PERSPECTIVE

doi:10.1111/j.1558-5646.2007.00100.x

A CENTENNIAL CELEBRATION FORQUANTITATIVE GENETICSDerek A. Roff

Department of Biology, University of California, Riverside, California 92521

E-mail: derek.roff@ucr.edu

Received December 6, 2006

Accepted January 28, 2007

Quantitative genetics is at or is fast approaching its centennial. In this perspective I consider five current issues pertinent to

the application of quantitative genetics to evolutionary theory. First, I discuss the utility of a quantitative genetic perspective in

describing genetic variation at two very different levels of resolution, (1) in natural, free-ranging populations and (2) to describe

variation at the level of DNA transcription. Whereas quantitative genetics can serve as a very useful descriptor of genetic variation,

its greater usefulness is in predicting evolutionary change, particularly when used in the first instance (wild populations). Second,

I review the contributions of Quantitative trait loci (QLT) analysis in determining the number of loci and distribution of their

genetic effects, the possible importance of identifying specific genes, and the ability of the multivariate breeder’s equation to

predict the results of bivariate selection experiments. QLT analyses appear to indicate that genetic effects are skewed, that at least

20 loci are generally involved, with an unknown number of alleles, and that a few loci have major effects. However, epistatic

effects are common, which means that such loci might not have population-wide major effects: this question waits upon (QTL)

analyses conducted on more than a few inbred lines. Third, I examine the importance of research into the action of specific genes

on traits. Although great progress has been made in identifying specific genes contributing to trait variation, the high level of

gene interactions underlying quantitative traits makes it unlikely that in the near future we will have mechanistic models for such

traits, or that these would have greater predictive power than quantitative genetic models. In the fourth section I present evidence

that the results of bivariate selection experiments when selection is antagonistic to the genetic covariance are frequently not well

predicted by the multivariate breeder’s equation. Bivariate experiments that combine both selection and functional analyses are

urgently needed. Finally, I discuss the importance of gaining more insight, both theoretical and empirical, on the evolution of the

G and P matrices.

KEY WORDS: Breeder’s equation, G matrix, microarrays, quantitative genetics, QTL analysis.

If we take the speculations of Yule presented at the Third Inter-

national Conference of Genetics (Yule 1906) on the relationship

between the biometrical and Mendelian approaches to heredity as

the foundations upon which the field of quantitative genetics is

based, then we have just passed the 100th birthday of quantita-

tive genetics. On the other hand, the 1918 publication of Fisher

might be taken as the real beginnings of quantitative genetics as

we know it (for a detailed account of Yule’s musings in relation

to Fisher’s contribution see Tabery 2004), in which case the cen-

tenary of quantitative genetics birth is but a few years away. No

matter which date we take, the fact remains that quantitative genet-

ics has been around for a long time, during which it has developed

with a very large statistical foundation that is still in the process of

being tested. Early work focused on the contribution of quantita-

tive genetics to animal and plant breeding but the work of Russell

Lande in the 1970s promoted the use of quantitative genetics by

those interested in evolutionary biology. A significant difference

between the interests of the breeder versus the evolutionary bi-

ologist is that whereas the breeder frequently is concerned with

the improvement of a single trait (or two traits combined into a

single index), the evolutionary biologist is generally faced with

addressing the evolution of multiple traits simultaneously. This

1017C© 2007 The Author(s). Journal compilation C© 2007 The Society for the Study of Evolution.Evolution 61-5: 1017–1032

PERSPECTIVE

change in focus has raised issues of methodology and approach

that are still being worked out: the purpose of this perspective is to

suggest that a singular contribution that quantitative genetics can

make to our understanding of organic evolution is in the area of

multivariate trait evolution and that the new fields of research in

genomics such as QTL and microarray analyses are contributing

to, and benefiting from, a quantitative genetic perspective.

The most general form in which quantitative genetics is used

in evolutionary biology is given by the equation �z = GP−1S,

where �z is the change in trait means, G is the genetic variance–

covariance matrix, P−1 is the inverse of the phenotypic variance–

covariance matrix, and S is the vector of selection differentials.

An alternate and equivalent formulation of this equation is �zi =∑n

j=1,n � j hi h jrAi j , where �zi is the response of the ith of n traits,

hj is the square root of the heritability of the jth trait, rAij is the

genetic correlation between traits i and j, and � j is the selection

gradient on the jth trait. I shall refer to these equations as the

multivariate breeder’s equation. In this perspective I shall highlight

five issues that bear upon the present and future contributions of

quantitative genetics to our understanding of evolutionary change:

(1) The utility of a quantitative genetic approach to measuring

genetic variation: In this section I outline the utility of a

quantitative genetic perspective in describing and analyzing

genetic variation at two very different levels of resolution,

namely genetic variation in natural populations and genetic

variation at the level of DNA transcription.

(2) Do the results of QTL analyses support the assumptions

of quantitative genetics? As a general descriptor in the two

circumstances discussed in section 1, the quantitative ge-

netic parameters may be useful in themselves, but what

we really desire is that the approach can actually be used

to predict evolutionary change. In this case we need to

consider whether the basic assumptions of quantitative ge-

netics are likely to be sufficiently accurate or robust for

at least short-term prediction and then whether selection

on multiple traits has produced results consistent with the

multivariate breeder’s equation. To address the question of

the number of loci and the distribution of their effects, I

use information recently obtained from QTL analyses, at

present possibly the premier method for investigating such

questions.

(3) What is the importance to quantitative genetics of identify-

ing specific genes? Recently there has been an enormous ef-

fort put into elucidating the molecular basis of variation with

attention being given to identifying genes of major effect.

Given that quantitative genetics focuses upon the totality

of genomic expression of a trait as expressed in a statisti-

cal description, does such research have any messages for

quantitative genetics?

(4) Testing predictions of the multivariate breeder’s equation. In

the fourth section I consider whether artificial selection on

multiple traits or evolutionary changes in wild populations

can be reasonably predicted by the multivariate breeder’s

equation.

(5) The evolution of the phenotypic and genetic variance co-

variance matrices. Application of the multivariate breeder’s

equation assumes that the variance–covariance matrices re-

main constant. In this section I examine this proposition

and suggest that the present hypothesis-testing approaches

should be replaced by an interval-estimation perspective.

The Utility of a Quantitative GeneticApproach to Measuring GeneticVariationA measure of genetic variation in a population and its potential

response to selection can be made by estimating G and P. The

latter is readily accomplished but the estimation of G presents

significant logistical problems. Three approaches can be used: (1)

Bring the organism into the lab and estimate the G matrix by

controlled breeding experiments, (2) use a sampling design in a

wild population that matches a standard pedigree design, such as

offspring on parent, (3) sample a population over a number of

generations and use the animal model.

The assumption of the first approach is that the estimate ob-

tained from a laboratory is equal or close to that which would be

obtained in the field. Because it was assumed that the environmen-

tal variance would be higher in the field than the lab, conventional

wisdom suggested that heritabilities and genetic correlations in

the field would be lower than in the lab. A meta-analysis of lab

and field studies showed that this was not the case for heritabil-

ities, though phenotypic variances tend to be reduced in the lab

(Weigensberg and Roff 1996). An assessment of the genetic cor-

relation or the genetic variances and covariances remains to be

undertaken. The results of the analysis on heritability show that

it is premature in the extreme to dismiss estimates from labora-

tory studies. Some studies in wild populations, most particularly

those on birds, have been able to estimate genetic parameters

from offspring on parent regression (e.g., Grant and Grant 1995;

Reale and Festa-Bianchet 2000; Roff et al. 2004). In general, how-

ever, a study of relationships among individuals in a wild popu-

lation will produce a convoluted set of relationships that cannot

be analyzed using such simple methods as half-sib or offspring–

parent regression. A solution to this dilemma is the animal model,

which does not require any specific pedigree (Knott et al. 1995;

Kruuk 2004). In addition to the important task of resolving the

question of how much genetic variation is found in wild popu-

lations (e.g., Reale et al. 2003; Kruuk 2004; Charmantier et al.

2006a), use of the animal model to estimate genetic parameters

1018 EVOLUTION MAY 2007

PERSPECTIVE

in wild populations has enabled detailed investigations into the

importance of maternal effects (Kruuk 2004; Wilson et al.

2005a,b; Charmantier et al. 2006b), genotype by environmen-

tal interactions (Kruuk 2003; Garant et al. 2004; Brommer et al.

2005; Nussey et al. 2005; Wilson et al. 2006), variation between

ages and sexes in genetic parameters (Pettay et al. 2005; Wilson

et al. 2005b; Charmantier et al. 2006c), and tests of sexual selec-

tion theory (Hadfield et al. 2006; Qvarnstrom et al. 2006). These

studies have demonstrated that genetic variation is usual in wild

populations and that long-term variation in trait values can only

be properly understood within a quantitative genetic framework.

Quantitative genetic approaches are also making significant

contributions at an entirely different level, namely variation at the

level of transcription of DNA. DNA microarrays have enabled

the visualization of the rates of transcription of hundreds to thou-

sands of genes (for overviews of the techniques see Brown and

Botstein 1999; Gibson 2002; Tarca et al. 2006). Early experiments

showed that rates of transcription varied among genotypes and that

transcription rates could themselves be viewed as heritable traits

(Schadt et al. 2003; Gibson and Weir 2005; Roelofs et al. 2006).

At a more general level, the analysis of microarray data can be

approached using the same statistical approaches as quantitative

genetics, namely mixed model analysis of variance, where both

genotypic and environmental sources of variation can be resolved

(Kerr et al. 2000, 2001; Wolfinger et al. 2001; Churchill 2002;

Chen et al. 2004; Nettleton 2006). At the present time use of mi-

croarrays is restricted by the costs of producing arrays for the

organism under study: even with model organisms the cost is suf-

ficiently high to preclude the analysis of hundreds of microarrays,

as would be necessary in a typical quantitative pedigree design.

Initial studies have used inbred lines (Jin et al. 2001; Rifkin et al.

2003; Schadt et al. 2003; crosses between isogenic lines (Drnevich

et al. 2004), different morphs of the same species (Derome et al.

2006), selected lines (Roberge et al. 2006), individuals from differ-

ent populations (Oleksiak et al. 2002; Vuylsteke 2005), or different

species (Rifkin et al. 2003). All cited studies showed genotypic

differences though only in a few cases were sample sizes suffi-

cient to attempt an estimate of variance components or a general

comparison with phenotypic variation.

Jin et al. (2001) examined rates of transcription in two inbred

strains of Drosophila melanogaster at ages one and six weeks and

separated variance components due to sex and genotype: sex con-

tributed most but the “genotypic contributions to transcriptional

variance may be of similar magnitude to those relating to some

quantitative phenotypes” (Jin et al. 2001, p. 389). In their analy-

sis of transcriptional variation in Arabidopsis thaliana, Vuylsteke

et al. (2005) found more than 30% of the genes had significant ad-

ditive effects and 5–20% of genes, depending on the cross, showed

nonadditive interaction. Most of the differences in transcriptional

variance in the fish Fundulus heteroclitus and F. grandis were

found within populations (coefficients of variation 5–15%) though

significant differences among populations and species were found

(Oleksiak et al. 2002).

Apart from the problem of sample size, the experiments us-

ing microarrays can suffer from a surfeit of data in the sense

that hundreds of genes may show differences. One could regard

the array as a variance–covariance matrix and calculate all possi-

ble variance and covariances, but this would generate enormous

problems of determining statistical significance. An alternative

approach is to collapse the array into a manageable number of un-

correlated variables using principal components analysis. Doing

this, Bochdanovits and de Jong (2004) were able to show sig-

nificant correlations between PC1 of gene expression and the two

traits, body weight and larval survival in D. melanogaster. Further-

more, PC analysis showed that variation in transcription rate was,

in addition to covarying with adult weight, a function of popula-

tion of origin and rearing temperature (Bochdanovits et al. 2003).

Whitefish (Coregonus clupeaformis) is found within a single

population in two morphs, a normal and a dwarf morph, that form

reproductively isolated ecomorphs (Derome et al. 2006). Com-

parison of transcriptional profiles of the two morphs collected

from two separate lakes, both morphs found in each lake, showed

both population- and morph-specific differences (Derome et al.

2006). Variation among gene expression has also been found in

the two phenotypic morphs, normal and “sneaker” (also known as

a “jack”) morph, of Atlantic salmon, Salmo salar (Aubin-Horth

et al. 2005a,b), and in territorial and nonterritorial males of the

cichlid, Astatotilapia burtoni (Hofmann et al. 1999; Hofmann

2003). Except for the whitefish study, where different populations

were raised in a common garden, separating environmental from

genetic components of variation was not possible in these exper-

iments, though the heritability of “jacking” in Chinook salmon

(Onchorynchus tshawytscha) is 0.67 (Mousseau et al. 1998), sug-

gesting that further testing for genetic differences in transcrip-

tional rates in the two morphs of Atlantic salmon would be prof-

itable. Genetic variation in transcription rates in Atlantic salmon

has been demonstrated by comparing strains selected for rapid

growth with wild strains. Five to seven generations of selection

produced heritable changes in gene transcription rates (Roberge

et al. 2006), but, because data on selection intensities are not avail-

able, heritabilities cannot be estimated.

Do the Results of QTL AnalysesSupport the Assumptions ofQuantitative Genetics?Prior to QTL analysis the estimation of the number of loci was

problematic and very uncertain. The advent of the use of molecu-

lar markers to divide the chromosome into many segments has

enabled QTL analysis, first conceived in 1923 (Sax 1923), to

EVOLUTION MAY 2007 1019

PERSPECTIVE

make great strides in enunciating the number of chromosomal

segments involved in quantitative genetic variation. Quantitative

trait loci analyses most frequently employ crosses between in-

bred lines, though methods exist for the analysis of outbred pop-

ulations (Lynch and Walsh 1998; for briefer, less mathematical

descriptions see Mackay 2001a or Mauricio 2001). Although the

statistical power of QTL analyses using inbred lines is generally

greater than those using outbred pedigrees (Erickson et al. 2004),

their weakness lies in their inability to detect more than two alle-

les at any locus. Thus even if a QTL analysis picks up relatively

few regions with significant effects we cannot immediately con-

clude that the assumption of a large number of genes of small

effect is violated, because there may still be numerous alleles at

each detected QTL or allelic variation at QTLs that happen to be

homozygous for the two inbred lines chosen. However, if QTL

analyses consistently found few regions of major effect we might

certainly begin to entertain the hypothesis that the assumption of

many genes of small effect may be incorrect, presuming that the

QTL segments are sufficiently small that they contain only a single

or possibly a few actual loci that affect the trait under study.

Early QTL analyses did indeed produce results that pointed

to relatively few regions of major effect. One would expect that

as sample size increased the number of QTLs detected would in-

crease, the percentage of phenotypic variance explained per QTL

would decrease, and the total variance explained would go up.

Rather surprisingly, though the first two predictions were upheld,

the third was not (see fig. 1.10 in Roff 1997). Using simulation,

Beavis (1994, 1998) showed that with small sample sizes QTL ef-

fects are grossly inflated and hence the effective number of QTLs

contributing to a trait is underestimated. This phenomenon has

become known as the Beavis effect and its theoretical basis inves-

tigated in detail by Xu (2003), though the general nature of the

problem was forecasted in the early 1990s both by the work of

Beavis and others (Kearsey and Farquhar 1998). To obtain reason-

ably accurate estimates of effects sample size must exceed 500,

whereas sample sizes much before the year 2000 were more typi-

cally in the range of 200 individuals (Roff 1997). It is still not clear

how many loci generally contribute to a trait or the distribution

of effects. In a review of QTL analyses in plants, Remington and

Purugganan (2003, p. S13) concluded “that individual genes with

relatively large effects on trait variation are probably important

in evolution,” but did not provide a meta-analysis to support this

statement. A meta-analysis of the distribution of QTL effects in

pigs and dairy did indicate that effects were skewed with a few

QTL of large effect, the total number of QTL for the dairy data

being estimated to lie between 50 and 100, depending on pop-

ulation size (Hayes and Goddard 2001). Mackay (2004, p. 254)

in reviewing QTL analyses in Drosophila drew the conclusion

that “the distribution of homozygous QTL effects is exponential,

with a large number of QTLs with small effects, and a smaller

number with large effects; the latter contribute most of the vari-

ation between parental lines.” To date I know of no study that

has carried out a meta-analysis of QTL effects from which gen-

eral statements about the number of QTLs and the distribution of

their effects can be made with statistical precision: such a study is

greatly needed.

Given that we know that there is not an infinite number of

loci, how many is enough to satisfy the assumption of normality

if each did indeed have a similar effect? The well-known answer

is that very few are required: four or five loci with two alleles per

locus will provide a distribution that is statistically very close to

normal. The problem lies in the fact that in such a situation selec-

tion can very rapidly erode genetic variation. A typical number

of QTL detected appears to be about 20 (Cheverud et al. 1996;

Vaughn et al. 1999; Mackay 2001a; Rocha et al. 2004; Nuzhdin

et al. 2005), though Walsh (2001, citing personal communication

with Mackay) gives an estimate of 130 genes for sternopleural

bristle number in D. melanogaster based on mutational effects.

Given the limitations of QTL detection, the number of loci might

well be typically in the dozens if not hundreds. What we do not

know, and need to know, is how many alleles typically segregate

at each locus (defining what is a locus at the molecular level it-

self presents difficulties, but here I refer only to QTL variation,

which admittedly is at best only a crude measure of a locus). The

number of QTL is probably sufficient to satisfy the assumption of

normality provided that the distribution of effects is itself close

to normal. The present QTL results, as expounded in the above-

cited reviews, suggest that the QTL effects are highly skewed.

On the other hand, this is not necessarily important, because the

multivariate breeder’s equation focuses upon the change in mean

trait values and hence even if the distribution of genetic effects

is not normal, by the central limit theorem, the distribution of

mean effects will be normal. Lack of normality is certainly ob-

served in many phenotypic distributions but these can be brought

into line by a suitable transformation. Theoretical and numerical

analyses have shown that the Gaussian approximation is satisfac-

tory even under strong selection, which produces large deviations

from normality (Turelli and Barton 1994). Thus, for single traits

the question of normality is probably not critical, at least for the

case of short-term (approximately 10 generations) selection. It is

not clear how important the assumption of multivariate normality

will be, and this question needs to be addressed via analytical, or

more likely, numerical analysis. If phenotypic effects mirror the

underlying additive genetic effects, then the question of multivari-

ate normality may be not be particularly significant because one

can find a suitable transformation. However, more troublesome is

the possibility that the distribution of additive genetic effects is not

the same as the composite phenotypic effects and hence a trans-

formation applied to the phenotypic scale does little or nothing to

improve the distribution on the additive genetic scale.

1020 EVOLUTION MAY 2007

PERSPECTIVE

But can we trust the distribution of effects as presently sug-

gested by the QTL analyses? Here we must consider the issue

of epistatic effects. First, it is very evident from analyses of line

crosses between inbred lines, different populations or different

species that both dominance and epistatic effects are exceedingly

common in both morphological and life-history traits, dominance

effects being demonstrated in more than 95% of cases and epistatic

effects demonstrated in more than 65% of cases (Roff and Emerson

2006). Quantitative trait loci analyses have made similar findings

(e.g., Cheverud and Routman 1995; Shook and Johnson 1999;

Mackay 2001b, 2004; Leips and Mackay 2002; Alonso-Blanco

et al. 2003; Carlborg et al. 2003; Caicedo et al. 2004; Carlborg

and Haley 2004; Weinig and Schmitt 2004; Malmber et al. 2005;

Mackay and Lyman 2005; Carlborg et al. 2006; Yi et al. 2006) de-

spite the fact that the power to detect epistatic interactions is low

(Flint and Mott 2001; Mackay 2001b; Carlborg and Haley 2004;

Erickson et al. 2004). If epistatic effects are so pervasive, the pres-

ence of alleles of large effect may be contingent on the particular

genetic background used in the QTL analysis, in which case the

effect of this “major” QTL may disappear when measured over

the entire complement of genomes present in a wild, outbreeding

population. In this scenario, epistatic effects could contribute sig-

nificantly to additive genetic variance but not epistatic variance.

This is the argument that Fisher himself used to dismiss the im-

portance of epistatic variance in large populations (Whitlock et al.

1995; Brodie 2000). In small populations, epistatic effects may

come to the fore and contribute to nonadditive genetic variance, a

consequence of which would be that the selection coefficient on a

locus in local populations may differ as a consequence of epistatic

effects, which is the argument Wright used in championing his

model of evolution (Hill 1989; Wade and Goodnight 1998). As

with QTL analysis, the detection of epistatic effects within pop-

ulations using traditional quantitative genetics approaches is ex-

tremely difficult, but this is itself no reason to ignore their possible

effects. In the light of the consistent evidence for epistatic effects,

we are in need of research both in the empirical investigation of

epistatic effects within populations, which will rely upon further

QTL analyses, and theoretical work on whether the effects as

presently observed could influence evolutionary trajectories.

At present, the conclusions on the importance of epistatic

variance, as opposed to epistatic effects, in modulating evolution-

ary responses is mixed. Keightley (1996) showed theoretically

that epistatic effects generated in metabolic pathways could cause

asymmetric responses to selection but empirical demonstration

is as yet absent. Other theoretical models have also shown that

epistatic effects could be important (Fuerst et al. 1997; Soriano

2000), but much remains to be done in working out the circum-

stances under which epistatic variance should be incorporated into

quantitative genetic models and analyses. Carlborg et al. (2006)

present an interesting case in which a single major QTL for growth

in chickens is actually composed of four interacting loci, the effect

of which is to produce a higher response to selection than would

be predicted by a single locus. Theoretical models incorporating

epistatic effects have also been studied in regards to mutation-

selection balance, the general finding being that, as with the ad-

ditive model, the final balance is sensitive to parameter values

(Hermisson et al. 2003; Hansen et al. 2006), about which we

know very little. Epistasis underlies canalization and may un-

der particular conditions be a source of cryptic variation (Hansen

2006). Several studies have shown that, as a result of the popu-

lation passing through a bottleneck, epistatic effects can be con-

verted into significant additive genetic variance (Goodnight 1988,

2000; Cheverud and Routman. 1996; Cheverud et al. 1999; Wade

2002) though its importance has been questioned by other studies

(Lopez-Fanjul et al. 2002, 2006b121; Hill et al. 2006; Turelli and

Barton 2006).

Finding considerable epistasis at the molecular level does not

mean that epistatic variance will be significant at the phenotypic

level at which most traits forming the focus of quantitative genetic

analysis are found. As discussed in the next section, epistatic in-

teractions are expected in such complex traits as morphology,

fecundity, or longevity but this may be irrelevant to quantitative

genetics if such effects are manifested as additive variance.

What is the Importance toQuantitative Genetics of IdentifyingSpecific Genes?Quantitative genetics is primarily a statistical description of the

action of genes and does not, in principle, concern itself with

the details of the genetic mechanism except in as much as such

mechanisms result in additive and nonadditive genetic variance.

On the other hand, such a broad brush approach to evolutionary

responses to selection or random sampling through drift may not

capture evolutionary responses in some instances. It is thus im-

portant to continually assess how the increasing information on

genetic mechanisms impacts quantitative genetic predictions. Re-

cent advances in genomics has led to the identification of specific

genes involved in traits of obvious evolutionary significance such

as morphology, life span, and resistance to pesticides (Table 1).

How do such findings impinge upon quantitative genetics?

Wing polyphenism is found in a large number of ant species

and is completely determinate in that particular castes, but not

all castes (queens in some species may be dimorphic for wings),

always exhibit the same phenotype. Although the same network

of gene interactions appear to be involved in the expression of

morphology, the point at which the network is interrupted dif-

fers among species (Abouheif and Wray 2002). This informa-

tion is important for an understanding of the genetic and physi-

ological regulation of caste development but does not affect the

EVOLUTION MAY 2007 1021

PERSPECTIVE

Tab

le1.

Exam

ple

so

fq

uan

tita

tive

trai

tsin

wh

ich

sin

gle

gen

esh

ave

maj

or

effe

cts

and

the

mo

lecu

lar

bas

iso

fre

gu

lati

on

has

bee

nst

ud

ied

.

Tra

itSp

ecie

sPa

thaf

fect

edN

otes

Sour

ce

Win

gpo

lyph

enis

mA

nts

Mul

tiple

Inte

rrup

tion

ofde

velo

pmen

taln

etw

ork

occu

rsat

diff

eren

tpl

aces

indi

ffer

ents

peci

esA

bouh

eif

and

Wra

y(2

002)

Gro

wth

ofin

sect

hind

legs

Num

erus

spec

ies

Ubx

and

abd-

Aex

pres

sion

Reg

ulat

orof

grow

thbu

tpre

cise

mol

ecul

arm

echa

nism

note

luci

date

dM

ahfo

ozet

al.(

2004

)

Bea

ksi

zeC

hick

ens,

duck

s,D

arw

in’s

finc

hes

Bm

p4D

iffe

rent

iale

xpre

ssio

nin

beak

mor

phog

enes

isA

bzha

nov

etal

.(20

04);

Wu

etal

.(20

04)

Hea

vym

etal

tole

ranc

eO

rche

sell

aci

ncta

Mt

Tra

nscr

iptio

nra

tere

gula

tes

Cd

excr

etio

nR

oelo

fset

al.(

2006

)

Bol

ting

A.t

hali

ana

FR

Ige

neen

code

sa

prot

ein

that

repr

esse

str

ansi

tion

tofl

ower

ing

Epi

stat

icin

tera

ctio

nw

ithF

LC

gene

spr

oduc

escl

inal

vari

atio

nSh

eldo

net

al.(

2000

);C

aice

doet

al(2

004)

Lif

esp

anD

.mel

anog

aste

rM

ultip

leM

ultip

lege

nes

indi

vidu

ally

have

maj

oref

fect

s(8

–85%

incr

ease

)Ta

ble

1in

Hug

hes

and

Rey

nold

s(2

005)

Lif

esp

anC

.ele

gans

Cel

l-si

gnal

ing

path

way

Up

to3×

incr

ease

p.43

2in

Hug

hes

and

Rey

nold

s(2

005)

.See

also

Ler

oi(2

001)

Res

ista

nce

A.t

hali

ana

Plas

ma

mem

bran

epr

otei

nth

atco

nfer

sab

ility

tore

cogn

ize

path

ogen

Not

driv

ento

fixa

tion

beca

use

ofa

trad

e-of

fw

ithse

edpr

oduc

tion

Tia

net

al.(

2003

)

Res

ista

nce

A.t

hali

ana

Aux

inre

spon

se3

mut

atio

nsaf

fect

ing

sam

epa

thw

ayR

oux

and

Reb

oud

(200

5)R

esis

tanc

eD

.mel

anog

aste

rJH

rece

ptor

Mut

antM

etal

lele

ssi

gnif

ican

tlyaf

fect

resi

stan

cean

dha

vest

atis

tical

lysi

gnif

ican

tple

iotr

opic

effe

cts

onlif

e-hi

stor

ytr

aits

Flat

tand

Kaw

ecki

(200

4)

Res

ista

nce

D.m

elan

ogas

ter

Ove

rtra

nscr

iptio

nD

iffe

rent

path

sca

nbe

affe

cted

(e.g

.,cy

toch

rom

eP4

50s,

glut

athi

one-

S-tr

ansf

eras

es,e

ster

ases

)L

eG

off

etal

.(20

03);

Fest

ucci

-Bus

elli

etal

.(2

005)

Res

ista

nce

Cul

expi

pien

sE

ster

ase

over

prod

uctio

nTw

olo

ciin

volv

ed,w

ithtw

ono

nexc

lusi

vem

echa

nism

sof

oper

atio

nB

ertic

atet

al.(

2002

)

Res

ista

nce

Myz

uspe

rsic

ae,

Mus

cado

mes

tica

Ove

rpro

duct

ion

ofca

rbox

ylas

esor

sodi

um-c

hann

elm

odul

atio

nPl

eiot

ropi

cef

fect

son

beha

vior

Fost

eret

al.(

2003

)

Res

ista

nce

Sacc

haro

myc

esce

revi

siae

Tra

nscr

iptio

nalr

egul

ator

sTw

ose

para

tem

utat

ions

,whi

chsi

ngly

incr

ease

resi

stan

cebu

ttog

ethe

rha

vene

gativ

eef

fect

son

fitn

ess

And

erso

net

al.(

2006

)

Res

ista

nce

Can

dida

albi

cans

Ove

rexp

ress

ion

ofdr

ug-r

esis

tanc

ede

term

inan

t3

diff

eren

tpat

tern

sev

olve

d,on

ein

volv

ing

asi

ngle

maj

orge

ne,t

heot

her

two,

whi

chw

ere

mor

eco

mm

on,

invo

lvin

gm

ultip

lege

nes

Cow

enet

al.(

2002

)

1022 EVOLUTION MAY 2007

PERSPECTIVE

general genetic model of caste determination nor does it imply

that wing development, or lack of, is a consequence of a single

gene or a single mutation. Caste determination in hymenoptera is

generally determined by environmental conditions during rear-

ing, including maternal inputs to the egg (Suzzoni et al. 1980;

Wheeler 1986, 1991), although there are cases of genetic differ-

ences among castes (Fraser 2000; Julian et al. 2002; Cahan and

Keller 2003). Genomic comparisons among castes have shown

that there is differential expression of numerous genes (Evans

and Wheeler 1999; Pereboom et al. 2005; Sumner et al. 2006),

though which ones are specifically required for determination is

not known. A general model for this mechanism of determina-

tion is the threshold model in which it is envisaged that at some

point in development the subsequent developmental trajectory is

determined by the value of some trait, called the liability, and a

threshold: values of the liability above the threshold shift develop-

ment into one trajectory whereas values below the threshold shift

development into the alternate path (Falconer 1965; Wright 1977;

Roff 1996a). The liability could indeed be equated to a single

gene that up- or downregulates some product, such as a hormone,

that controls future development. On the other hand, the liability

may be a function of a large number of factors, in which case

the liability may show a continuous distribution. In the former

case, evolution can be modeled using simple Mendelian popula-

tion genetics, whereas in the latter a quantitative genetic approach

is appropriate. With respect to wing dimorphism, it is intrigu-

ing to find that in holometabolous development, as found in the

hymenoptera, the vast majority of cases can be modeled using a

single locus model with winglessness being dominant, but in those

insects with hemimetabolous development a polygenic model best

fits the data (Roff and Fairbairn 1991).

Insects show enormous variation in the relative size of their

hind legs, which can be related to variation in the pattern of expres-

sion of the Ubx and abd-A genes (the method of detection could not

distinguish between these two and so their relative contributions

are not known; Mahfooz et al. 2004). Similarly, the activity of

the Bmp4 gene correlates with adult beak size in Darwin’s ground

finches (Abzhanov et al. 2004). Does this mean that leg length or

beak size is determined by the action of only one or two genes? It

is readily observed that there is continuous phenotypic variation

within populations and estimates of heritability of morphological

traits are relatively large (approximately 0.4, Mousseau and Roff

1987), which is inconsistent with single gene action. Morphol-

ogy is a result of a sequence of developmental processes, which

both affect and are affected by the expression of particular genes

such as Ubx, abd-A, and Bmp4. Even if we knew all the genes

involved in the developmental process, it is unlikely that we could

predict the results of selection on a single trait better than that

done by quantitative genetics (for reasons discussed below, the

jury is still out on whether the prediction of multivariate evolution

will typically require more than a traditional quantitative genetic

model).

An excellent illustration of the relationship between single

gene action and quantitative genetics is given by the study of

Roelofs et al. (2006) on additive genetic variation in metallothio-

nen expression in the collembolan Orchesella cincta. Tolerance

to heavy metals in this species is mediated by cadmium (Cd) ex-

cretion, which has been shown to have a heritability between 0.33

and 0.48 (Posthuma et al. 1993). It is known that the gene mt plays

a significant role in Cd excretion. Using quantitative polymerase

chain reaction (PCR), Roelofs et al. (2006) determined variation

in transcription rate of this gene and from parent–offspring regres-

sion estimated the heritability of transcription rate to be between

0.36 and 0.46, which agrees very well with the previously esti-

mated heritability for Cd excretion. Cadmium excretion is largely

under the control of a single gene (mt) but the expression of this

gene is itself modified by the action of other genes, thereby pro-

ducing continuous genotypic and phenotypic distributions.

Another example in which a single gene plays a key role

but its effect may be modeled by a quantitative genetic approach

is the gene FLC, which controls the onset of flowering in A.

thaliana (Sheldon et al. 2000). Flowering is controlled by the

induced transcription rate of FLC, variation in which is a func-

tion of both allelic variation at the FLC locus and the action of

other genes (Sheldon et al. 2000; Caicedo et al. 2004; see Rem-

ington and Purugganan 2003 for a review of other genes affect-

ing flowering time in plants). Epistatic interaction between the

genes FRI and FLC is responsible for clinal variation in flow-

ering time (Caicedo et al. 2004). It would be extremely inter-

esting to know if this epistatic interaction resulted in significant

epistatic variance.

Numerous mutations affecting life span in D. melanogaster

and C. elegans have been isolated (Table 1). Life span in

D. melanogaster has been the subject of intense study, both using

quantitative and genomic approaches. Life span responds readily

to selection with attendant correlated responses in physiology and

life-history traits, the mechanisms for which are still unresolved

(Valenzuela et al. 2004; Rose et al. 2005; Vermeulen and Bijlsma

2006). Single gene manipulations have shown that life span can be

substantially increased (up to 85%) and that no single gene deter-

mines this trait or even a unique mechanism by which longevity is

altered (see table 1 in Hughes and Reynolds 2005). Genomic anal-

yses have identified up to 25 QTL affecting longevity (Nuzhdin

et al. 2005). Eleven QTL were identified on chromosome 3 con-

taining from 12 to 170 positional candidate genes (Wilson et al.

2006). Quantitative trait loci analyses have also shown significant

dominance, epistatic and genotype by environment interactions

(Leips and Mackay 2002; Forbes et al. 2004). It is evident that

longevity is a highly complex trait likely involving a large ar-

ray of different physiological components. Although single gene

EVOLUTION MAY 2007 1023

PERSPECTIVE

mutations can have significant effects on longevity, the antagonis-

tic effects on other fitness components may exclude their invasion

into most natural populations: in the absence of such effects we

would expect these genes to be generally favored and spread to

fixation at which point they no longer contribute to variation (of

course high extrinsic mortality will greatly reduce the selective

advantage of longevity genes). The presence of dominance and

epistatic effects is not unexpected: life-history traits typically show

directional dominance (Roff 1997) and the complexity of phys-

iological components of longevity would argue for interactions

among loci. Whereas dominance effects may be revealed by con-

tributions to genetic variance, epistatic effects, even of large effect,

may contribute little to genetic variance, as illustrated, for example

by the lack of epistatic variance in Drosophila bristle number but

significant epistatic interaction revealed by QTL analysis (Mackay

and Lyman 2005). It remains to be shown if the epistatic effects

in longevity could play a significant role in evolutionary change

and thus need to be incorporated into a quantitative genetic model

of the evolution of life span.

Major gene effects conferring increased resistance to pes-

ticides, herbicides, and drugs have frequently been observed in

natural populations of animals and plants (Table 1; Jasieniuk et al.

1996; ffrench-Constant et al. 2004). In many cases the molec-

ular mechanism underlying this resistance is an upregulation of

transcription (Table 1; Taylor and Feyereisen 1996). Major gene

action is common in the evolution of insecticide resistance in nat-

ural populations but artificial selection appears to act on polygenic

variation (McKenzie and Batterham 1994). The precise reasons for

this are still debated (McKenzie and Batterham 1998; McKenzie

2000) but certainly a contributing factor is that the relevant muta-

tions are likely to be absent in laboratory populations but available

in the much larger natural populations. An understanding of the

potential genetic mechanisms available for resistance is, in this

case, important for predicting the circumstances under which par-

ticular evolutionary trajectories will be taken.

In summary, detailing the genetic mechanisms is an impor-

tant enterprise but, with relatively few exceptions, knowledge of

those mechanisms does not contribute to the prediction of the

evolutionary trajectory of traits that fall within the purview of

quantitative genetics. At present, although it is possible to simu-

late simple gene networks and follow their evolutionary change

(Frank 1999; Omholt et al. 2000; Hasty 2001; de la Fuente et al.

2002; Nijhout 2002; Bergman and Siegal 2003), we are nowhere

close to simulating the complexity of genetic interactions involved

in the determination of such traits as fecundity, longevity, or

body size.

An important area of research that is highlighted by the search

for specific genetic mechanisms is that of determining the number

of alternate paths to a single phenotype. Selection in the “classi-

cal” quantitative genetic model assumes equality of all loci, with

the result that the change in allelic frequencies during selection

may differ due to chance. Under this scenario two lines selected

in the same direction could display the same phenotype but differ

at particular loci. Because of nonadditive genetic interactions, a

cross between two such selected lines would not then necessarily

produce the same phenotype. For example, crosses between lines

of mice selected for growth rate revealed extensive nonadditive

interactions (Mohamed et al. 2001). Differences in genetic mecha-

nism have also been demonstrated in mice selected for thermoreg-

ulatory nest-building behavior (Bult and Lynch 1996). Perhaps,

even more intriguing is the possibility of different morpholog-

ical, physiological, or behavioral pathways leading to the same

selection response. Examples in this category include selection

on competitive ability in Drosophila (Joshi and Thompson 1995),

growth rate patterns in mice (Rhees and Atchley 2000), wheel

running in mice (Garland et al. 2002), and adaptive evolution to

growth media in Escherichia coli (Fong et al. 2005). Different

pathways to the same phenotype have also been found in natural

populations of D. subobscura. Near identical clines in wing size

is found in D. subobscura populations in Europe, South America,

and North America, but the components of the wing show striking

differences (Gilchrist et al. 2004). Crosses among populations of

D. melanogaster also suggest that different clines in wing size

have different genetic bases (Gilchrist and Partridge 1999). Such

results do suggest that research incorporating quantitative genetic

and mechanistic approaches are fundamental to the prediction of

evolutionary change and that we need to develop models that com-

bine these two components.

Testing Predictions of theMultivariate Breeder’s EquationWhereas QTL analysis can provide direct evidence for or against

the assumptions underlying the quantitative genetic framework,

indirect tests are provided by the ability of quantitative genetic

models to predict the rate and direction of evolutionary change.

Perhaps more importantly, the results of such experimental com-

parisons inform us on the robustness of the models to the un-

derlying assumptions. In this respect the record on predictions

for single trait responses to artificial selection is very good, ex-

cellent predictions being made for the first 10–15 generations of

selection, followed generally by the predicted decline in response

as variation is eroded (Hill and Caballero 1992; fig. 2.5 in Roff

2002). Artificial selection experiments also tend to support the

results from QTL analyses that genes of large effect frequently

occur (Hill and Caballero 1992). The analysis of trait variation

in wild populations, particularly responses following changes in

biotic or abiotic conditions, depends generally upon being able to

predict multivariate responses, and here even the results of artifi-

cial selection experiments are somewhat discouraging.

1024 EVOLUTION MAY 2007

PERSPECTIVE

Tab

le2.

Asu

rvey

of

biv

aria

tear

tifi

cial

sele

ctio

nex

per

imen

ts.

Spec

ies

Tra

it1

Tra

it2

Com

pare

dto

Res

ult

Ref

eren

cepr

edic

ted?

Sele

ctio

nin

allf

our

dire

ctio

nsB

icyc

lus

anya

naA

nter

ior

eyes

pot

Post

erio

rey

espo

tN

oB

oth

trai

tsre

spon

ded

Bel

dade

etal

.(20

02)

Bic

yclu

san

yana

Fore

win

gar

eaB

ody

wei

ght

No

Bot

htr

aits

resp

onde

dFr

anki

noet

al.(

2005

)M

ouse

12to

21-d

ayw

eigh

tgai

n51

day

wei

ght

Yes

Goo

din

two

dire

ctio

ns(H

–H;H

–L),

poor

inth

eot

her

two

(L–L

;L–H

)B

erge

ran

dH

arve

y(1

975)

D.m

elan

ogas

ter

Cox

als

Ster

nopl

eura

lbri

stle

sY

esG

ood

fiti

nea

rly

gene

ratio

n(1

0)po

orfi

tin

late

rge

nera

tion

(22)

Sher

idan

and

Bar

ker

(197

4)

Trib

oliu

mca

sten

eum

13-d

ayla

rval

wei

ght

Pupa

lwei

ght

Yes

Poor

,par

ticul

arly

for

anta

goni

stic

sele

ctio

nB

ella

ndB

urri

s(1

973)

Trib

oliu

mca

sten

eum

14-d

ayla

rval

wei

ght

30-d

ayla

rval

wei

ght

Yes

Poor

,par

ticul

arly

for

anta

goni

stic

sele

ctio

nO

kada

and

Har

din

(196

7)

Trib

oliu

mca

sten

eum

Pupa

lwei

ght

Egg

layi

ngY

esG

ood,

cons

iste

ntw

ithes

timat

esC

ampo

and

dela

Fuen

te(1

991)

One

dire

ctio

nof

sele

ctio

nre

info

rcin

gan

da

seco

ndan

tago

nist

icO

ntho

phag

usac

umin

atus

Hor

nle

ngth

Bod

ysi

zeN

oR

espo

nse

sam

ein

both

dire

ctio

nsE

mle

n(1

996)

Rei

nfor

cing

sele

ctio

nM

ouse

Post

wea

ning

wei

ghtg

ain

Litt

ersi

zeat

birt

hN

oB

oth

trai

tsre

spon

ded

Doo

little

etal

.(19

72)

D.m

elan

ogas

ter

Abd

omin

albr

istle

sSt

erno

pleu

ralb

rist

les

No

Bot

htr

aits

resp

onde

dSe

nan

dR

ober

tson

(196

4)Tr

ibol

ium

cast

eneu

mPu

palw

eigh

tFa

mily

size

Yes

Poor

,but

good

for

sing

letr

aits

Ber

ger

(197

7)Pl

ant

Hei

ght

Num

ber

ofle

aves

Yes

Goo

dM

atzi

nger

etal

.(19

77)

Ant

agon

istic

sele

ctio

nM

ouse

Tail

leng

thB

ody

wei

ght

No

Bot

htr

aits

resp

onde

dC

ockr

em(1

959)

Mou

seFo

odin

take

,or

gona

dalf

atpa

d,or

fatp

adB

ody

wei

ght

No

Bot

htr

aits

resp

onde

dSh

arp

etal

.(19

84)

Bra

ssic

ara

paFi

lam

entl

engt

hC

orol

lale

ngth

No

Bot

htr

aits

resp

onde

dC

onne

r(2

003)

Boa

rD

aily

wei

ghtg

ain

betw

een

30–8

0kg

Bac

kfa

tind

exat

80kg

No

Bot

htr

aits

resp

onde

dO

llivi

er(1

980)

Mou

seTa

ille

ngth

Bod

yw

eigh

tY

esPo

orR

utle

dge

etal

(197

3)M

ouse

Wei

ghta

t5w

eeks

Wei

ghta

t10

wee

ksY

esPo

orM

cCar

thy

and

Doo

little

(197

7)M

ouse

6-w

eek

body

wei

ght

Litt

ersi

zeat

birt

hY

esPo

orE

isen

(197

8)M

ouse

12-w

eek

fatw

eigh

tC

onst

ant1

2-w

eek

body

wei

ght

Yes

Fair

inon

edi

rect

ion,

poor

inth

eot

her

Eis

en(1

992)

Mou

se8-

wee

kbo

dyw

eigh

t3–

5w

eek

wei

ghtg

ain

Yes

Poor

von

But

ler

etal

.(19

86)

Mou

seW

eigh

tgai

n,bi

rth

to10

days

Wei

ghtg

ain,

28da

ysto

56da

ysY

esG

ood

inon

ere

gim

e,po

orin

anot

her

Atc

hley

etal

.(19

97)

Trib

oliu

mca

sten

eum

Bod

ysi

zePu

palw

eigh

tY

esPo

orC

ampo

and

Ray

a(1

986)

Trib

oliu

mca

sten

eum

Lar

valw

eigh

t,or

deve

lopm

entt

ime,

orpu

palw

eigh

t

Inde

xof

othe

rtw

oY

esG

ener

ally

poor

Sche

inbe

rget

al.(

1967

)

Trib

oliu

mca

sten

eum

Pupa

lwei

ghta

t21

days

Adu

ltbo

dyw

eigh

tat2

1da

ysY

esG

ood

inon

edi

rect

ion,

poor

inot

her

Cam

poan

dV

elas

co(1

989)

Chi

cken

Egg

wei

ght

Bod

yw

eigh

tY

esPo

orFe

stin

gan

dN

ords

kog

(196

7);

Nor

dsko

g(1

977)

Tur

key

Day

ste

sted

Egg

wei

ghta

ndra

teof

lay

Yes

Acc

urat

efo

rth

eon

ege

nera

tion

test

edG

arw

ood

etal

.(19

78)

Tur

key

8-w

eek

body

wei

ght

24-w

eek

body

wei

ght

Yes

Mod

erat

eA

bpla

nalp

etal

.(19

63)

Mai

zeY

ield

Ear

heig

htY

esPo

orM

olle

tal.

(197

5)So

ybea

nPr

otei

nco

ncen

trat

ion

Oil

cont

ent

Yes

Goo

din

one

dire

ctio

n,po

orin

othe

rO

pens

haw

and

Had

ley

(198

4)

EVOLUTION MAY 2007 1025

PERSPECTIVE

The general finding of artificial bivariate selection experi-

ments is that antagonistic selection, meaning selection opposite

to the sign of the genetic correlation, frequently does not accord

with prediction (Table 2). Various reasons have been advanced for

the poor response: incorrect initial estimates, maternal effects, ge-

netic drift, asymmetry in gene frequencies, type of index selection

applied, and functional constraints. However, in no case has the

cause of the irregularity in response been adequately analyzed.

If quantitative genetic theory cannot account for response to ar-

tificial bivariate selection then it will be severely limited in how

useful it can be in understanding short-term evolutionary change

in wild populations.

The breeder’s equation has been applied to explain selection

response in three natural populations: changes in a diapause com-

ponent, KP, in the lepidopteran, Hyphantria cunea (Morris 1971);

the evolution of body components in Darwin’s medium ground

finch, Geospiza fortis (Grant and Grant 1995); the evolution of ju-

venile hormone esterase (JHE) activity in the Bermuda population

of the sand cricket, Gryllus firmus (Roff and Fairbairn 1999). For

H. cunea, Morris (1971) successfully used the single trait breeder’s

equation to predict the change in Kp in three populations over 12

years (for a summary and discussion see Roff 1997, p. 157–159).

Roff and Fairbairn (1999) successfully predicted the correlated

response of JHE activity to changes in proportion macropterous

(long-winged and capable of flight) female G. firmus using genet-

ical parameters derived from laboratory rearings. Finally, Grant

and Grant (1995) obtained good agreement between observed and

predicted response to natural selection in G. fortis using genetical

parameters estimated from offspring–parent pedigrees in the same

population. Multivariate selection was overwhelmingly reinforc-

ing on G. fortis, meaning that selection was in the direction of

the genetic correlations, which is the case most likely in theory to

produce predictable responses (this also appears to be supported

by the empirical findings in Table 2, though the number of cases

I have been able to locate is surprisingly few).

To address the utility of the multivariate breeder’s equation

we need bivariate selection experiments in which both functional

and genetic factors that could restrict the evolutionary trajectory

can be explored. Such experiments will most likely be achievable

using an invertebrate or plant system, though a fast growing ver-

tebrate such as guppies might also be useful. Possible candidates

for which we have considerable information on functional and

genetic parameters are D. melanogaster (e.g., Roff and Mousseau

1987; Flatt et al. 2005; Chippindale et al. 2003; Rose et al. 2005),

Arabidopsis (e.g., Pigliucci 1998; Ungerer and Rieseberg 2003;

Ungerer et al. 2003; Koornneef et al. 2004), Manduca sexta (e.g.,

D’Amico et al. 2001; Davidowitz et al. 2005; Nijout et al. 2006,

2007), Bicyclus anynana (e.g., Beldade et al. 2002; Brakefield

et al. 2003; Zijlstra et al. 2003; Frankino et al. 2005), Onthoph-

agus sp. (Emlen 1996, 2000, 2001; House and Simmons 2005;

Emlen et al. 2006; Moczek 2006), and G. firmus (e.g., Roff and

Fairbairn 1999, 2001, 2006; Roff et al., 2002; Zera and Harshman

2001).

The Evolution of the Phenotypicand Genetic Variance–CovarianceMatricesA fundamental assumption of the foregoing discussion is that the

variance–covariance matrices do not themselves evolve. This is

clearly not the case but we presently lack a detailed theory on how

the matrix will change over time (Arnold et al. 2001; McGuigan

2006; Phillips and McGuigan 2006). Schluter (1996), assuming

that the G matrix remains constant, pointed out that evolution

would tend to follow the trajectory in which additive genetic vari-

ances are maximal: thus, for example, with two traits the evolu-

tionary path would at least initially tend to be in the same direction

as the major axis of the bivariate distribution. On the other hand,

we would also expect that variances and covariances would be

selected such that the resulting major axis of the bivariate distri-

bution would be in the direction of selection, that is, the G ma-

trix aligns itself to selection (Lande 1980; Cheverud 1984; Arnold

1992; Arnold et al. 2001). Some understanding of the evolution of

the G matrix under different types of selection has been achieved

by simulation (Jones et al. 2003, 2004) but empirical descriptions

of the manner of variation in the G matrix are still rather few

and general patterns have yet to emerge with which theoretical

analysis can be compared.

To date most empirical studies of the G matrix have focused

upon the question of whether G matrices vary among populations

or species (Roff 2000; Steppan et al. 2002). It comes as no surprise

that given sufficiently large sample sizes statistically significant

variation among G matrices is very common, if not ubiquitous. It is

time to depart from this hypothesis-testing approach and consider

the question of interval-estimation, that is, asking not whether

two matrices differ but what is the amount and pattern of differ-

ences (a point also pressed by Phillips and McGuigan 2006). A

potential stumbling block is the logistical difficulty of determin-

ing G matrices. One solution may be to use the P matrix as a

surrogate, which for morphological traits can be justified by the

close correspondence between the phenotypic and genetic corre-

lations (Cheverud 1988; Roff 1996b). However, a comparison of

how the P and G matrices interpreted variation among species

of crickets suggested that using P as a surrogate for G can be

misleading even for morphological traits (Begin and Roff 2004).

Because it is an important component of the breeder’s equation,

a study of variation in the P matrix is also of importance in its

own right, regardless of its possible use in place of G (Roff and

Mousseau 2005).

1026 EVOLUTION MAY 2007

PERSPECTIVE

ConclusionsQuantitative genetics has shown itself to be an extremely fruitful

approach to the analysis of quantitative variation. The intellectual

achievement of bringing together Mendelian genetics and statis-

tics was a landmark in evolutionary biology. The breeder’s equa-

tion, in either its singular or multivariate formulation, is elegant

in its simplicity yet has proven to be of high explanatory abil-

ity, though the predictive ability of the multivariate version needs

much more testing.

As a descriptor of genetic variation in a population the quanti-

tative genetic perspective has been extremely important. Analyses

of wild populations have shown that genetic variation is rampant

and generally ample for rapid evolutionary responses. At the level

of the genome the quantitative genetics perspective has played a

major role in bringing order to the vast amount of data extracted

from microarrays. The potential of this combination has yet to

be realized, but surely will be as the cost of microarray analy-

sis drops to a point at which it can be applied to standard ped-

igree designs.

The underlying assumptions of the breeder’s equation, in ei-

ther its singular or multivariate forms, have always been known

to be mathematical approximations of what is actually happening

at the level of the gene. The important question is simply how

good are these approximations? The results of single trait selec-

tion suggest that they are reasonable for short-term selection but

predictable deviations occur over the long term. Quantitative trait

loci analyses have shed more light on the number of loci and

the distribution of genetic effects but much remains to be learned

about the number of alleles and the distribution of genetic ef-

fects in a large outbreeding population. In particular, do QTLs of

major effect show such effects across the large array of genetic

backgrounds expected in an outbreeding population?

The considerable research done at the level of molecular ge-

netics has revealed extensive networks of interacting genes. Fre-

quently, genes of large effect are found and these may indeed be

common, though research tends to be directed towards detecting

such genes. While it is important to elucidate the genetic mecha-

nisms underlying traits, those of interest to quantitative geneticists

will generally be composed of such a large array on interacting

components that at this stage there is no possibility of creating

a useful mechanistic model for such traits. Quantitative genetics

cuts through this Gordian knot to provide a convenient and pow-

erful summary tool of these interactions. Further developments in

the mathematics of gene networks may provide a means of con-

necting mechanism and statistical description, but it remains to be

seen whether such would provide greater explanatory power than

presently provided by the quantitative genetic approach.

An area in which quantitative genetics has been surprisingly

unsuccessful is that of the quantitative prediction of multivariate

evolution when selection is antagonistic to the genetic covariances.

In large part this failing is due to a paucity of bivariate selection

experiments with follow-up analyses of the mechanistic causes for

the deviations from expectation. The recent acknowledgment of

the utility of selection experiments (Gibbs 1999; Brakefield et al.

2003; Conner 2003; Garland 2003; Fuller et al. 2005; Swallow and

Garland 2005) and of experimental evolution approaches (Bennett

and Lenski 1999; Stearns et al. 2000; Mery and Kawecki 2002;

Rose et al. 2005; Roff and Fairbairn 2007) will likely remedy

this situation.

Just as genetic variances are expected to evolve under the

force of selection so too are the G and P matrices expected to

evolve. Theoretical and numerical analyses of such evolution is

beginning, as is the description of variation of the matrices in wild

populations in relation to possible factors of selection, but we are

still at the early stages and this area is ripe for further study.

Quantitative genetics has proven itself of great utility over

the last 100 years. The advent of massive computing power and

the ability to delve into the molecular foundation of genetic vari-

ation promises to contribute to an increasing refinement of the

multivariate breeder’s equation: there is no reason to expect that

the contribution of quantitative genetics to our understanding of

the basis and evolution of trait variation will diminish in the

near future.

ACKNOWLEDGMENTSThis work is supported by National Science Foundation (NSF) grant DEB-0445140. I am very grateful for the constructive criticisms of the tworeviewers.

LITERATURE CITEDAbouheif, E., and G. A. Wray. 2002. Evolution of the gene network underlying

wing polyphenism in ants. Science 297:249–252.Abzhanov, A., M. Protas, B. R. Grant, P. R. Grant, and C. J. Tabin. 2004.

Bmp4 and morphological variation of beaks in Darwin’s finches. Science305:1462–1465.

Alonso-Blanco, C., L. Bentsink, C. J. Hanhart, H. Blankestijn-de Vries, and M.Koornneef. 2003. Analysis of natural allelic variation at seed dormancyloci of Arabidopsis thaliana. Genetics 164:711–729.

Anderson, J. B., N. Ricker, and C. Sirjusingh. 2006. Antagonism between twomechanisms of antifungal drug resistance. Eukaryotic Cell 5:1243–1251.

Arnold, S. J. 1992. Constraints on phenotypic evolution. Am. Nat. 140(Suppl.):s85–s107.

Arnold, S. J., M. E. Pfrender, and A. G. Jones. 2001. The adaptive landscapeas a conceptual bridge between micro- and macroevolution. Genetica112–113:9–32.

Atchley, W. R., S. Xu, and D. E. Cowley. 1997. Altering developmental tra-jectories in mice by restricted index selection. Genetics 146:629–640.

Aubin-Horth, N., C. R. Landry, B. H. Letcher, and H. A. Hofmann. 2005a.Alternative life histories shape brain gene expression profiles in malesof the same population. Proc. R. Soc. B Biol. Sci. 272:1655–1662.

Aubin-Horth, N., B. H. Letcher, and H. A. Hofmann. 2005b. Interaction ofrearing environment and reproductive tactic on gene expression profilesin Atlantic salmon. J. Hered. 96:261–278.

EVOLUTION MAY 2007 1027

PERSPECTIVE

Beavis, W. D. 1994. The power and deceit of QTL experiments: lessons fromcomparative QTL studies. Pp. 250–266. Proceedings of the Forty-NinthAnnual Corn and Sorghum Industry Research Conference, AmericanSeed Trade Assoc., Washington, D.C.

———. 1998. QTL analyses: power, precision and accuracy. Pp. 145–162 inA. H. Patterson, ed. Molecular dissection of complex traits. CRC Press,New York.

Begin, M., and D. A. Roff. 2004. From micro- to macroevolution through quan-titative genetic variation: positive evidence from field crickets. Evolution58:2287–2304.

Beldade, P., K. Koops, and P. M. Brakefield. 2002. Developmental con-straints versus flexibility in morphological evolution. Nature 416:844–847.

Bell, A. E., and M. J. Burris. 1973. Simultaneous selection for two correlatedtraits in Tribolium. Genet. Res. 21:24–46.

Bennett, A. F., and R. E. Lenski. 1999. Experimental evolution and its role inevolutionary physiology. Am. Zool. 39:346–362.

Berger, P. J. 1977. Multiple-trait selection experiments: current status, prob-lem areas and experimental approaches. Pp. 191–204 in E. Pollack,O. Kempthorne and J. T. B. Baily, eds. Proceedings of the Interna-tional Conference on Quantitative Genetics. Iowa State University Press,Ames.

Berger, P. J., and W. R. Harvey. 1975. Realized genetic parameters from indexselection in mice. J. Anim. Sci. 40:38–47.

Bergman, A., and M. L. Siegal 2003. Evolutionary capacitance asa general feature of complex gene networks. Nature 423:549–552.

Berticat, C., G. Boquien, M. Raymond, and C. Chevillon. 2002. Insecticideresistance genes induce a mating competition cost in Culex pipiensmosquitoes. Genet. Res. 79:41–47.

Bochdanovits, Z., and G. de Jong. 2004. Antagonistic pleiotropy for life-history traits at the gene expression level. Proc. R. Soc. Lond. B 271:S75–S78.

Bochdanovits, Z., H. van der Klis, and G. de Jong. 2003. Covariation of larvalgene expression and adult body size in natural populations of Drosophilamelanogaster. Mol. Biol. Evol. 20:1760–1766.

Brakefield, P. M., V. French, and B. J. Zwaan. 2003. Development and thegenetics of evolutionary change within insect species. Ann. Rev. Ecol.Evol. Syst. 34:633–660.

Brodie, E. D. I. 2000. Why evolutionary genetics does not always add up. Pp.3–19 in J. B. Wolf, E. D. B. III and M. J. Wade, eds. Epistasis and theevolutionary process. Oxford Univ. Press, Oxford.

Brommer, J. E., J. Merila, B. C. Sheldon, and L. Gustafsson. 2005. Naturalselection and genetic variation for reproductive reaction norms in a wildbird population. Evolution 59:1362–1371.

Brown, P. O., and D. Botstein. 1999. Exploring the new world of the genomewith DNA microarrays. Nat. Genet. Suppl. 21:33–37.

Bult, A., and C. B. Lynch. 1996. Multiple selection responses in house micebidirectionally selected for thermoregulatory nest-building behavior:crosses of replicate lines. Behav. Genet. 26:439–446.

Cahan, S. H., and L. Keller. 2003. Complex hybrid origin of genetic castedetermination in harvester ants. Nature 424:306–309.

Caicedo, A. L., J. R. Stinchcombe, K. M. Olsen, J. Schmitt, and M. D. Pu-rugganan. 2004. Epistatic interaction between Arabidopsis FRI and FLCflowering time genes generates a latitudinal cline in a life-history trait.Proc. Nat. Acad. Sci. U.S.A. 101:15670–15675.

Campo, J. L., and M. B. d. l. Fuente. 1991. Efficiency of two-stage selectionindices in Tribolium. J. Hered. 82:228–232.

Campo, J. L., and L. G. Raya. 1986. Realized genetic-parameters from an an-tagonistic selection index in Tribolium-castaneum. Can. J. Genet. Cytol.28:358–364.

Campo, J. L., and T. Velasco. 1989. An experimental test of opti-mum and desired gains indexes in Tribolium. J. Hered. 80:48–52.

Carlborg, O., and C. S. Haley. 2004. Epistasis: too often neglected in complextrait studies? Nat. Rev. Genet. 5:618–625.

Carlborg, O., S. Kerje, K. Schutz, L. Jacobsson, P. Jensen, and L. Andersson.2003. A global search reveals epistatic interaction between QTL for earlygrowth in the chicken. Genome Res. 13:413–421.

Carlborg, O., L. Jacobsson, P. Ahgren, P. Siegel, and L. Andersson. 2006.Epistasis and the release of genetic variation during long-term selection.Nat. Genet. 38:418–420.

Charmantier, A., C. Perrins, R. H. McCleery, and B. C. Sheldon. 2006a. Quan-titative genetics of age at reproduction in wild swans: support for antag-onistic pleiotropy models of senescence. Proc. Nat. Acad. Sci. U.S.A103:6587–6592.

———. 2006b. Evolutionary response to selection on clutch size in a long-term study of the mute swan. Am. Nat. 167:453–465.

———. 2006c. Age-dependent genetic variance in a life-history trait in themute swan. Proc. R. Soc. B Biol. Sci. 273:225–232.

Chen, J. J., R. R. Delongchamp, C.-A. Tsai, H. -m. Hsueh, F. Sistare, K.L. Thompson, V. G. Desai, and J. C. Fuscoe. 2004. Analysis of vari-ance components in gene expression data. Bioinformatics 20:1436–1446.

Cheverud, J. M. 1984. Quantitative genetics and developmental constraints onevolution by selection. J. Theor. Biol. 110:155–171.

———. 1988. A comparison of genetic and phenotypic correlations. Evolution42:958–968.

Cheverud, J. M., and E. J. Routman. 1995. Epistasis and its contribution togenetic variance components. Genetics 139:1455–1461.

———. 1996. Epistasis as a source of increased additive genetic variance atpopulation bottlenecks. Evolution 1042–1051.

Cheverud, J. M., E. Routman, J., F. A. M. Duarte, B. Van Swinderen, K.Cothran, and C. Perel. 1996. Quantitative trait loci for murine growth.Genetics 142:1305–1319.

Cheverud, J. M., T. T. Vaughn, L. S. Pletscher, K. King-Ellison, J. Bailiff,E. Adams, C. Erickson, and A. Bonislawski. 1999. Epistasis and theevolution of additive genetic variance in populations that pass through abottleneck. Evolution 53:1009–1018.

Chippindale, A. K., A. L. Ngo, and M. R. Rose. 2003. The devil in the detailsof life-history evolution: instability and reversal of genetic correlationsduring selection on Drosophila development. J. Genet. 82:133–145.

Churchill, G. A. 2002. Fundamentals of experimental design for cDNA mi-croarrays. Nat. Genet. 32:490–495.

Cockrem, F. 1959. Selection for relationships opposite to those predicted bythe genetic correlation between two traits in the house mouse (Mus mus-culus). Nature 183:342–343.

Conner, J. K. 2003. Artificial selection: a powerful tool for ecologists. Ecology84:1650–1660.

Cowen, L. E., A. Nantel, M. S. Whiteway, D. Y. Thomas, D. C. Tessier,L. M. Kohn, and J. B. Anderson. 2002. Population genomics of drugresistance in Candida albicans. Proc. Nat. Acad. Sci. U.S.A. 99:9284–9289.

D’Amico, L. J., G. Davidowitz, and H. F. Nijhout. 2001. The developmentaland physiological basis of body size evolution in an insect. Proc. Roy.Soc. Biol. Sci. Ser. B 268:1589–1593.

Davidowitz, G., D. A. Roff, and H. Nijhout. 2005. A physiological perspectiveon the response of body size and development time to simultaneousdirectional selection. Integr. Comp. Biol. 45:525–531.

de la Fuente, A., P. Brazhnik, and P. Mendes. 2002. Linking the genes: inferringquantitative gene networks from microarray data. Trends Genet. 18:395–398

1028 EVOLUTION MAY 2007

PERSPECTIVE

Derome, N., P. Duchesne, and L. Bernatchez. 2006. Parallelism in genetranscription among sympatric lake whitefish (Coregonus clupeaformisMitchill) ecotypes. Mol. Ecol. 15:1239–1249.

Doolittle, D. P., S. P. Wilson, and L. L. Hulbert. 1972. A comparison of multipletrait selection methods in the mouse. J. Hered. 63:366–372.

Drnevich, J. M., M. M. Reedy, E. A. Ruedi, S. Rodriguez-Zas, and K. A.Hughes. 2004. Quantitative evolutionary genomics: differential gene ex-pression and male reproductive success in Drosophila melanogaster.Proc. R. Soc. Lond. B 271:2267–2273.

Eisen, E. J. 1978. Single-trait and antagonistic index selection for litter sizeand body weight in mice. Genetics 88:781–811.

———. 1992. Restricted index selection in mice designed to change bodyfat without changing body weight: direct responses. Theor. Appl. Genet.83:973–980.

Emlen, D. J. 1996. Artificial selection on horn length-body size allome-try in the horned beetle Onthophagus acuminatus. Evolution 50:1219–1230.

———. 2000. Integrating development with evolution: a case study with beetlehorns. Bioscience 50:403–418.

———. 2001. Costs and the diversification of exaggerated animal structures.Science 291:1534–1536.

Emlen, D. J., Q. Szafran, L. W. Corley, and I. Dworkin. 2006. Insulin signalingand limb-patterning: candidate pathways for the origin and evolutionarydiversification of beetle horns. Heredity 97:179–191.

Erickson, D. L., C. B. Fenster, H. K. Stenøien, and D. Price. 2004. Quantitativetrait locus analyses and the study of evolutionary process. Mol. Ecol. 13:2505–2522.

Evans, J. D., and D. E. Wheeler. 1999. Differential gene expression betweendeveloping queens and workers in the honey bee, Apis mellifera. Proc.Nat. Acad. Sci. U.S.A. 96:5575–5580.

Falconer, D. S. 1965. The inheritance of liability to certain diseases, estimatedfrom the incidence among relatives. Ann. Hum. Genet. 29:51–76.

Festing, M. F., and A. W. Nordskog. 1967. Response to selection for bodyweight and egg weight in chickens. Genetics 55:219–231.

Festucci-Buselli, R. A., A. S. Carvalho-Dias, M. de Oliveira-Andrade, C.Caixeta-Nunes, H. M. Li, J. J. Stuart, W. Muir, M. E. Scharf, and B.R. Pittendrigh. 2005. Expression of Cyp6g1 and Cyp12d1 in DDT re-sistant and susceptible strains of Drosophila melanogaster. Insect Mol.Biol. 14:69–77.

ffrench-Constant, R. H., P. J. Daborn, and G. LeGoff. 2004. The genetics andgenomics of insecticide resistance. Trends Genet. 20:163–170.

Flatt, T., and T. J. Kawecki. 2004. Pleiotropic effects of methoprene-tolerant(Met), a gene involved in juvenile hormone metabolism, on life-historytraits in Drosophila melanogaster. Genetica 122:141–160.

Flatt, T., M. P. Tu, and M. Tatar. 2005. Hormonal pleiotropy and the juvenilehormone regulation of Drosophila development and life history. Bioes-says 27:999–1010.

Flint, J., and R. Mott. 2001. Finding the molecular basis of quantitative traits:successes and pitfalls. Nat. Rev. Genet. 2: 437–445.

Fong, S. S., A. R. Joyce, and B. O. Palsson. 2005. Parallel adaptive evolutioncultures of Escherichia coli lead to convergent growth phenotypes withdifferent gene expression states. Genome Res. 15:1365–1372.

Forbes, S. N., R. K. Valenzuela, P. Keim, and P. M. Service. 2004. Quantita-tive trait loci affecting life span in replicated popidations of Drosophilamelanogaster. I. Composite interval mapping. Genetics 168:301–311.

Foster, S. P., S. Young, M. S. Williamson, I. Duce, I. Denholm, and G. J.Devine. 2003. Analogous pleiotropic effects of insecticide resistancegenotypes in peach-potato aphids and houseflies. Heredity 91:98–106.

Frank, S. A. 1999. Population and quantitative genetics of regulatory networks.J. Theor. Biol. 197:281–294.

Frankino, W. A., B. J. Zwaan, D. L. Stern, and P. M. Brakefield. 2005. Naturalselection and developmental constraints in the evolution of allometries.Science 307:718–720.

Fraser, V. S. 2000. Genetic influence on caste in the ant Camponotus conso-brinus. Behav. Ecol. Sociobiol. 47:188–194.

Fuerst, C., J. W. James, J. Soelkner, and A. Essl. 1997. Impact of dominanceand epistasis on the genetic make-up of simulated populations underselection: a model development. J. Anim. Breed. Genet. 114:163–175.

Fuller, R. C., C. F. Baer, and J. Travis. 2005. How and when selection experi-ments might actually be useful. Integr. Comp. Biol. 45:391–404.

Garant, D., B. C. Sheldon, and L. Gustafsson. 2004. Climatic and temporaleffects on the expression of secondary sexual characters: genetic andenvironmental components. Evolution 58:634–644.

Garland, T. J. 2003. Selection experiments: an under-utilized tool in biome-chanics and organismal biology. Pp. 23–56 in V. L. Bels, J. -P. Gasc andA. Casinos, eds. Vertebrate biomechanics and evolution. BIOS ScientificPublications Ltd., Oxford.

Garland, T., M. T. Morgan, J. G. Swallow, J. S. Rhodes, I. Girard, J. G. Belter,and P. A. Carter. 2002. Evolution of a small-muscle polymorphism inlines of house mice selected for high activity levels. Evolution 56:1267–1275.

Garwood, V. A., P. C. Lowe, and B. B. Bohren. 1978. A replicated singlegeneration test of a restricted selections index in poultry. Theor. Appl.Genet. 52:227–231.

Gibbs, A. 1999. Laboratory selection for the comparative physiologist. J. Exp.Biol. 202:2709–2718.

Gibson, G. 2002. Microarrays in ecology and evolution: a preview. Mol. Ecol.11:17–24.

Gibson, G., and B. Weir. 2005. The quantitative genetics of transcription.Trends Genet. 21:616–623.

Gilchrist, A. S., and L. Partridge. 1999. A comparison of the genetic basisof wing size divergence in three parallel body size clines of Drosophilamelanogaster. Genetics 153:1775–1787.

Gilchrist, G. W., R. B. Huey, J. Balanya, M. Pascual, and L. Serra. 2004. Atime series of evolution in action: a latitudinal cline in wing size in SouthAmerican Drosophila subobscura. Evolution 58:768–780.

Goodnight, C. J. 1988. Epistasis and the effect of founder events on the additivegenetic variance. Evolution 42:441–454.

———. 2000. Quantitative trait loci and gene interaction: the quantitativegenetics of metapopulations. Heredity 84:587–598.

Grant, P. R., and B. R. Grant. 1995. Predicting microevolutionary responsesto directional selection on heritable variation. Evolution 49:241–251.

Hadfield, J. D., M. D. Burgess, A. Lord, A. B. Phillimore, S. M. Clegg, and I.P. F. Owens. 2006. Direct versus indirect sexual selection: genetic basisof colour, size and recruitment in a wild bird. Proc. R. Soc. B Biol. Sci.273:1347–1353.

Hansen, T. F. 2006. The evolution of genetic architecture. Ann. Rev. Ecol.Evol. Syst. 37:123–157.

Hansen, T. F., J. M. Alvarez-Castro, A. J. R. Carter, J. Hermisson, and G.P. Wagner. 2006. Evolution of genetic architecture under directionalselection. Evolution 60:1523–1536.

Hasty, J. 2001. Computational studies of gene regulatory networks: in numeromolecular biology. Nat. Rev. Genet. 2:268–278.

Hayes, B., and M. E. Goddard. 2001. The distribution of the effects ofgenes affecting quantitative traits in livestock. Genet. Sel. Evol. 33:209–229.

Hermisson, J., T. F. Hansen, and G. P. Wagner. 2003. Epistasis in polygenictraits and the evolution of genetic architecture under stabilizing selection.Am. Nat. 161:708–734

Hill, W. G. 1989. Sewall Wright and quantitative genetics. Genome 31:190–195.

EVOLUTION MAY 2007 1029

PERSPECTIVE

Hill, W. G., and A. Caballero. 1992. Artificial selection experiments. Ann.Rev. Ecol. Syst. 23:287–310.

Hill, W. G., N. H. Barton, and M. Turelli. 2006. Prediction of effects of geneticdrift on variance components under a general model of epistasis. Theor.Pop. Biol. 70:56–62.

Hofmann, H. A. 2003. Functional genomics of neural and behavioral plasticity.J. Neurobiol. 54:272–282.

Hofmann, H. A., M. E. Benson, and R. D. Fernald. 1999. Social status regulatesgrowth rate: consequences for life-history strategies. Proc. Nat. Acad.Sci. U.S.A. 96:14171–14176.

House, C. M., and L. W. Simmons. 2005. The evolution of male geni-talia: patterns of genetic variation and covariation in the genital scle-rites of the dung beetle Onthophagus taurus. J. Evol. Biol. 18:1281–1292.

Hughes, K. A., and R. M. Reynolds. 2005. Evolutionary and mechanistictheories of aging. Ann. Rev. Entomol. 50:421–445.

Jasieniuk, M., A. L. Brule-Babel, and I. N. Morrison. 1996. The evolution andgenetics of herbicide resistance in weeds. Weed Sci. 44:176–193.

Jin, W., R. M. Riley, R. D. Wolfinger, K. P. White, G. Passador-Gurgel, and G.Gibson. 2001. The contributions of sex, genotype and age to transcrip-tional variance in Drosophila melanogaster. Nat. Genet. 29:389–395.

Jones, A. G., S. J. Arnold, and R. Borger. 2003. Stability of the G-matrix in apopulation experiencing pleiotropic mutation, stabilizing selection, andgenetic drift. Evolution 57:1747–1760.

———. 2004. Evolution and stability of the G-matrix on a landscape with amoving optimum. Evolution 58:1639–1654.

Joshi, A., and J. N. Thompson. 1995. Alternative routes to the evolution ofcompetitive ability in two competing species of Drosophila. Evolution4:616–625.

Julian, G. E., J. H. Fewell, J. Gadau, R. A. Johnson, and D. Larrabee. 2002.Genetic determination of the queen caste in an ant hybrid zone. Proc.Nat. Acad. Sci. U.S.A. 99:8157–8160.

Kearsey, M. J., and M. G. L. Farquhar. 1998. QTL analysis in plants; whereare we now? Heredity 80:137–142.

Keightley, P. D. 1996. Metabolic models of selection response. J. Theor. Biol.182:311–316.

Kerr, M. K., and G. A. Churchill. 2001. Statistical design and the analysis ofgene expression microarray data. Genet. Res. 77:123–128.

Kerr, M. K., M. Martin, and G. A. Churchill. 2000. Analysis of variance forgene expression microarray data. J. Comput. Biol. 7:819–837.

Knott, S. A., R. M. Sibly, R. H. Smith, and H. Moller. 1995. Maximum likeli-hood estimation of genetic parameters in life-history using the “animalmodel”. Ecology 9:122–126.

Koornneef, M., C. Alonso-Blanco, and D. Vreugdenhil. 2004. Naturally oc-curring genetic variation in Arabidopsis thaliana. Ann. Rev. Plant Biol.44:141–172.

Kruuk, L. E. B. 2004. Estimating genetic parameters in natural populationsusing the “animal model”. Phil. Trans. R Soc. B Biol. Sci. 359:873–890.

Lande, R. 1980. Sexual dimorphism, sexual selection, and adaptation in poly-genic characters. Evolution 34:292–305.

Le Goff, G., S. Boundy, P. J. Daborn, J. L. Yen, L. Sofer, R. Lind, C. Sabourault,L. Madi-Ravazzi, and R. H. ffrench-Constant. 2003. Microarray analy-sis of cytochrome P450 mediated insecticide resistance in Drosophila..Insect Biochem. Mol. Biol. 33:701–708.

Leips, J., and T. F. C. Mackay. 2002. The complex genetic architecture ofDrosophila life span. Exp. Aging Res. 28:361–390.

Leroi, A. M. 2001. Molecular signals versus the Loi de Balancement. TrendsEcol. Evol. 16:24–29.

Lopez-Fanjul, C., A. Fernandez, and M. A. Toro. 2002. The effect of epistasison the excess of the additive and nonadditive variances after populationbottlenecks. Evolution 56:865–876.

Lopez-Fanjul, C., A. Fernandez, and M. A. Toro. 2006. The effect of geneticdrift on the variance/covariance components generated by multilocusadditive x additive epistatic systems. J. Theor. Biol. 239:161–171.

Lynch, M., and B. Walsh. 1998. Genetics and analysis of quantitative traits.Sinauer Associates, Sunderland, MA.

Mackay, T. F. C. 2001a. Quantitative trait loci in Drosophila. Nat. Rev. Genet.2:11–20.

———. 2001b. The genetic architecture of quantitative traits. Ann. Rev. Genet.35:303–339.

———. 2004. The genetic architecture of quantitative traits: lessons fromDrosophila. Cur. Opin. Genet.Dev. 14:253–257.

Mackay, T. F. C., and R. F. Lyman. 2005. Drosophila bristles and the nature ofquantitative genetic variation. Phil. Trans. R. Soc. B Biol. Sci. 360:1513–1527.

Magnhagen, C. 1991. Predation risk as a cost of reproduction. Trends Ecol.Evol. 6:183–186.

Mahfooz, N. S., H. Li, and A. Popadic. 2004. Differential expression patternsof the hox gene are associated with differential growth of insect hindlegs. Proc. Nat. Acad. Sci. U.S.A. 101:4877–4882.

Malmberg, R. L., S. Held, A. Waits, and R. Mauricio. 2005. Epistasis forfitness-related quantitative traits in Arabidopsis thaliana grown in thefield and in the greenhouse. Genetics 171:2013–2027.

Matzinger, D. F., C. C. Cockerham, and E. A. Wernsman. 1977. Single char-acter and index mass selection with random mating in a naturally self-fertilizing species. Pp. 503–518 in E. Pollack, O. Kempthorne and T. B.B. Jr., eds. Proceedings of the International Conference on QuantitativeGenetics. Iowa State Univ. Press, Ames.

Mauricio, R. 2001. Mapping quantitative trait loci in plants: uses and caveatsfor evolutionary biology. Nat. Rev. Genet. 2:370–381.

McCarthy, J. C., and D. P. Doolittle. 1977. Effects of selection for independentchanges in two highly correlated body weight traits of mice. Genet. Res.29:133–145.

McGuigan, K. 2006. Studying phenotypic evolution using multivariate quan-titative genetics. Mol. Ecol. 15:883–896.

McKenzie, J. A. 2000. The character or the variation: the genetic analysis ofthe insecticide-resistance phenotype. Bull. Ent. Res. 90:3–7.

McKenzie, J. A., and P. Batterham. 1994. The genetic, molecular and pheno-typic consequences of selection for insecticide resistance. TREE 9:166–169.

———. 1998. Predicting insecticide resistance: mutagenesis, selection andresponse. Phil. Trans. R. Soc. Lond. B Biol. Sci. 353:1729–1734.

Mery, F., and T. J. Kawecki. 2002. Experimental evolution of learning abilityin fruit flies. Proc. Nat. Acad. Sci. U.S.A. 99:14274–14279.

Moczek, A. P. 2006. Integrating micro- and macroevolution of developmentthrough the study of horned beetles. Heredity 97:168–178.

Mohamed, S. A., O. Rottmann, and F. Pirchner. 2001. Components of heterosisfor growth traits and litter size in line crosses of mice after long-termselection. J. Anim. Breed. Genet. 118:263–270.

Morris, R. F. 1971. Observed and simulated changes in genetic qual-ity in natural populations of Hyphantria cunea. Can. Ent. 103:893–906.

Mousseau, T. A., and D. A. Roff. 1987. Natural selection and the heritabilityof fitness components. Heredity 59:181–198.

Mousseau, T., K. Ritland, and D. D. Heath. 1998. A novel method forestimating heritabilities using molecular markers. Heredity 80:218–224.

Nettleton, D. 2006. A discussion of statistical methods for design and analy-sis of microarray experiments for plant scientists. Plant Cell 18:2112–2121.

Nijhout, H. F. 2002. The nature of robustness in development. BioEssays24:553–563.

1030 EVOLUTION MAY 2007

PERSPECTIVE

Nijhout, H. F., G. Davidowitz, and D. A. Roff. 2006. A quantitative analysis ofthe mechanism that controls body size in Manduca sexta. J. Biol. 5:16.

Nijhout, H. F., G. Davidowitz, and D. A. Roff. 2007. Artificial evolution:the response to simultaneous selection on two fitness traits. Physiol.Biochem. Zool.: In press.

Nussey, D. H., E. Postma, P. Gienapp, and M. E. Visser. 2005. Selectionon heritable phenotypic plasticity in a wild bird population. Science310:304–306.

Nuzhdin, S. V., A. A. Khazaeli, and J. W. Curtsinger. 2005. Survival analysisof life span quantitative trait loci in Drosophila melanogaster. Genetics170:719–731.

Omholt, S. W., E. Plahte, L. Oyehaug, and K. Xiang. 2000. Gene regula-tory networks generating the phenomena of additivity, dominance andepistasis. Genetics 155:969–980.

Oleksiak, M. F., G. A. Churchill, and D. L. Crawford. 2002. Variation in geneexpression within and among natural populations. Nat. Genet. 32:261–266.

Pereboom, J. J. M., W. C. Jordan, S. Sumner, R. L. Hammond, and A. F.G. Bourke. 2005. Differential gene expression in queen-worker castedetermination in bumble-bees. Proc. R. Soc. B Biol. Sci. 272:1145–1152.

Pettay, J. E., L. E. B. Kruuk, J. Jokela, and V. Lummaa. 2005. Heritability andgenetic constraints of life-history trait evolution in preindustrial humans.Proc. Nat. Acad. Sci. U.S.A. 102:2838–2843.

Phillips, P. C., and K. L. McGuigan. 2006. Evolution of genetic variance–covariance structure. Pp. 310–325 in C. W. Fox and J. B. Wolf, eds.Evolutionary genetics. Oxford Univ. Press, Oxford.

Pigliucci, M. 1998. Ecological and evolutionary genetics of Arabidopsis.Trends Plant Sci. 3:485–489.

Posthuma, L., R. F. Hogervorst, E. N. G. Joosse, and N. M. V. Straalen. 1993.Genetic variation and covariation for characteristics associated with cad-mium tolerance in natural populations of the springtail Orchesella cincta(L.). Evolution 47: 619–631.

Qvarnstrom, A., J. E. Brommer, and L. Gustafsson. 2006. Testing the geneticsunderlying the co-evolution of mate choice and ornament in the wild.Nature 441:84–86.

Reale, D., D. Berteaux, A. G. McAdam, and S. Boutin. 2003. Lifetime selectionon heritable life-history traits in a natural population of red squirrels.Evolution 57:2416–2423.

Rhees, B. K., and W. R. Atchley. 2000. Body weight and tail length divergencein mice selected for rate of development. J. Exp. Zool. 288:151–164.

Remington, D. L., and M. D. Purugganan. 2003. Candidate genes, quantitativetrait loci, and functional trait evolution in plants. Int. J. Plant Sci. S7–S20

Rifkin, S. A., J. Kim, and K. P. White. 2003. Evolution of gene expression inthe Drosophila melanogaster subgroup. Nat. Genet. 33:138–144.

Roberge, C., S. Einum, H. Guderley, and L. Bernatchez. 2006. Rapid parallelevolutionary changes of gene transcription profiles in farmed Atlanticsalmon. Mol. Ecol. 15:9–20.

Rocha, J. L., E. J. Eisen, L. D. Van Vleck, and D. Pomp. 2004. A large-sampleQTL study in mice: I. Growth Mam. Genome 15:83–99.

Roelofs, D., L. Overhein, M. E. de Boer, T. K. S. Janssens, and N. M. vanStraalen. 2006. Additive genetic variation of transcriptional regulation:metallothionein expression in the soil insect Orchesella cincta. Heredity96:85–92.

Roff, D. A. 1996a. The evolution of threshold traits in animals. Q. Rev. Biol.71:3–35.

———. 1996b. The evolution of genetic correlations: an analysis of patterns.Evolution 50:1392–1403.

———. 1997. Evolutionary quantitative genetics. Chapman and Hall, NewYork.

———. 2000. The evolution of the G matrix: selection or drift? Heredity84:135–142.

———. 2002. Life-history evolution. Sinauer Associates, Sunderland, MA.Roff, D. A., and D. J. Fairbairn. 1991. Wing dimorphisms and the evolution of

migratory polymorphisms among the Insecta. Am. Zool. 31:243–251.———. 1999. Predicting correlated responses in natural populations: changes

in JHE activity in the Bermuda population of the sand cricket, Gryllusfirmus. Heredity 83:440–450.

———. 2001. The genetic basis of dispersal and migration and its conse-quences for the evolution of correlated traits. Pp. 191–202 in C. Clobert,J. Nichols, J. D. Danchin and A. Dhondt, eds. Causes, consequences andmechanisms of dispersal at the individual, population and communitylevel. Oxford Univ. Press, Oxford.

———. 2007. Laboratory evolution of the migratory polymorphism in thesand cricket: combining physiology with quantitative genetics. Physiol.Biochem. Zool.: In press.

Roff, D. A., and T. A. Mousseau. 1987. Quantitative genetics and fitness:lessons from Drosophila. Heredity 58:103–118.

———. 2005. The evolution of the phenotypic covariance matrix: evi-dence for selection and drift in Melanoplus. J. Evol. Biol. 18:1104–1114.

Roff, D. A., S. Mostowy, and D. J. Fairbairn. 2002. The evolution of trade-offs:testing predictions on response to selection and environmental variation.Evolution 56:84–95.

Roff, D. A., T. Mousseau, A. P. Møller, F. d. Lope, and N. Saino. 2004.Geographic variation in the G matrices of wild populations of the barnswallow. Heredity 93:8–14.

Rose, M. R., H. B. Passananti, A. K. Chippindale, J. P. Phelan, M. Matos, H.Teotonio, and L. D. Mueller. 2005. The effects of evolution are local:evidence from experimental evolution in Drosophila. Integr. Comp. Biol.45:486–491.

Roux, F., and X. Reboud. 2005. Is the cost of herbicide resistance expressed inthe breakdown of the relationships between characters? A case study us-ing synthetic-auxin-resistant Arabidopsis thaliana mutants. Genet. Res.85:101–110.

Rutledge, J. J., E. J. Eisen, and J. E. Legates. 1973. An experimental evaluationof genetic correlation. Genetics 75:709–726.

Sax, K. 1923. The association of size differences with seed-coat pattern andpigmentation in Phaseolus vulgaris. Genetics 8:552–560.

Schadt, E. E., S. A. Monks, T. A. Drake, A. J. Lusis, N. Che, V. Colinayo, T.G. Ruff, S. B. Milligan, and C. G. Lamb, J. R., P. S. Linsley, M. Mao, R.B. Stoughton, S. H. Friend. 2003. Genetics of gene expression surveyedin maize, mouse and man. Nature 422:297–302.

Scheinberg, E., A. E. Bell, and V. L. Anderson. 1967. Genetic gain in pop-ulations of Tribolium castaneum under uni-stage tandem selection andunder restricted selection indices. Genetics 55:69–90.

Schluter, D. 1996. Adaptive radiation along genetic lines of least resistance.Evolution 50:1766–1774.

Sen, B. K., and A. Robertson. 1964. An experimental examination of meth-ods for the simultaneous selection of two characters, using Drosophilamelanogaster. Genetics 50:199–209.

Sharp, G. L., W. G. Hill, and A. Robertson. 1984. Effects of selection ongrowth, body composition and food intake in mice. I. Responses in se-lected traits. Genet. Res. 43:75–92.

Sheldon, C. C., D. T. Rouse, E. J. Finnegan, W. J. Peacock, and E. S. Den-nis. 2000. The molecular basis of vernalization: the central role ofFLOWERING LOCUS C (FLC). Proc. Nat. Acad. Sci. U.S.A. 97:3753–3758.

Sheridan, A. K., and J. S. F. Barker. 1974. Two-trait selection and the ge-netic correlation. II. Changes in the genetic correlation during two-traitselection. Aust. J. Biol. Sci. 27:89–101.

EVOLUTION MAY 2007 1031

PERSPECTIVE

Shook, D. R., and T. E. Johnson. 1999. Quantitative trait loci affecting survivaland fertility-related traits in Caenorhabditis elegans show genotype-environment interactions, pleiotropy and epistasis. Genetics 153:1233–1243.

Soriano, V. J. M. 2000. Components of variation of polygenic systems withdigenic epistasis. Genet. Mol. Biol. 23:883–892.

Stearns, S. C., M. Ackermann, M. Doebeli, and M. Kaiser. 2000. Experimentalevolution of aging, growth, and reproduction in fruitflies. Proc. Nat.Acad. Sci. U.S.A. 97:3309–3313.

Steppan, S. J., P. C. Phillips, and D. Houle. 2002. Comparative quantitativegenetics: evolution of the G matrix. TREE 17:320–327.

Sumner, S., J. J. M. Pereboom, and W. C. Jordan. 2006. Differential geneexpression and phenotypic plasticity in behavioural castes of the prim-itively eusocial wasp, Polistes canadensis. Proc. R. Soc. B Biol. Sci.273:19–26.

Suzzoni, J. P., L. Passera, and A. Strambi. 1980. Ecdysteroid titre and caste de-termination in the ant, Pheidole pallidula (Nyl.) (Hymenoptera: Formi-cidae). Cell. Mol. Life Sci. 36:1228–1229.

Swallow, J. G., and T. Garland Jr. 2005. Selection experiments as a tool inevolutionary and comparative physiology: insights into complex traits—an introduction to the symposium. Integr. Comp. Biol. 45:387–390.

Tabery, J. G. 2004. The “Evolutionary Synthesis’’ of George Udny Yule. J.Hist. Biol. 37:73–101.

Taylor, M., and R. Feyereisen. 1996. Molecular biology and evolution ofresistance to toxicants. Mol. Biol. Evol. 13:719–734.

Tarca, A. L., R. Romero, and S. Draghici. 2006. Analysis of microarray exper-iments of gene expression profiling. Am. J. Obstet. Gynecol. 195:373–388.

Tian, D., M. B. Traw, J. Q. Chen, M. Kreitman, and J. Bergelson. 2003.Fitness costs of R-gene-mediated resistance in Arabidopsis thaliana.Nature 423:74–77.

Turelli, M., and N. H. Barton. 1994. Genetic and statistical analyses of strongselection on polygenic traits: what, me normal? Genetics 138:913–941.

———. 2006. Will population bottlenecks and multilocus epistasis increaseadditive genetic variance? Evolution 60:1763–1776.

Ungerer, M. C., C. R. Linder, and L. H. Rieseberg. 2003. Effects of geneticbackground on response to selection in experimental populations of Ara-bidopsis thaliana. Genetics 163:277–286.

Ungerer, M. C., and L. H. Rieseberg. 2003. Genetic architecture of a selectionresponse in Arabidopsis thaliana. Evolution 57:2531–2539.

Valenzuela, R. K., S. N. Forbes, P. Keim, and P. M. Service. 2004. Quantita-tive trait loci affecting life span in replicated populations of Drosphilamelanogaster. II. Response to selection. Genetics 168:313–324.

Vaughn, T. T., L. S. Pletscher, A. Peripato, K. King-Ellison, E. Adams, C.Erikson, and J. M. Cheverud. 1999. Mapping quantitative trait loci formurine growth: a closer look at genetic architecture. Genet. Res. 74:313–322.

Vermeulen, C. J., and R. Bijlsma. 2006. Changes in genetic architecture duringrelaxation in Drosophila melanogaster selected on divergent virgin lifespan. J. Evol. Biol. 19:216–227.

von Butler, I., J. Aumann, and F. Pirchner. 1986. Antagonistic selection for cor-related body weight traits in different mouse populations. Theor. Appl.Genet. 71:698–702.

Vuylsteke, M., F. van Eeuwijk, P. Van Hummelen, M. Kuiper, and M. Zabeau.2005. Genetic analysis of variation in gene expression in Arabidopsisthaliana. Genetics 171:1267–1275.

Wade, M. J. 2002. A gene’s eye view of epistasis, selection and speciation. J.Evol. Biol. 15:337–346.

Wade, M. J., and C. J. Goodnight. 1998. The theories of Fisher and Wright in thecontext of metapopulations: when nature does many small experiments.Evolution 52:1537–1553.

Walsh, B. 2001. Quantitative genetics in the age of genomics. Theor. Pop.Biol. 59:175–184.

Weigensberg, I., and D. A. Roff. 1996. Natural heritabilities: can they bereliably estimated in the laboratory. Evolution 50:2149–2157.

Weinig, C., and J. Schmitt. 2004. Environmental effects on the expression ofquantitative trait loci and implications for phenotypic evolution. Bio-Science 54:627–635.

Westoby, M., E. Jurado, and M. Leishman. 1992. Comparative evolutionaryecology of seed size. TREE 7:368–372.

Wheeler, D. E. 1986. Developmental and physiological determinants of castein social hymenoptera: evolutionary implications. Am. Nat. 128:13–34.

———. 1991. The developmental basis of worker caste polymorphism in ants.Am. Nat. 138:1218–1238.

Whitlock, M. C., P. C. Phillips, F. B. G. Moore, and S. J. Tonsor. 1995. Multiplefitness peaks and epistasis. Ann. Rev. Ecol. Syst. 26:601–29.

Wilson, A. J., D. W. Coltman, J. M. Pemberton, A. D. J. Overall, K. A. Byrne,and L. E. B. Kruuk. 2005a. Maternal genetic effects set the potential forevolution in a free-living vertebrate population. J. Evol. Biol. 18:405–414.

Wilson, A. J., L. E. B. Kruuk, and D. W. Coltman. 2005b. Ontogenetic patternsin heritable variation for body size: using random regression models ina wild ungulate population. Am. Nat. 166:E177–E192.

Wilson, A. J., J. M. Pemberton, J. G. Pilkington, D. W. Coltman, D. V. Mif-sud, T. H. Clutton-Brock, and L. E. B. Kruuk. 2006. Environmental cou-pling of selection and heritability limits evolution. PLoS Biol. 4:1270–1275.

Wilson, R. H., T. J. Morgan, and T. F. C. Mackay. 2006. High-resolution map-ping of quantitative trait loci affecting increased life span in Drosophilamelanogaster. Genetics 173:1455–1463.

Wolfinger, R. D., G. Gibson, E. D. Wolfinger, L. Bennett, H. Hamadeh, P.Bushel, C. Afshari, and R. S. Paules. 2001. Assessing gene significancefrom cDNA microarray expression data via mixed models. J. Comput.Biol. 8:625–637.

Wright, S. 1977. Evolution and the genetics of populations: a treatise in fourvolumes. Vol. 3 Experimental results and evolutionary deductions. Univ.of Chicago Press, Chicago.

Wu, P., T. -X. Jiang, S. Suksaweang, R. B. Widelitz, and C. -M. Chuong. 2004.Molecular shaping of the beak. Science 305:1465–1466.

Xu, S. 2003. Theoretical basis of the Beavis effect. Genetics 165:2259–2268.

Yi, N., D. K. Zinniel, K. Kim, E. J. Eisen, A. Bartolucci, D. B. Allison, andD. Pomp.2006. Bayesian analyses of multiple epistatic QTL models forbody weight and body composition in mice. Genet. Res. 1–16.

Yule, G. U. 1906. On the theory of inheritance of quantitative compoundcharacters on the basis of Mendel’s laws—a preliminary note. Report ofthe 3rd International Conference of Genetics:140–142.

Zera, A. J., and L. Harshman, G. 2001. The physiology of life-history trade-offsin animals. Ann. Rev. Ecol. Syst. 32:95–126.

Zijlstra, W. G., M. J. Steigenga, P. Brakefield, and B. J. Zwaan. 2003. Simul-taneous selection on two fitness-related traits in the butterfly Bicyclusanynana. Evolution 57:1852–1862.

Associate Editor: M. Rausher

1032 EVOLUTION MAY 2007