GENOMIC selection (GS) is a new technology that

Transcription

1 Copyright Ó 2009 by the Genetics Society of Americ DOI: /genetics The Accurcy of Genomic Selection in Norwegin Red Cttle Assessed by Cross-Vlidtion Tu Lun,*,1 John A. Woollims,*, Sigbjørn Lien, Mtthew Kent,*, Morten Svendsen nd Theo H. E. Meuwissen* *Deprtment of Animl nd Aquculturl Sciences nd Centre for Integrtive Genetics, Norwegin University of Life Sciences, N-1432 Ås, Norwy, The Roslin Institute (Edinburgh), Royl (Dick) School of Veterinry Studies, University of Edinburgh, Roslin, Midlothin EH25 9PS, United Kingdom nd Geno Breeding nd Artificil Insemintion Assocition, 1432 Ås, Norwy Mnuscript received July 15, 2009 Accepted for publiction August 12, 2009 ABSTRACT Genomic Selection (GS) is newly developed tool for the estimtion of breeding vlues for quntittive trits through the use of dense mrkers covering the whole genome. For successful ppliction of GS, ccurcy of the prediction of genomewide breeding vlue (GW-EBV) is key issue to consider. Here we investigted the ccurcy nd possible bis of GW-EBV prediction, using rel bovine SNP genotyping (18,991 SNPs) nd phenotypic dt of 500 Norwegin Red bulls. The study ws performed on milk yield, ft yield, protein yield, first lcttion mstitis trits, nd clving ese. Three methods, best liner unbised prediction (G-BLUP), Byesin sttistics (ByesB), nd mixture model pproch (MIXTURE), were used to estimte mrker effects, nd their ccurcy nd bis were estimted by using cross-vlidtion. The ccurcies of the GW-EBV prediction were found to vry widely between 0.12 nd G-BLUP gve overll the highest ccurcy. We observed strong reltionship between the ccurcy of the prediction nd the heritbility of the trit. GW-EBV prediction for production trits with high heritbility chieved higher ccurcy nd lso lower bis thn helth trits with low heritbility. To chieve similr ccurcy for the helth trits probbly more records will be needed. GENOMIC selection (GS) is new technology tht is expected to revolutionize niml breeding. It is distinct from trditionl selection methods where phenotype nd pedigree informtion is combined to predict breeding vlues nd where t lest one source is necessry for prediction. Estimtion of GS breeding vlue is bsed on the estimtion of mrker effects covering the whole genome nd combines these estimtes with the mrker genotypes to obtin breeding vlue estimtes. Given sufficiently dense genomewide mrker mp, ll the genetic vrince is expected to be explined by the mrkers, nd ll quntittive trit loci (QTL) re in linkge disequilibrium (LD) with t lest one mrker (Clus et l. 2008). This llows GS to predict genomewide estimtes of breeding vlues (GW- EBV) without the need of phenotyping the selection cndidtes. A potentil cost reduction of up to 90% cn be chieved for breeding progrm by GS (Scheffer 2006), becuse only moderte number of individuls re required to hve both known mrker genotypes nd phenotypes. These individuls form reference dt set for the estimtion of GW-EBV. The knowledge obtined from the reference dt set cn be pplied to the 1 Corresponding uthor: Deprtment of Animl nd Aquculturl Sciences, Norwegin University of Life Sciences, Box 5003, N-1432 Ås, Norwy. E-mil: tu.lun@umb.no clcultion of GW-EBV for the selection cndidtes on the bsis of their mrker genotypes, with n ccurcy tht is found in the vlidtion of the prediction (Goddrd nd Hyes 2007). For successful ppliction of GS, bsed on reference dt set, to usully much lrger popultion of selection cndidtes without phenotypic records, ccurcy of the prediction is key issue to consider (Goddrd nd Hyes 2009). Since GS ws first proposed by Meuwissen et l. (2001), mny reserch works using simulted dt hve been performed on this issue (Clus nd Veerkmp 2007; Hbier et l. 2007; Kolbehdri et l. 2007; Clus et l. 2008; Solberg et l. 2008). The recent vilbility of genomewide dense SNP mrker mps hs mde GS with rel dt fesible. Studies of the ccurcy of genomic predictions hve emerged in some niml species, including mice (Lee et l. 2008; Legrr et l. 2008), chickens (Gonzlez- Recio et l. 2009), nd cttle (Hyes et l. 2009), nd in plnt species [for exmple, brley (Zhong et l. 2009)]. For GS pplied to diry cttle, ccurcies for the GW- EBV hve been reported in North Americn Holstein (VnRden et l. 2009), Austrlin Holstein Friesin (Hyes et l. 2009), nd New Zelnd Holstein Friesin nd Jersey diry cttle (Hrris et l. 2008). In the present work we pplied GS to Norwegin Red diry cttle to investigte the ccurcy nd possible bis Genetics 183: (November 2009)

2 1120 T. Lun et l. of GW-EBV prediction for the phenotypes of milk production, clinicl mstitis, nd clving ese, by using rel bovine genotyping dt. Three methods, best liner unbised prediction, Byesin sttistics, nd mixture model pproch were used in the study, nd their ccurcies nd bises of the GW-EBV were compred. To estimte the ccurcy nd bis of the GW-EBV the pproch of cross-vlidtion ws employed, mking use of estimtes of breeding vlue from the Norwegin Red diry cttle breeding scheme. MATERIALS AND METHODS Genotypic nd phenotypic dt: There were 500 Norwegin Red bulls selected for this study with 466 sons of 34 sires, with no son lso being sire. Sons hd been progeny tested between 2001 nd 2006, nd sires tested before The numbers of sons chosen for yers 2006, 2005, 2004, 2003, 2002, nd 2001 re 36, 44, 98, 98, 100, nd 90, respectively. All sons nd sires were genotyped t CIGENE ( using the 25K MIP-SNP chip rry from Affymetrix (Sn Diego). All dt from n individul SNP were deleted if () pedigree informtion exposed.2.5% non-mendelin sire offspring inheritnce ptterns, (b) its genotype probbilities significntly devited from the Hrdy Weinberg proportions (P, 0.01%), (c) cross smples.25% genotypes were missing, or (d) its minor llele frequency (MAF),2.5%. A totl of 18,991 SNPs remined fter filtering. The phenotypic dt of ll 500 bulls used for the study re dughter-yield devitions (DYDs) (Wiggns et l. 1992) for the trits: metric tons of milk yield, kilogrms of milk ft yield, kilogrms of milk protein yield, clving ese, nd clinicl mstitis (cm). Clinicl mstitis ws considered in three trits defined by period of first lcttion: cm1, dys in milk; cm2, dys in milk; nd cm3, dys in milk. The dt were bsed on the verge of 1038 dughters, vrying from 111 to 21,391, nd were vilble for ll bulls for ll trits. Accurcy of DYD for trit is defined s the verge of the ccurcies of the DYDs of 500 bulls for the trit nd ws obtined together with DYD from BoviBnk Ltd. ( The ccurcies of DYDs re listed in Tble 1. The genotype dt nd phenotype dt of ll 500 bulls constitute the complete dt used in the present work. Trining dt: The trining dt sets were ech obtined by msking the phenotype, i.e., setting the phenotype unknown, for defined number of individuls. The individuls whose phenotype ws msked were selected in two different wys. The first wy ws through rndom selection: here 100 individuls t time were rndomly selected, without replcement, to produce five nonoverlpping trining dt sets; i.e., every phenotype ws msked precisely once in the trining dt sets. In this rticle this wy is referred to s 20% rndom msking. The second wy ws to select individuls on the bsis of their yer of progeny testing: seven trining dt sets were obtined for yers 2006, 2005, 2004, 2003, 2002, 2001, nd before The number of phenotype-msked individuls in trining dt set for yer of testing is the number of bulls selected for this yer. We clled this wy of selection cohort msking. The nonmsked dt were nlyzed by the models described in the dt nlysis section to predict the msked phenotypes. This resulted in ech bull hving predicted phenotype from ech msking method nd this ws compred to the relized DYD. The correltion coefficient between the predicted nd relized DYDs ws clculted nd used s mesure of the ccurcy of the GW-EBV predictions. Additionl trining sets for production trits were generted to test the impct of incresing the rndom msking to TABLE 1 Heritbility nd ccurcy of DYD for studied trits Trit h 2 Accurcy Milk yield Ft yield Protein yield cm cm cm Clving ese % by rndomly llocting ech individul to one of two trining sets. This implies tht there were only 250 individuls with phenotypes in the trining dt set, insted of 400 s in 20% rndom msking. To obtin stndrd errors, for both 20% nd 50% rndom msking the division into sets nd ll the subsequent nlyses described in the Dt nlysis section were replicted six times. Dt nlysis: Three models were used to estimte the mrker effects: best liner unbised prediction (G-BLUP), Byesin sttistics (ByesB), nd MIXTURE. G-BLUP estimtes the effects of the mrkers by best liner unbised prediction (Henderson 1975), ssuming tht every mrker explins n equl proportion of the totl genetic vrince. ByesB is described in detil by Meuwissen et l. (2001) nd estimtes the vrince explined by every mrker, using prior distribution tht ssumes tht this vrince is smll, denoted s s 2, with probbility (1 g B ); i.e., the mrker hs virtully no effect or comes from n inverse-chi-squre distribution with probbility g B. The probbility g B represents the probbility tht mrker hs substntil effect nd ws vried in the dt nlysis since it is generlly unknown. Meuwissen et l. ssumed s 2 ¼ 0 for mrkers with smll estimted effects, but by hving s 2 slightly lrger thn zero, the model cn be implemented s Gibbs smpling lgorithm, which hs computtionl dvntges. Here, the smll vrince s 2 ws estimted from the dt, i.e., from the genes with smll effect. In the Gibbs chin s 2 ws smpled from the conditionl posterior, which is SS x 2 n 2, where x 2 n 2 is rndom devite from the inverse-chi-squre distribution with n 2 d.f.; n is the number of SNPs with smll effect in the current itertion of the chin; SS ¼ SI i 2, where I i i is n indictor vrible tking vlues 1 if SNP i belongs to the SNPs with smll effects in the current itertion nd I i ¼ 0 otherwise; nd i is the current solution of the effect of SNP i. As mentioned bove, if SNPs were ssumed to hve substntil effect, they hd n individul vrince estimted. If this individul vrince ws,s 2, the SNP effect ws removed from the set of SNPs with substntil effect, to ensure tht the substntil effect SNPs lwys hd higher vrince thn the smll effect SNPs. This is similr to including polygenic term in the ByesB model (Clus nd Veerkmp 2007; Solberg et l. 2008), but where the correltion mtrix of the polygenic effects is defined by the mrkers with smll effect insted of by the pedigree. Since ByesB mkes quite strong ssumptions bout the prior distribution of the mrker effects, which my not be true in rel dt, we lso used model tht ttempts to estimte this prior distribution. For the ltter, we mde use of property of mixtures of norml distributions, nmely tht they cn be used to pproximte ny other (prior) distribution (Silvermn 1996). In the MIXTURE model we ssumed tht the mrker effects cme from mixture of two distributions: one distribution with lrge vrince (ccommodting lrge mrker effects) nd one with smll vrince (ccommodting smll mrker

3 effects). This model ws lso implemented in Gibbs smpling lgorithm s described by George nd McCulloch (1996) except tht the vrince of the smll SNP effects is estimted here. The distribution to which the mrker belongs is smpled from the Bernoulli distribution, with prmeter g M. The prmeter g M, which reflects the proportion of the mrkers belonging to the lrge nd the smll vrince distribution, is smpled using noninformtive Bet distribution s prior. The vrinces of the two distributions underlying the mixture (s 12 nd s 22 ) re estimted using noninformtive chi-squre distribution (Sorenson nd Ginol 2007). The model of nlysis tht ws used by G-BLUP, ByesB, nd MIXTURE ws Accurcy of Genomic Selection 1121 y ¼ m 1 XNm X j j 1 e; j¼1 where y is N 3 1 vector of phenotypes (DYDs); N m is the number of mrkers fitted; j is the effect of the mrker; X j is N 3 1 vector denoting the genotype of the individuls for mrker j, with X ij ¼ 0 if individul p i is homozygous for the first llele t locus j, X ij ¼ 1= ffiffiffiffiffi p H j if heterozygous, Xij ¼ 2= ffiffiffiffiffi H j if individul pi is homozygous for the second llele t locus j, nd X ij ¼ 2q j = ffiffiffiffiffi H j if the mrker genotype is missing, where qj is the frequency of the second mrker pffiffiffiffiffi llele nd H j is the mrker heterozygosity. The division by H j stndrdizes the vrince of the mrker genotype dt to 1. The vrince of j is ssumed to be V s /N m for G-BLUP, is estimted by ByesB, nd in MIXTURE equls s 12 or s 22, depending on whether the mrker effect is smll or lrge nd s 12 nd s 22 re both estimted. Since the trits re DYDs, V s is the sire vrince, which is one-qurter of the totl genetic vrince, nd ws obtined from Interbull ( together with the trit heritbilities (Tble 1). Given the estimtes of the mrker effects nd the mrker genotypes, genetic vlues for the msked individuls re predicted s GW-EBV i ¼ XNm X ij â j ; where X ij is the mrker genotype of individul i for mrker j coded the sme s bove, nd â j is the estimted effect of mrker j. By dding the overll men, m, to the GW-EBV i, nd ssuming tht the residul effect of the DYDs is on verge 0, predicted phenotype ws obtined for every bull (whose phenotype ws msked). Since every bull s phenotype ws msked once in one of the trining sets, totl of 500 predicted phenotypes were obtined for ech model for trit for msking strtegy. The correltion coefficient between the predicted nd relized phenotypes ws clculted nd used s mesure of the ccurcy of the GW-EBV predictions. The regression of the relized phenotypes on the predicted phenotypes is used s mesure of the bis of the GW-EBV, where regression coefficient of 1 denotes no bis,,1 implies tht extreme high (low) vlues of the GW-EBV over- (under)- predict the relized phenotypes, nd vice vers for regression coefficient.1. These summry sttistics were exmined both overll nd within ech msked set. For ByesB clcultion, the length of the Gibbs chin ws 15,000 itertions nd 5000 itertions were used for burn-in. For MIXTURE, the chin length ws 12,000 itertions nd burn-in ws 8000 itertions. To ensure the convergence of the Gibbs chins used for ByesB nd MIXTURE, 10 distinct chins were run for milk yield nd the estimted ccurcy ws clculted from pooling the chins. It ws found tht the estimted ccurcy did not chnge to three significnt numbers fter pooling 3 chins. This finding ws tested for j¼1 Figure 1. Accurcy of GW-EBV prediction with the ByesB method for the milk yield trit with respect to the number of mrkers with effect. other production trits nd helth trits. Consequently ll results presented for Gibbs nlyses re the verge of 3 distinct Gibbs chins. RESULTS Determintion of the number of mrkers with effects: The number of mrkers with substntil effect in ByesB clcultion determines the probbility g B of mrker with substntil effect. In this study, this number is defined seprtely for different wys of msking dt for ech trit, by set of ByesB clcultions with different numbers of effective genes. For exmple, for the rndom msking dt for milk yield, we pplied ByesB to the dt with the number of effective genes 800, 1600, 2400, 3200, 6400, 9600, nd 12,800, respectively. The result in Figure 1 shows tht the ccurcy for GW-EBV prediction ws ffected little by the number of mrkers with n effect. Accurcies vried from 0.56 to 0.58 with respect to numbers of effective genes used. The mximum ccurcy chieved for rndom msking in Figure 1 suggests tht 3200 ws pproximtely optiml, nd thus g B ¼ (3200/18,991) ws used for milk yield. The g B vlue for milk yield for cohort msking of dt ws determined similrly, nd the lower vlue of g B ¼ ws found to be slightly better thn other vlues of g B. For other production trits nd helth trits, the sme pproch ws pplied to set g B, nd the vlues re shown in Tble 2. Tble 2 lso lists g M vlues for MIXTURE, together with s 12 nd s 22 s the vrinces of the two distributions underlying the model. In contrst to ByesB, optiml numbers of effective genes cn be determined during the MIXTURE clcultions, nd Tble 2 shows tht the g M vlue for MIXTURE is mostly lower thn the g B for ByesB. Accurcy of GW-EBV prediction: Tble 3 shows the ccurcy of the GW-EBV prediction by the ByesB, MIXTURE, nd G-BLUP methods. For 20% rndom msking, Tble 3 shows the men predictive ccurcy

4 1122 T. Lun et l. TABLE 2 Estimtes of g B for ByesB nd g M, s 12, nd s 22 for MIXTURE for rndom msking nd cohort msking Trit Rndom msking: Cohort msking: ByesB MIXTURE ByesB MIXTURE g B g M 2 s 1 2 s g B g M 2 s 1 2 s Milk yield Ft yield Protein yield cm cm cm Clving ese obtined for predicting the 100 individuls in the vlidtion set for nlysis of the 400 in the trining set. The men is therefore n verge of 30 vlues, 5 from ech rndom division of the bulls into 5 sets of 100, nd then replicted six times. The stndrd error is bsed on the vrince between the replicte mens. However, for cohort msking, the ccurcy is combined using the single GW-EBV obtined for ech of the 500 bulls. It is shown in Tble 4 tht in cohort msking, ccurcies vry within considerble rnge for offspring subsets with different popultion size nd yer of progeny test. For most trits, the prediction of the msked sire cohort using phenotypes of their offspring cohorts chieved higher ccurcy thn those of msked cohort offspring. TABLE 3 Accurcy of GW-EBVs obtined by G-BLUP, MIXTURE, nd ByesB Trit G-BLUP MIXTURE ByesB Cohort msking Milk yield Ft yield Protein yield cm cm cm Clving ese Rndom msking Milk yield Ft yield Protein yield cm cm cm Clving ese Approximte SE The ccurcy for cohort msking is shown s combined ccurcy estimted for 500 selected individuls, while the ccurcy for rndom msking is shown s the men of the ccurcies for five trining dt sets nd the pooled pproximte stndrd error. The generl conclusion from Tble 3 is tht for the trits studied the differences between the methods re smll, nd re smll compred to their stndrd errors. For rndom msking, ll three methods used give similr men ccurcy nd stndrd error. There is trend mong the methods for G-BLUP to hve higher ccurcy thn other methods for cohort msking. Among the three production trits the ccurcy for milk yield is in generl lower thn tht for ft yield nd for protein yield, but gin the difference between the ccurcies is within the rnge of the stndrd error. For helth trits, Tble 3 shows tht the ccurcies of GW-EBV re considerbly lower thn the ccurcies for production trits. In ddition, compred to the production trits, the helth trits show bigger differences between men ccurcy nd combined ccurcy. This cn be seen in Tble 3 by the difference between men ccurcy nd combined ccurcy for cm1 nd cm2, which is beyond the rnge of stndrd error of the ccurcy. Tble 5 presents overll verge ccurcy nd bis bsed on men ccurcies nd bises for six replictes of 50% nd 20% msking. Results in Tble 5 show tht ccurcy for 20% msking with 400 phenotypes in the TABLE 4 Men, minimum, nd mximum ccurcies for six offspring trining subsets nd ccurcy for sire dt set in GW-EBV prediction for cohort msking with ByesB Offspring Trit Men Min Mx Sire Milk yield Ft yield Protein yield cm cm cm Clving ese

5 Accurcy of Genomic Selection 1123 TABLE 5 Accurcy nd bis of GW-EBV prediction for rndom msking with 250 DYDs nd 400 DYDs in the trining dt set Overll men ccurcy Overll men bis Trit 250 DYDs 400 DYDs 250 DYDs 400 DYDs G-BLUP Milk yield Ft yield Protein yield MIXTURE Milk yield Ft yield Protein yield ByesB Milk yield Ft yield Protein yield Approximte SE The ccurcy nd bis re shown s the overll men ccurcies nd bises for five trining dt sets nd six replictes nd the pooled pproximte stndrd error. trining dt set is significntly higher compred to 50% msking with 250 phenotypes in the trining dt set. Bis of GW-EBV prediction: The degree of bis from the methods is judged by compring the regression coefficients of phenotypes on predicted phenotypes with the vlue 1. Tble 6 presents the bis of the GW-EBV prediction for the trits studied. As for the presenttion of ccurcy, for rndom msking, Tble 6 shows the overll men nd the stndrd error of the bis of the predictions for six replictes of five trining dt sets, while for cohort msking, it is the combined bis estimted for ll 500 selected individuls. The results show tht for production trits the GW-EBV predictions for rndom msking hd lower bis compred to those for cohort msking, but these differences were within the stndrd errors. It is observed for the three mstitis trits in Tble 6 tht there is less bis if the prediction is more ccurte. For exmple, for cm1, Tble 3 shows the combined ccurcy of the prediction for cohort msking is higher thn the men ccurcy for rndom msking, nd Tble 6 shows the combined bis of cohort msking is lower thn the men bis for rndom msking. Among the four helth trits, GW-EBV prediction for clving ese hs the highest ccurcy (Tble 3), nd the prediction is in generl lest bised (Tble 6). Accurcy nd bis for subset of mrkers: To investigte the effect of the number of mrkers fitted on the ccurcy of the GW-EBV, for production trits, we rndomly removed mrkers in the complete dt sets nd repeted the nlyses described in mterils nd methods. In this work, 25, 50, nd 75% of 18,991 mrkers were rndomly selected nd removed. This process ws replicted six times to obtin stndrd errors TABLE 6 Bis of GW-EBVs obtined by G-BLUP, MIXTURE, nd ByesB G-BLUP MIXTURE ByesB Cohort msking Milk yield Ft yield Protein yield cm cm cm Clving ese Rndom msking Milk yield Ft yield Protein yield cm cm cm Clving ese Approximte SE The bis for cohort msking is shown s combined bis estimted for 500 selected individuls, while the bis for rndom msking is shown s the men of the bises for five trining dt sets nd the pooled pproximte stndrd error. nd results for cohort msking re shown in Tbles 7 nd 8. In generl the results for the reduced mrker dt sets show similr fetures to those for the complete dt with respect to the different trits, methods of nlysis, nd msking of the phenotypes. As expected, the ccurcy of the prediction reduces s the number of mrkers becomes smller. However, the decrese of the ccurcy ws smll. For exmple, for G-BLUP pplied to the three production trits, the combined ccurcies of the GW-EBV decrese,9% of their originl vlue for the subset with 75% of the mrkers removed. DISCUSSION This study pplied genomic selection to rel rther thn simulted phenotypes in setting in which it would be used in prctice nd where the predictive ccurcy cn be ssessed by comprison with reltively precise estimtes of breeding vlues obtined from phenotypic mesurements nd genetic evlution using pedigrees. The existence of reltively precise comprison llowed this study to compre the effectiveness of the different methods tht might be employed. A totl of 519,000 mesurements were mde on individul diry cows, to obtin the 500 DYD phenotypes on individul bulls used in the nlysis. The GW-EBVs for individul bulls were clculted from the estimtes of effects of 19,000 SNP mrkers lone nd the ccurcy of the estimtes ws determined by the correltion between predicted nd relized DYDs, r DYD,GW-EBV. The estimtes of the mrker

6 1124 T. Lun et l. TABLE 7 Accurcy of GW-EBV prediction for cohort msking with 25, 50, nd 75% of ll mrkers msked % of ll mrkers msked G-BLUP Milk yield Ft yield Protein yield MIXTURE Milk yield Ft yield Protein yield ByesB Milk yield Ft yield Protein yield Approximte SE The ccurcy is shown s the verge combined ccurcies cross six different replicted mrker mskings (see results) nd the pooled pproximte stndrd error. effects cme from trining dt sets nd r DYD,GW-EBV derived from using cross-vlidtion. Generlly, the estimted ccurcies will underpredict the observed ccurcy of selection, i.e., the correltion between GW-EBV nd true breeding vlues, r GW-EBV,TBV, becuse the relized DYDs re not perfectly predicting the true breeding vlues. The expected correltions between the DYDs nd genetic vlue, r DYD,TBV, re given in Tble 9. A better estimte of the ccurcy of the TABLE 8 Bis of GW-EBV prediction for cohort msking with 25, 50, nd 75% of ll mrkers msked % of ll mrkers msked G-BLUP Milk yield Ft yield Protein yield MIXTURE Milk yield Ft yield Protein yield ByesB Milk yield Ft yield Protein yield Approximte SE The bis is shown s the verge combined bises cross six different replicted mrker mskings nd the pooled pproximte stndrd error. TABLE 9 Accurcy of the GW-EBV prediction (r DYD,GW-EBV ), the expected correltion between the DYDs nd genetic vlue (r DYD,TBV ), nd r GW-EBV,TBV for studied trits Trit r DYD,TBV r DYD,GW-EBV r GW-EBV,TBV Milk yield Ft yield Protein yield cm cm cm Clving ese r DYD.GW-EBV is represented by the combined ccurcy of the G-BLUP method pplied to the cohort msking dt set. GW-EBV (r GW-EBV,TBV ) my be obtined by clculting r DYD,GW-EBV /r DYD,TBV, where r DYD,TBV equls the ccurcy of DYD (Tble 1). In Tble 1, there is strong reltionship between heritbility nd the ccurcy of DYD, i.e., r GW-EBV,TBV. This suggests tht dt sets of.500 bulls re needed to chieve comprble ccurcies for the less heritble trits, i.e., the helth trits s shown by Detwyler et l. (2008). TheG-BLUPmethodgveoverllthehighestr DYD,GW-EBV nd little bis of the GW-EBV. The G-BLUP method mkes no ssumptions bout the distribution of the sizes of the SNP effects. ByesB nd MIXTURE ssumed tht some SNPs explin more vrince thn others. This outcome suggests tht the distribution of true effects is sufficiently spred mong loci, tht there is insufficient benefit from fitting the more complex models, tht t lest the mjority of the SNPs explin smll mount of genetic vrince, nd tht ccounting for some outlier SNPs tht explin substntilly more vrince, s in the ByesB model, does not improve GW-EBVs. The ltter is probbly becuse there re too few such outlier SNPs nd the genetic vrince they explin is too smll reltive to tht explined by ll the SNPs with smll effects. A contributing fctor to this outcome my be tht the SNP density is lso too low for the benefits of ByesB or MIXTURE to be fully pprent. In the bsence of sequence dt, the custive SNPs re unlikely to be in the dt nd t low density more SNPs will be required to cpture QTL. This result tht most genetic effects re smll grees with recent lrge-scle genomewide ssocition study conducted for height in humns, where 20 vrints were detected tht explined together only 3% of the vrition (Weedon et l. 2008). For trit whose genetic vrince cn be explined by smll number of genes, ByesB might be expected to do better thn G-BLUP. For exmple, previous study with the Holstein Friesin cttle breed (Riquet et l. 1999) identified QTL for milk production trits, especilly milk ft. The positionl cndidte cloning of the QTL identified the cndidte gene coding cylcoa:

7 Accurcy of Genomic Selection 1125 dicylglycerol cyltrnsferse 1 (DGAT1) (Grisrt et l. 2002). One my expect tht ByesB might chieve higher ccurcy thn G-BLUP for the prediction of breeding vlues for milk production trits of Holstein Friesins. However, so fr there is no published result vilble showing the segregtion of the DGAT1 gene in the smple of Norwegin Red cttle used for the present work. It my be tht the DGAT1 gene is not segregting in Norwegin Red cttle, the genetic vrince in ll the milk production trits of Norwegin Red cttle might be explined by mny smll genes, nd hence G-BLUP might be in fvor of chieving higher ccurcy for the GW-EBV prediction thn ByesB s observed here. When reducing the number of mrkers by fctor of 2or4,r DYD,GW-EBV ws not much reduced (Tble 7). This my be becuse the G-BLUP, which ws found to give the highest r DYD,GW-EBV, merely uses the mrkers to estimte the reltionship between the bulls, i.e., to estimte the frction of lleles the nimls hve in common (Hbier et l. 2007). Thus the use of fewer mrkers did not reduce the ccurcy of the estimte of the reltionship mtrix much (Hyes et l. 2003), which is centrl to G-BLUP. The SNP detection method my lso hve ffected this result, in tht the sequencing of smll chromosoml segments results in some of the detected SNPs being very close to ech other; i.e., the SNPs re unevenly distributed cross the chromosome nd clusters of very closely linked SNPs occur. If one or few of the SNPs within such cluster re omitted, this would not reduce the mrker informtion content very much, since often severl SNPs remin within the cluster in close LD with the one omitted; i.e., the cluster is still informtive. Detwyler et l. (2008) studied fctors tht ffect the ccurcy of prediction, using genomewide pproch. With the formul derived by the uthors we cn clculte n estimte of the number of independent loci tht contribute to the genetic vrince for trit (n G )by the ccurcy of the breeding vlue prediction (r), the number of phenotypes used for the prediction (n P ), nd the heritbility of the trit (h 2, obtined here s squre of the ccurcy of DYD in Tble 1) s n G ¼ n P [h 2 /r 2 h 2 ]. We pplied the formul to the result of G-BLUP for rndom msking of dt for milk yield nd got n G ¼ 734. We lso hd vilble smller dt set of Holstein cttle nd we used the estimte of n G to predict wht ccurcy might be obtined for milk yield using the methods described here, from trining set of 255 records. When this ws done, we obtined predicted vlue of 0.46, which compres to the observed vlue of This gives us some optimism tht degree of predictbility of these ccurcies might be obtined. Cohort msking, grouping the DYDs by yer of progeny test of the bulls, in the cross-vlidtion more closely resembles the prcticl ppliction of genomic selection, where GW-EBV of contemporries is required. The decresing ccurcy for the men of the cohorts is first explined by the smller vrince of the EBVs within cohort, 80% of the whole set: ssuming constnt regression line, then the first pproximtion of this impct is to reduce the ccurcies, being correltions, by 10%. Further reductions of the correltion within ech cohort might be expected becuse of chnges in hplotype nd llele frequencies rising from genetic chnge over time in this selected popultion nd incomplete mixing of lleles over the different yer groups. Overll our results indicted tht cohort msking ws not substntilly worse thn rndom msking of the dt, which suggests tht the popultion structure for predicting GW-EBV of contemporry bulls is pproximtely s eqully suited to genomic selection s the prediction of rndom set of Norwegin Red bulls. The ltter my be different in different species, breeds, nd/ or selection progrms. In generl, the ccurcies of the GW-EBV vry widely between 0.12 nd 0.62, where the lower ccurcies pply to the mstitis trits tht hve low heritbility, i.e., down to s low s An ccurcy of 0.75 is probbly sufficient for the (pre)selection of young bulls t young ge (Scheffer 2006). To chieve this for the popultion structure of the 500 bulls, it is predicted tht trining set of 1000 bulls would be required for milk production trits, using Detwyler et l. (2008), nd more bulls for helth trits. However, in prctice lrger trining sets would be required, first to be confident of chieving comprble ccurcies within cohort nd second to chieve ccurcies for helth nd fitness trits tht re comprble to those for milk production. Therefore this rticle demonstrtes the fesibility of developing GW-EBV in prctice, but t the sme time indictes the scle of trining dt sets required to compete with existing pedigree nd phenotype pproches in diry cttle breeding. Such pproches in diry cttle re generlly considered to be well optimized, nd so in other species nd for other objectives the size of the trining set my not necessrily be s lrge to be competitive. This rticle represents the uthors views nd does not necessrily represent position of the Europen Commission, who re not lible for the use mde of such informtion. Helpful comments of two nonymous reviewers re grtefully cknowledged. This reserch project hs been cofinnced by the Europen Commission, within the 6th Frmework Progrmme, contrct no. FOOD-CT ( SAB- RE Cutting Edge Genomics for Sustinble Animl Breeding). LITERATURE CITED Clus, M. P. L., nd R. F. Veerkmp, 2007 Accurcy of breeding vlues when using nd ignoring the polygenic effect in genomic breeding vlue estimtion with mrker density of one SNP per cm. J. Anim. Breed. Genet. 124: Clus, M. P. L., T. H. E. Meuwissen, A.P.W.de Roos nd R. F. Veerkmp, 2008 Accurcy of genomic selection using different methods to define hplotypes. Genetics 178: Detwyler, H. D., B. Villnuev nd J. A. Woollims, 2008 Accurcy of predicting the genetic risk of disese using genomewide pproch. PLoS ONE 3: e3395.

8 1126 T. Lun et l. George, E. I., nd R. E. McCulloch, 1996 Stochstic serch vrible selection, pp in Mrkov Chin Monte Crlo in Prctice, edited by W. R. Gilks, S. Richrdson nd D. J. Spiegelhlter. Chpmn & Hll/CRC, London/New York. Goddrd, M. E., nd B. J. Hyes, 2007 Genomic selection. J. Anim. Breed. Genet. 124: Goddrd, M. E., nd B. J. Hyes, 2009 Mpping genes for complex trits in domestic nimls nd their use in breeding progrmmes. Nt. Rev. Genet. 10: Gonzlez-Recio, O., D. Ginol, G. J. M. Ros, K. A. Weigel nd A. Krnis, 2009 Genome-ssisted prediction of quntittive trit mesured in prents nd progeny: ppliction to food conversion rte in chickens. Genet. Sel. Evol. 41: 3. Grisrt, B., W. Coppieters, F. Frnir, L. Krim, C. Ford et l., 2002 Positionl cndidte cloning of QTL in diry cttle: identifiction of missense muttion in the bovine DGAT1 gene with mjor effect on milk yield nd composition. Genome Res. 12: Hbier, D., R. L. Fernndo nd J. C. M. Dekkers, 2007 The impct of genetic reltionship informtion on genome-ssisted breeding vlues. Genetics 177: Hrris, B. L., D. L. Johnson nd R. J. Spelmn, 2008 Genomic selection in New Zelnd nd the implictions for ntionl genetic evlution. Proceedings of the Interbull Meeting, Nigr Flls, NY. Hyes, B. J., M. Crrick, P. Bowmn nd M. E. Goddrd, 2003 Genotype x environment interction for milk production of dughters of Austrlin diry sires from test-dy records. J. Diry Sci. 86: Hyes, B. J., P. J. Bowmn, A. J. Chmberlin nd M. E. Goddrd, 2009 Invited review: genomic selection in diry cttle: progress nd chllenges. J. Diry Sci. 92: Henderson, C. R., 1975 Best liner unbised estimtion nd prediction under selection model. Biometrics 31: Kolbehdri, D., L. R. Scheffer nd J. A. B. Robinson, 2007 Estimtion of genome-wide hplotype effects in hlf-sib designs. J. Anim. Breed. Genet. 124: Lee, S. H., J. H. J. vn der Werf, B.J.Hyes, M.E.Goddrd nd P. M. Visscher, 2008 Predicting unobserved phenotypes for complex trits from whole-genome SNP dt. PLoS Genet. 4: e Legrr, A., C. Robert-Grnie, E. Mnfredi nd J. M. Elsen, 2008 Performnce of genomic selection in mice. Genetics 180: Meuwissen, T. H. E., B. J. Hyes nd M. E. Goddrd, 2001 Prediction of totl genetic vlue using genome-wide dense mrker mps. Genetics 157: Riquet, J., W. Coppieters, N. Cmbisno,J. J.Arrnz, P. Berzi et l., 1999 Fine-mpping of quntittive trit loci by identity by descent in outbred popultions: ppliction to milk production in diry cttle. Proc. Ntl. Acd. Sci. USA 96: Scheffer, L. R., 2006 Strtegy for pplying genome-wide selection in diry cttle. J. Anim. Breed. Genet. 123: Silvermn, B. W., 1996 Smoothed functionl principl, components nlysis by choice of norm. Ann. Stt. 24: Solberg, T. R., A. K. Sonesson, J. A. Woollims nd T. H. E. Meuwissen, 2008 Genomic selection using different mrker types nd densities. J. Anim. Sci. 86: Sorensen, D., nd D. Ginol, 2007 Likelihood, Byesin nd MCMC Methods in Quntittive Genetics. Springer-Verlg, New York. VnRden, P. M., C. P. Vn Tssell, G.R. Wiggns, T. S. Sonstegrd, R. D. Schnbel et l., 2009 Invited review: relibility of genomic predictions for North Americn Holstein bulls. J. Diry Sci. 92: Weedon, M. N., H. Lngo, C. M. Lindgren, C. Wllce, D. M. Evns et l., 2008 Genome-wide ssocition nlysis identifies 20 loci tht influence dult height. Nt. Genet. 40: Wiggns, G. R., P. M. VnRden nd R. L. Powell, 1992 A method for combining United-Sttes nd Cndin bull evlutions. J. Diry Sci. 75: Zhong, S., J. C. M. Dekkers, R.L.Fernndo nd J. L. Jnnink, 2009 Fctors ffecting ccurcy from genomic selection in popultions derived from multiple inbred lines: brley cse study. Genetics 182: Communicting editor: G. Gibson