Additive and Nonadditive Genetic Variance inFemale Fertility of Holsteins

INA HOESCHElEDepartment of Dairy SCience

Virginia Polytechnic InstiMe and State UniversityBlacksburg 24061.()315

ABSTRACT

Additive and nonadditive genetic vari­lICes were estimated for cow fertility ofHolsteins. Measures of fertility were firstlactation days open and service period asItCOl'ded and with upper bounds of 150IIIId 91 d. respectively. Six million in­seminations from the Raleigh, North Car­olina Processing Center were used toform fertility records of 379,009 cows.Data were analyzed with a model ac­counting for all additive, dominance, andadditive by additive covariances tracedthrough sires and maternal grandsires.Variance components were estimated bythe tilde-hat approximation to REML.Heritability in the narrow sense was 2%for days open and .8% for service period.DooJinaoce and additive by additive vari­llI¥:t as a percentage of phenotypic varia­tiro strongly depended on imposition ofupper bounds. Heritabilities in the broadseuse ranged from 2.2 to 6.6% and were• least twice as large as heritabilities indie narrow sense. Effect of 25% inbreed­ing was only around an additional 3 dopen. Specific combining abilities amongbills were estimated as sums of domi­nance and additive by additive interac­tions removing effect of inbreedingdepression. Differences between maxi­IIItB and minimum estimates were in theorder of twice the estimated standarddeviation, ranging from 1.5 to 6.7 d Ef­fects of inbreeding and specific combin­il3 ability could be jointly considered inmIing programs following sire selection.(Key words: nonadditive genetic vari­ance, female fertility, approximate re­Ilricted maximum likelihood)

I&ceiYcd September 20, 1990.Ita:qIIed November 5, 1990.

IfI J DIiJy Sci 74:174~1752

Abbreviation key: A x A =additive by addi­tive, CPU =central processing unit, DO =daysopen, MGS = maternal grandsire, MME =mixed model equations, SeA = specific com­bining ability, and SP = service period.

INTRODUCTION

Profitability of dairy cattle does not onlydepend on milk production but also on non­production characteristics such as fertility andhealth traits. The phenotypic and genetic struc­ture of fertility is more complex than that ofyield for several reasons. Fertility, defined asthe nonreturn event, is a synergistic trait (10)affected by three individual components (pater­nal, maternal, and filial), each of which consistsof a genetic and a pennanent environmentaleffect Repeatabilities of fertility measures areoften much higher than the small heritabilitiesin the narrow sense [e.g., (7, 8)], allowing forthe presence of nonadditive genetic variance.Measures of fertility are not approximately nor­mally distributed but either discontinuous (non­return event, services per conception) or contin­uous with substantial skewedness (days open,days to first breeding, service period).

Very few estimates of nonadditive geneticvariance for dairy cattle traits are currentlyavailable. VanRaden (24) and Tempelman andBurnside (22) recently estimated small nonad­ditive variance components (around 5% ofphenotypic variance) for production traits in USand Canadian Holsteins, respectively. In theCanadian study (22), dominance variance forone trait (fat yield) was significant and esti­mated at 24% of total variation. This estimatewas probably biased upward for several reasonslisted by the authors including common envir­onment of full sisters within herds. Tempelmanand Burnside (23) also estimated dominancevariance for conformation traits with estimatesranging from 3 to 16%.

1743

1744 HOESCHELE

ill a study of six inbred lines of Holsteinsand their reciprocal crosses (2), estimates ofspecific combining abilities were significant fordays open (DO) but not for production traits.Beckett et al, (2) concluded that "specific genecombinations and the way in which they are as­sembled can have an important influence on re­productive performance" (p. 619).

About two-thirds of all cows in the US areunder some mating program (16). Mating deci­sions following selection should be based onnonadditive genetic variation, inbreeding, andnonlinear economics. Additive by additive (A xA) effects minus sire and dam contributionsand dominance effects are each composed of asire-dam combination effect plus Mendeliansampling (14, 27). Sire-dam combination ef­fects are inherited (14, 27) through eight ances­tor pathways (interactions of sire with dam'sparents, of dam with sire's parents, and ofsire's parents with dam's parents). For popula­tions in which dams have few offspring, combi­nation effects can be defined as sire-maternalgrandsire (MGS) interactions. Best linear unbi­ased predictions of combination effects withand without individual records can be obtainedfrom mixed model equations (MME).

Algorithms to compute inverses of additive,dominance (for a noninbred population), and Ax A (for any population) relationship matricesat costs only linearly increasing with populationsize are available (11, 12, 14, 27). The MMEusing such inverses predict individual additiveand nonadditive merits and also sire-dam or

TABLE 1. Summary of data edits.

Records remaining

sire-MGS combination effects.This paper presents estimates of additive,

dominance, and A x A genetic variances aswell as effects of inbreeding and specific c0m­

bining ability among bulls for female fertilitytraits of Holsteins.

MATERIALS AND METHODS

Data

Breeding records were provided by theDairy Records Processing Center at Raleigh,NC. A total of 6,732,444 inseminations werereceived; these included breedings betweellSeptember 1982 and September 1989 in Ver­mont, Virginia, North Carolina, Georgia, Flori­da, illdiana, Kentucky, Tennessee, and Texas.Data edits are outlined in Table 1. For each firilactation, four fertility traits were computdincluding DO, DO with an upper bound of ISOd, service period (SP), and SP with an upperbound of 91 days. These and alternative mea­sures of fertility were described by Hansen ~

al, (7). Retaining only one record per cow withvalues for the four traits described and furtheredits listed in Table 1 reduced the data set from5,842,276 Holstein inseminations to 887,Oljcow records.

Original pedigree information on fertilityrecords was only sire of cow. Dam and MGSwere found by matching fertility records with

Total Percentage Edits

6,732,4445,842,276

887,015

379,009

100.086.8

13.2

5.6

Inseminations received from RaleighInseminations of HolsteinsOne record per cow with four trait values: days open (DO),

D0150, SP, and SP91 in first lactation; additional edits:20 mo ;5; APe! ;5; 40 mo25 d ;5; DFS2 ;5; 200 d

5 d ;5; sp3 ;5; 200 d270 d ;5; DSc4 ;5; 290 dServices: n ;5; 4Sires with > 30 daughters, or maternal grandsires with > 10

granddaughters; herd-year-seasons with > 1 sire

lAPC = Age at first calving.

2DFS = Days to fIrst service (days between calving and fIrst service).

3Sp = Service period (days between first and last insemination).

"uSC = Days to subsequent calving (days between last service and subsequent calving).

Journal of Dairy Science Vol. 74, No.5, 1991

NONADDITIVE VARIANCE IN FERm..ITY 1745

the USDA cow evaluation file. A list of bullswith either 30 or more daughters in the data or10 or more maternal granddaughters was pre­pared. Cows whose sire appeared in this listand whose MGS either appeared in the list orwas unknown were retained. In the [mal dataset of 379,009 cows, 50.3% of the MGS wereunknown.

Data Model

Instead of an animal model including addi­tive (a), dominance (d), and additive by addi­tive (aa) genetic values of individual cows, asire-MGS model (13) was employed, where sireand MGS were defined as sire and MGS of thecow. The sire-MGS model was derived fromthree genetic recurrence relationships (11, 14,19, 27):

a = .5l1sire + .25aMGS + rnaaa = .25allsire + .0625aaMGS + cilsire,MGS

+ maad = C<!sire,MGS + md

where the m terms represent Mendelian samp­ling plus residual genetic effects associatedwith unknown dams, ca is combination effectof sire with MGS due to interactions of genesin the sire with genes in the MGS at differentloci, and cd is combination effect of sire withMGS due to interactions of genes in the sirewith genes in the MGS at the same loci.

For sire j, let Sj = .5aj and SSj = .25aaj' Thesire-MGS model for analyzing the data was

Yijkl = hysj + b X fjjkl + Sj + .sSk + SSj+ .25sSk + Cdjk + Cajk + ~jkl [1]

where

y \]1:1 is an observation on an individualcow,

hysj is fIxed effect of herd-year-seasoni,

fjjkl is the inbreeding coefficient of acow,

b is the coefficient for the regres­sion of trait value on inbreedingcoefficient,

!jl sk> SSj, sSk, Cajk, and cdjk are random geneticeffects as defined previously forsire j and MGS k, and

eijkl is a random residual.

For the special case of sire identical toMGS, recurrences for a and aa effects reduce to

a = .75ilsire + rnaaa = .5625aasire + ffiaa

where the aa recurrence derives from the equal­ity of combination effect of the sire with him­self and one quarter of the sire's aa effect (27)or casire,sire = .25ailsire' In Model [1], the part Sj+ .5Sk + SSj + .25sSk + Cajk must be replaced by1.5 Sj + 2.25 SSj'

Model [1] can be viewed as an enhancementof the model of Allaire and Henderson (1) withthe added benefit that Model [1] allows differ­ent genetic effects (additive, A x A, domi­nance) to be separated by accounting directlyfor their covariance structure, assuming rela­tionships can be traced fully through sires andMGS. Model [1] can be rewritten in matrixnotation as

y = Xh + bf + Zs + Uss + Wca+ Vcd + e [2]

where

Y is the data vector,h is the vector of fIxed hys effects,f is the vector of inbreeding coefficients,s is the vector of additive sire effects,

ss is the vector of A x A sire effects,ca is the vector of Ax A sire-MGS combi­

nation effects,cd is the vector of dominance sire-MGS

combination effects,e is the vector of residuals,

X is a known matrix relating cows to hys,Z is a known matrix with two nonzero ele-

ments per row of 1 pertaining to sireand .5 to MGS if MGS is known, andwith one nonzero element of I for sire ifMGS is unknown or of 1.5 for sire ifsire is identical to MGS,

U is a known matrix with two nonzeroelements per row of I pertaining to sireand .25 to MGS if MGS is known, andwith one nonzero element of 1 for sire ifMGS is unknown, or of 2.25 for sire ifsire is identical to MGS, and

Journal of Daily Science Vol. 74, No.5, 1991

1746 HOESCHELE

W and V are known matrices relating cowsto sire-MGS combinations; W and V in­clude zero rows for cows with missingMGS; W also contains zero rows forcows with sire identical to MGS,

The variance-covariance structure associatedwith model [2] is

Acr; 0 0 0 0

Bl1cr;s B12cr;s 0 0

B22cr;s 0 0

symmetric C~ 0

R

where cr; = .2~, cr;s = .06~, ~ =

.0625cri; 0-;, ~aa' and cri are additive, A x A,

and dominance genetic variance, respectively;A is the additive genetic relationship matrixamong bulls due to sires and mgs; Bl1 is the Ax A genetic relationship matrix among bullsequal to A # A with # denoting the Hadamardproduct; B12 is the relationship matrix amongA x A main and combination effects; B22 is therelationship matrix among A x A sire-MGScombination effects; C is the relationship ma­trix among dominance sire-MGS combinationeffects; R is a diagonal matrix of residual vari­ances.

Elements of the relationship matrix C can becomputed from additive relationships asdescribed by Hoeschele and VanRaden (14).Elements of B22 are obtained analogously (27)except multiplied by .5 because Var(ca) =

.5cr;s' Nonzero elements in B 12 link the A x A

effects of the bulls in ss to the combinationeffects among the sires and MGS of the bullsincluded in ca. This variance-covariance struc­ture allows separate estimation of dominanceand A x A combination effects, although theelements in cd and ca are linked to the recordsby the almost identical incidence matrices V

Journal of Dairy Science Vol. 74, No.5, 1991

and W, through their different paths of inheri·tance.

Residual variance (diagonal element of R),

when MGS is known, is ~ = ~ (1 - .3125h;.

.09765625 h~ - .0625 h~) and is 0-;. = ~(1­

.25h; - .0625 h~) when MGS is unknown,

where ~ is phenotypic varianch; =

O-;/~, h~ = ~/~, and h~ = <&~. V11len

sire or MGS are inbred, residual variance ureduced due to smaller Mendelian samplingvariance. Under inbreeding, variance of Men·delian sampling in the recurrence for an addi·tive effect given earlier is Var(mJ = (.6875-

.25fsire - .0625fMGS) h;~, and variance of

Mendelian sampling in the recurrence for an Ax A effect is Var(maa> = {(I + f)2 - [.3125+

.25(fsire + .25fMGs) + f]2 }h~~, where fsireJ

fMGS , and f are inbreeding coefficients of sire,MGS, and individual, respectively. Hence, foranoninbred individual with sire and MGS inbred

by any amount f. = fsire + .25fMGS, ~ il

appropriately reduced by subtracting .25f.h~~2 2 ~and (.15625f. + .0625f.) haa<rp.

The variance-covariance structure associatedwith Model [2] is correct under Cockerham's(4) assumptions, specifically in absence of rna·jor genes, linkage, and inbreeding. The effectsof inbreeding on variances and covariances areaccurately include-Ai in A and B (11, 27), but ifdominance variation and inbreeding coexis~

some coefficients in C are incorrect (14), addi·tive and dominance effects of inbred individu·als are correlated, and dominance covariancesmay not be fully explained by covariancesamong combination effects. These joint effectsof inbreeding and dominance will be ignoredhere. An exact treatment (3, 5,9, 15,21) wouldprohibit analysis of large data sets (21), and theadditionally required covariance parameters canprobably not be accurately estimated at lowlevels of inbreeding (3).

Mixed Model Equations

Mixed model equations are based on Model[2] and require the inverse relationship matricesA-1, B-1, and C-1. The inverses were computeddirectly by algorithms described elsewhere (11,

NONADDITIVE VARIANCE IN FERTILITI 1747

14, 27). These algorithms allow computation ofinverses at costs linearly related to dimensionsof matrices but require including tie ancestorsof bulls and of sire-MGS combinations.

Variance ratios used were ka =cr;/cr; =(256

8 2 2 2 2 22- Oha- 25haa - 16hd)/64ha, kaa = ~/cr;,s =(256 - 80h; - 25h~ - 16h~)/16h~, and kct =

~/~ = (256 - 80h; - 25h~ - 16h~)/16h~.Individual inbreeding coefficients in f were

computed by applying a modified form of thetabular method to individual sire-MGSpedigrees (26).

Variance Component Estimation

Variance components were estimated withthe tilde-hat approximation to REML (18, 25)because the coefficient matrix of the MMEcould not be inverted with conventional orsparse matrix methods. Let Sh sSh cah and Cdirepresent elements of the vectors s, SS, ca, andcd, respectively. Approximate solutions neededin the tilde-hat method were

where M = 1- X(X'X)-IX', 6 is the estimate ofbfro}ll the MME, and the variance ratios ka, kct,and kaa are evaluated at current estimates of thevariance components. New estimates of the var­iance components were computed from the es­timation equations

a; = §'A-IS/I, [(Z'MZ)n!«Z 'MZ)iii

+ Alii kJ]~ = [§S'Bllss + ca'B22ea + is'B l2ea

ss + ca'B21SS]/{I, [(U'MU)n!«U'MU)iii

+ B~lkaa)] +I, [(W'MW)idi

«W'MW)ii + B~2kaa)]}

cd'C-ICd/I, [(V'MV)n!«V'MV)iii

-1~+ Cii kd)]

er. = (y'My - rMy*6 - §'Z'My - is'U'Mye _ ca'W'My - Cd'V'My)/[N - 1

- rank (X)]

where §, is, ca, and cd are solutions to theMME evaluated at previous variance compo­nent estimates and

Computing Strategy

Computations were performed using twoFORTRAN programs with the first one cal­culating inbreeding coefficients and the non­zero elements of A-I, B-1, and C-l and thesecond one processing the data and the sortedinverse coefficients to calculate solutions foreffects and variance components (FORTRANprograms available from the author). Solutionsto the MME were obtained by iteration on data(20). The data set and the coefficients of theinverse relationship matrices were read onlyonce during the first round of iteration andstored in memory for subsequent rounds.

Data were sorted by herd-year-season, anddata within herd-year-season were processedtwice within each round of iteration with thefirst processing yielding a new herd-year-sea­son solution and the second used to accumulateright-hand sides, adjusted for herd-year-season,of the genetic effects. After processing all datarecords, solutions for the genetic effects werecomputed while processing coefficients of theinverse relationship matrices. In this part, right­hand sides of genetic effects were adjusted byGauss-Seidel within and across different typesof genetic effects (order additive, dominance, Ax A), but right-hand sides of individual geneticeffects had been adjusted during data proces­sing for effect of MGS if bull appeared as sireand vice versa by Jacobi. Similarly, right-handsides for sire-MGS combination effects hadbeen adjusted previously for individual effects

Journal of Dairy Science Vol. 74, No.5, 1991

1748

TABLE 2. Data characteristics.

HOESCHELE

No. of records (one record per cow)No. of herd-year-seasonsNo. of sires and maternal grandsires in dataNo. of bulls added for relationship tiesNo. of cows with maternal grandsires knownNo. of sire maternal grandsires subclasses in dataNo. of subclasses added for relationship tiesAverage no. of records in sire-maternal grandsires subclassMaximum no. of records in sire-maternal grandsires subclassDimension of A-I (no. of nonzero coefficients)1Dimension of c-1 (no. of nonzero coefficients)2Dimension of 1>1 (no. of nonzero coefficients)3Maximum inbreeding coefficient, %Average inbreeding coefficient, %Percentage cows with nonzero inbreeding coefficient, %

1A is additive genetic relationship matrix.

2C is dominance genetic relationship matrix.

3B is additive by additive genetic relationship matrix.

379,00930,749

2652291

188,31469,746

117,7972.7

8632943 (21,703)

183,037 (7,020,992)188,220 (7,180,229)

26.5625.4

21

of sires and MGS. This mixture of Gauss­Seidel and Jacobi was combined with succes­sive overrelaxation for genetic effects.

RESULTS AND DISCUSSION

Computational Aspects

Convergence for variance components wasassumed to occur when the absolute changebetween two successive rounds was less than.2% of the current estimate for all three geneticvariance components. Convergence for geneticeffects solutions was accepted when

L (fiP+IJ - fii[lJ/ < .0001 [Lfi~][l+IJi

was satisfied, where u stands for any type ofgenetic effect (s, ss, cd, or ca) and 1 for iterationnumber. For the trait DO, 80 rounds of iterationwere required for the variance component solu­tions to achieve convergence and a total of 319rounds on the genetic effects solutions. Totalcentral processing unit (CPU) time for the iter­ation program was 4.5 hours on an mM 3090.Number of rounds and CPU times for the otherthree traits were very similar and are, therefore,not presented. With variance ratios fixed andstarting values of zero for all effects, about 40rounds of iteration on the genetic effects solu­tions were needed to attain convergence.

Journal of Dairy Science Vol. 74, No.5, 1991

The program required 82.8 Mb of memoryfor the data set described in Table 2 with379,009 records, 404,950 equations, and a totalof 14,222,924 nonzero coefficients from thethree inverse relationship matrices, when dataand inverse coefficients were stored in memoryafter the first reading. On computers with smallamounts of memory, the iteration program canbe run by reading data and inverse coefficientsin each round of iteration at increased CPU butdecreased memory requirements. With this op­tion, analysis of the data set in Table 2 wouldrequire only 7.6 Mh. Storing of data and non·zero inverse coefficients would be requiredwhen using vectorization. However, major partsof the iteration program did not vectorize be­cause of dependencies and short loops.

Although the genetic effects solutions con·verged rather quickly (convergence rates simi·lar to MME for additive effects only), conver·gence of the variance component solutions wasslow. For models with a single random effectbesides residual (e.g., additive sire model), con·vergence rate of estimation-maximizationREML and approximate REML algorithms wasgreatly enhanced by subtracting the expectedamount of residual variance contained in thecorresponding quadratics (25). For several ran·dom effects models, subtracting expectedamounts of all variance components, except theone being estimated, from the quadratic mightspeed convergence of estimation-maximization

NONADDITIVE VARIANCE IN FERTll.ITY 1749

REML and tilde-hat algorithms substantiallyand should be investigated.

With unbalanced data and for models withseveral random effects such as different typesof genetic effects, where there are substantialcovariances among variance component esti­mates, no conservative procedure for approx­imating standard errors is currently available(17) but should be developed. In this paper,therefore, variance component estimates arepresented without standard errors.

Variance Component Estimates

Table 3 gives estimates of variance compo­nents for the four fertility traits. Imposing anupper bound reduced residual variance and ad­ditive genetic variance for both traits DO andSP, reduced the nonadditive variance compo­nents, in particular dominance variance, forDO, and increased the nonadditive componentsfor SP.

Ratios of the genetic variance components tophenotypic variance are listed in Table 4. Esti­mates of heritability in the narrow sense,

~ow = cr;/o;, were in good agreement with

the literature [e.g., (7)]. Generally, heritability

in the broad sense, h~oad = (cr; +~ + ~)Jcr;,

was more than twice as large as h~ow' Impos­ing the upper bound of 150 d on DO did notaffect the percentage of phenotypic variance ex­plained by additive and A x A variance butmarkedly reduced ratio of dominance to pheno­typic variance. For SP, the upper bound of 91 dcaused an increase in ratio of dominance to

phenotypic variance.For more than half of the cows represented

in the data, MGS was missing so that inbreed­ing coefficients could not be computed. Be­cause ignoring inbreeding in these cows couldhave inflated the estimates of the nonadditive,in particular dominance, variance components,a reduced data set containing only cows withknown MGS was also analyzed. For the

2 2reduced data set, both ~ow and hbroad were

slightly higher (last row of Table 4) than for thefull.

Inbreeding and Specific Combining Ability

Table 5 presents estimates of the linear re­gression of trait values on inbreeding coeffi­cients multiplied by 25 to yield effect of 25%inbreeding (e.g., sire =MGS). Inbreeding at the25% level caused cows' DO to be around 3 dlonger and extended service period to an addi­tional 3 d. Beckett et al. (2) found much largereffects of inbreeding on fIrst lactation DO insix inbred lines of Holsteins with a pooledestimate of 18.5 d per 25% inbreeding. Theinbreeding level averaged 12.49% across linesversus only .4% (Table 3) for the entire data setand .8% for the subset of cows with sire andMGS known in this study. The effect of in­breeding depression might have been somewhatunderestimated because inbreeding coefficientsof cows were computed from relationshipsamong their sires and MGS only.

The effects of inbreeding in Table 5 can becompared with the effects of specillc combin­ing ability (SeA) among bulls for cow fertility

TABLE 3. Variaoce component estimates for fertility traits.

Variance componen~

00 1426.5 29.7 17.5 35.100150 1041.4 22.6 12.5 5.3SP 1082.0 9.4 .2 15.1SP91 923.9 7.3 2.8 27.1ooJ 1366.6 38.9 6.9 49.9

100 =Days open, DOl50 = days open with an upper bound of 150 d, SP = service period (days between first and lastinsemination), SP91 = service period with an upper bound of 91 d.

2Uni! is days squared.

30n1y cows with known maternal grandsires included.

Journal of Dairy Science Vol. 74, No.5, 1991

1750 HOESCHELE

TABLE 4. Genetic parameter estimates for fertility traits.

Variance as percentage of phenotypic

Trait I h2 h2 h2~ad2a aa d

DO 2.0 1.2 2.3 5.5D0150 2.1 1.2 .5 3.8SP .8 .0 1.4 2.2SP91 .8 .3 2.8 3.6D03 2.7 .5 3.4 6.6

IDO =Days open, 00150 =days open with an upper bound of 150 d, SP =service period (days between first andilstinsemination), SP91 = service period with an upper bound of 91 d.

22 __2+22_2hbroad - 100 (u;,: aaa + ad)/crp·

30nly cows with known maternal grandsire included.

given in Table 6. Size of difference among sire­MGS combinations in SCA was quantified bythe difference between estimated maximum andminimum SCA (ESCAmax - ESCAIniIJ withESCA = fa + cd and by twice the estimatedstandard deviation of SCA with

~CA = ~ + .50;s· Difference in SCA evalu­ated from ESCA was mostly smaller than2o-SCA because of shrinkage toward zero due toaverage subclass size of only 2.7 cows with amaximum of 863. Differences in SCA were inthe order of 2 to 7 d and, hence, equal or largerthan the effects of 25% inbreeding.

The analysis of the fertility data set couldhave been performed under an animal modelfitting additive, A x A and dominance geneticeffects of cows. Inclusion of Ax A and domi­nance sire-dam combination effects as ancestoreffects of the individual A x A and dominanceeffects permits computation of the inverse rela­tionship matrices at costs only linearly relatedto the order of the matrices (14, 27), thusallowing formation of MME for a population aslarge as or larger than the one described inTable 1. Analysis under an animal model in­stead of a sire model yields equal or largerestimates of additive genetic variance (6). Themodel options of the FORTRAN program em­ployed in this study includes animal model,reduced animal model, and sire-MGS models.The sire-MGS option was chosen to limit com­puting cost by reducing the order of the MME.

Nonadditive genetic variance was equal orlarger than additive variation but nonadditive,in particular dominance, variance dependedstrongly on whether or not upper bounds were

Journal of Dairy Science Vol. 74, No.5, 1991

applied to fertility measures. Variation in fe­male fertility is due to differences among COW!

in ability to conceive and in ability of theembryo to survive. Variation in embryo sur·vival was not fully accounted for because sireand MGS of cow were included in the modelbut sire of fetus was not. Genetic variation inability to conceive and in embryonic surviv~

may have been reduced because all cows werefertile as heifers and were successful concep­tions themselves. Hence, larger additive andnonadditive variances might exist for heiferfertility. Larger nonadditive and, in particular,dominance variation and larger effects of in·breeding and SCA on fertility may be foundwhen considering service bull and sire of cowin the model instead of sire and MGS of COW,

and this should be investigated.

TABLE 5. Estimates of effects of inbreeding on fertili~

traits.

Effectof 25%

Traitl inbreeding

(d)

DO 3.300150 2.9SP 2.6SP91 2.5D02 3.3

IDO = Days open, D0150 = days open with an upperbound of 150 d, SP = service period (days between fillland last insemination), SP91 = service period with an upperbound of 91 d.

20nly cows with known maternal grandsires included.

NONADDITIVE VARIANCE IN FERTILITY 1751

TABLE 6. Estimates of differences in specific combiningabilities (SCA) among bulls excluding inbreeding. I

Difference in SCAevaluated as

Trait2ESCAmax- ESCAmin3 2crSCA

(d)

00 3.7 5.500150 1.5 1.5SP 2.2 1.9SP91 2.9 3.6004 4.4 6.7

lSum of dominance and additive by additive combina­tion effects.

200 =Days open, D0150 = days open with an upperbound of 150 d, SP = service period (days between lustand last insemination), SP91 =service period with an upperbound of 91 d.

~SCA is the BLUP of SCA.

40n1y cows with known maternal grandsires included.

CONCLUSIONS

Simultaneous estimation of additive, A x A,and dominance effects and variance compo­nents as well as specific combining abilities ofanimal pairs from large data sets is now feasi­ble. Additive genetic variance for cow fertilityis small, and nonadditive variation is onlyslightly larger and dependent on imposition ofupper bounds on fertility measures. Effects ofSCA among dairy sires for cow fertility aresmall but at least as important as effects ofinbreeding and could be jointly considered inmating programs following sire selection.

ACKNOWLEDGMENTS

J. Clay at the Dairy Records ProcessingCenter at Raleigh, NC is thanked for providingthe breeding records. Assistance of C. Cassadyin data editing is gratefully acknowledged. Fi­nancial support for this study was provided bythe National Association of Animal Breedersand by Eastern Artificial Insemination Cooper­ative.

REFERENCES

1Allaire, F. R., and C. R. Henderson. 1965. Specificccmbining abilities among dairy sires. J. Dairy Sci. 48:1096.

2Beckett, R. C., T. M. Ludwick, E. R. Rader, H. C.

Hines, and R Pearson. 1979. Specific and generalcombining abilities for production and reproductionamong lines of Holstein cattle. J. Dairy Sci. 62:613.

3 Cbevalet, C., and M. Gillois. 1977. Estimation of geno­typic variance components with dominance in smallconsanguineous populations. Proc. Int Conf. QuantGenet., Iowa State Univ. Press, Ames.

4 Cockerham, C. C. 1954. An extension of the conceptof partitioning hereditary covariance for analyses ofcovariance among relatives when epistasis is present.Genetics 39:859.

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