An Application of Index Selection to the Improvement Of

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AN APPLICATION OF INDEX SELECTION TO THE IMPROVEMENT OF

SELF.POLLINATED SPECIES

J. PESEK' and R. J. BAKERResearch Statiort, Canada Deportment of Agriculture, Winnipeg 19, Canada.

Contribution No. 399, received November 7, 1969'

ABSTRACTResults of a genetic study of four quantitative desired genetic gains rather than relative eco'characters in-a cross of two cultivirs of Tri- nomic w;ights o=f traits, is explained in detailticunt aestivum L. em Thell. indicated that and applied to selection for maturity, heightheritability of yield was lower than the herita- and yield from a hybrid population ofbilities of maturity and height and that inter- wheat. The methods and problems of usingactions between genotypic- effects and year index selection in self-polfinated species areenvironmental effects were nonsignificant. The discussed.modified seleclion index method. based uoon

INTR.ODUCTION

Smith (16) first suggested the use of the concept of a "discriminant function" as

a logical and systematic manner of selecting plant lines to improve several quanti-

tative characters simultaneously. He applied this technique to wheat. Since thattime, this method has become known as index selection and has been used ex-

tensively in the improvement of various animal species. The application of indexselection to the improvement of self-pollinated plant species, for which it was

first suggested, has been rare.The object of index selection is to maximize the average "genetic worth" of

a population. Genetic worth is the sum of products of the genotypic values of themeasured characters and their respective "economic weights". Thus, genetic worthreflects the overall value of a particular line or individual. Economic weightsexpress the relative importance of one trait to another in making up the overallvalue of a line. Since genotypic values cannot be observed or measured directly,it is necessary to develop a linear function of the observable phenotypic values

which will best discriminate among genotypes of different genetic worth. Flence,

the original term for index selection was "a discriminant function for plant selec-tion". Once a selection index has been constructed, it is possible to predict thedifference between the mean of a proportion selected by truncation and the meanof the original population for each character. This "expected response" may beused to evaluate beforehand the consequences of several alternative selection pro-cedures. "Observed response" implies that the selection has already been done.

Selection indexes may be used as a basis for the simultaneous improvementof more than one character by selection, or for enhancing the effectiveness ofselection for one character by incorporating information on one or more secondarycharacters. The latter use has been most common in plant breeding (I,'7,9,II, 13,15) because there is no need to assign economic values to all traits in thisapplication. To improve the primary trait, such as yield, as much as possible,the economic values of the secondary traits are all set al zeto and that of theprimary trait as unity. This method has generally permitted good results in selec-tionforyield (7, 11). Exceptions were noted by Panse and Khangonker (13) incotton and Abraham ( 1) in rice. For improvement of several characters simul-taneously, however, it is necessary to assign economic weights to the characters

lPostdoctorate Fellow (permanent address: Research Institute for Basic Agrotechnique, Brno-Hrusovany, Czechoslovakia).

Can. J. Platrt Sci, 50: 267-276 (May 1970)

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268 CANADIAN JOURNAL OF PLANT SCIENCE

and this is often very elaborate and in some cases almost impossible. For instance,

the economic value of a character may depend upon its reaching a certain threshold

value. Protein content in wheat must be above a certain minimum level before

a line is acceptable. Above that level, protein content becomes relatively less

important than yield. Since Smith's (16) paper, two other approaches to thediscriminant problem in selection have been proposed but both incorporate the

economic weights concept. Kempthorne and Nordskog (10) developed the theory

of restricted selection indexes and applied it to selection in poultry. Tallis (17)

derived a further modification in the terms of an "optimum genotype". These

modifications allow for the maintenance of one or more characters at the level of

the population mean or at some pre-chosen optimum level. Difficulties in assign-

ment of relative economic weights led us to the problem of ranking measures of

several quantitative attributes when nothing is to be assumed about economic

weights. The concept of "desired genetic gains" (14) which removes all needs forassigning relative economic weights provides one answer.

In this study we report the results of a quantitative genetic study in a crossof two cultivars of hard red spring wheat, Triticum aestivum L. em Thell., and

apply the modified selection index method to selection in this cross.

MATERIALS AND METHODS

The parental cultivars for this study were 'Garnet' and 'Kenya 360.H'. With

respect to the four characters measured in this study, Gamet headed earlier, ripened

earlier, had shorter straw, and was lower yielding than Kenya 360.H. Lines were

advanced from single seeds in the F, generation up to single seeds in the F" genera-

tion by single seed descent, as suggested by Goulden (6). Seed from random F.

plants was bulked and grown as plots to produce the F, generation. Bulk seed

from 48 F, plots and the two parental cultivars was sown in replicated yield trials(two replicates) at Brandon and Regina in 1961 . Seed harvested from the yield

plots was again sown at these two places in 1968. Days to heading (DH)' days

to ripening (DR), height in centimeters (HT) and yield in decagrams per plot(Y) were recorded for all plots in all trials.

A combined analysis of variance and covariance was performed on the data.

Mean squares for each character and mean cross products for each pair of charac-

ters were calculated for sources of variation relating to genotypes, years, places,

the interactions, and error. Components of variance and covariance were then

estimated as outlined by Comstock and Moll (4). Phenotypic and genotypic cor-

relations were estimated by the methods outlined by Baker et al. (3).

Pesek and Baker's (14) modification of the theory of index selectioninvolves

calculation of index coefficients accordins to the following matrix formulation:

b:G-th. ?z

where b is the vector of index coefficients, G-' is the inverse of the genotypic

variance-covariance matrix, /z is the vector of desired genetic gains and p/zis lhereciprocal of the selection differential in standard units.

Since p/z is constant for any experiment, an equivalent solution can be ob-

tained from:

b:G-lh.

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PESEK AND BAKER-INDEX SELECTION

The above expression represents the following set of simultaneous equations forthe specific example of four characters:

b*n I bzgtz I ba*z * bqu -- ht

hgrz I bzgzz -f 6:9:: -f bqzt : hz

bqn I hzgzz * b;Brr I bqzq : htb$rt I bz7z+ I b*tr * b4++ : h+

where the bo's are the index coemcients to be solved for, g,,, is the genotypic co-variance between characters i and j, and ho is the desired genetic gain for the i'ncharacter.

After estimating the genetic components of covariance, the b,'s were evaluatedfor two different sets of desired genetic gains. The resulting b,'s were then com-bined with the character means of each of the 48 lines to sive a selection indexfor each line of the form:

Ie : brXLn I brXre f- btXre I brXt*

/" being the index value of the k'" line and X,,,, X",,, X",, a;fld X,* being the meanvalues of the four traits for that particular line. The five lines having the highestindex values were chosen as the selected population, and their means were com-pared with those of the original population and with the means of the parentalcultivars.

RESULTS

Estimates of components of variance and heritabilities of each of the four charactersare given in Table 1. Heritability has been expressed on a line mean basis, themean being taken over two replicates at each of two places in each of two years.

An approximate test of significance for a difference from zero is given by com-paring an

estimate to twice its standard deviation. By this criterion, it is apparentthat the genotype x year interaction component of variance is unimportant for allcharacters. For yield, the genotype x place interaction component is nonsigni-ficant and the genotype component of variance would be judged as just approachingsignificance. The heritability estimates indicate that relative yields of lines aremore dependent on environmental influence than the other three traits.

The genotypic and phenotypic correlations among the four characters arelisted in -Iable 2. All phenotypic correlations are positive and significant at the77o leveI of probability. The genotypic correlations between yield and the othercharacters are larger than the corresponding phenotypic correlations.

Table 1. Estimates of variance comporlents and heritabilitl. (n'rean basis)

Componentx I)a1s to head Dill's to ripen Height (cm) Yield (dkg)

269

62,62,^,

6'ctrn2

o2"

h'(%)

7 .03+t.670.18+0.152 .01+0.,190.41+0 180.93+0.09

8+.2

13.01+3.070. 28+0.562.+1+0.921 .35+0. 784.78+0.48

85. 1

5+.91+ 5.033 .03+3. 293 . 81+3 .413 .03+ 1 .689.93+ 1 .03

91 .0

7 .94+1 .O23.26+3 -792.10+3.6r

12 .74++ -8021 .7t+2.18

48. 1

1t2s : component of variance due to genotypic difierences among lines, 6t I : component of variance due to theinteraction of genotypic and year effects, dtr, : component of variance due t; the inteiacLion of genotvpic and placeefiects, dzrrJ : component of variance due to the second order interaction of genotypes, places and years, t2e : thevariance due to plot-to-plot environmental variations.

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Table 2. Genot-vpic and phenotypic correlations among four traitsJ

DH DR HTY

Da1's to head (DH)

Da.vs to ripen (DR)Height (HT)Yield (Y)

0.980.570.6+

0.91+*

0.570. 74

0..48*x

0.52*x0.7+

0.26xx

0.32**0. 55**

t*Significant at th.e 17o lcvel ni probrbilitt.fPhenotypic correlarjons abor e the djagonal. gPnot] l ic belo\'.

The flrst example of application of the modified method (14) of index selec-

tion was based on desired gains of: (1) a decrease of 2.75 days (5% ) in days to

heading, (2) a decrease of 4.83 d,ays (5%) in days to ripen, (3) a decrease of

1.63 cJntimeterc (2Vo ) in height, and (4) an increase of 3.25 decagrams (about

3.2 bu/acre, i.e., to%) in yield. By using these values and the estimates of

genetic covariances and variances in the four linear equations, the following index

ioefficients were obtained: b,: 15.70, b,: -14.14, b": -1.97, and bn: 6.84.Thus, the index value of a line is obtained by multiplying its average days to head

by 15.70, subtracting 14.14 times the number of days to ripen, subtracting 1.97

times the height in centimetels, and adding 6.84 times the yield psr plot i1 dega;

grams. For the index value of line 1, which averaged 52.8 days to head, 95.1

days to ripen,82.6 centimetels in height and 39.92 decagrams per plot in yield,

one obtains:

1s.70(52.s) - 14.14(95.1) - 1.97(82.6) + 6 81(39.92) : -405 4

Desired genetic gains for the second example allowed for some delay in

maturity in hope of a greater increase in yield. Thus, the desired genetic gains

were a 5Vo inuease in days to heading(2.1

5),a 5Vo increase in days to ripel.

(4.83), a IVo decrease in height (-0.81) and a 2o7o increase in yield (6.50).

The index coefficients werei br : 5.20, b": -4.42, b": -I.37, and b' = 3'58'

The index value of the first line was:

5,20(s2.8) - 1.42(95.1) - r.37(82.6) + 3.58(39.92) : -116 0

The mean values for each character and the two index values for each line are

presented in Table 3. The index values have all been made positive by subtracting

their minimum value.

The five lines with the highest index value were then selected, and the means

of the various characte$ were compared with what would have been expected on

a theoretical basis and with the original parents of the cross. These data are

summarized in Table 4. The ranking of selected lines indicates that use of a

selection index often leads to the selection of lines which do not excal in any

one character but tend to be more intermediate. Yield, which has the most

weight in the desired gains, is represented by lines which tend to rank high. Ex-

pected gains, calculated by prediction equations (5, 8), are distributed in proportion

to the desired gains. However, most of the realized gains depart from those ex-

pected both in sign and magnitude.

DISCUSSION

Application of index selection to self-pollinated species may meet with the unique

situation of selection among homozygous lines where the selected line or lines will

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PESEK AND BAKER-INDEX SELECTION

-fable 3. 'fable of means and index values of lines and parents

271

Line No

Height

(cm, Index B

Da.vs to Da.vs to

head ripen

Yield

(dkg) Index Ai2

3

45

67

8

910

11

72

l.)

7+

1.)161n

18t9202122

23nt

2526272829

30JI

3233343536

38394041A'

+.1

444J

46

48

Mean

GarnetKenya 360.H

52 .8

55. 8

51 .254. 8

.)o . .')

.)+.r54.4.)/.652 .854. 1

52 .665.258 .'i.50. (,53.253 .452 .053.452.0JI. I

52.+5,1 .855.853.4.)J. Z

J.). I

53 .553. 1

53. 1.).). I

58. 5

5+.256.454.6.).) . o

62.6s3.551 .154.558.056.453.052.954.5

52.959.457 .9

.).). t,

51.961 .1

95. 1

100. t)

97 .495.298.497 .69+ -r9'1.1

101 .994.095 .,1

92 .5108.898.898.096.1.93.992.892.691 .492 .195.095 .496.993 .6

100.599 .991 .296.4

95 .095.8t02.295.996.098. 8

98.6105.695. 8

93.295.299 .297 .293.294.493. 1

91 .9i01.1i00.8

96.6

91 .6107.4

82.686.485 .3tJ.l

85. 1

80.873.785. 1

83 .380.881 .07+.282.882.86.) ..i80.076.478.5tr.l77.776.780.388.682 .377.281 .5

80.882.8

81 .087.993.086 .981 .092.786.683 .676 .570.9

80. 8

7+.975.281 .380.881 .589 .485. 1

81 .3

39 .9241 .6834.9835.0833.51.)r.lt29.2031 .8829.413t.6129.7529 .8933.7930.8832.9533 .0530.3232.8126.0633 .6533.3533 .0639.1636.99.)l . Jr26.7930.7633 .3932 .05

33 .4829 .9239 .9530. 75

32.3+37 .9630.7930. 19

25.7626.9529.06.tl -.).)32.3529 .5237.7935 .36

31.0036. 11

28.90

32.51

27 .9+45. 58

126.+133.8t01 .780.262.396.6

105. 1

105. 7

35 .488. 8

76.0107 .985 .099.782.576.699.1

105.797 .9

132.8t2+.4

79 .1140 .4128.5110.0

0.041 .5

i09.058.4

91.595.265.9

12t.468.950.463.342.760. 990 .4

103.2116.499.8

125.8153 .7774.2105 .645.5

57 .060.340.940.226.338.241 .937 .+1+.234.628 .143.038.637 .032.033 .539 .343.t36.553 .351.033.95,/. t.)+.+43.90.0

zr.t43.621 .2

38.022.741 .021 .946.629.017.825.315.226.1JJ. J41 .949 .739.2.)+. /

60.7

4t.7+r .7l.l . .t

25.959.0

81 .3111 .5

81 .887 .6

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PESEK AND BAKER-INDEX SELECTION 273

be the final product of selection. We see no value for index selection in this in-stance, since the goals of the program will depend upon what is available forselection and since evaluation of the final product is already complete. Theeffectiveness of index selection will be useful in programs of recurrent selection.cycles

ofrecurrent

selection can be obtained by ielecting a portion of the popu-lation and recombining the genetic material of tie selected portion to form u tre*population which is to be the foundation of a new cycle o1 selection.

At first look, the large discrepancies between expected and realized gains raisedoubt as to the validity of the general theory of index selection. Howiver, esti-mates of both expected and realized, gains ire subject to error, the error of thedifference thus being compounded. A minimum estimate of the standard deviationof the difference between the expected and. realized gains can be obtained bytaking the standard deviation of the realized gains as (V/s + v/4g),', where itis the estimate of the phenotypic variance of line means. Having done this, thedifferences between realized, and expected gains all fall within thJ range of twicetheir standard

deviations. . The discrepancies between realized, and exp"ected gainsare thus well within the limits of random environmental variability und th"rJfor"should not discredit index selection methods.

The sizes of the expected gains deserve comment, for they are small relativeto the gains that are desired of this particular wheat cross. Aimitting some levelof error.inthese expectations, it is s?iil clear that several cycles of selection wouldbe required to obtain the desired results. The realized gain estimated for yieldwas greater than the expected gain. The large error associated with this measure-ment, however, casts doubt on comparisons oirealized with expected gains for yield.

. As will always be !rye in the application of this method (14), the exp-ectedgains are a constant multiple of the desired gains. Thus, one'would

"*p""t

thut

the desired gains should be obtained if ind& selection is continued foi enoushcycles. This will not be true in actual practice if pleiotropic effecrs impose lirii-tations on the gain that can be realized.. If this should be the case, one wouldobserve changes in genetic parameters during cycles of selection. The nature ofthese changes would indicate whether the deiired gains could be achieved.

- .It tl interesting to ask what economic weights would have to be assigned toobtain the same selection results as are obtainJd by the modifled method, whichbypasses this step. By using the relation pb = da of conventional theory andinserting the index coefficients of the first example (b) and the phenotypic (p) andgenotypic (G) variance-covariance matrixes, it is possible to esiimate the economicvalues (a) fhat would have resulted in identical expectations. For the first ex-

?-pl-"' the equivalent economic values would have been 2.0 for days to head,, -2.2for days to ripen, -0.3 for height in centimeters and 1.0 for yleld per plot indecagrams. These values appear to be nonsense from un e.orro-i" point oi view,but do serve to indicate our inability to consider as a whole the genetic inter-relationships among four traits.

The equivalent economic values for the second example, in spite of changes inselection aims, are similar to those of the first except for a general reduction inmagnitude._ Il may also be seen that the index coefficients oflhe second exampleare similar both in sign and magnitude to those of the first. If we take into accor]ntthe large positive correlations among all four characters and express our two goalsas attempts to decrease three (or one) characters and increase the other on"- (ot

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three), we can see that the insensitivity of the index coefficients is due to tho

manifold interrelationrhip, u-ong the characters. This is further demonstrated

by noting that days to ilead unJ duy, to ripen are given.p,o,ttiiu"

and negative

weights, respectively, so that their combined influence on yield is not detrimental

to the goals of the Program.Such considerations raise doubt as to whether an early maturing, high yielding

cultivar could be a.u"top"a from this cross. one would need several cycles of

selection to reach tn" !6uf. Palmer (12) has indicated that recurrent selection

holds great promise foi ttre breeders of self-pollinated crops as far as any one

character is concerned. This is no less true for the simultaneous improvement. of

several quantitative characters. In our case, his procedure would involve selecting

the two best lines with regard to index values and intercrossing to start a new

cycle. with the method used in the present study, each.cycle.would require at

least five years. Hence, the overall program would be prohibitively time consuming

and methods of shortening the cycle time would have to be devised.

A modification of thi"s type of recurrent selection can be suggested inthe light

of Baker's results (2), which indicate that intermating in a self-pollinated crop

such as wheat or barley is technically feasible. Rather than selecting just the best

two lines for intercrossing, several lines could be intermated to produce a founda-

tion population for u n"# cycle of selection. This procedur-e would also help to

reduce the random genetic'deviations associated with small sample sizes (2)'

One would be advised to start a recurrent selection program with- divergent gen-etic

material and calculate selection indexes based on long term goals of the breeding

program. Lines excelling in one or--several traits could be extracted from the

iroltu- and evaluated foi ability to fi1l immediate needs during any cycle. Selec-

tion of lines to start the next cycle would, however, be on the basis of the index

system, which tends to retain individuals whose performance inrespect to numerous

u'Auptiu" traits is close to the population means, and tends to exclude those with

extreme expression of a single triit, ut can be seen from rank values in Table 4.

From our examples it is clear that the main requisites for using index selectiort

are quantitative data, estimates of genetic parameteis and a statement of the goals

of th" progru-. Ttre first requirerient m"itts that visual ratings such as "good" or

,,bad,,'muit be replaced ty ratings on a suitable scale. If the data for a given

trait are discontinuour (..g.ratin!'s of 1 to 5) or if the trait is controlled by few

genes, one should anticipite sigriificant deviations from theoretical expectations'

Methods of estimating g"tt.1i" parameters necessaly for construction of selec-

tion indexes fall into four" Jategories analogous to those employed in estimating

genetic variances for one trait] They may be derived -from(l) regression of

progeny means on parental values for all possible combinations of traits' (il)differences between genetically homogeneous and heterogeneous populations,.(lli)

data from F, and bJckcross populations, and (iv) combined variance-covariance

analysis. In the modified p"iig."" method of selection, as used here, it is natural

to replicate essentially homozygous genotypes over several environments which

slows down cycle time. Nonsignincant estimates of genotype T yeq variance in

this study uod io another (3) iniicate that the cycle time could be reduced by one

year by testing in one instead of two years'-Intergeneration comparisons, as between F, and Fn, constitute a form of repli-

cation *oittty of investigation relative to early generation selection' These com-

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PESEK AND BAKER-INDEX SELECTION 275

parisons afford estimates of genetic variances and covariances in much the same

way as animal breeders obtain information necessary for the application of indexselection. Such estimates could be obtained in early generations and thus shortenthe time required for each cycle of a recurrent selection program. Once estimatesof genetic parameters are available, it is merely routine to incorporate the desired

gains of the selection program into a selection index that constitutes an objectivebasis for the simultaneous imorovement of ouantitative characters.

It should be noted that bur method can also be used for simultaneous indexselection of a primary trait (say yield) along with selection of a set of secondarytraits (components of yield). If no information is available for the suitable assign-ment of desired gains in the secondary traits, the desired responses for each traitcan be simply derived from the formula:

, li'tj : rij!*_

r,

where subscripts i, j refer to primary and secondary traits respectively, h's atedesired gains, g's the genetic variances of the traits and r is the genetic correlationbetween traits i and j.

Selection for quantitative traits is complicated by qualitative characters suchas disease resistance. For example, can disease reaction, which is simply in-herited, be incorporated into a selection index? Of course such factors cannotbe incorporated, but it is possible to apply the methods of index selection to thoselines that have been proven to be disease resistant. There is a distinct possibility,however, that selection for disease resistance will have an adverse effect on subse-quent improvement of quantitative traits. For example, in cases of repulsionlinkages between genes for resistance and genes for yield, which might be expectedin a cross between a high yielding cultivar and a disease resistant cultivar, selection

for disease resistance would likely reduce the mean yield. Hence, greater improve-ment would be necessary to attain the original goals. Research on interrelation-ships of qualitative and quantitative characters is needed. If one were to adopt a

long term recurrent selection program for quantitative traits, it might be ad-vantageous to select first for quantitative traits under disease-free conditions and

subsequently to introduce those genes necessary for survival by backcrossing.The modified index theory introduced by Pesek and Baker (14) and pre-

sented here in terms of two worked examples should prove useful to those workersinvolved directly in the improvement of economic species. The method combinesthe goals of the breeder with the genetic restrictions of the population with whichhe is working, into an objective rule for selection. The necessary calculations are

difficult if more than four or flve characters are involved, but no more so than themethod of Smith (16) and much less so than the methods of Tallis (17) andKempthorne and Nordskog (10). With access to electronic computers, the matrixmanipulations are routine.

This new modification, besides eliminating the need for assignment of eco-nomic weights, can replace the methods of Tallis and of Kempthorne and Nordskog.To replace the restricted index method of Kempthorne and Nordskog (10), onespecifies zero desired genetic gain for the traits to be restricted. By specifying adesired genetic gain which will result in the optimum being approached, the opti-mum genotype index method (17) can be approximated. If a breeder should

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want to realize certain restrictions in the first cycle of selection, this method would

be inferior in that the restrictions are not realized at the expense of the improve-

ment in other characters. This criticism can be overcome adequately by calcu-

lating several sets of index coefficients corresponding to difierent sets of desired

gainJ, and comparing the gains to be expected by the use of each index'

ACKNOWLEDGEI\{ENTS

We gratefully acknowledge a Postdoctorate Fellowship from the National Research

Council of Canada held 6y the senior author during the course of this study' We

are indebted to Dr. A. e. Campbell of this station for providing data and for

comments on the manuscfipt. The data were collected by the cereal breeders of

the Brandon and Regina Risearch Stations, whose assistance we appreciate'

1. ABRAHAM T. P. 1953.

Vol. 18, p. 3 in Proc. 4th

F.A.O., Rome.

2. BAKER, R. J. 1968. Extent of intermating in selj-Pollinated species necessary to

counteract the effect of genetic drift. Crop Sci' 8: 547-550'

3.BAKER,R.J.,BENDELOW,V.M.andKAUFMANN,M'L'1968'Inheritanceandinterrelationshrp u-ong li"fd and several quality traits in common wheat. Crop Sci' 8:

725-728.

4. COMSTOCK, R. h,. and MoLL, R. H. 1963. Genotype environmental interaction'

p. 164-196 iz Statisticaf genetics and plant breeding, NAS-NRC 982' Washington' D'C'

5. FINNEY, D. J. 1962. Genetic gains under three methods of selection. Genet. Res'

Camb.3: 417-423.

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