GENETICS AND BREEDING

Potential Improvements in Rate of Genetic Gain from Marker-AssistedSelection in Dairy Cattle Breeding Schemes

T.H.E. MEUWISSENResearch InstiMe for Animal Production ·Schoonoord"

PO Box 5013700 AM Zeist, The Netherlands

J.A.M. VAN ARENDONKDepartment of Animal Breeding

Wageningen Agricultural UniversityPO Box 338

6700 AH Wageningen, The Netherlands

ABSTRACT

The value of marker-assisted selectionin dairy cattle breeding schemes is pre­dicted by a detenninistic model. In theseschemes, associations between markersand milk production were assessed fromproduction records of daughters of agrandsire by a multiple regression modelwith random marker effects. By tracingmarkers from the grandsire to grandoff­spring, deviations of grandoffspring fromtheir full-sib family mean were predict­ed. Predictions of the within-family vari­ance of the grandoffspring accounted forby markers amounted to up to 13.3%.This figure decreased when the numberof daughters of the grandsire analyzeddecreased and, less markedly, when thedistance between flanking markers in­creased

Prediction of within-family deviationshardly improved rates of genetic gain inconventional progeny testing schemes;equal numbers of young bulls were bornannually. Genetic gain and improvementof genetic gain because of prediction ofwithin-family deviations were muchhigher in nucleus schemes. In theseschemes, with short optimized genera­tion intervals, conventional selection wasmainly for pedigree information and didnot use the within-family variance.Analysis of highly polymorphic markersin daughters of both grandsires ac­counted for 4.1 to 13.3% of the within-

Received June 17, 1991.Accepted February 11, 1992.

1992 J Dairy Sci 75:1651-1659

family variance, which increased rates ofgain by 9.5 to 25.8% and 7.7 to 22.4% inopen and closed nucleus schemes, re­spectively. Risk of breeding schemes,measured by the variance of the selectionresponse, was not increased by the use ofmarkers.(Key words: markers, selection, dairycattle, breeding schemes)

Abbreviation key: MAS = marker-assistedselection, MOET = multiple ovulation andembryo transfer, QTL = quantitative trait loci.

INTRODUCTION

In current animal breeding schemes, predic­tion of genetic differences between animals isbased on phenotypic observations, which de­pend on genetic and environmental factors.Restriction fragment length polymorphism (1),variable number of tandem repeats (12, 17),and polymerase chain reaction (19) make itpossible to identify genetic differences directlyat the DNA level. These differences, which arecalled genetic markers, are not likely to bequantitative trait loci (QTL) themselves, butthey may be linked to QTL (23). In a breedingscheme, use of phenotypic and marker datacould provide more information than pheno­types alone. When marker data are included inthe selection criteria, this process being re­ferred to as marker-assisted selection (MAS),accuracy of selection may be increased.Marker data can be collected early in life,allowing selection at an early age, and, in thisrespect, MAS is similar to juvenile indicatortraits (25).

The use of genetic markers in animal breed­ing involves four steps: 1) search for genetic

1651

1652 MEUWISSEN AND VAN ARENDONK

markers, 2) establishment of a linkage map ofthe markers, 3) detection of associations be­tween markers and QTL, and 4) use of marker­QTI.. associations in the breeding program.Herein steps 3 and 4 will be considered.

Marker and QTI.. associations may be foundby multiple regression of performance data onthe number of marker alleles present for allmarkers (14, 22, 21). This method requireslinkage disequilibria between markers andQTL across the population. Over generations,crossovers make linkage disequilibria small.The procedure is useful when the populationhas hybridized recently or when a large num­ber of markers are available, wliich increasethe size of the linkage disequilibria by increas­ing the probability of having a marker close tothe QTI.. (14).

Even loose linkage will cause linkage dise­quilibria within families, which may be usedfor within-family selection (23). Geldermann(7) proposed the term "chromosome segmentsubstitution effect" to account for possiblelinkage of a marker to several linked QTI... Theeffect of the chromosome segment is due toone or more QTI.., which lie on that chromo­some segment. More than one QTI.. constitutea cluster. Markers can be used within familiesto detect which of the two parental chromo­some segments is inherited by an individual. Inthis way, markers explain part of the singleparent Mendelian sampling variance (4). Thismay be especially useful in breeding schemeswith short generation intervals, by which selec­tion among full sibs is inaccurate or random,e.g., multiple ovulation and embryo transfer(MOET) nucleus schemes (18).

The aim of this paper is to assess potentialextra genetic gain that was due to MAS inconventional progeny testing and open andclosed MOET nucleus schemes. It is assumedthat the number of markers available is rathersmall, and, hence, within-family linkage dise­quilibria are used to predict deviations fromthe family mean. First, the fraction of thewithin-family variance explained by markers isestimated. Second, the additional genetic gainfrom prediction of within-family deviations isassessed.

MATERIALS AND METHODS

Statistical Analysis

Associations between the clusters of QTLcontaining one or more QTL and the markerswill be estimated separately within each familybecause effects of QTL clusters and linkagephase may differ among families. The QTLclusters stem from the grandsire, an exten­sively used bull (Table 1). He and many of hisdaughters will be scored for their marker geno­types. Also, mates of the grandsire will bescored if necessary for tracing markers fromgrandsire to daughter. The production recordsof the daughters of the grandsire are analyzedby the multiple regression model:

Y = JlI + Zm + e, [1]

where Y=a vector of production records of thedaughters of the grandsire; I = a vector ofones; m = a vector of differences betweeneffects of marker alleles at the marker loci; Z

OffsprinrGrandsireYear

TABLE l. The marker-assisted selection breeding plan with generation intervals of 2 yr. The grandoffspring are selectedfor their marker genotype based on marker and quantitative trait loci (Q1L) associations (assoc.) in the daughters.

Grand-offsprmg2

o123456

bornselected ----.~----------.,I .

'---bom '---bornselectOO-

start lactations L--oommarter-Q'n--assoc. ---information I selection

lCommercial daughtus of the grandsire resulting from AI services of the grandsire.

20ffspring of high genetic merit, i.e., nucleus offspring in nucleus schemes and young bulls in progeny testingschemes.

Iournal of Dairy Science Vol. 75, No.6, 1992

MARKER-ASSISTED SELECIlON 1653

= an incidence matrix linking differences be­tween marker alleles to production records:element ij is 1 if daughter i inherited the firstof the two marker alleles of locus j and zerootherwise (the numbering of the marker allelesis arbitrary but should be consistent across alldaughters of the grandsire); and e =is a vectorof error terms.

Differences between the effects of Q1Lhaplotypes formed by the Q1L situated be­tween two flanking markers are denoted byQ'ILj. The variance because of Mendelian

sampling of these Q1L haplotypes is .25Q1Lf.

The expectation of Q'ILj is zero, and the ex­

pectation of .25QTLf is .25~n: Because the

sum of the Mendelian sampling variances ofthe Q1L haplotypes equals the total variancedue to Mendelian sampling in offspring of the

grandsire's Q1L (.250;), ~1L=o;t({NM - 1)

Nc)' where 0;, NM, and Nc are the additive

genetic variance, the number of marker lociper chromosome, and the number of chromo­somes, respectively. This assumed that NM ~ 2(at least one marker bracket), two markers aresituated at the chromosome ends, markers areequidistant, the distribution of Q1L across thegenome is uniform, and double recombinationscan be neglected within a marker bracket. Fol­lowing methods of Fernando and Grossman (6)and Goddard (1991, unpublished), differencesbetween effects of marker alleles are treated asrandom effects in Model [1]. The variances ofy, m, and e are ZMZ' + R, M, and R, respec-

tively, where R = 0;1, and M is for one

chromosome with equidistant markers and onemarker at each chromosome end (Goddard,1991, unpublished):

2 11 4 1

1 4 11

~1L 6' [2]

1 4 11 2

for instance, Var(ml) = Var(UIQ1LI) =

E(uiQ1Li) - E2(uIQTLI) = E(ui)E(QTLi) =lhO'Q1L2, where ml is the effect of the first

marker, and UI is the fraction of the effectQTLI of the first QTL picked up by the firstmarker. If there is no QTL at the first bracket,QTLI = O. The rest of the effect QTLI ispicked up by the second marker. The fractionUI =(r - rl)/r, where r and rl are the recombi­nation rates between flanking markers and be­tween the first marker and the first QTL, andfraction UI is assumed to be uniformly distrib­uted between 0 and 1. This implies that doublerecombinations are neglected and that QTL areuniformly distributed over the genome. The

error variance 0; is approximately 0; - lho;,where 0; is the phenotypic variance.

The BLUP estimates of m are obtainedfrom Henderson's (10) mixed model equa­tions:

l'Z ] [jl] = [l'Y]Z'Z+M-la~ rn Z'Y·

The variance of rn is M - (Z'Z/o; + ~Irl.

The expectation of the elements ij of the sym­metric matrix Z'Z is

for j > i, and lhN, for j =i. For example, withfour flanking markers, the expectation of Z'Zis

[

1 (I - r) (I - r~ + r 2 (I - r)3 + 3(1 _ r)r 2 jIhN 1 (1 - r) (1 _ r)2 + r 2

1 (1 - r)

symm. 1

Prediction of WIthIn-Family DevIationsof Grandoffsprlng

It is assumed herein that the transmission ofall markers is traceable; i.e., markers arehighly polymorphic. For marker locus i, thepredicted genetic value of an offspring of thegrandsire is lqrnio where lq = 1 when theoffspring inherited the first allele at markerlocus i and let =0 when it inherited the secondThere are two possible genotypes for thegrandoffspring: 1) they inherited the marker of

Jownal of Dairy Science Vol. 75, No.6, 1992

1654 MEUWISSEN AND VAN ARENDONK

the grandsire of which the effect is estimatedor 2) they inherited the marker of the grand­dam, which has an intermediate effect. Here,QTL of the granddam are assumed to have, onaverage, the same genetic values as those ofthe grandsire. Hence, the predicted genotypicvalues of the marker locus i are kimh and Ihmhrespectively. 1be predicted family mean is.5(ki + .5)mh and predicted within-family devi­ations are (.5lq - .25)mi or -(.5lq - .25)mhwhen the grandsire's marker is inherited ornot, respectively. When p contains the factors(.5ki - .25) or -(.5ki - .25), which depend onthe marker genotype, p'", is the predictedwithin-family deviation of the grandoffspring.1be variance of this predictor is p'(M -(Z'Z/cr; + M-I)-I)p.

The size of the cattle genome is about 30 M(Morgan) distributed over 30 chromosomes.Hence, the average length of the chromosomesis 100 cM. The number of recombinationsbetween the markers on a chromosome followsa binomial distribution with a maximum of NM- 1 recombinations. If the number of recombi­nations is Nr, the number of p vectors possibleis (NM - 1)!/(Nr!(NM - Nr - I)!). Each pvector is defined by the sites of the recombina­tions. For example, with a recombination ratebetween the markers of 20 cM, i.e., six mar­kers on the chromosome of 100 cM (onemarker at each chromosome end), and recom­binations after the second and the fourth mark­er, p' = [.25, .25, -.25, -.25, .25, .25] or p' =[-.25, -.25, .25, .25, -.25, -.25], which provide

the same variance p'(M - (Z'Z/cr; + M-l)-I)p.

The average variance of the predictor is ob­tained by weighting the variances for all pvectors possible by their probabilities of occur­rence.

By tracing markers from both grandsires,the within-family variance explained by mar­kers will be doubled. In the following, theextra genetic gain from prediction of within­family deviations of grandoffspring will beassessed using marker information of bothgrandsires.

Prediction of Genetic Gain

For the prediction of genetic gain, the deter­ministic model of Meuwissen (15) was used.The model predicted genetic gain using selec-

Journal of Dairy Science Vol. 75, No.6, 1992

tion index theory. Selection indices includedall available information, including the in­dividual's performance, information from fulland half sibs, from the sire and the dam andtheir full and half sibs, and progeny perform­ances. Furthermore, the marker index p'lil wasincluded. The marker index predicted devia­tions within full-sib families and was not cor­related with sib and pedigree information. Itwas available when selection candidates werel-yr-<lld (fable 1) and for all selection paths,except the cows to breed cows path, in whichselection was random (fable 2). Correlationsbetween breeding value estimates of relativesdecreased because of inclusion of the markerindex. The variance of the marker index p'(M- (Z'Z/cr; + M-I)-I)p was assumed to equal 0,

.05, .10, or .25 times the within-family vari­ance.

The model accounted for variance reductionfrom selection, which included the Bubner ef­fect (2), and for reduction of selection differen-

TABLE 2. Parameters of the open and closed nucleus andconventional progeny testing schemes. I

Nucleus size or twice number of young 512bulls tested, I yr

Total number of cows. x loS 10Number of test records per young bull 100

(only in progeny testing scheme)Number of nucleus or bull-sires 8Number of nucleus or bull-dams 64Number of offspring per nucleus 8

or bull-damNumber of AI sires (used for commercial 30

cows)Selection of dams of commeccial cows RandomGeneration intervals are optimized

imposing the restrictionsOpen or closed nucleus schemes. yr 2-10Progeny testing scheme

Sire. yr 6-10Dam, yr 4-10

Involuntary culling ratesBulls, % 52Cows,% 3~

lMilk production data collection from all nucleus andcommercial cows.

2pive percent of the number of young bulls (samenumber for all age classes). Por use as nucleus or bull­sires, there is sufficient frozen semen available from (in­voluntary) culled bulls.

3nnrty percent of the number of cows present withinan age class.

MARKER-ASSISTED SELECTION 1655

TABLE 3. The fraction of within-family variance ofgrandoffspring predicted by marker analysis of bothgrandsires. The marker analysis was performed on thedaughters of !he grandsires.

tials because of the finite population size andcorrelations between predicted breeding valuesof relatives (11) using the approximation ofMeuwissen (16). Within-family variances and,consequently, variances of the marker indexwere not reduced by the Bulmer effect.Changes in variances because of frequencychanges of Q1L alleles was not included. Al­so, variance of genetic gain was predicted (15).Variance of genetic gain is a measure of therisk of the breeding scheme. Inbreeding has astrong relation with variance of the selectionresponse (3).

100 500 1000

1nf0000000000e daughtersper grandsire

by markers. The within-family variance ex­plained by markers decreases 1 to 5% withincreasing distances between the markers. Theeffect of increasing marker distances is largerfor larger numbers of daughters tested. Byincreasing the number of daughters from 500to 1000, the explained variance increases by 24to 27%. The maximum fraction of the within­family variance explained by the markers was13.3% and required 1000 daughters and a dis­tance between flanking markers of 5 cM.

Genetic Gain Because of Predictionof WIthin-Family Deviations

The increase in genetic gain from predictionof within-family deviations was small inprogeny testing schemes (see Table 4). Inprogeny testing schemes, a considerableamount of the within-family variances was ex­plained by individual or progeny performancedata. Thus, MAS cannot contribute much tothe accuracy of selection. However, in nucleusschemes, in which selection was mainly forpedigree and sib data and in which within­family deviations are not explained. geneticgains may be improved substantially. The im­provement was mainly due to the increase in

.1329

.1324

.1309

.1301

.1286

.1260

.1048

.1046

.1038

.1033

.1026

.1011

.0416

.0416

.0414

.0414

.0413

.0411

(cM)

5.010.020.025.033.350.0

Distance betweenflanking markers

IPraction of the variance of within-family deviationexplained by markers.

TABLE 4. The effect of predicting within-family devia­tions on genetic gains (E(&O», their standard deviations(80(&0», the standardized selection differentials (is), ac­curacies of selection (mu>, and generation intervals <Ls>of bull nucleus sires.

Breeding Plans

Parameters of the open and closed nucleusand conventional progeny testing plans aregiven in Table 2 and were also used byMeuwissen (15). In the closed nucleus plan, allnucleus dams are selected from nucleus cows,but, in the open nucleus and progeny testingplan, commercial cows are available for selec­tion. In the progeny testing scheme, bulls andcows are eligible for selection when progenytest results and an individual lactation recordare available, respectively.

Selection is for milk production, Le., anaggregate trait that might include milk. fatyield, and protein yield The heritability andgenetic and phenotypic correlations betweenlactations are .25, 1, and .4, respectively.

RESULTS

Fraction of Genetic VarianceDetected by Markers

Table 3 shows the fractions of within­family variances of grandoffspring explained

.00

.05

.10

.25

.00

.05

.10

.25

.00

.05

.10

.25

E(&O) 80(&0) is rm. Ls(O'g units/yr) (yr)

Conventional progeny testing plan

.240 .017 2.32 .906 6.1

.242 .017 2.32 !:xlT 6.1

.245 .017 2.32 .9m 6.1

.253 .017 2.32 .908 6.1

Open nucleus plan

.284 .081 2.03 .313 2.0

.317 .077 2.13 .376 2.0

.343 .079 2.16 .419 2.0

.408 .082 2.19 .515 2.0

Closed nucleus plan

.297 .147 2.07 .364 2.0

.325 .133 2.14 .397 2.0

.350 .124 2.16 .431 2.0

.412 .116 2.19 .520 2.0

Journal of Dairy Science Vol. 75, No.6, 1992

1656 MEUWISSEN AND VAN ARENDONK

accuracy of selection. Also, selection differen­tials increased because of reduction of correla­tions between estimated breeding values ofrelatives. 1bese correlations are high whenselection is mainly based on pedigree and sibinfonnation and relatives have more or less thesame pedigree and sibs. Information on within­family deviations differs among relatives, so itreduces correlations between breeding valueestimates of relatives.

The standard deviation of the genetic gainwas hardly affected by prediction of within­family differences (see Table 4). This suggeststhat inbreeding rates are also not much affectedby MAS. Within-family information decreasescorrelations between breeding value estimatesof relatives and thus decreases the probabilityof selecting relatives, which reduces the stan­dard deviation of the selection response. In theopen nucleus schemes, the fraction of the nu­cleus dams that are themselves nucleusanimals increases from 31 to 70% (results notshown) when the explained fraction of thewithin-family variance increases from 0 to25%. This implies that the open nucleusscheme becomes "more closed", which in­creases the standard deviation of the selectionresponse (compare open and closed nucleusschemes in Table 4). The latter effect causesthe increase of the standard deviation of theselection response when the explained within­family variance is large in open nucleusschemes. 1bese almost neutral effects of MASon variance of the selection response and, per­haps, on inbreeding is in contrast with theeffects of most other new techniques that in­crease genetic gain. For instance, MOETstrongly increases variance of the selectionresponse and inbreeding (IS).

DISCUSSION

Marker and QTL Associations: Assumptions

Marker effects were assumed to be due toclusters of Q1L, each Q1L having a smalleffect. Under this assumption, gene frequencychanges of individual Q1L will be small, and,thus, genetic variance will not decrease muchbecause of changes in gene frequencies. HMAS would mainly increase the gene fre­quency of Q1L with large effect, it would onlybe superior over conventional selection in theshort term, less than ± 5 generations (20). Inthe long tenn, both selection methods would

Journal of Dairy Science Vol. 75, No.6, 1992

fix the positive allele of the Q1L and would~hievethemaximumpo~~eresponsefur

this Q1L. But the conventional selectionmethod allocated less selection differential tothe fixation of the major gene and thus moreselection differential to Q1L with small effect.Hence, conventional selection would be super­ior in the long term, when QfL with largeeffect are present.

Realization of equidistant markers in ~­tice depends on the total number of markersavailable from which the equidistant markersare chosen. When equidistant markers are notavailable, the variance-covariance matrix ofthe marker effects M (Fonnula [2]) should beadjusted. The variance of the effect of marker iis adjusted proportionally to the size of themarker brackets, which involve marker iCovariances between the effects of flankingmarkers i and j are adjusted proportionally tothe size of the marker bracket fonned by mar­kers i and j. Genetic variance explained bymarkers is probably quite robust against fluctu­ations of distances between markers because itis not much reduced by increasing distances(Table 3).

Two markers on each chromosome wereassumed to be situated at the chromosomeends; i.e., the probability of a Q1L betweenthe chromosome end and the marker situated atthat end is negligible. This distribution of mar­kers ~ross the chromosome is not optimal (4).The variances of the effect of the outmostmarkers in Fonnula [2] may be adjusted ac­cording to the variances of the Q1L outsidethese markers and the fraction of these vari­ances picked up by the outmost markers. Also,if information about the distribution of QfLacross the genome is available, it can be usedto adjust these variances. It was assumed herethat Q1L were distributed uniformly acro~ thegenome, which implies that virtually no infor­mation about the distribution of the QTL wasavailable.

The probability of double recombination be­tween flanking markers was neglected in For­mula [2]. When accounting for double recom­binations, the fraction u1 of the effect of theQfLl picked up by the first marker is (r - rV(1 - rl)!(r(l - r», where rl and r2 are therecombination rates between Q1LI and thefirst and the second marker, respectively (seeexample explaining Formula [2]). Assumingno interference between recombinations [the

MARKER-ASSISTED SELECTION 1657

Haldane (9) mapping function], E(u~) values

are 11.7, 5.6, 3.2,2.1, .5, and .1% lower thanone-third, which was used in Formula [2], fordistances between flanking markers of 50, 33,25,20, 10, and 5 cM, respectively. Hence, thefraction of the within-family variance ex­plained by markers, which are 50 cM apart, issubstantially overestimated by approximately11.7% because of neglect of double recombi­nations.

For the prediction of the within-family vari­ances of the offspring explained by the mar­kers, the QTI. of the granddam were assumedhave on average the same genetic value asthose of the grandsire. More within-family var­iance can be explained when accounting fordifferences in estimated breeding value. Forinstance, when the grandsire has a higher ex­pected breeding value than the granddam,grandoffspring could be selected based on thefraction of the markers derived from the grand­sire. This leads to selection of grandoffspringthat resemble the grandsire as closely as possi­ble. However, the goal of the mating of thegrandsire and the granddam is to obtain amixture of their genes in the offspring and toselect offspring that are superior to both thegrandsire and the granddam. Consequently,prediction of within-family differences becauseof the differences in breeding value of thegrandsire and the granddam will increase re­sponse rates in the first generation of selectionbut probably decreases response rates over sev­eral generations of selection. Further researchis needed to verify this.

It was assumed that all markers could betraced from the grandsire to the selection can­didates. Assuming n alleles of equal frequency,the probability that a marker allele is traceablefrom the grandsire to his grandoffspring is (1 ­1/0 - 1/02)(1 - 1/02) (13). This probabilityapproaches 1 for highly polymorphic markers.When individual markers are not highly poly­morphic, marker haplotypes may be formedfrom a number of closely linked markers. Ifthis is not possible, the results of Table 3 haveto be multiplied by the probability that amarker is traceable.

WithIn-Family VarianceExplaIned by the Markers

Estimates of marker effects were not testedfor their statistical significance. Testing for

significance will lead to 1) neglect of smalleffects, which leads to (small) decreases ingenetic gains; and to 2) fewer significantmarker effects and thus lower response rateswhen the distance between flanking markersbecomes shorter. The latter is due to statisticalconfounding of marker estimates. With smalldistances between the markers, many daugh­ters are needed to detect that one marker has asignificantly larger effect than its flankingmarkers. Also, because marker effects were nottested for significance, it was not necessary tomake distributional assumptions about thesizes of QTI. effects. Marker effects were uti­lized regardless of their size.

A sequential testing procedure for markereffects partially avoids the problems of con­founding (5). Markers with the largest effects,e.g., based on a multiple regression of allmarkers, are sequentially included in the mul­tiple regression model. This procedure isstopped when the last included marker did nothave a significant effect. With sequential test­ing, the sizes of the chromosome segmentstraced by the markers are larger than withmultiple regression analysis of all markers.The reduction in genetic gain because of thelatter effect is probably small, because theeffect of the distance between flanking markerson the variance explained by them is rathermoderate (see Table 3).

The increase of the within-family variancewith decreasing distances between flankingmarkers (1 to 5%) is moderate because 1) thevariance explained by each marker decreaseswith increasing numbers of markers, 2) theinformation provided by an additional markeris confounded with the information from theother markers, and 3) double recombinationsare neglected in the variance of the markereffects (Formula [2]), which caused over­predicted variances explained by markers whendistances between markers were large.

The costs may be high to determine themarker genotype of many daughters of a sirein order to estimate marker and QTI. associa­tions. 1bese costs are reduced by not evaluat­ing the daughters for all markers known, butonly evaluating them for a subset of markersknown to be associated with QTI. from previ­ous studies. Costs may be reduced further byevaluating the selection candidates (grandoff­spring) only for markers with moderate to

Journal of DaiJy Science Vol. 75, No.6, 1992

1658 MEUWISSEN AND VAN ARENDONK

large estimated effects. This reduction in costsis minor, because the number of selection can­didates is usually small compared with thenumber of test daughters. Also, a granddaugh­ter design (24) will reduce the costs, but ge­netic gains will be reduced because the grand­grandoffspring of the grandsire will be selectedbased on their markers, i.e., an additional gen­eration is lost compared with the daughterdesign (Table 1). Further research is needed toreduce the costs of MAS breeding schemeswithout large reductions in genetic gains.

Increased Rates of Gain

Selection responses in Table 4 apply to anymethod that predicts within-family deviationsof young animals. Also, juvenile indicatortraits of milk production may be used to pre­dict within-family deviations, as was suggestedby Woolliams and Smith (25).

Table 4 shows that MAS does not increaserates of gain in conventional progeny testingschemes; equal numbers of young bulls areborn annually. Kashi et al. (13) predicted anincrease of 20 to 30% in genetic gain, whenMAS was applied in progeny testing schemesin which young bulls were selected on markergenotypes and only selected bulls entered theprogeny test In this scheme, the number ofyoung bulls entering the progeny test is re­stricted; i.e., numbers tested determine thecosts of the breeding scheme. The presentresults apply to schemes in which the numberof young bulls born annually is restricted; i.e.,number of embryo transfers determines costs.Intermediate assumptions are probably mostrealistic. Table 4 shows that MAS progenytesting schemes are at best competitive to nu­cleus schemes; hence, MAS should be appliedto nucleus schemes. The MAS increased ge­netic gains in nucleus schemes very effectively(Table 4). In nucleus schemes not using MAS,there is no information on individual andprogeny performances that predict within­family deviations because of the short genera­tion intervals (see Table 4). Therefore, re­sponse because of MAS adds to the regularselection response without interfering. The in­crease in genetic gain is highest in theseschemes.

In the open and closed nucleus schemes,detection and estimation of marker..qrL as-

Journal of Dairy Science Vol. 75, No.6, 1992

sociations were based on records of commer­cial cows because family sizes within the nu­cleus are too small. In these schemes, selected2-yr-old nucleus sires are also used for servingcommercial cows. This requires that farmersaccept AI bulls with breeding values of lowaccuracy to serve their cows.

The fraction of the within-family varianceaccounted for by markers was 4.1 to 13.3%.From these figures and the results of Table 4,interpolation shows that MAS increases ratesof gains by 9.5 to 25.8% and 7.7 to 22.4% inopen and closed nucleus schemes, respectively,when highly polymorphic markers are used,

ACKNOWLEDGMENTS

We are indebted to Ina Hoeschele, JohnWoolliams, and an anonymous reviewer foruseful comments and corrections on the manu­script.

REFERENCES

1 Botstein, D., R. L. White, M. Skolnick, and R. W.Davis. 1980. Construction of a genetic linkage map inman using restriction fragment length polymorphisms.Am. J. Hum. Genet. 32:314.

2 Bulmer, M. G. 1971. The effect of selection on ge­netic variability. Am. Nat. 105:201.

3 Crow, J. F., and M. Kimura 1970. An introduction topopulation genetics theory. Harper and Row PubI.,New York, NY.

4 Dekters, J.C.M, and M. R. Dentine. 1991. Quantita­tive genetic variance associated with chromosomalmarkers in segregating populations. Theor. Appl. Ge­net. 81:212.

5 Edwards, M. D., C. W. Stuber, and J. F. Wendel.Molecular-marker-facilitated investigations of quan­titative trait loci in maize. I. Numbers, genomic distri­bution and types of gene action. Genetics 116:113.

6 Fernando, R. L., and M Grossman. 1989. Markerassisted selection using best linear unbiased predic­tion. Genet. SeI. EvoL 21:467.

7 Geldermann, H. 1975. Investigations on inheritance ofquantitative characters in animaIs by gene markers. I.Methods. Thcor. Appl. Genet. 46:319.

8 Reference deleted in proof.9 Haldane, J.B.S. 1919. The combination of linkage

values and the calculation of distances between loci oflinked factors. 1. Genet. 8:299.

10 Henderson, C. R. 1984. Applications of linear modelsin animal breeding. Can. CataI. Publ. Data, Univ.Guelph, ON. Can.

11 HiI1, W. G. 1976. Order statistics of correlated vari­ables and implications in genetic selectionprogrammes. Biometrics 32:889.

121effreys, A. J., V. Wilson, and S. L. Thein. 1985.Hypervariable "minisatellite" regions in human DNA.Nature (Lond.) 314:67.

13 Kashi, Y., E. Ha1Ierman, and M SoUer. 1990. Marker-

MARKER-ASSISTED SELECTION 1659

assisted selection of candidate bulls for progeny test­ing programmes. Anim. Prod. 51:63.

14 Lande, R., and R. Thompson. 1990. Efficiency ofmarker-assisted selection in the improvement of quan­titative traits. Genetics 124:743.

15 Meuwissen. T.H.E. 1991. Expectation and variance ofgenetic gain in open and closed nucleus and progeuytesting schemes. Anim. Prod. 53:133.

16 Meuwissen. T .H.E., 1991. Reduction of selection dif­fC2'entials in finite populations with a nested full-halfsib family structure. Biometrics 47:195.

17 Nakamura, Y., M. Leppert. P. O'Connell, R. Wolff, T.Holm, M. CulvC2', C. Martin, E. Fujimoto, M. Hoff, E.Kumlin, and R. White. 1987. Variable number oftandem repeat (VNTR) markers for human gene map­ping. Science 235:1616.

18 Nicholas, F. R., and C. Smith. 1983. Increased rates ofgenetic change in dairy cattle by embryo transfer andsplitting. Anim. Prod. 36:341.

19 Saiki, R. K., D. H. Gelfand, S. Stoffel, S. J. Scharf, R.Higuchi, G. T. Hom, K. B. Mullis, and A. H. Erlich.

1988. PrimC2'-directed enzymatic amplification ofDNA with thennostabile DNA polymerase. Science239:487.

20 Saefuddin, A., and J. P. Gibson. 1991. Selectionresponses in populations with a transgene. J. Anim.Sci. 69. (SuppL 1):215.(Abstr.)

21 Smith, C. 1967. Improvement of metric traits throughspecific genetic loci. Anim. Prod. 9:349.

22 Smith, C., and S. P. Simpson. 1986. The use ofgenetic polymorphisms in livestock improvement. J.Anim. Breed. Genet. 103:205.

23 Soller, M. 1978. The use of loci associated withquantitative effects in dairy cattle improvement.Anim. Prod. 27:133.

24 Weller, J. I., Y. Kashi, and M. Soller. 1990. Power ofdaughter and granddaughter designs for determininglinkage between marker loci and quantitative trait lociin dairy cattle. J. Dairy Sci. 73:2525.

25 Woolliams, J. A., and C. Smith. 1988. The value ofindicator traits in the genetic improvement of dairycattle. Anim. Prod. 46:333.

Journal of Dairy Science Vol. 75, No.6, 1992