for -

ward manner w i t h rnortality d a t a , bemuse mortal i ty &ita

g i v e you a measuremant of f i t n e s s from zero t o 1. You see,

mor ta l i ty is zero, so your f i tcess is 1. S3 LE such a

c learcu t cas2, your Load-iTatLo methoc: would w m k . Most of

the exampies a re w i t h m o r t a l i t y data. Xy inpression i s ,

aga in , exac t ly t h e opposi te . Cf a lL t h e hunan data we can

c o l l e c t , a o r t a l i t y da ta are the l e a s t usable, 2 . ~ d 1'11 t e l l . . <

you why.

% r e i s a type of family, an2 t h i s is t h e number

of b i r t h s and the nunb9r of dea ths [tu0 births ;an6 zero

deakhs], number e l ive , two. X o r t a l l t y is zero. You have

two children. Everybody survived. The mortality i s zero.

In another type of family, the b i r t h s a re 8, 3 died, and 5 suzvived. The c o s t a l i t y i s .375; 37 per cent mortal i ty .

This is f i n e . When you t a l k -about f i t n e s s , what can you say

here? The moztality people would say tha t the mor ta l i ty of

tha first family i s zero. T h i s I s the highest frequency.

I call i t I. T h i s moTtality is 37 per cent , so it should be

l e s s f i t . T h i s i s not th;? c a s e a t a2.l. These m a r t a l i t y d a t a

410

do not t e l l us t h e f i tness , because , i f you take t h e number

of l i ve ch i ld ren , t h i s contr ibuted only two chi ldren, and

the second famt ly cont r ibu ted f ive . Whi l e these mor ta l i ty

da t a a r e u s s fu l , t h e usual impression of people who a r e not

deal ing w i t h mor. ta l i ty data is t h a t t h e higher the mortal i ty ,

t h e l e s s c h i l d r e n you have. T h i s is assuming t h a t t h e num-

ber of b i r t h s remain constant. The more who died, of course,

the less a r e l e f t . But t h i s i s not t rue in human populations

a t all. The opposite i s t rue . The h i g h e r the mortal i ty ,

the l a rger the s ize of t h e fami ly . Yor ta l i ty is p o s i t i v e l y

associated w i t h s i z e . The larger family has mortal i ty , and

the smaller family does not.

How a r e we going

oreer to ca1culat .e the load?

LEWONTIN: May I

p o s i t i v e c o r r e l a t i o n between

is obvious.',from what you a r e

t o assume the f i t nes s va lue i n

ask, Dr. Li, whether the observed

mor ta l i t y and f e r t i l i t y , which

saying--do you assume t h i s is a

g e n e t i c c o r r e l a t i o n or a socioeconomic correlation?

L I : Whatever i t i s , i t is t he re .

LEWONTIN: But suppose t h e c o r r e l a t i o n were t h e

oppos i t e , gene t i ca l ly ; would you not take th i s out by your

socioeconomic regressions, which we ta lked about on t h e f i rs t

day? I don* t k ~ o w . Would you o r xouldnt t you?

Ni33L : No, you wotlld not .

LE',!OMTIN: A13 r i g h t . NEi3L: A t l eas t , the k inds ws t a lked about would

n o t g e t a t t h a t .

XMPST?3R: Yes, but i t s e e m to me that the ques-

t i o n a r i s e s , i n n e g a t i v e c o r r e l a t i o n , i f that should be r e -

cent , say, in terms of two or three thousand years in human

experience, due to socioeconomic factors, then, t h e s i z e of

the family is now a u s e l e s s measurement f o r us, but t h e mor-

t a l i t y remains, and i t may s t i l l represent a genotype having

the same impact a s it d i d many years ago. That is a p o s s i b i l -

I

i t y .

411

NEEL : I agree, and I can on ly say wetre doing

our bes t to ge t da ta o f tha t na ture on very primitive popu-

l a t i o n s r i g h t now.

DEEIIPSTTR :

mor ta l i t y avay because

rmx, : NO,

about i t .

LI: ALL I

So I don't think ws can j u s t throw

of t h i s corFe2ation.

but we can ra i se SOB& st-r lous qu.e s t ions

can do.is r a i s e a question. I don*t

claim tha' t every family i s like this.

MORTON: IS i t genera l ly t rue tha t people agree

t h a t the number of s teznopleural b,-€s",las is something i n

which we should all be i n t e r e s t e d , 5ut mor t a l i t y i s something

ws shouldn't be?

DICKERSON: I won ' t buy t h a t .

DOBZHANSKY: Absolutely, Since Professor Dempster

ascr ibed t o me an opinion t h a t 1etha.ls were what k e p t man

going, I th ink t ha t I can ascr ibe , that opinion to Dr. Lewontin.

L I : kll, the l a s t po in t i s correspondence. The

correspondence always bothers me a good t?eal. T h i s neans,

when you ge t a body of human data , you can c a l c u l a t e a l l k i n d s

of things. This, I will c a l l t h e s t a t i s t i c a l o r observed

e f f e c t s . On the o ther s ide , ws have a s e t o f genet ic parame-

t e r s which a r e s p e c i f i e d by our selectior, , the loa< r a t i o , the

def in i t i on o f t he l oad , and so on. 'de have one s e t o f observed

things, and, on the other s ide, we have one set o f abs t r ac t

thinking. How are we t o establish the correspondence between

the two?

I think, 'ir! one paper , the d i s t r ibu t ion of number

of chi ldren in f a m i l i e s was mentioned as an index of n a t u r a l

s e l e c t i o n , and so on and so f o r t h . But, on the o ther hand, i f you say t ha t t h e d i s t r i b u t i o n of the nunlSor of s i z e ? has nothing

to Co w i t h na tu ra l s e l ec t ion , I i t would ba equa l ly t rue , a t

t h i s moment of ignoracce, because, if we a r e a l l of the same

genotype, we s t i l l have a d i s t r i b u t i o n of nunber of c h i l e r e n i n

the population. In going th2ough thses papers, I think,

therefore , some of u s have t -?ken for granted that each sta-

t i s t i c a l o b s e r v a t i o n h a s a gene t ic core ; so t h i s parsmeter

corresponc?ed %o t h a t , anc? t h i s w i t h t h a t . T h i s , I h v e

grave doubts about.

Before :.!e csn apply t h i s ~z';t=oci, ~8 ha-&? t o be

c lear about a l l theze f i v e p i n t s . Any oEe of ths f i v e

would cast doubt on the neaning o f t h e r a t i o . >!hat I have

been tcll.lting about, then, i s rea1f.y a s e t of prelininary and

elementary considerations behind the things t ha t 9r. Crow

talked about, o n the o k h o ~ s i 6 e of t h e Soaxl . If we could

not get any agreement Or, a np Of r ive po i n t s f i rs t , then, I clonft see any concrote physical mesning of t h i s

r a t i o a t a l l .

No. 6, and I 2zonised you I wouldn't t a lk about

t h i s , so Irll j t t s t put t h a t i t l e $own ar,d leave i t [Social

Well, I am p r i v L l e g e d t o have a f r o n t row, sc) I

car, watch ~y var ious f r i ends r zac t . I I:no*;t you a r e a11 ex-

per i rnental sc ient is ts , but i f ' you devote a small fi-action o f

your time t o studyizg socio_l.ogy, I t,h(r,%, you will agree v i t h

me tha t human beir,gs are nore interast i r -g than corn, g ice ,

o r Drosophi1.a.

NEEL: Dr. Li, before you s i t b l : ~ n , ucder yc3ur

KO. 1 c l a s s i f i c a t i o n , you points \? out, other mort,els which

should be brought into t h e p ic ture . ';.!oul? you care t o e labo-

r a t e on t h a t a l i t t l e b i t ?

L I : Wel l , as I said, I would be the f i r s t one t o

admit my ignorance, b;lt our ignorance has nothing t o do wi th

t h e t r u e s t a t e of na tum. Just t o g i v s p u one exanple of t h e

kind w 8 have been ta lk ing about , mio t ic d r ive , mJphiLosophy is

that each ty?e of equilibrium has a s t o r y Set;ir,d i t ; each t y r e

af e g i l i b r i u m h a s t o be s t u d i e d ;3er SF?, You S ~ Z , i f wo k 3 e p

a c t the Fear, we have t o c a l l I t a pear. If we p i c k i 5 c u t ,

we c a n m t force it; t o be e i t h e r a n a p p l e o r a banana.

I can g ive you a t h i r 2 kin?. A certain gene

413

frequency may not be ab le t o be maintained by heterozygous

advantage alone. thybe, the advantage i s on ly s l i gh t ly ad -

vantageous, but the gene, for instance, i s higher t h m t ha t

t h a t can be explained by th is . On the o ther hand, i t cannot

be explained by mutat ion ra te a lone. It could very well and

e a s i l y be tha t we have a Iow'mutat ion ra te and a low he te ros i s .

These two fac tors co inc ide .

Then, f i n a l l y , WF? get an equi l ibr iun . This is the

point; t h i s he t e ros i s and th,e mta t ion a r e no t nu tua l ly ex -

c lus ive . Why do we have to d iv ide them so clearcut? Mutations

occur a l l t h e t i m e , i n a l l p o s l a t i o n s , i n a l l . l oc i , and , i n

some of the hterozygous, the heterozygous are better, and i n

o ther cases , they a re worse than the normal heterozygotes. With

both of t h e f o r c e s , s h a l l we say , ex is t ing in the popula t ion ,

why should we force t h i s populat ion into one category o r t h e

o the r?

DIC?%,?SON: Are you simply saying that i t could b;e

a cont inuous d i s t r ibu t ion , more o r 14ss, in degree of dominance

o r something of tha t sor t , sild t ha t you are ob jec t ing to a

sharp l i n e of demarcation?

L I : Well, t h a t ' s too s t r o r g a statement. I am

not object ing. I thought we sqrt of imposed o u r a r b i t r a r y

s tandard on nature instead of t r ea t ing ca tu re a s i t is.

NEEL: I wmder, C.C. , If he i s n ' t b r i n g i n g out a

po in t tha t shou1.d be brought out; namely, that you do have

mixed l o c i . ?lost ce r t a in ly , you have nixed l o c i , t h e mathe-

matics of which are scarcely touched up to now, and which mag

do sone very strange things.

L I : Yes, t h i s is a good word. I usual ly t a l k

about mixed l o c i , and we can ta lk about mixed fo rces i n na tu re .

FALCOKER: Is tbere , possibly, a third type of " - -*Ice t ha t ve have--

CROY!: We haven't even heard the f i r s t yet .

FAJLONER: --where nu ta t ion r a t e i s not negl ig i5 le

i n r e l a t i o n t o s e l e c t i o n p r e s s u r e , where se l ec t ion p re s su re

. is smalier t h a n a u t a t i o n r a t e , and ve have a balanced poly-

morphism, naintained by muta t ion i n oppos i t e d i r ec t ions?

NOW, I don't !mow, t h i s may not be r e a l i s t i c , b u t c a n we

completely neglect i t as a p o s s i b i l i t y ?

CIIOW: We car, neglect a l o t of t h i n g s a s f i r s t

approximztions,, but i t i s t r u e t h a t i n such a locus, where

both fac tors a re involved , the segrega t iona l component and

the mutational cornponent a r 9 no t s t r i c t ly compar tnen ta l i z -

ab le and addi t ive, but t h i s doesn' t mean you can ' t dea l w i th

a s i t u a t i o n l i k z this . Theoret ical . ly , I choose not to do it

.in t h i s discussion, but--

NEEL: Eut t h i s . may be the most meaningful.

CEOW: No, I don't- t h i n k it i s .

YXL: I t c e r t a i n l y i s t h e xost comnotl s i t u a t i o n .

CR0;J: Kot, not u n l e s e h e t e r o t i c l o c i are very

frequent , which I am inc l ined t o th ink they a re no t .

?EEL: Let me r e s t a t e i t : t h s t where we 6is-

c u s s h e t e r o t i c l o c i , t h i s i s the most comaon.

CROW: but then, I think, I can s ay f a i r ly , for

z o s t h e t e r o t i c loci, the segregat ional comaonent i s n o t im-

por tant . NEZL: But the i nb reed ing e f f ec t s you ge t from

s u c h l o c i a r e what I'm ta lking about .

CR@W : I t h i n k t h e y a r e c l e a r l y due ma inl-y t o

the segregat ional component, too. I *on* t th ink you a r e

neglect ing very much of s igrdf icance when you neglect segre-

g a t i o n r a t e s a t a seprega t iona l locus . This can be worked ou t .

It i s n ' t t h a t you j u s t neglect something. You work i t out

and see tha t i t is small.

BODNE3: 1snr.t what you r e saying, i n a way, Jim, I

t h a t there i s a vesy narrow razge of s e l e c t i o n c o e f f i c i e n t s

:!fiere you have a h e t e r o t i c locus, where both the nutation and

t h e k e t e r c t i c componect cont r ibu te more o r l e s s cornparable

aaoun t s?

CROW : Ye s . BODMR: That, over rnost vaiues of s e l e c t i o n

coef f ic ien ts , one o r t h e o ther is predominant.

CROW: Yes. If t h e h e t e r o t i c e f f e c t i s of t he

ordsr of OT so, t h a t i s , the same order of mutation,

tksre a r e a nurnber of cornpl.icatior?.s, but t b s e a r e n ' t c o n t r i -

but ing very much,

DICICEESOrI: It ?s a s t r o n g l y bimodaL popuZation;

i s t h a t r i g h t ?

:Y%IGIiT : There is another kind of balance that, it

seems to me, i s important, o r I have considered i t a s mast

important. I n my 1931- paper, which vas t o qu i t e an ex ten t

concerned with modes of balance, t h q kin1 t k a t I s t r e s s e d most

was one t h a t wouid g i v e r ise t o what you might c a l l immigra-

t i ona l l oad , i nmig ra t iona l ac t s l ike mutation, but a tremend-

ously more poverfu l fac tm than nu ta t ion . If you have a popu-

l a t i o n i n a l a r g e a r e a , w i t h su f f i c i en t i so l a t i . on in d i f f e r e n t

regions so t h a t s e l e c t i o n c a n o p r a t e d i f f e r e n t l y in d i f f e r e n t

regions, many pa3 ple have c r i t i c i z e d me f o r s a y i n g a l l d i f -

f e r s n t i a t i o n was random . d r i f t between regions, but t h a t i s not

the case a t a l l . Thdse same people u sua l ly a rgue t ha t d f f f e r -

e n t i a t i o n was due t o d i f f e rence i n t he cond i t iom o f s e l ec t ion

i n d i f f e ren t r eg ions .

I don ' t t h ink there wotlld bs much Cisagreenent

about there being differecces i n t h e condi t ions of s e l e c t i o n

in Ci f fe ren t reg ions , vh ich xear,s t ha t $here is a favored--

well , l e t ' s j u s t aut i t on the basis of a s i i l g l e gem: t ha t

one a l l e l e is favored in one r eg ion , an6 t he o the r a l l e l e i s

favored i n the other regzon. Eut now, i f thsy a r s n o t com-

p le t e ly i so l a t ed , . t he re t.:oulc!.bs a leakace there , so t h a t t h e

immigrants would be going f ron each region to the o the r , pu l l -

ing i t down from what I t would be i f they were coxple te ly iso-

l a t e e ; so that both of these regions will be suf fer ing from an

inmigrat ional load that i s in .ba lance wi th adverse se lec t ion .

YOU c a n ' t put thea on the same bzs i s , because the

best genotype i n the two regions i s d i f f e r e n t . They a r e simply

not comparable. They a r e q u a l i t a t i v e l y d i f f e r e n t . But each

region will be ir, b alance between immigrations, tending: to

pull i t down. As f a r a s i t is concerned, i t i s a good gene

i n t h e other region, but pul l ing i t down a s f a r a s t h a t r e g i o n

is concerned.

S e l e c t i m i s o y r a t h g a g g i n s t t h a t i n p r e c i s e l y

the same way as your mutat lbnal load operates , but , in that

case, the gene Prequercies may very well be h igh , in the

neighborhood of .30, .4C o r .TO and so 03, becatlse inmigra-

t i o n i s such an ingortant, powerful factor,more so than muta-

t i o n . You have sofiething, therefore, that i s very .mch l ike

mutational load, except tha t the charac te r i s t ic geQe f r e -

quencies o r the equilibrium f?equ.encies are not of t h e order

o f , gerhaps, one i n t e n thousand btlt may be in the neighbor-

hooc? of one h a l f , Like the segregat'onal load.

C3Oh': I thought about t h i s quite a b i t , Dr.

Wright, but-

3CRIC;HT: So i t s e e s t o me tha t it would o r d i n a r i l y

be the case tha t you would have polymorphism in each of these

regions, due not a t ull to heterotic advar, tage of the hetero-

zygote, but dce t o the balance Setween immigrants that are

unfavorable from the standpoint of reaching this equat ion.

MULLE3: Could I say soneth ing i n addT-tion t o t h a t ?

It won't take long . To extend t h e ;nech,r,isms of balance and

load. s t i l l f u r t h e r , a l l loads s x i s t i n g i n an equi l ibr ium

c o r r e l a t i o n a r e , o f course, balanced. I might give an example

which I mentioned i n !ay 1945-47 pzper a s a sample o f t h i s ,

which I th ink a l o t of people have a l r e a d y r e a l i z e d ; namely,

of genes-an6 I th ink F isher mentioned t h i s sor t of thing, too--

and It has nothing to do w i t h segregat ion load in the sen=

of he te ro t ic , a l though tha t might work w i t h i t .

Our advantages are advantageous when present ln a

g iven Pcpula t ioa , in a small freqcancy, azd become disadvastage-

OUS a t a h i g h f requency, l ike the hypothet ical case of nesr-

s igh tedness in kcman communities, which would be advantageous ;

a s f a r 3s p7oducing indLvi2uals'who we7e h e l p f u l i n making

417

arrowheads or other f ine work tha t was usefu l , and disad-

vantageous beyond a c e r t a i n p o i n t .

N R I G H T : Yes. Dr.Dobzhansky and I discussed t h a t

in a paper a good many years ago , espec ia l ly as appl ied to

regions in rdhich the,re i s something of d iv is ion of l abor .

WLLEE: However, I th ink tha t is a very ra re

s o r t of th i f ig , compared with t h i s great majority of things we

a re talking about.

CEIO'd: There i s some thing more important to say,

ar,d tha t is , loci that are maintained t h i s way will not be

spec ia i ly respns ive to inbreeding . Therefore , ':!,e &'A

r ' a t i o s t i l l a rgues for a nutational hypothesis.

IU'RIGHT: The immigrational l o a d is precisely the

same a s mutation load, because i t a c t s l i n e a r l y .

CR0I.J: It will hav.e a d i f f e ren t i nb reed ing e f f ec t ,

though, because of t h e d i f f e r e n t gene frequencies you are

l i k e l y to f ind under these conditions.

WXGET: That i s e s sen t i a l ly t he po in t ; t ha t gene

frequencies will be an8 i n f i v e , and mutation load will be

very low, one i n ten thousand.

CROW: I really th ink you can d i s t i n g u i s h between

the mutational component and everything e lse , throwing this

i n w i t h the E st, which I am t ry ing to 23.

WRIGHT: T h i s behaves very d i f fe ren t ly in the

segrega t ional load.

CROW: Not a s r e l a t e6 t o i nb reed ing .

ElCRTON: A t ciose range, you wouldn't know i n a

particular case whether a s eg re i a t iona l sys t em a t a d i f f e r e n t

frequency would change a11 t he s e l ec t ion coe f f i c i en t s .

LEWONTIN: As a matter of f a c t , you can show quite

simply that if you e v a l u a t e , t h e f i t n e s s a t e q u i l i b r i u m , e i t h e r

ths heterozygote must be i n f e r i o r or sugeyior to get i t .

YRIGHT: I r r e s p e c t i v e of j u s t how i t a c t s , t h e r e

is a th i rd type of load , t h a t i s poss ib ly ve ry d i f f e ren t from

ei ther mutat ional or segl-egat ional .

418

CROW: And it is important to t r y t o i s o l a t e i t .

All I was t r y i n g t o s a y for the moment, so f a r a s t h i s dls-

cussion is concerned, i s t h a t I think we can throw th is

f a i r l y e a s i l y i n w i t h the S class without rnaking a se r ious

mistake. I tk ink t h i s will apgear inmost of the experiments

ve have talked about i n t h e S c lass .

I want t o say, before Dr. Lils discuss ion s tops ,

I don ' t r ea l ly want to 6 i scuss the de ta i led i t ems , I t o 5, t ha t he has talke2 about and which he put i n p r i n t . My own

opinion is t h a t Dr. L i i s r a i s i n g , i n some cases, semantic

quest ions and, in some other cases , he has not rea l ly under -

stood the problem. I a l s o wish , con t r a ry t o h i s w i s h , t h a t

there were l e s s i s o l a t i o n . I th ink t ha t most of t h e p i n t s

he has ra ised, two o r three hours of discussion would c l a r i f y .

I don ' t want t o do i t in a l a rge group l i k e t h i s , where the re

seem t o be more important issues than the understanding o f

pa r t i cu la r de f in i t i ons o f s eve ra l yea r s ago. But I don't want

t o be in te rpre ted as agree ing wi th most of what he said. I

disagree qui te profcxxl ly .

NEEL: Jim, i s it your plan today to get to t h e

i n t e rp re t a t ion o f B/A r a t i o s ?

CROW: riot spec i f Ica l ly , no . There a re severa l

people who have soaething to s a y about it. I would l i k e t o

be f r e e t o comment, but I have sa id so m c h on t h i s subject

i n p r i n t t h a t I w'ould hate t o regeat i t here.

NEEL: Well, t o sone of us, t h i s problen comes up:

The B/A r a t i o s f o r r a r e , n i c e , c l e a n c u t r e c e s s i v e t r a i t s r u n

of the order of 80 t o 100 or 150. Newton has ca lcu la t ed

those fo? fa i r ly recess ive d i seases . Now, a l i t t l e b i t of

a B/A r a t i o of that magnitude, lsO:l, goes a long way i n

raising the B/A r a t i o .

LEWONTIN: No, i t doaen ' t . It has t h e reverse

e f f e c t . h%EL: I meag, i f you have coaponents i n the B/A

r a t i o t h a t a r e 15O:l or 100:1, how do you i n t e r p r e t a n o v e r a l l

B/A r a t i o o f , l e t ' s say, 10, which has been mentioned? T h i s

is an i s sue tha t , I think, i t would ke worth discussing here.

LINORTIM: Well, Jim, I spent the l a s t month r e -

viewing a l l of the b iases I could f ind in B/A r a t i o s and a l l

t h e ex?z:-icsnts, and I described myself yGsterday a s being

a comple te ly un in te res tee pa r ty ra ther than a 2 i s i n t e r a s t e d

party. I am un in te re s t ed i n t he s ense t ha t , t o me, i t i s not

a c r i t i c a l i s s u e i n evoZutionary theory. But I have become

in t e re s t ed in i t , and I think, i f I cou ld have a few minutes

t h i s afternoon, I could probably sunmarize a good deal of

these biases and experimental. situations.

CROW: I was going t o c a l l on Dick Lewontin this

morning. I wonder if t h i s is the time t o do i t ?

NZEL: If you are ready, I think, perhaps, t h i s is>

t h e t i n e t o do i t .

LE'VJONTIN: A 1 1 r i g h t ; becaus it r e l a t e s s p e c i f i -

c a l l y t o th i s po in t you just; r a i s e d a b o u t s p e c i f i c t r a i t s

an6 so on. I th ink what I will say is completely unexception-

ab le .

LEVENE: Impossible! [Laughter]

DICKEESO3J : We '11 see.

LEWONTIN: I took a look a t t h i s question over t h e

last rnonth in p repara t ion f o r this conference, and simply

asked myself, what is t h e p rope r ty of the B/A r a t i o a s a

d e t e c t i o n system? I am not concernec about the biological

meaning of load i n t h i s pa r t i cu la r contex t , but siaply, say,

someone o f f e r s me an instrument for a d e t e c t i o n problem; what

are i t s d e t e c t i o n c h a r a c t e r i s t i c s , i t s s e n s i t i v i t i e s o v e r

the various mrts o f the range, and the way i t shoaid be used,

and so on? That's a l l I'm concerned with.

,';..seems t o m t h a t this coQld bs looked a t i n

s e x r a l wzys. Fil*st of a l l , 1s t he B//A r a t i o t o be used as a

M x c t i o n system, i n the case of single c learcut recessive

t r a i t s ? Ny conclusion i s t ha t i t i s not. I would like t o doc!:?.

ment t h i s . I t h i n k t h a t i t has uses, but t h i s i s the wrong

420

place to use them, f o r a very simple reason--and I think

t h a t Jim agrees with this--

. CROW: Oh, yes.

LZ'vJOPU'TIN: A t l e a s t , I think, he hasn' t made

t h i s point here, but; you do agree with this .

C2OU: Yes, i f I understand what you're saying.

LZ1;JONTIN: It s what I wrote t o you i n ny l e t t e r . I

LSWN'E : Use the yellow chal.8 so we can see it.

LE!!JOKTIN: By a recessive t r a i t , I nean nothing

about f i tness. I do not conmit myself on the quest ion of re-

c e s s i v i t y o f f i t n e s s , b u t , r a t h e r , zecess iv i ty o f the defec t

which we can measure i n a human popI.ation.

PULLER: Excuse me, but as soon a s you u s e t h e ,

word, t tdsfect , t ! you commit yourself w i t h r e g a r d t o f i t n e s s .

LEVONTIN: All r i g h t ; a chzracter is t ic--no, I

don't . It may be a de fec t which has no e f fec t on the gene t ic

f i t n e s s . T h e r e a r e l o t s and lots of de fec t s which, presumably,

have no e f f ec t on ge r , e t i c f i t nes s , Profzssor XulJ-er.

MULLER: I'm sorry, but I don't use the word, !!de-

fect,!! in tha t sense . I

LE'JOKTIN: A l l r i g h t 4 I WOR t use the word, !!de-

fect.!! I111 say we have a human t r a i t ; which I s recognized by

t h e nedicai man a s a so-cal led human d i so rde r , o r va r i an t o f

some kind. I don ' t want t o g e t i n t o t h a t .

McKUSICK: 'dhg c20n1t you say l'phenotypelt?

MULLER: l!Deviant,tf i f you l i k e .

LEWOMTIN: The e s sen t i a l po in t is that , f rom a

medical standpoint, human genet ic s tacdpoin t , we c l a s s i f y t h e

populat ion into affected persons and unaffected persons. I f

t h e a f fec ted persons a re homozygotes for some gene, then, we

t r y t o c a l c u l a t e the B/A r a t i o , The point i s t h a t we have

confounded, i n t he una f fec t ed class, two genotypes.

T h i s means t h a t when we take t h e maxizum fitiless 7

i n the population, whether we- use mortal i ty , fecundi ty , o r

anything e lse , we a r e , in fac t , t ak ing an average of the

421

f i t n e s s o f those two confounded genctypes. You see, we a r e

saying that these individuals have a h igher f i tness than

these. These mag regresent the maximun f i t n e s s , and they

a r e confounded. LC0mparir.g Ba t o A , and a to AA.] MOW, f o r a gene which is p a r t i a i l y dominant on

t h e f i t n e s s z a l e , t h a t i s t o say, i f t h i s ' i s less f i t than

t h a t , i f t h i s i s less f i t , i n t u rn , than tha t , t h i s confounding

has absolute?-y no de tec tab le e f fec t on the B/A r a t i o , f o r the

obv ious r eason t ha t t he re r ea i ly i sn ' t much confounding here, :

because nearly a l l th2 individusls in the populat ion a re AA;

anyway, so the mean f i t n e s s o f these things 5 s so close to

t he mean f i t n e s s .of A A t h a t %here i s no problem. I won't go

through that .

But l e t US ask i f , perchance, on t h e f i t n e s s

scale , the genes should be h e t e r o t i c , I n t h a t c a s e , if we

take t h e f i t n e s s o f t h a t c l a s s a s r e p r e s e n t i n g t h e star.dard

f i t n e s s , we have confounded the two f i t n e s s e s . The ~ s u l t is

that the apparent maximum f i t n e s s a t e q u i l i b r i u m is as fo l lows:

tlhat becomes apparent t o us, because of t h i s confounding, is

simply 1 - S/S + 2 , T. That i s w h t i t appears t o be.

If we then pu t tha t in to the ca lcu la t ion of load i n

t h e outbred population, the apparent load--and t h i s i s appar-

e n t load in the outbye6 popuiation--Lt comes o u t t o be, a s a

matter of f a c t , ST2/S +T. The apparen! l o a d i n t h e inbred

population, of course, does not suffer from t h i s confoundipg.

WAiLAC3: I s n ' t t h e r e a parenthesis around S +T?

LEI~IOMTIN: Yes, I m sorry. The apparent load in

the inbred population becomes t h i s [(T(S+T)/S+T) 1 I c a l c u l a t e the inbred component fron! the non-

a f f e c t e d i n d i v i d u a l s ' f i t n e s s . I do not re fe r myself back t o

the outbred component t o g e t t h e maximum f i t n e s s . I eo t h i s ,

c lear ly , because an inbred cornponent not only is inbred w i t h

respec t t o t h i s gene, but also with resilect t o a l l o ther genes;

so if I want t o know t h e marg ina l f i t nes s due to t h i s gene,

I nus t coapa re t hese s t r i c t iy w i th in t h e inbred component.

,

422

Having'done t h i s , I come out w i t h a l oad r a t io

as fol lows--and, to s imglify i t , l e t me say tha t s i s equal

t o K )I t . It turns out , then, that the inbred-to-outbred

r a t i o is 1 -(K)\x 1+ t v i c e K over IC, which, f o r my s f ia l l

value of K, i s approxinately equal t o 1 / K .

What does K mean here? It nearrs the proport ional

d i s a b i l i t y of these homozygotes, so-called normal ind iv idua l s ,

norslal from the point of view of the medical Sefect , as cos-

pared w i t h these; so we would assurne gene ra l ly t ha t t hese i n -

dividuals are probably not very Sadly o f f i n corngarison w i t h

these. These a re nos t baC.ly off because o f t h e i r d e f e c t , and

these a re bac!ly o f f f o r some other reason [comparing AA t o A I .

K, then, i s gene ra l ly a small number. A A might have a f i t n e s s

of 98 per cent of t h e heterozygote, and aa, 89 per cent--a

reasonable value, because'K i s 10,

You see what t h i s means. It means, f o r such a

s 2 e c i f i c e f f e c t , t h e apparent load ra t io looks l ike the appar -

e n t l o a d r a t i o f o r semidominant chain, where the load ra t io

i s progor t iona l to 1/H.

You remember t h a t t h e l o a d r a t i o f o r a semidomi-

nant chain i s 1/2--is t h a t s i g h t ? 2H?

DICKERSON: Your K is simply T over S.

CROW: Dick, could I say something a t t h i s point?

T h i s i s a l l appa ren t ly co r rec t , but -1 rea l ly ought to say ,

somewhat defens ive ly , tha t we have known i t a l l a long; that is,

Newton and I have known it, and'we have not used the Load-

r a t i o c r i t e r i o n e x c e p t for t r a i t s where the re is an optiaurn from

t!hiCh YOU can measure the t e v i a t i o n ; so t h i s confounding of

the homozygote on heterozygote c lasses doesnl t enter here .

t h i s was used f o r a . t r a i t Like deafness, it was used to

r u l e out a very def in i te hypothes is , namely, t h a t all homozy-

go te s were deaf, and t h a t t h e d e a f n e s s t r a i t was due t o s e l e c -

t i o n on the charac te r , th rough the t ra i t i t se l f , no t th rough

Some o t h e r t r a i t . I agree, a s I th ink Newt does, t h a t t h i s i s

a Pre t ty implaus ib le hypothes is , in t h e f i r s t p l a c e , and i t is

423

ru led ou t w i t h a grea t dea l of r i g o r .

The onl:? o%hes way i n which gene t i c load prin-

c i p l e was used, i n questions having to do w i t h ind iv idua l

hurnan t rs i ts , was vhere i t had to do Rot w i t h B/A r a t i o , 2 s

here, but i t had to do riIth my poiht No. 11, i n which I

asked what the totail segregation l o a d is, contributed by

such a locus. That i s not biased by t h i s kind of considera-

t i o n , and l e t me exp la in why, because I think you h o w but

not everybody in the rmm t o s s .

\!hen YOU .measure tke segregst ion b a e from obser-

va t ion of a s i n g l e t r a i t such a s deafness, you do t h i s by

Deasuring the f i tness loss by the dea fness t r a i t , and then you

have an inequal i ty which says that the minimu3 number of

a l l e l e s o r t h e n a x i m n ntlmber of a lLeles , i s sonething or

o5her. WOW, i f I yake a n is take i n measuring t h e f i tness of

t h i s t r a i t and, instead of measuring i t from the o?timum

heterozygote, but measure i f f ron t h e homozygote to the

heterozygote, I have unc?erestimated i t , and my inequa l i ty is

still here, 5 p r i o r i .

LEWONTIP:: But t h i s dexonstrat ion is not made i n

any way to point an accusing f i n g s r a t arybody, but t o draw

i t t o t h e a t t e n t i o n of

that they ought not t o

forward manner.

CEObi: 8u t

:z:*psmR: i;Iforms t ion.

LE'dOiJT I)! :

people who may not havernalized this,

use the l o a t r a t i o i n t h i s s t r a i g h t -

ncbody has.

YGV. can ' t d.0 i t . you don t get t h e I

Then, I nisunderstood Jim i n t h i s case.

Did you Rot a s k whether th i s n ight no t be done?

iEF,L: Ply comment was t o imply t ha t it couid not

5e bone.

CRO'd: I t h i n k we can agree t o t h a t . LEWCYTIN: Then, I f n so r ry I wasted your tine.

I assumed there were some people, and I know there i s a t l e a s t

one person, i n t h e room who thought that the best ::lay t o use

424

. . - 8 .

the B/A r a t i o was, i n f a c t , t o take a s i n g l e human t r a i t ,

which was a very c lear one, and take the affected persons and

the nonaffected persons, and use the nonaffected persons as

giving the maximum ' f i t nes s .

DEMPSTER: How would you ever get a r a t i o . t h a t

way? There's no way i n which you can get a r a t i o , so, if the

person t r ied to use i t , he wouldn't have a r a t i o t o work on.

LZ!!ONTIN: O f course , he wouldn 't . DEMPSTER: So what r a t i o do you t a k e , i n t h a t

case? You have t o have three values t o get t h i s r a t i o , and

I donr t see what three values you take from the population.

UWONTIP?: I'm sorry, but you have cous in aa t ings

and you have outbred matings.

CROW: You can take the frequency of the rate.

LEWONTIN: Yes. 1 don ' t see any d i f f icu l ty there .

DEMPSTER: Oh, yes.

CROW: You can do this concept, but I don ' t th ink

anybody who understood the nature of the theory would ever do

it tha t way.

LEWONTIN: Then, I 've wastee a l i t t l e time. I

simply wanted to say, please, never use B/A r a t i o s - -

CROW: Unless you know what you're doing. [Laughter]

LE'VJOI,JTIN: No, wait a minute. Never use B/A r a t i o s

f o r spec i f i c human t r a i t s where you cannot t e l l t h e heterozygote.

Do you agree? ,

CROI! : Oh, sure.

LEWONTIN: If you -can t e l l t he he t e rozygo te fo r a

spec i f i c human t r a i t , you do not need the B/A r a t i o . Is t h a t

cor rec t?

CROW : I ' m sor ry ; I was thinking about your f i r s t

statement.

LEWONTIN: If you can detect the heterozygote, you do

not need the B/A r a t i o t o answer the question involved.

NEEL: Then, would you l ike to t ake the next s tep?

€raving to ld us we can never use B/A r a t i o s f o r s p e c i f i c t r a i t s - -

425

CROW: I'm not quite sure t h i s i s t r u e . b y b e ,

we can f ind a way of doing i t .

NEEL: Then, can we use i t f o r d a t a which cons is t

of a a ix tu re of s s e c i f i c t r a i t s ?

LEljJOrrTIN: &. Let me expla in tha t , or a t l e a s t

Let me say what I t h i n k you can do when you a r e n i t d e a l i n g

w i t h a mixture of t r a i t s . I th ink i t i s a quest ion of averag-

ing out, bu.t I'LL g e t t o t h a t .

The quest ion is, you cannot use i t f o r s p e c i f i c

t r a i t s . Then, .it must be used simply a s the gross picture of

f i t n e s s i n inbred and outbred conponants of the population.

The f i r s t t h i n g we mst obsezve i s t h a t i f you want to u se i t

i n t h i s way, i t nust be used in such a way t h a t you es t imate

t h e f i t n e s s e s of the components, t h e ir,bred and outbred corn-

ponents of the population, under the sme conditions ir,

which t h e s e l w t i o n was zoing on, because HowarZZ has provided

us w i t h a manuscript , and'I believe i t is now i n p r i n t , show-

ing how the B/A r a t i o c a n be very sens l t ive to depar tures from

equilibrium, cr .supposed equilibrium, o f s e l ec t i on coe f f i c i - ,

e n t s ; t h a t i s t o say, i? the selection measure i s not the

select ion under which the popuh t ion i s a t equ i l ib r iua , t hen ,

the B/A r a t i o can be very misleading.

Using Howar6's argumank, then, which I f i n d f a u l t -

less, I must say tha t if you want t o use the B/A r a t i o , t h e

second , t h i n g you rnust do is t o rnaasuze the comaonents of f i t -

n e s s i n ' t h e same environmenks. These components of f i t n e s s

must be the components undar which the population has been se-

l ec ted .

blULLER: May I say in tha t connec t ion tha t I t h i n k

i t was recognized in our jo in t paper tha t t h i s was the case,

b c t that i t was recognized to work i n a ce r t a ig d i r s c t i o n ,

Hamly, to minimize t h e r a t i o fount?.

LEWONTIN: But t h i s is, infact , not the conclusioi l

h'oward has corn@ to . i'f you look a t t he g raphs of the paper

which he has now published, he shows t i l a t , i n f a c t , t h e r e are

425

4

many cases where the B/A r a t i o f o r h e t e r o t i c t r a i t c a n be

badly of f in the trrong d i r ec t ion . Is tha t no t comect ,

Ifowsrd, t h a t you can get a very l a rge B/A r a t i o ? I

LLlEN2: Ita sorry I di6n t br ing the s l ide .

LESiGI?TIN: But i s t h a t not c o r r e c t ?

CROW: Is there any reason wky they should devi-

a t e more o f t e n i n t h i s d r rec t ion than i n the o ther? I don l t

know. If the argument here i s t h a t you can coc t r ive s i tua-

t i ons i n which t h i s would be a misleading resul t , obviously,

yes.

LEIJIONTIN: I ' m t rying to f ind a s i tua t ion under

which we a l l would agree that the 3 / A r a t i o is a s good a s

you can make it . O X ?

MULLER: No, i would l i k e t o come back to that

point. 1sn:t i t t rue t ha t , i n gene ra l , the environmental con-

d i t i o n s have been improving so a s t o minimize the ratio as

found by the method we used, and making i t lower than i t

would. have been if doae under t h e condi t ions in which the

equilibrium had beer1 obtained?

LEVOI!TIN: Excuse me, Prcfessos :fuller, but I

think the main point I want t o mzke here, and I haven't fin-

ished, is not that it ought to be used in human pokuiations,

where, I think, your statement is cor rec t , bu t i t ought not to

be applied to Drosophila. I th ink it i s a gross error t o take

a sample from a Drosophila population, bring i t into the iabo-

ra tory , a rd measure t he f i tness of various components under at

c o m p i e t e l y a r t i f i c i a l set o f 'conditions, which have no r e l a -

t i onsh ip t o the condi t ions which es tabl ished the equi l ibr ium

i n the Drosophila population, and expect a necessa r i ly s ens ib l e

r e s u l t . When we come t o human populations, 1'11 have something

e l s e to say, but I th ink you have t o ba very carefu l .

If you can be sure that the cond i t ions i n the

l abora tory a re such tha t your se lec t ion es t imates , your e s t i -

mates of f i t n e s s , d e v i a t e i n c? known d i r e c t i o n from the selec-

t i o n which has gone on in na ture , then, you know the d i rec t ion

of b i a s , but un le s s you do know t h a t , your e s t ima tes of f i t -

ness bear an unknown r e l a t i o n s h i p t o the f i t n e s s in a n a t u r a l

population. This is what we u s u a l l y do in Drosophi la , af ter

a l l . We do !mow the measure of f i t n e s s i n t h e n a t u r a l po;u-

l s t i c n .

'If this is t x e , then hov can one usa t h e 3 / A

r a t io? Wel l , man Fs the obvious place vt-,e;.e you use the B/A

Tatio, for the reason that the es t imatesof f i trxss which you

take do not in any way l i . S h i * b the popAat ion; tha t i s t o

say, you do z o t change tke sel.w",on cuefficiel?. ts when YOU

take the e s t i m t e s of fitness. T h y a x the es t imates of

f i t n e s s i n t h e s t a n d i a g pcpUlafiOi1.

Now, s f m e we have tile resu2.t t h a t O i l e must never

take an error.eous, o r , ssy, take the l e s s t e;.;.oneous gossfble

measxrcs of the selec ' i icn i n crde? tka'; t h i s lack-of-equi l ib-

rlurll al-gumsnt i I O t upset us, i t fo l lcws t h a t VJS ,nust, whera

we can, avoid taking partial conbonants of f i t n a s s , s ime

ally one p a r t i a l component of f i t n e s s is r n t i t se l f a a r e d i c t e r

of the equi l ibr ium.

Pian, again, is z s i t m t i m where we can do t h i s ,

because we can get the con!plete a p - s g e c i z i c rnar ta l i ty and

fecundi ty schedules f o r mail, xa1:ke fo=l any other organism In

t h e world. T h i s i s a d i f f i c u l t t h i n g to do,. and 1 am on ly

t r y i n g t o s e t up tke kind cf data v h i c h $ I t h i n k , would give

t h e best klnd of B/A e s t i n a t e . Whak I rsqul re , then , fs t h e

complete age-spaciPic nortaii.f;y and fecandi ty schedales for

t h following three compo,rlsnts CJE the population, because I have t o allow maternal effect , unfox-tunatsly, for the general

random component of the popclation, t h e so-called outbred

acpulation, f o r o f f sp r ing which arr3 themselves inbred t o v a r i -

c c s degrces aad offspr ing wt;lcI; a x not necesseFiiy themsclves

inbred, but which corn2 f ~ o a inb,-ed rnoti?2rs. Ons must exzrnfne

211 t h ree of these. If we lrp~ lucky, the inbred nother > ] a r t

make any diffezence, i n which cas8 ou: pxblem is eesie;., but

I do say completa age-specific ncmi;aiI.ty and fecuzti i ty.

428

ROBERTSON: ?lay I j u s t i n t e r r u p t ? T h e o f fspr ing

of t h e a a t i n g s are going t o be inbred?

L W C N T I N : In sone cases, yes, because YGU have

cousin raarriage.

ROi3ERTSON: Are you going to take those on and.

see what t h e i r own fecundi ty is?

SEWONTIN: That would be nice if vou could do i t .

ROBERTSOV: It seems t o me t ha t i s e s s e n t i a l .

LEWONTIN: Well, you must know the fecundi ty of

an inbred individual and the fecundi ty of--yes, c e r t a i n l y

you have t o know the fecundi ty of inbred individuals; abso-

l u t e l y .

LEVENi3: If you had the Cata on inbred mothers,

you could g e t i t on inbred fa thers . These, of tours, will

be of different ages , probably.

LEWONTIN: T h i s i s not an easy d a t a - c o l l e c t i n c : job,

Howard. I don't propose t h a t i t is, but I propose that i t

e l imina tes many of the ob jec t ions Professor L i has ra i sed to

the B/A r a t i o . You ?re depending on the r e a l s e l e t i o n busi-

ness goir,g on i n t h e population, an aqe-spec i f ic se lec t ion ,

which d e t e r n i n e s t h e t o t a l s e l e c t i o n ir, the human population.

CROW: I th ink i t i s r e a l l y Rovard's po in t r a the r

than Dr. L i r s , b u t t h a t ' s a l l r i g h t - - j u s t to keep the record

s t r a i g h t . LEWONTIN: If t h a t is the case, I had seve ra l o the r

points. Ye come t o the l a s t - -

MORTON: I foliow you completely up t o the point

where you are es t imat ing A . Tell ne whzt t h i s means when you

use fecundity.

- LE!trONTIM: No, i t .is age-specif ic mortal i ty and fe-

cundi ty , mul t ip l ied in t h e proper way t o give you an es t imate

o f 3 .

DEXPSTER: How abou t t he ques t im , how do you cone

t o your A ?

LEXONTIX : I have two more , m i n t s t o aake. One i s

0

Now, a s has been pointed out repeatedly, and I

t h e b i a s ing e f f ec t of A. bdhat we a re do ing , i n e f f ec t , i s

t r y i n g t o draw a r e g r e s s i o n l i n e , and trie a re t ry ing t o ge t

B, B being the slope, and A , the in te rcept . The point has

been raised over and over again that the A is above some un-

known level , and, so lcng 2s i t i s above some unknown l e v e l ,

we do not know what the real value of A is.

don't have t o go through i t aga in , the e f fec t of such a b i a s

is to lower the ra t io ; tha t i s to say, i f A is measured from

100 per cent, or three childr-en per family, when i t should

be measure6 from two chi ldren aer fami ly , then , the e f fec t is

t o lower the ra t io . If A is rea l ly remarkably l a rge , if t h i s

dev ia t ion from the groper Eeasurement point is r e a l l y remark-

ably Large , r e l a t ive t o t h e deviat ion f rom your assuaed

point, then, of course, the lowering will be very large ; and

so t h i s i s where we come t o t h i s quest ion of t h e one-sided

detect ion system that we a re t a lk ing abou t .

It is c h a r a c t e r i s t i c of t h i s detection system that,

if t h e r a t i o is very large, under the condi t ions .1 have speci-

f i e d of age-s2ecif ic mortality and fecundity, then, t h i s bias

cannot be t h e cause of this inf la ted B/A r a t i o . But i f the

B/A r a t i o is very small, i t may be, indeed, one of t h e con-

t r ibu t ing causes , and there i s no way you can get around t h i s

problem, a s f a r a s . I call sea.

MORTON: It's c l e a r t h a t you are taking fecundity;

the B/A r a t i o i s not only small but i t is negat ive ; tha t is ,

the reasonable model f o r f i t n e s s i n t e r m s of our enthv-siasm

for. parameters would be the adaptive value i n t he r i g h t sense,

o r E t o A minus BF, so B/A--

LEuJONTIN: Well, now, wait a minute.

PI3RTOIT: I don ' t th ink i t * s g o h g t o be pos i t i ve .

CROW: 1 doni t th ink you can do t h i s kind of ex-

geriaent meaningfully.

LEWONTIN: We don' t do t h i s , an'pay.

M03TCN: The pro.blem i s wi2h fecundi ty . I t ' s

430 something like a minus BF, because e i ther A represents the

mean fecundi ty , and the amount o f inbzeeding will lower i t ,

so the exponent ia l tern will be B minus EF on t ha t model.

This doesn' t mean anything, then.

LEW3IJTfN: Excuse me, k t S you havs lowai*ed f e - curid:i& yoa have an estimated fecundity load, don't you?

MORTON: T h i s i s a gecundity which dossn ' t seem

to have a c l e a r meaning. Fecundity [balance i:laudible due

t o t h e f a c t t h a t h a l f a dozen people were saeaking a t once . ]

LEMONTIN: I don't use t & u sepa ra t z ly , anyway.

What I would c a l l U I s nothing bit t h e i n t r i n s i c r a t e o f in-.

crease of R--knowing nothiag about humans but sone.t;:lL?gabout

Drosophila. I would t r y t o e s t i z a t e R from the equat ion

summation, e i t h e r minus R M X aquals 1 o r L. YOU see, if

the re 1 s such a t h i n g a s a s t a b l e age d i s t r i b u t i o n , which the re

Probably i sn ' t , t h e n , whme LX is the aor t a l f ty s chedu le ,

t h i s gi-ves me an est imate of--

K W T O N : SUPPOSS you were doing t h i s f o r a popu-

l a t i o n t h a t wasn!t i x r e a s i n g o r d e c x a s i n g ; ~ O U would e s t i -

mate :'Our Malthusian parameter as x c o . That is your A ,

apparent ly , and then yau ge t a B f o r h ibreeding e f fec t . Your

B/A r a t i o i s enormous. It seeOs t o $13 t ha t t h e f a i l u r e t o de-

f i n e your A allows you t o g e t posi t ive, negat ive 01" i n f i n i t e

r e s u l t s .

LEWOPJTIX: H w would you dcf i2.e the A ?

NORTON: That rs the pzoblen.

LEWOMTIN : All r i g h t .

XORTOM: Ther.e a r e soms ways of t ry ing to do it ,

but-- e

LEWONTIN: I wocl! be happy to hear them. So t h e r e

i s t h i s unknown b ia s , fa12 emilgh, c.,cl,;Iccially foi. fecundity, a s

y c t l point oGt, since you could maL:a "the mxi0=~..;1 fecundi ty 143

if >-at? wanted to .

431 ..

LEWONTIN: No, I arn proposing to go o u t , o r t h a t

somebody go o u t and get complete mortality and fecundi ty

schedules.

CROW: But thepoint i s t h a t no Drosophila ex-

per ime9ts ever tz ied to answer t h i s ques t ion in t h i s way.

I don' t th ink i t can be done.

LEWONTIN: I don ' t th ink t h e Drosophila experi-

ments can do i t .

NEEL: Let me i n t e r j e c t and say that such data

can be obtainec! f o r man, 'but f hope we will have a d i s c u s s i o n

a s t o whether they will yielc! c r i t i c a l r e s u l t s .

LZVONTIN : The l a s t point I want t o nake is the

one ra i sed severa l t imes a l ready ir, the discussion--the e f -

f e c t of mixtures of t i f f e r e n t k i n d s .

CROW: I'm not sure I r e a l l y understand t h e pur-

pose of t h i s discussion. I s i t t o show,where you a re dea l ing

w i t h f e r t i l i t y d a t a , t h i s i s a hard c r i t e r i o n t o apply?

LEWONTIM : Yes . CROW: d e l l , t h i s is ce r t a in ly ag reed .

LEtV'ONTIM: There a r e a i l s o r t s 'of t h ings t ha t you

know ant! t h a t some o ther people know whLch other people don't

know; I mean, I'm saying everything which seems so pa ten t ly

obvious to me t h a t I f e e l a l i t t l e sii3y, but when I t a l k t o

people about t h i s , there i s a t l s a s t one person i n t h e room

who hasn't thought about one of these things, so I don ' t t h ink

I'm wasting time completely. I may be wrocg. O f course, you

know every one of these things and you agree w i t h them. That 's

what I'm saying.

. ROBERTSOlY : What do you pro pose t o do wi t h these

?ata when you've go t them?

LFXONTIN: What I'm saying i s t h a t the only way

you can hope t o use the B/A r a t i o i s i f you had the complete

s e l e c t i o n d i s t r i b u t i o n o f your population.

NEEL: But, Dick, i s n ' t t h i s t h e q u e s t i o n a t i s s u e ?

I th ink t ha t we could, i n man, with a g rea t dea l of labor , g e t

t h e kind of d a t a you have requested. Let us assume t h a t t h e

S/A r a t i o , however we cor rec t f o r the environmental compon-

ent i n A , which is a s l i d i n g s ca l e , obvious ly , came o u t t o

1C"

IIEiJOiJ"TIN: Y s s ; I ' n a3x . t t o d e a l w i t h t h a t point.

IjEEL: Then, will we g e t a c r i t i c a l i n t e r p r e t a t i o n ?

NEEL : That s my l a s t point.

CROW: A f e : t t l l i t y nezn o r some th iq .

FEEL: The w h l e gernisch..

LE!d3?1TX: That :s the pc int I'm t r y i n g t 3 l ead up

t o i n the end. T h i s comes t o t h s qu*stion of t h e s e n s i t i v i t y

of t h e t e t e c t i o n s y s t e a . Yhat we a r e askiag is, sup?ose t h a t

a p ropor t ion of :he l o c i , X, is minta ined segrega t iona l ly ,

and tha t a proportion, 1-K, is xaintaLned m t a t i o n a l l y ; what

happeas t o t h e l o a d r a t i o ? T h a t ' s what wetre r ea l ly a sk ing .

It i s very simple to dexons t ra te . Jim has eemonstratsd i t .

I won't bother to.

hZEL: Please deaonstrate i t .

LEWONTIY: A 1 1 r i g h t , I'LL denonstrate i t . Sup- .'

pose t h a t I kave a hundred g i n s s tka t a re na in ta ined by a nu-

t a t i o n a l l o a d , and one gene that, is rair- ts ined by a segrega-

t ional load mechanisa; what we a r e g0ir.r t o a s k is, what will

t h e r a t i o of the outbrezding to );he in t reee ing Load be? Notice,

we do not take t h e averaga of t he r a t io s . t ake t he r a t i o

of the averages, because you go i n a x ? determine outbred load,

LC in the populat ion, ind this is t h e r e s u l t of analerage of

a hundred nutatiorial geces an6 oze segregational gene. Then,

you do the same f o r iribred load, and so you are t ak ing the

r a t i o of two averages. Nb? What a r e you ac tua l ly do ing?

CR3W: Tha t ' s r i gh t , excep t t ha t you want t o

troa4 the whole. thing down.

LP,ldI::'O!~!TIN: I 7eal i .e that . T h i s i s w h a t ycuii*e

ac tua l ly do ing in p rac t ice . You e s t i m a t s the load i n t h e c u t -

bred po,ruiation, you est imate t h e locc! i n t h e inbrgd populatfgn,

and you put one over the o.l:lar. €3.1'; tJhen vou e s t i n a t e the l o a d

433

i n t h e outbred population, i t i s an average of the two corn-

ponents of the load, and when you e s t i aa t e t he i nb red POPU-

l a t i o n , i t is the average of two components of the load.

Therefore, t h e r a t i o t h a t you take comes o u t t o be a r a t i o

of averages and not an average of ra t ios .

If you do tha t , t hen , i n order for the contr ibu-

t i o n t o t h i s s a . t i o t o be equal between mutational and segre-

ga t iona l load , for example, you would need-

CROW: Equal in the outbred population?

LEWONTIN: Yes, equal in the outbred populat ion;

--you would need many hundrees nore" t i n e s n u t a t i o n a l l o c i

than segregat ional loci , because each segregat ional locus

con t r ibu te s a much l a r g e r amount t o the load than each muta-

t i ona l l ocus f o r thosereasonable values of s e l e c t i o n t h a t we

have been talking about. Therefore, i t t akes a hundred muta-

t i o n a l l o c i t o equal, i n i t s load e f fec t , one segrega t iona l

locus.

Therefore, every t iae you add a s ingle segrega-

t i ona l l ocus , you tend t o make th i s numera tor l a rger , tha t is,

you are adding a l a rge va lue t o t h i s numerator, and you a r e

also adding a l a rge va lue t o t h e denoainator, and t h e r e s u l t

of t h a t r a t i o is tha t the va lue of t h e r a t i o g e t s c l o s e r and

c l o s e r t o 1; in o the r words, every time you add a s ing le

locus, which has a h igh load e f fec t , you add a big number t o

both numerator and denominator fraction, and therefore you

tend t o reduce the 'size of t he f r ac t ion .

What I am saying, then, i s that without any

numerical examples--in fact, I did a l i t t l e test f o r myself,

f n which I allowed an average degree of dominance of de le te r i -

ous genes of 2 . 5 per cent , a number I just picked out of t he

a i r , of course--

MULLER: No, it is not ou t o f the a i r . [Laughter ]

LENONTIN: That was a joke intended t o be a t my 1

own expense, ~ O f e S S o r Muller: [Laughter] I assumed a hundred

l o c i , w i t h a 2.5 Per cent average dominance and a s ing le

434

he tero t ic locus , w i t h an average heterosis of 2.5 per cent ,

t h a t i s t o say, the two hoaozygotes were 5qua1, and when I do

t h a t , w i t h a 1 O O : l r a t i o of those two kinds of l o c i , I come

out with a l o a d r a t i o of approxinatzly 4.2 o r something. I

c a n ' t reme:nber what i t comes out to, but i t i s a low load

r a t i o .

\!;hat I arn saying, then, is t h a t i f you asked Jim's

quest ion No. 2, which is t h e proportior. of l o c i vhl.ch a r e

h e t e r o t i c as opposed t o mu!xtionai, t h i s d e t e c t i o n system is

a one-sided detection system to anssJer that question, because

the load ra t io , r?, when p lo t ted against t h e proport ion of .

h e t e r o t i c l o c i , looks l i k e t h i s [drawing curve], which means

t h a t when the p.1-oportion of h e t e r o t i c l o c i i s indeed very

. smal l , the load ra t io i s high, but this curve d r o p s so r a p i d l y

t h a t when you g e t to a3out 1 per c e n t o r less h e t e r o t i c l o c i ,

St has already dropped down ,?ear i t s symptote , which i s 2.

That being the case, we c a n c a l l t h i s a one-sided

detect ion system; namely, i f 1 go t o Eature and I discover

t h a t the load r a t i o i s 25 o r 30 , I c m say t h a t h s t e 2 o t i c l o c i

a r e not very cammon, but, i f I d i s c w s r a load r a t i o of 4, I

cangot say how comnon they a r e . It i s o x - s i d e e i n t h i s re -

spect, but I wanted t o say--

?J"r=Z'L: Then, t h i s mans , w i t h the kind of load

r a t i o s t h a t a r e beginning to CGYE i n , we are in an indeterminate

s i t u a t i o n . You are subscr ib ing to ' tha t?

LEKONTIN: Rxcept t h a t t h e r e a r s o t h e r b i a s e s which

a l s o tend t o lower t h e l oad r a t i o .

NEEL: All r i g h t .

LEUONTIN: Now, it is one-sided f o r t h i s reason,

and i t i s om-sideC because i t a l so n i s -es t imates A and a l s o

t ends t o make i t a one-sided hypothesis, so t o spzak; i n O i ; k r

words, i t is a de tec t ion sys ten which, i f you got an extreniely

high value and you thought t h e population was a t e q u i i i b r i u m

w i t h respect t o t he s e l ec t ion fo rces you have estimated--

flULLRR: Or o u t of e q u i l i b r i u a , i n the d i r e c t i o n i n

435

0

which i t is, probably.

LEWONTIN: Yes, o r ou t o f equi l ibr ium in the

proper direct ion. In any one o f these cases , then, I would

regard the B/A r a t i o as a go& one-sided tes t . It becomes

no t e s t a t a l l i f there are biasgs pushing the ra t io i n the

o the r d i r ec t ion and , fo r t h i s r ea son , I kave asked par t icular-

l y t h a t we ge t an es t imate o f coef f ic ien t which i s re levant

to the populat ion o r a t l e a s t i n t h e r i g h t d i r e c t i o n f o r t h e

population. Eut I do thin!{ i t i s a two-sided t e s t of what

is t o me a nore importar,t hypothesis, and t h a t is Jim's ques-

t i o n No. 3, where we are no t d i scuss ing the number of loci,

which, in my opinion, is a t r i v i a l q u e s t i o n e x c e p t a s i t bears

on nore inportant questions, but uhere we are ask ing , what i s

the pmportion o f gene t i c va r i a t ion i n t he popu la t ion which

can be ascr ibed to these two kinds of l o c i ?

In t h i s case, I would like t o po in t ou t t ha t ,

i~& f a c t o , a low r a t i o means tha t t he re i s a l o t of v a r i a t i o n

from however many l o c i there may be, being contr ibuted by

segrega t iona l loci, even i f t h e y a r e v e r y m a l l in number,

whereas a high ra t io neans , ipso facto., that even i f they were

very l a rgs in nunber , which they couldn't be, but whatever

t h e i r number, they a re not contribufiRg a g r e a t d e a l t o t h e

gene t ic var ia t ion.

That is why I disagreed w i t h Jim when he sa id he

thought i t was a one-s ided tes t of quest ion 2. I th ink i t i s

a two-sided t e s t of quest ion 3.

CROW: Yes, I t h i n k t h a t ' s a l l r i g h t .

LEWCNTIM: That i s what I wanted t o say. It is,

indeed, a one-s ided tes t of-. 2, because of b i a ses and because

of t h i s r a t i o cf average effect , but i t can be a two-sided t e s t

fo r 3.

CROW: Let me put two o r three numerical eyam?! x

on t h e board.

LEWONTIN: That * s what I wanted to say. I don't

think everybody knows t h i s .

0

436

CROW: This is r i g h t along t h e l i n e of what you

talked about. E4aybe, one ought to do i t . Suppose I consider

the examples uncler which the A or a nuta t iona l corngonent and

a segregat ional cornnor.ent f o r inbred and f o r ranc?.om come

i n t o i t . H O W , suppose t h a t the nutational conponent and the

segreca t iona l component a re equa l i n t he random-mated popula-

tion--and Jirn Nee1 d i d p r a c t i c a l l y the sane thing once in one

of h i s papers--but suppose each o f these is equa l t o 10, f o r

convenience. 'i'?:s, on inbreeding, will increase by a f a c t o r , "

aaking i t perhaps 40 or 50, t o ' t ake a convenient round number-=

no, I want a higher factor than that , don ' t I?

h%J% : Yake i t LOO.

CROW: Yes, LOO, which i s p r e t t y low f o r t h e u s u a l

l e v e l s of doninance, but say 100 f o r convenience. Just say

there a re on ly two a l l e l e s , so t h i s changes t o 20. If I now

average the averages, t h i s i s going to be, c o l l e c t i v e l y , a

r a t i o of 120/20, which is 6. T h i s t e l l s me tha t the inbred

load i s considerably nore mutat ional than segregat ional , but

i t has been pret ty uninfor&tlve a s t o what i s happening I n t h e

general population, desp i t s t h e f ac , t t ha t t h i s is p r e t t y

high. This i s r e a l l y t h e p o i n t I *n t rp ing to make, and i t is

simply paraphrasing what Dick said, but he expressed i t not

i n terns of nuaber of a l l e l e s i nvo lved bu t t he t o t a l ccn t r ibu -

t i o n of t h e s e a l l e l e s .

This one exanple i s probably enough, because I

happened t o p ick jus t about what I wanted it t o do. This

means t h a t this value has to be p r e t t y low t o o f f e r much e v i -

dence on the random population.

NEZL: Yes; but then would you agree, Jirn, t h a t i f

the values do come o u t t h a t low, they do offer-..

CROV: Now, t h i s i s what I say: They seem t o me

t o be inpossible t o i n t e r p r e t u n l e s s you can d i s t i ngu i sh the

gene t i c f roa t h e environmental components of A .

NCEL: Yell, can we t a l k a b o u t t h a t a l i t t l e bit?

C9GW: Let me say t h i s , t h a t i t i s undoubtedly

437

t r u e , if t h i s va lue tu rns ou t to be 2, ar.d you can ru,Le ou t

any environmental conponent to e i the r t h e nunerator o r de-

nominator, that i s not incons is ten t , JOU see, w i t h your sag-

regat ional hyp3thesis .

ZZidJOXTIN: it i s c o ; ~ isb:~-L with a Caiz x x b a r

uf mxta t iona l loc i . Again, i t is the nxxber ar,d r:gt tke e f -

f e c t .

CRO'J: If i t i s e x s c t l y 2.

LE"If0KTIN: Oh, well, if i t Is e x a c t l y 2--

CI!2l.I : But '3ven f f it * s 2, 5 21- 2.3.

LZdONTIN: I th ink y c u c c ~ l . d g e t =In equal ncmber

of segregat ions1 2nd rn t a tLona1 i cc i giving y m c 2.5.

C W d t You don't nean e q m l n u b s r s o f l o c i ; you

mean equal coxhd5ut ions t o the random LDad.

LEWONTIN: No. Bupposz t he re wsre e q u a l numkers

of l o c i , what would the load r a t i o be? Dretty close to 2?

CX!!f: Yes, p r e t t y close t o 2. kt, I agree with

yo^, t h s t i s not t h e i n t e re s t ing ques t ion . One wa3C,s t o k ~ o w

more.

MORTON: I be l i eve , i f you have a mutational Load

of the type of exti-ernely s z a l l hoaoqrgous e f f e c t , such tha.t

mutat ions are re tarded i n both d i r e c t i o n s t o keep i t going i n

the popu2ation, then, you could g e t a lot! r a t i o . But if the

gene frequency i s c lose to 50 per cent--

CRCW: Y e s , t he re I s $ h a t ? o s s i S i l i t y .

NEEL : One question. We kaen ta lk ing hopefu l ly

sbout dis t inguishing the two coa2onents of A , the genet ic and

nocgenetic. Actually, I think, one of the fac2.s t h a t shakes

u s East about ' the Japanese data that we havs is t h a t we have

j u s t a s nice a ccnsanguini ty effect on the f requency o f d i s e a s e s

t h a t you would classI.i"y 2 s being of an i r , fec t lw.s e t io logy as

we do on conEenLta1 o r tdiopathi*? diseases. %ow, t h i s r a i s e s

i n ny mind the quest ion of uhe t her you <.on' t have two wetges

h e r e i n terms of gene t ic anC nongexet ic contr ibut ion to any

p a r t i c u l a r Ceath, and is t h i s a 'wi l l -of- the-wis?, t o th ink tha t

we can ever break A i n to two components?

LSWONTIII: I believe you can put a rnaximrn value

on A f o r human populations. I would l i k e t o know, i f you

do put t h i s maximum r a t i o , what the expacted bias is. I t h i n k

you can put i t on ;n tha following way: If you look s t it as

t h e i n t r i n s i c r a t e of increase of R, o r a s a ivIalthusian

parameter-- le t ' s not forget , in an overlapping pcpulat ion o r

a population of overlapping generat iocs , i t is the ea r ly

b i r t h s t h a t c u u n t . T h i s i s the most important thing from

the standpoint of t h e spread of a genotype in a population,

t o g e t those f i r s t k i d s i n e a r l y , and. we don't care about the

few;",at ';'cu have a t t h e much l a t e r ages,

T h i s being the case, I th ink tha t one can aake

from what one knows about how long i t t a k e s t o t e r n h a t e a

pregnancy successful ly--f i rs t of a l l , a s f a r a s m o r t a l i t y is

concerned, the absolute maxinum mortalicy i s z e r o , a l l r i g h t ?

We can therefore agree tha t the minimum m o r t a l i t y or maximum

l iveabiLi ty , if you l i k e - -

SLATIS: Ma!te i t mininum.

LEWONTIN: Well , when i t comes t o . caxirnurn f e r -

t i l i t y , you can ce r t a in ly a s s ign a maximum reaso lab le human

f e r t i l i t y , a spec i f ic fe r t i l i ty schedule . For example , you

can say that ' a woman might have twenty-five children if she

conce ived every par and brought them successful ly t o term, but

t h e l a s t f i f t e e n c h i l d r e n make r e l a t i v e l y l i t t l e c o n t r i b u t i o n

to the Malthusiasm parameter as compared t o t h e f i r s t t e n .

I can draw out a maximum human age - spec i f i c f e -

cundity schedule; I can jus t wrlte i t down on the board, and,

u s ing t ha t -maximum human age-spec i f ic fecundi ty t ab le and the

opt imal mor ta l i ty t ab le , which is e s s e n t i a l l y z e r o , I can tal-

cu la t e what t h e a b s o l u t e l y l a r g e s t r a t e of increase of such a

population would be

Now, I should ask myself, given t h i s value, how

s e r i o u s l y does i t b l a s t h e r e s u l t s which we get? If i t tu rns

out t o blas them immensely, then, wet re in r e a l t rouble .

439

Suppose, however, t h a t i t doesn ' t b ias them immensely-

CROV: I think the proper quest ion to ask is,

t h i s de f ines t h e load space, as Jim Nee1 calls i t , and how

nany polymorphisms can be maintained within t h i s superman,

o r whatever you c a l l him, and the average of the population?

LEWONTIN: No, not how; rcany polymorphisms, because

I think, again, we agree we don't cam. Ye know the answer

to load space --period.

MO9TON: D o n f t you have t o take a supremely i m -

por tan t po in t , tha t if you ask what i s the optilnum phenotype

for man over a long period o f time, it is not a woman having

two hundred children, because t h i s i s just inconceivable--

she couldn't raise them--but, under primitive conditions, a

child born once every three years , v iable , i s about as much a s

the woman can maintain, as you point ou t , over a r a t h e r s h o r t

i n t e r v a l of time. The optimal fecundity, under these p r i m i -

t ive condi t ions , therefore , is probably not much g rea t e r t han

the mean fecundi ty now. It i s not an enormous thing.

DOBZHANSKY: Is t h a t your d e f i n i t i o n of optimum

genotype? I would like very much t o have i t spe l led ou t .

MORTON: I th ink o.ptimum phenotype i s the thing

t h a t causes t h e confusion here. The optimum i s something in-

conceivable, It i s a man the s ize of a dinosaur, reproducing

every half hour by binary fus ion .

DOBZHANSKY: And doing a very good job a t t h a t .

[Laughter 3 MORTON: 'he phenotype has t o be more o r l e s s what we

recognize as the spec ies charac te r i s t ic , under the condi t ions

t h a t evolved him. T h i s means t h a t t h e r e a r e r e a l l i n i t s on

what the optimum f e r t i l i t y i o u l d be.

DOBZHANSKY: I would l i k e you very much to s p d 7 x t

t h i s optimum phenotype limit; j u s t make spec i f i ca t ions .

MORTON: All we need i s the optimum phenatype f o r

t h i s .

LE!JONTIN: I proposed a spec i f ica t ion a l ready .

.

440

make . DOBZHANSKY: O.K. Then, rnake a committee cons l s t -

ing of Lewmtf-?, Morton and, I assume, Jim Crow, and l e t them

drald up s p e c i f i c a t i o n s f o r 'an optimum human genotype. It

would be ve ry i n t e re s t ing .

LEWOMTIN: Mot an optimum genotype, but an optimum

fecundity schedule . DOBZHANSKY: O.K., but draw it up, P l ease .

MORTON: There i s one o the r way t o do what D i c k .

wants t o do--

CRON: Then, what do you want t o do w i t h i t?

MORTON: Jim's theory about t h e phenotypic selec-

t i o n , which suggests something about the r e l a t i v e rnagnitude

of t h e phenotypic selection as It ope ra t e s on mor t a l i t y and

fecundi ty , a lso can be used to get some idea of how Large the

concept of A is , a t l e a s t a t t h e p r e s e n t , t i m e and for any de=

f ined popu la t ion , r e l a t ive t o what i t is for mor ta l i ty . I

th ink t hese two methods could be used, and we ought t o g e t

reasonable agreement . LEWONTIN: I .would sugges t , t o r e f ine t he problem

a l i t t l e b i t , we would have t o make the following two assump-

t i ons : t ha t ove r a short range of human evolut ion, t h e ges-

ta t ion per iod does not have cons iderable gene t ic var ia t ion ,

l e t 's say. O f c o u r ~ ~ , you can always make a ges ta t ion per iod

of two months, but l e t ' s ho ld ges ta t ion a t n ine months, and

l e t ' s hold the age o f puber ty a t some reasonably gar ly age.

If we hold those two constant, then, I think, we can--

DOBZHANSKY: But why should we? Why shouldn't we

make a ges t a t ion o f two months and age of puberty a t f i v e

years? Wouldn't t h a t be even more optimum? Why not?

LEWGNTIN: Why not make man i n t o a Drosophila?

DOBZHANSKY: Well, i f you measure the optimum g e m - ;

type a t maximum power, surely, - t h i s procuces chi ldren-- -

441

CROW: I think this is not a fruitful argument

at t h i s stage.

M3EL: Let 's have lunch!

[Th sesslor, adjourned at twalve-f:ft> 3tclock. 1