Prediction of the reliability of genomic breeding values for crossbred performance

Transcription

1 Vandenplas et al. Genet Sel Evol :43 DOI /s Genets Seleton Evoluton RESERCH RTICLE Open ess Predton of the relablty of genom breedng values for rossbred performane Jéréme Vandenplas * Jak J. Wndg and Maro P. L. Calus bstrat Bakground: In rossbreedng programs varous genom predton models have been proposed for usng phenotyp reords of rossbred anmals to nrease the seleton response for rossbred performane n purebred anmals. possble model s a model that assumes dental sngle nuleotde polymorphsm SNP effets for the rossbred performane trat aross breeds SGM. nother model s a genom model that assumes breed-spef effets of SNP alleles BSM for rossbred performane. The am of ths study was to derve and valdate equatons for predtng the relablty of estmated genom breedng values for rossbred performane n both these models. Predton equatons were derved for stuatons when all phenotypng and genotypng data have already been olleted.e. based on the genet evaluaton model and for stuatons when all genotypng data are not yet avalable.e. when desgnng breedng programs. Results: When all genotypng data are avalable predton equatons are based on seleton ndex theory. Wthout avalablty of all genotypng data predton equatons are based on populaton parameters e.g. hertablty of the trats nvolved genet orrelaton between purebred and rossbred performane effetve number of hromosome segments. Valdaton of the equatons for predtng the relablty of genom breedng values wthout all genotypng data was performed based on smulated data of a two-way rossbreedng program usng ether two losely-related breeds or two unrelated breeds to produe rossbred anmals. The proposed equatons an be used for an easy omparson of the relablty of genom estmated breedng values aross many senaros espeally f all genotypng data are avalable. We show that BSM outperforms SGM for a spef breed f the effetve number of hromosome segments that orgnate from ths breed and are shared by seleton anddates of ths breed and rossbred referene anmals s less than half the effetve number of all hromosome segments that are ndependently segregatng n the same anmals. Conlusons: The derved equatons an be used to predt the relablty of genom estmated breedng values for rossbred performane usng SGM or BSM n many senaros and are thus useful to optmze the desgn of breedng programs. Senaros an vary n terms of the genet orrelaton between purebred and rossbred performanes hertabltes number of referene anmals or dstane between breeds. Bakground Several lvestok produton systems are based on rossbreedng shemes e.g. 1 3 and take advantage of the nreased performane of rossbred anmals ompared to purebred anmals along wth breed omplementarty. For suh produton systems based on rossbreedng the breedng goal for the purebred populatons s to optmze *Correspondene: jereme.vandenplas@wur.nl nmal Breedng and Genoms Centre Wagenngen UR Lvestok Researh P.O. Box H Wagenngen The Netherlands the performane of rossbred desendants. However the seleton of purebred anmals for rossbred performane has not been extensvely mplemented n lvestok partly due to the dffulty of routne olleton of pedgree nformaton on rossbred anmals 4. Wth the advent of genom seleton varous genom predton models have been proposed whh use phenotyp reords of rossbred anmals to nrease the seleton response for rossbred performane n purebred anmals e.g These approahes predt breedng values for rossbred performane of seleton The uthors 217. Ths artle s dstrbuted under the terms of the Creatve Commons ttrbuton 4. Internatonal Lense whh permts unrestrted use dstrbuton and reproduton n any medum provded you gve approprate redt to the orgnal authors and the soure provde a lnk to the Creatve Commons lense and ndate f hanges were made. The Creatve Commons Publ Doman Dedaton waver publdoman/zero/1./ apples to the data made avalable n ths artle unless otherwse stated.

2 Vandenplas et al. Genet Sel Evol :43 Page 2 of 19 anddates usng the estmated allele substtuton effets of many sngle nuleotde polymorphsms SNPs. The SNP allele substtuton effets are estmated from phenotypes of genotyped referene anmals. In the ontext of rossbreedng several breeds and ther rosses are nvolved n genom predton and purebred and rossbred performanes are often onsdered to be dfferent but orrelated trats e.g Therefore estmates of SNP allele substtuton effets for purebred and rossbred performane trats may not be the same for purebred and rossbred populatons e.g. due to genotype by envronment nteratons. ssumng only addtve gene aton one approah to aommodate ths s to model dfferenes between allele substtuton SNP effets usng a multvarate genom model that assumes a orrelaton struture between the effets of SNPs aross the purebred and rossbred populatons or equvalently by assumng a genet orrelaton struture aross the trat measured n purebred and rossbred populatons 9 1. These multvarate genom models are referred to hereafter as aross-breed SNP genotype models SGM sne the estmates of SNP allele substtuton effets for the rossbred performane trat are also used to predt breedng values for rossbred performane of purebred seleton anddates regardless of ther breed of orgn 4 6. Thus estmates of SNP effets for the rossbred performane trat usng SGM are not breed-spef. However a number of fators may have an mpat on the effet that an be measured for a SNP for the rossbred performane trat. Frst the two parental alleles at a SNP n a rossbred anmal may have dfferent effets on the phenotype due to dfferent levels of lnkage dsequlbrum LD wth a quanttatve trat lous QTL n the parental purebred populatons. Seond dfferent genet bakgrounds suh as domnane or epstat nteratons an result n the effets of the same QTL to be dfferent n purebred versus rossbred anmals. nd thrd purebred and rossbred anmals may be exposed to dfferent envronments leadng to genotype by envronment nteratons. Beause of these reasons estmated allele substtuton effets at SNPs for the rossbred performane trat may be breed-spef. To aommodate all these dfferenes prevously an approah was proposed 3 6 that estmates breed-spef allele substtuton effets for the rossbred performane trat BSM assumng that the breed orgn of SNP alleles n rossbred anmals s known. Results from smulatons have shown that BSM an result n greater auray of genom estmated breedng values EBV of purebreds for rossbred performane than SGM under some ondtons In order to be able to evaluate many dfferent breedng program desgns that apply genom predton for rossbreedng performane t would be useful to be able to predt the relablty of genom EBV usng for example dfferent genom models or dfferent breedng shemes. Predton of relablty should preferably onsder the genotype data of all referene anmals and seleton anddates when avalable although t s also desrable to be able to predt the relablty when genotype data of e.g. seleton anddates s not avalable.e. when desgnng breedng programs. ous equatons have been proposed n the lterature to predt the relablty or the auray.e. the square root of relablty of genom EBV for groups of anmals. The nvestgated genom predtons rely on sngle-populaton genom models and on SGM When genotypes are avalable for both referene anmals and seleton anddates predton equatons are derved usng seleton ndex SI theory whle before avalablty of all genotypng data they are derved usng populaton parameters e.g. hertablty number of referene anmals However to our knowledge equatons for predtng the relablty of genom EBV for rossbreedng performane for groups of anmals have not yet been reported. The prmary am of ths study was to derve equatons for predtng the relablty of genom EBV for rossbred performane based on SGM or BSM. Predton equatons were derved for stuatons when all genotypng data are avalable for both referene anmals and seleton anddates referred to as wth avalablty of genotypng data and for stuatons when the genotypng data are not avalable referred to as wthout avalablty of genotypng data. The seond am was to ompare the predtons of the relablty of genom EBV wthout avalablty of genotypng data to the predtons obtaned from the equatons wth avalablty of genotypng data beause the former are an approxmaton of the latter. Both relabltes have the same expetaton sne they both rely on predton error varanes PEV and assume absene of seleton. Fnally the equaton for predtng relablty wthout avalablty of genotypng data was used to nvestgate the expeted ranges of relabltes of genom EBV usng BSM for a pg breedng program. Methods The frst part of ths seton desrbes equatons for predtng the relablty of genom EBV for rossbred performane usng SGM or BSM. For the dervatons of these equatons we assumed a rossbreedng program wth two breeds and B wth ther F1 beng rossbred anmals. In order to smplfy the dervaton of the equatons we assumed that phenotypes are orreted for all fxed and random effets other than addtve genet effets. Furthermore referene anmals are defned as

3 Vandenplas et al. Genet Sel Evol :43 Page 3 of 19 anmals wth genotypes and phenotypes and seleton anddates are defned as anmals wth genotypes but wthout ther own phenotype. The assumpton that all referene anmals have genotypes s lkely to be orret n the near future as genotypng osts ontnue to derease. The am s to predt the relablty of genom EBV for rossbred performane for seleton anddates of breed. For the referene populaton three senaros were nvestgated: 1 the referene populaton nludes only breed anmals PB PB.e. purebred PB phenotypes are used to predt EBV for rossbred CB performane of PB seleton anddates; 2 the referene populaton nludes only rossbred anmals CB PB.e. CB phenotypes are used to predt EBV for CB performane of PB seleton anddates; and the referene populaton nludes both rossbred and breed anmals CB + PB PB.e. CB and PB phenotypes are used to predt EBV for CB performane of PB seleton anddates. These senaros represent stuatons where rossbred anmals are termnal anmals n ommeral herds of pgs and hkens. The seond part of ths seton desrbes smulatons of the three senaros used to valdate the predton equatons wthout avalablty of genotypng data. In the equatons below referene anmals are ndated by upperase letters whle seleton anddates are ndated by lowerase letters. ross breed SNP genotype models Equatons for predtng the relablty of genom EBV for rossbred performane usng SGM were developed for the three senaros. s SGM s assumed breed and rossbred anmals an be onsdered as belongng to dfferent populatons assumng the genet orrelaton between the PB and CB performane trats r to be the genet orrelaton between these breed and rossbred populatons. Therefore equatons for predtng the relablty of genom EBV for rossbred performane for the three senaros usng SGM an be derved from prevous studes by for example Daetwyler et al. 12 and Wentjes et al. 1 wthout avalablty of genotypng data and by VanRaden 15 wth avalablty of genotypng data. PB PB senaro The PB PB senaro onsders breed anmals for both referene anmals and seleton anddates. Phenotypes are therefore assoated wth the purebred performane trat whle the trat of nterest s the rossbred performane trat. Indeed seleton anddates must be seleted to optmze rossbred performane of ther rossbred desendants. Wentjes et al. 1 developed equatons for predtng the auray of aross-populaton genom EBV values wthout and wth avalablty of genotypng data. ssumng addtve gene aton dfferenes n allele substtuton effets that underle the populaton-spef trat of nterest were modelled by the genet orrelaton between trats whh mples a multvarate genom model. Smlarly for the PB PB senaro dfferenes n allele substtuton effets that underle the purebred and rossbred performane trats an be onsdered n terms of the genet orrelaton between the purebred and rossbred performane trats r Therefore followng Wentjes et al. 1 wth avalablty of genotypng data the average predted relablty of genom EBV for rossbred performane aross-breed seleton anddates usng breed referene anmals an be omputed as follows based on SI theory: r 2 P_SGM_wth 1 N a where N a s the number of breed seleton anddates; h 2 a σ 2 a σ 2 a +σ 2 e s the hertablty of the purebred performane trat wth σa 2 beng the genet varane of the purebred performane trat and σe 2 the resdual varane of purebred performane trat; r σ a σ 2 a σ 2 wth σ a beng the genet ovarane between the purebred and rossbred performane trat and σ 2 the genet varane of the rossbred performane trat; matrx G s the N N genom relatonshp matrx for the N referene anmals of breed ; vetor G a s the row orrespondng to the th seleton anddate of breed of the N a N genom relatonshp matrx G a between seleton anddates of breed and referene anmals of breed ; G a a s the dagonal element orrespondng to the th seleton anddate of breed of the N a N a genom relatonshp matrx G aa between seleton anddates of breed ; and matrx I s the dentty matrx. Matres G G aa and G a are parts of the genom relatonshp matrx among all referene anmals and G G a seleton anddates of breed.e. G 1 N a r 2 P_SGM_wth G r 2 a. G a G aa Wthout loss of generalty and smlar to Wentjes et al. 1 matrx G s omputed followng the seond method of VanRaden 15.e. G ZZ m where m s the number of SNP genotypes and matrx Z ontans the standardzed genotypes as Z lk M 2pk lk 2p k 1 p k wth M lk beng the SNP genotype oded as for one homozygous genotype 1 for the heterozygous genotype or 2 for the alternate 1Ga G + I 1 h2 a h 2 a G a a 1

4 Vandenplas et al. Genet Sel Evol :43 Page 4 of 19 homozygous genotype of the lth anmal of breed for the kth lous and p k s the allele frequeny at the kth lous. Wthout avalablty of genotypng data the predted relablty of genom EBV for rossbred performane of breed seleton anddates and usng breed referene anmals an be omputed as 1: r 2 C_SGM_wth 1 N a 1 N a r 2 C_SGM_wth G a G + I 1 h2 h 2 G a a 1Ga 3 rp_sgm_wthout 2 N h 2 r2 a 2 N h 2 a + Me where h 2 σ 2 a where Me a s the effetve number of hromosome segments that are shared between seleton anddates and referene anmals of breed. If the term r 2 s gnored or equal to 1 Eq. 2 has the same form as the equaton proposed by Daetwyler et al. 12. One of the assumptons n the dervaton of ths equaton was that the error varane was approxmately equal to the phenotyp varane beause only one lous was taken nto aount at a tme and eah lous explans only a small part of the addtve genet varane However as explaned by Daetwyler et al. 12 n the ppendx of ther paper ths approxmaton results n slght underestmaton of the predted relabltes beause the error varane dereases when multple lo are used. In ddtonal fle 1 of the urrent study we proposed a dervaton of Eq. 2 based on the mxed model theory and gnorng the term r 2. We assumed that a sngle populaton was used and that effets of all ndependent lo are estmated smultaneously. Our dervaton leads to the same equaton as proposed by Daetwyler et al. 12 n the ppendx of ther paper whh orrets for the fat that the error varane dereases when multple lo are used. Ths dervaton usng the mxed model theory an be extended for dervng predton equatons usng SGM and t wll be also the bass for dervng predton equatons usng BSM. σ 2 +σ 2 e s the hertablty of the rossbred performane trat wth σe 2 beng the resdual varane; matrx G s the N N genom relatonshp matrx between the N rossbred referene anmals; and vetor G a s the row orrespondng to the th seleton anddate of breed of the N a N genom relatonshp matrx G a between breed seleton anddates and rossbred referene anmals. Smlarly to Wentjes et al. 1 the genom relatonshp matrx between breed seleton anddates and rossbred referene anmals G s omputed followng the seond method of VanRaden 15 but takng nto aount that the seleton anddates and referene anmals belong to two dfferent populatons. It then follows that G G G a G a G aa ZZ m where m s the number of SNPs and matrx Z ontans the standardzed genotypes as Z ljk M ljk 2p jk wth M ljk beng the SNP 2p jk 1 pjk genotype oded as prevously of the lth ndvdual from the jth populaton.e. purebred or rossbred for the kth lous and p jk s the allele frequeny of the jth populaton at the kth lous. Wthout avalablty of data an equaton that predts the relablty of genom EBV for rossbred performane of breed seleton anddates usng N rossbred referene anmals an be smply wrtten as follows: CB PB senaro The referene populaton for the CB PB senaro nludes genotyped rossbred anmals that have phenotypes for the rossbred performane trat. The seleton anddates are breed anmals that are related to the referene populaton and that must be seleted to optmze rossbred performane of ther rossbred desendants. Beause the trat of nterest s the rossbred performane trat and beause allele substtuton SNP effets are estmated from rossbred data the average predted relablty of genom EBV for rossbred performane aross breed seleton anddates usng a rossbred referene populaton an be omputed wth avalablty of genotypng data as follows 1: rc_sgm_wthout 2 N h 2 N h 2 + Me a where Me a s the effetve number of hromosome segments shared by breed seleton anddates and rossbred referene anmals 1. CB + PB PB senaro The referene populaton for the CB + PB PB senaro nludes anmals of breed wth phenotypes for the purebred performane trat and rossbred anmals wth phenotypes for the rossbred performane trat. The seleton anddates are anmals of breed that are related to the referene populaton. Sne the rossbred performane trat s the trat of nterest the average 4

5 Vandenplas et al. Genet Sel Evol :43 Page 5 of 19 predted relablty of genom EBV aross seleton anddates for rossbred performane of breed seleton anddates usng breed and rossbred referene anmals an be omputed wth avalablty of genotypng data as follows 1: r 2 C+P_SGM_wth 1 N a 1 N a 1 G a a r G a G + I 1 h2 a h 2 a r G r 2 C+P_SGM_wth G a G r Wthout avalablty of genotypng data the predton equaton for the relablty of genom EBV for rossbred performane of breed seleton anddates usng breed and rossbred referene anmals an be wrtten as follows 14: r 2 C+P_SGM_wthout r r Breed spef allele substtuton models In rossbred populatons SNP effets may be breed-spef due to a number of fators 4 nludng dfferent extents of LD between SNP and QTL between breeds whh an be aommodated by usng BSM whh fts breed-spef allele substtuton effets 3 4. In ths seton t s assumed that the breed orgn of SNP alleles s known as requred by BSM. Moreover only the CB PB and CB + PB PB senaros are onsdered sne the PB PB senaro nvolves data on only one breed. To our knowledge equatons for predtng the relablty of genom EBV usng BSM have not prevously been developed. CB PB senaro For the CB PB senaro assumng that eah ndvdual has one phenotyp reord orreted for all effets other than the addtve genet effets BSM for the rossbred performane trat an be wrtten as follows 3 4: where y s the vetor of orreted reords of rossbred performane; Z ZB ontans the standardzed breed B SNP alleles of eah rossbred anmal; β β B G + I 1 h2 h 2 h 2 r a h 2 Me a Me a h 2 a Me a + 1 N r h 2 a h 2 h 2 a h 2 Me a Me a h 2 a Me a h 2 Me a. Me a Me a h 2 Me a + N 1 y Z β + Z B βb + e 1 r G a G a s the vetor of breed B-spef allele substtuton effets for all SNPs; and e s the resdual vetor. Entres of matrx Z are defned as Z lk M lk p k 2pk 1 p k where element M lk s set to or 1 when the kth lous of the lth ndvdual has breed allele 1 or 2 respetvely; and p k s the frequeny at the kth lous for breed. Matrx Z B s defned smlarly. Expetatons and varanes of β and β B are assumed to be E Iσ 2 β β β B β β B Iσ 2 β B and where σ 2 σ 2 s the varane of the breed B-spef allele substtuton effet and σ 2 β β B σ 2 B s the addtve genet varane due to alleles from populaton B n the rossbred populaton for the rossbred performane trat 3 4. Equvalently BSM for the rossbred performane trat an be wrtten as 3: y + B + e where Z β B ZB βb s the vetor of breed B of orgn addtve genet effets for the rossbred performane trat. It then follows that expetatons and varanes of and B are defned as E B and B Z σ Z 2 m Z B ZB I σ 2 B m σ 2 G B σ 2 B where GB s the breed B partal genom relatonshp among the N rossbred anmals 3. These assumptons mply that and B as well as β and β B are ndependent of eah other. Based on SI theory genom EBV for rossbred performane of seleton anddates from breed a an be predted from reords of rossbred referene anmals as follows: ĉ a Usng the model desrpton t an then be shown that the varane of y s equal to: Cov a y 1y y. I σ 2 m I σ 2 B m y G σ 2 + G B σ 2 B + Iσ 2 e

6 Vandenplas et al. Genet Sel Evol :43 Page 6 of 19 and that the ovarane between a and y s equal to: Cov a y Cov a + B + e Cov a + Cov a B + Cov a e Cov a a σ 2 wth matrx a m 1 Z a Z beng the breed -spef partal genom relatonshp matrx between the N a seleton anddates of breed and the N rossbred referene anmals. The relablty of ĉ a of the th seleton anddate of breed s then equal to: Cov ĉ rc_bsm_wth 2 a 2 a ĉ a ĉ a a a 1 a + σ GB 2 B a a σ 2 Wth avalablty of genotypng data the average predted relablty of genom EBV aross all breed seleton anddates s equal to: rc_bsm_wth 2 1 rc_bsm_wth 2 N 1 a N a + h 2 GB B h 2 where h 2 σ 2 σ σ 2 B 2 +σ 2 e h 2 B + I σ2 e σ 2 1 a a a + I h2 1 2 h2 B h 2 σ 2 B σ σ 2 B 2 +σ 2 e 1 a. 1 a s the breed B-spef hertablty of rossbred performane. Sne no equaton has prevously been proposed to predt the relablty of genom EBV for BSM wthout avalablty of genotypng data here we put forward a dervaton based on mxed model theory 17 assumng that allele substtuton effets for breeds and B are estmated smultaneously. Equvalene between the mxed model and SI theores has prevously been shown under ertan ondtons nludng the use of the same estmates of the fxed effets Our dervaton of the equaton for predtng the relablty of genom EBV for BSM wthout avalablty of genotypng data.e. Eq. 8 below s detaled n ddtonal fle 2 and the result s brefly desrbed n the followng. Consder N unrelated genotyped rossbred referene anmals. For smplty t s assumed that the breed -spef effet β of eah kth ndependent lous 7 explans an equal amount of the breed -spef addtve genet varane σ 2.e. σ 2 Me a σ 2 β wth Me a beng the effetve number of hromosome segments underlyng the rossbred performane trat for breed and segregatng n both breed seleton anddates and rossbred referene anmals. The same assumpton s made for the breed B-spef effet β B. The genom EBV a for the th seleton anddate of breed an be predted as follows: ĉ a za ˆβ where za s a vetor of the standardzed genotypes for the Me a ndependent lo of the th seleton anddate of breed and ˆβ s the vetor of the predtons of β. Followng mxed model theory the relablty of ĉ a an be omputed from the predton error varane ĉ a a and s equal to: ĉ r 2 C BSMwthout 1 z a ĉ a ssumng that the allele substtuton effet β of eah kth ndependent lous explans an equal amount of the breed -spef addtve genet varane σ 2 and that the relablty of the estmated effet r 2 β s the same for eah lous t follows that: Relablty r 2 β an be approxmated as follows. Let ŷ be the vetor of phenotypes orreted for all other fxed effets for the breed -spef allele substtuton effets other than the kth effet ˆβ as well as for the breed k B-spef allele substtuton effets ˆβ B. The predton of β for the kth lous an then be performed usng the followng model: a a a a za za ˆβ z a ˆβ z a. β za ˆβ rc_bsm_wthout 2 ŷ z k β + ε k β r 2 β. β

7 Vandenplas et al. Genet Sel Evol :43 Page 7 of 19 where vetor z k ontans the standardzed breed alleles of rossbred referene anmals and ε k s the resdual vetor. The varane of ŷ s equal to: ŷ z k β + ε k from whh t follows that after some algebra and assumng unrelated genotyped anmals see ddtonal fle 2 for detals: where σp 2 σ 2 e s the phenotyp resdual varane of the rossbred performane trat. Therefore followng mxed model theory the predton of β z k z k σ 2 β ε k ŷ z ˆβ k z k σ 2 I 1 r 2 2 β I ˆβ + σ 2 B 2 s equal to: + ε k σ 2 β and the relablty of ˆβ s equal to see ddtonal fle 2 for more detals: r 2 β It then follows that wthout avalablty of genotypng data the predted relablty of the genom EBV for breed seleton anddates s equal to see ddtonal fle 2 for more detals: By gnorng the term 1 2 h2 r 2 1 a 2 h2 B r 2 a B h 2 and h 2 B the predton equaton smplfes to: σp 2 σ 2 2 r2 β σ 2 B 2 r2 β B z k β r 2 C_BSM_wthout r2 β 1 r 2 β B + σ 2 e Iσ 2 ε 1σ z k σε 2 + σ 2 2 β ε z k ŷ N σε 2 σ 2 β N σε 2 σ β r 2 C_BSM_wthout N h 2 + 2Me a ˆβ β β N h h2 r 2 a N h 2 N h 2 + 2Me. a 1 2 h2 B r 2 B a. for low 8 CB + PB PB senaro For the CB + PB PB senaro the referene populaton nludes breed and rossbred referene anmals eah wth ther own phenotypes. The BSM for the rossbred performane trat assumng that eah ndvdual has one reord orreted for all effets other than addtve genet effets an be wrtten as follows 3 4: y y Z Z + Z B β a β β B where y s the vetor of orreted reords of purebred performane Z ontans the standardzed SNP genotypes of breed referene anmals and β a s the vetor of breed allele substtuton effets for all SNPs for purebred performane. Equvalently the prevous BSM an be wrtten as 3: y a e y + B + e where a Z β a s the vetor of addtve genet effets for the purebred performane trat. Expetatons and varanes and ovaranes of a a and B are assumed to be E and B a Z σ Z a 2 m Z σ a Z m B Z σ a Z m Z σ 2 Z m Z B σ 2 ZB B m σ a 2 σ a σ a σ 2 G B σ 2 B where s the breed genom relatonshp matrx between N referene anmals of breed and s the breed -spef partal genom relatonshp matrx between N seleton anddates of breed and N rossbred referene anmals 3. Based on the SI theory genom EBV for the rossbred performane trat for breed seleton anddates a an be predted from reords of breed referene anmals and of rossbred referene anmals: ĉ a Cov a y wth y. y Based on the model desrpton the varane of y s equal to: + y y 1y e e

8 Vandenplas et al. Genet Sel Evol :43 Page 8 of 19 y y y sne: σ 2 + Iσ 2 e σ a σ a σ 2 + G B σ 2 B + Iσe 2 Cov y y Cov a + e Cov a + B Cov a + B + e σ a. Smlarly the ovarane between a and y s equal to: Cov a y a σ a a σ 2. The relablty of ĉ a of the th seleton anddate of breed s then equal to: Cov ĉ rc+p_bsm_wth 2 a 2 a ĉ a a 1 a a σ a 1 σ 2 a + Iσ 2 e G a a σ a r G a G a B + I 1 h2 a h 2 a r G ĉ a a a σ 2 Wthout avalablty of genotypng data the predton equaton for the relablty of genom EBV based on BSM rc+p_bsm_wthout 2 an be derved smlarly to the predton equaton for the CB PB senaro rc_bsm_wth 2. The dervaton s based on mxed model theory and assumes that ndependent allele substtuton effets for breeds and B for both purebred and rossbred performanes were estmated smultaneously. The detaled dervaton an be found n ddtonal fle 3. Consder N unrelated genotyped breed referene anmals and N unrelated genotyped rossbred referene anmals. Smlar to the CB PB senaro the genom EBV a for the th seleton anddate of breed an be predted as ĉ a za ˆβ and ts relablty s equal to: ĉ rc+p_bsm_wthout 2 a ˆβ k r 2 a β. σ a σ 2 + G B σ 2 B + Iσe 2 + GB where the breed -spef genet orrelaton between purebred and rossbred performane trats r s equal to r σ a. σa 2 σ 2 Wth avalablty of genotypng data the average predted relablty of genom EBV aross all breed seleton anddates s therefore equal to: rc+p_bsm_wth 2 1 rc+p_bsm_wth 2 N 1 a a a r G h 2 B h 2 + I h2 1 2 h2 B h 2 r G a G a B 1 a σ a a σ 2 1 r G a a β Relablty r 2 β an be approxmated as follows. The predton of β for the kth ndependent lous an be performed usng the phenotypes of both purebred and ŷ rossbred performanes ŷ orreted for all other 1 + I 1 h2 a h N a 2 a r G a a r G + GB r G h 2 B h 2 + I h2 1 2 h2 B h 2 1 9

9 Vandenplas et al. Genet Sel Evol :43 Page 9 of 19 fxed effets as well as for the breed B-spef allele substtuton effets and orrelated effets usng the model: ŷ ŷ z k z k and the relablty of ˆβ s equal to: ˆβ a εk k ˆβ + ε k k where ε k s the resdual vetor. For smplty we wll εk Iσ 2 assume that ε ε k Iσε 2 wth σε 2 beng the resdual varane assoated wth ŷ. Then followng mxed model theory the predton of βa k β s equal to: k ˆβ a k z ˆβ k Iσ 2 ε z k z Iσε 2 k z k r 2 β β k z k z k Iσ 2 ε Iσ 2 ε ˆβ β β ŷ σ 2 β ŷ where PEV ˆβ s the predton error varane of ˆβ k and s equal to the dagonal element of the nverse of the left-hand sde of the mxed model equatons assoated wth the predton of k β a β. fter some algebra whh s detaled n ddtonal fle 3 t follows that the predted relablty of genom EBV for breed seleton anddates wthout data s equal to: rc+p_bsm_wthout 2 r2 β r h 2 a r h 2 a Me a + N 1 r h 2 Me a 2Me a h 2 h 2 a 2Me Me a a h 2 a Me a h 2 2Me a r Computaton of the effetve number of hromosome segments Me The predton equatons wthout avalablty of genotypng data requre the effetve number of hromosome segments that are ndependently segregatng n a populaton nludng seleton anddates S and referene anmals R.e. that are shared between the two h 2 2Me a PEV ˆβ σ 2 β h 2 a Me a h 2 + 2Me N 1 a 1 1 populatons Me SR. The value of Me SR an be omputed as proposed by Wentjes et al. 14: 1 Me SR SG 2 SR SR where G SR s the genom relatonshp matrx between seleton anddates and referene anmals SR s the pedgree relatonshp matrx and S 2 G SR SR s the empral varane of the dfferenes between orrespondng elements of G SR and SR. In our study G SR and SR were saled to the same base populaton by resalng the nbreedng level n G SR to the nbreedng n SR as follows 2: G SR 1 F G SR + 2 FJ σ 2 1 β + a σ β a β σ β a β σ 2 β where F s the average pedgree nbreedng level omputed from the pedgree and J s a matrx flled wth 1s. The proposed omputaton of Me requres genotypes for both seleton anddates and referene anmals whh may be nonsstent wth ts use n the omputaton of relabltes wthout avalablty of genotypng data. However t s reasonable to assume that genotypes are already avalable for a lmted number of anmals for example at least 1 that have the rght famly struture that s representatve of the evaluated senaro suh that an aurate approxmaton of Me an be omputed 14. The effetve number of hromosome segments orgnatng from a spef breed b and that are shared between purebred seleton anddates S of ths breed and rossbred referene anmals R Me b SR s requred for the predton equatons for BSM. In ths study Me a s requred n Eqs. 8 and 1 and was assumed to be equal to Me a whh s requred n Eqs. 2 and 6. The equalty Me a Me a was assumed sne the seleton anddates were the same for Eqs and 1 the number of referene anmals R and R was large and the parents of breed and rossbred referene anmals were sampled from the same fnte pool. Smulated data Data were smulated to valdate Eqs and 1 whh predt the relablty of genom EBV for rossbred performane usng SGM or BSM wthout avalablty of genotypng data. Two extreme senaros were onsdered n whh ether two losely-related or two unrelated breeds were used to produe rossbred 1

10 Vandenplas et al. Genet Sel Evol :43 Page 1 of 19 anmals. The relabltes predted by Eqs and 1 were valdated aganst the relabltes omputed wth the orrespondng predton equatons wth avalablty of genotypng data that s Eqs and 9. The relabltes predted by equatons wth avalablty of genotypng data are equvalent to those omputed from PEV assoated wth seleton anddates of a genom best lnear unbased predton nludng both referene anmals and seleton anddates based on phenotypes orreted wth the best lnear unbased estmates of the fxed effets and assumng the absene of seleton 15. Generaton Breed 5 F 5 M Breed 8 F 5 M Hstoral populaton 5 M - 5 F 5 M - 5 F 1 M 1 F Breed B 5 F 5 M Breed B 8 F 5 M Populatons Frst hstoral and breed populatons were smulated usng the QMSm software 21; seond a two-way rossbreedng program wth fve generatons of random seleton was smulated usng a ustomzed Fortran program. For the hstoral populaton 1 dsrete random matng generatons wth a onstant sze of 1 ndvduals were smulated whh was followed by 1 generatons n whh the populaton sze was gradually dereased to 2 ndvduals. In these 2 hstoral generatons half of the smulated anmals were males and the other half were females. Offsprng were produed by the random unon of gametes from the male and female gamet pools and the number of offsprng was equal to the number of anmals requred n the next generaton. To smulate the two breed populatons and B two random samples were drawn from the last generaton of the hstoral populaton.e. generaton 2 eah nludng 5 males and 5 females. Subsequently wthn eah of the breeds 1 or 1 generatons of random matng were smulated before the two-way rossbreedng sheme was begun. These two senaros.e. a ommon orgn ether 1 or 1 generatons ago wll be referred to as related and unrelated breeds respetvely. For the 1 and 1 generatons of random matng a ltter of four offsprng two males and two females per female was smulated. From these offsprng 5 males were seleted at random for the next generaton. The number of females seleted randomly for the next generaton was gradually nreased from 5 to 8 durng the frst four generatons of the smulaton of the breed populatons n order to enlarge the sze of the populaton Fg. 1. In a seond step a two-way rossbreedng program wth fve generatons of random seleton was smulated. The anmals of breeds and B that were used to start the rossbreedng program were sampled from generaton 21 for the related breeds and from generaton 21 for 2+x 21+x 22+x Breed 8 F 5 M F 3 M 1 3 F 1 M F 3 M 1 23+x 1 M 3 F 25+x 1 M 3F Breed B 8 F 5 M B F 3 the unrelated breeds. Durng the rossbreedng program and for both breeds anmals of breeds and B were randomly seleted and mated to smulate the next generaton of a onstant sze of 1 males and 3 females for eah breed. From eah of these fve generatons anmals of breeds and B were randomly rossed to produe fve generatons of 4 rossbred anmals. Purebred anmals used as parents of rossbred anmals ould also be parents of the next generaton of purebred anmals Fg. 1. B B M 1 B 3 F 1 M B F 3 B M 1 B 3 F 1 M B 3 F 1 M Fg. 1 Shemat representaton of the smulaton. The rossbreedng program started at generaton 21 + x wth x beng equal to 1 for the senaro wth related breeds and equal to 1 for the senaro wth unrelated breeds. The number of males M and females F per generaton are reported wthn brakets. Referene anmals were randomly seleted from generaton 22 + x n bold. Breed seleton anddates were randomly seleted from generatons 23 + x 24 + x and 25 + x n tal haraters

11 Vandenplas et al. Genet Sel Evol :43 Page 11 of 19 Genotypes The total length of the smulated genome was 1 Morgans M 1 hromosomes of 1 M and 4 SNPs eah. The postons of SNPs and of reombnatons were randomzed per hromosome and a reurrent mutaton rate of was assumed. ll SNPs wth a mnor allele frequeny MF hgher than or equal to.5 n the last hstoral generaton.e. generaton 2 and were used to smulate the SNP genotypes of the purebred and rossbred anmals. For subsequent analyses 2 SNPs were randomly seleted from these SNPs for eah hromosome. The breed orgn of eah allele for eah rossbred anmal was reorded. ll senaros nludng the hstoral populatons were replated 1 tmes. Valdaton of predton equatons wthout avalablty of genotypng data The valdaton requred a set of known genotypes as desrbed prevously but no phenotype sne the relabltes predted wthout avalablty of genotypng data were valdated aganst the relabltes predted wth avalablty of genotypng data. However estmates of hertabltes and genet orrelatons between purebred and rossbred performane were requred. Hertabltes of.2.4 and.95 were used for both the purebred and rossbred performane trats. hgh hertablty suh as.95 and a sngle reord per referene anmal an be assumed when phenotypes of referene anmals are derved from hghly relable EBV e.g. deregressed EBV 1. Genet orrelatons between purebred and rossbred performane trats were assumed to be equal to.3 or.7. In the smulated data two groups of referene anmals and one group of seleton anddates were defned for eah senaro of related and unrelated breeds. For the senaros wth related and unrelated breeds the two groups of referene anmals were randomly seleted from generatons 212 and 212 respetvely. For senaros PB PB and CB PB the two groups of referene anmals nluded 2 and 4 anmals that were randomly hosen from breed and rossbred anmals respetvely. For senaro CB + PB PB the frst group nluded 4 randomly hosen breed anmals and 2 randomly hosen rossbred anmals and the seond group nluded 4 breed anmals and 4 rossbred anmals. For the seleton anddates for senaros PB PB CB PB and CB + PB PB 1 breed anmals were randomly seleted from eah generaton startng from generaton 213 for the related breeds senaro and from generaton 213 for the unrelated breeds senaro to reate the groups of seleton anddates. In the followng seleton anddates from generatons 213 or 213 are referred to as G1 seleton anddates. Smlarly seleton anddates from generatons 214 and 214 and from generatons 215 and 215 are referred to as G2 and G3 seleton anddates respetvely. For eah referene populaton-seleton anddates ombnaton and for eah senaro relabltes of the genom EBV for rossbred performane were omputed usng Eqs and 9 for the senaros n whh all data was avalable and usng Eqs and 1 for senaros wthout avalablty of genotypng data. The requred genom relatonshp matres and values of Me were omputed usng our n-house software al_grm 22. The predted relabltes were averaged aross the 1 replates. pplaton of a predton equaton The proposed equatons an be used to nvestgate the relablty of genom EBV for rossbred performane n rossbreedng shemes. s an llustraton Eq. 1 whh predts the relablty of genom EBV usng both purebred and rossbred anmals as referene anmals by BSM was used to predt the relablty of genom EBV for a pg produton system for whh 1 breed anmals were prevously genotyped and phenotyped. The am was to nvestgate the effet of the addton of rossbred anmals to the referene populaton on the relablty of genom EBV for rossbred performane. hertablty of.2 was assumed for both purebred and rossbred performane trats and the genet orrelaton between purebred and rossbred performane trats for breed r ranged from. to 1.. Both values of Me requred by Eq. 1.e. Me a and Me a were assumed to be equal to based on the equaton Me 2N e L/ln 4N e L 23 wth N e beng the effetve populaton sze and L beng the total length of the genome n M. For N e and L we assumed values of 8 and 27 respetvely based on the study of Landrae pgs by Umar and Tapo 24 and the study by Ln et al. 25. The use of equal values of Me for the purebred and rossbred populatons was based on the assumpton that breed parents of purebred and rossbred anmals were sampled from the same pool. Results Ths seton frst presents the results of the valdaton of the equatons for predtng relablty wthout avalablty of genotypng data. s defned prevously the relabltes wthout avalablty of genotypng data were valdated aganst the relabltes omputed wth avalablty of genotypng data. The seond part of ths seton desrbes the nrease n relabltes from the addton of rossbred anmals to a purebred referene populaton n a pg breedng program.

12 Vandenplas et al. Genet Sel Evol :43 Page 12 of 19 PB PB senaro For the PB PB senaro the results show that relabltes predted wthout avalablty of genotypng data were of the same order of magntude as relabltes omputed wth avalablty of genotypng data Fgs For the senaro wth related breeds and r.3 Fg. 2 the predted relabltes wth avalablty of genotypng data were around.1 for h 2 a.2 n the range.2;.3 for h 2 a.4 and n the range.4;.5 for h 2 a.95 aross all three groups of G1 G2 or G3 seleton anddates and wth 2 referene anmals from breed. When r.7 Fg. 3 the orrespondng Fg. 2 Relabltes wth a purebred referene populaton and a genet orrelaton equal to.3. Relabltes of genom estmated breedng values for rossbred performane wth W/ and wthout W/O avalablty of genotypng data usng a referene populaton wth 2 or 4 breed anmals whh are separated from breed seleton anddates by one G1 or three G3 generatons. Hertabltes of.2.4 and.95 were assumed. Results were averaged aross replates Fg. 3 Relabltes wth a purebred referene populaton and a genet orrelaton equal to.7. Relabltes of genom estmated breedng values for rossbred performane wth W/ and wthout W/O avalablty of genotypng data usng a referene populaton wth 2 or 4 breed anmals whh are separated from breed seleton anddates by one G1 or three G3 generatons. Hertabltes of.2.4 and.95 were assumed. Results were averaged aross replates predted relabltes wth avalablty of genotypng data were n the range.5;.7 for h 2 a.2 n the range.1;.15 for h 2 a.4 and n the range.2;.28 for h 2 a.95. For both senaros wth r.3 and r.7 the addton of 2 breed referene anmals slghtly nreased the predted relabltes Fgs Relabltes predted wthout avalablty of genotypng data were always lower than those predted wth avalablty of genotypng data whh agrees wth theory see PB PB senaro seton n the Methods seton. For the senaro wth related breeds and r.3 Fg. 2 the dfferenes between relabltes predted wthout and wth avalablty of genotypng data were around. for h 2 a.2 n the range.2;. for h 2 a.4 and n the range.2;.1 for h2 a.95 aross all three groups of G1 G2 or G3 seleton anddates and wth 2 breed referene anmals. When r.7 Fg. 3 the orrespondng dfferenes between relabltes predted wthout and wth avalablty of genotypng data were n the range.3;. for h 2 a.2 n the range.6;.2 for h2 a.4 and n the range.11;.4 for h 2 a.95. The largest dfferenes between relabltes predted wthout and wth avalablty of genotypng data were always observed for the G1 seleton anddates. Smlar results were obtaned for the senaro wth unrelated breeds see ddtonal fle 4: Tables S1 S2. Suh smlar results were expeted sne the dstane between breeds s not taken nto aount by SGM. The SD of the relabltes aross replates were n the range.;.1 see ddtonal fle 4: Tables S1 S2. CB PB senaro Relabltes wth and wthout avalablty of genotypng data are presented n Fg. 4 for related breeds and n Fg. 5 for unrelated breeds. The CB PB senaro nluded both SGM and BSM. For both models the relabltes predted wthout avalablty of genotypng data underestmated the relabltes predted wth avalablty of genotypng data. Underestmaton was lose to when h 2.2 and nreased up to.1 wth nreasng h2 and number of rossbred referene anmals. Smlar to the PB PB senaro the underestmaton of relabltes predted wth avalablty of genotypng data by the relabltes predted wthout avalablty of genotypng data was largest for the G1 seleton anddates. For the G1 seleton anddates the relabltes for SGM wth avalablty of genotypng data were around.9 wth 2 rossbred referene anmals ndependent of the relatonshp between the breeds and around.16 wth 4 rossbred referene anmals usng h 2.2 Fgs Dfferenes between the relabltes predted wthout and wth avalablty of genotypng data were

13 Vandenplas et al. Genet Sel Evol :43 Page 13 of 19 Fg. 4 Relabltes wth a rossbred referene populaton that orgnated from two related breeds. Relabltes of genom estmated breedng values for rossbred performane wth W/ and wthout W/O avalablty of genotypng data based on an aross-breed SNP genotype model SGM or on a breed-spef allele substtuton effets model BSM and usng a referene populaton wth 2 or 4 rossbred anmals. Referene anmals were separated from breed seleton anddates by one G1 or three G3 generatons. Hertabltes of.2.4 and.95 were assumed. Results were averaged aross replates Fg. 5 Relabltes wth a rossbred referene populaton that orgnated from two unrelated breeds. Relabltes of genom estmated breedng values for rossbred performane wth W/ and wthout W/O avalablty of genotypng data based on an aross-breed SNP genotype model SGM or on a breed-spef allele substtuton effet model BSM and usng a referene populaton wth 2 or 4 rossbred anmals. Referene anmals were separated from breed seleton anddates by one G1 or three G3 generatons. Hertabltes of.2.4 and.95 were assumed. Results were averaged aross replates around.1 for both 2 and 4 rossbred referene anmals. The orrespondng relabltes usng h 2.95 were around.37 and.58 wth 2 and 4 rossbred referene anmals respetvely. The orrespondng dfferenes between relabltes predted wthout and wth avalablty of genotypng data were n the range.13;.8. For G1 seleton anddates wth related breeds the relabltes for BSM wth avalablty of genotypng data were around.6 and.11 wth 2 and 4 rossbred referene anmals respetvely when usng h 2.2 Fg. 4. Dfferenes between relabltes predted wthout and wth avalablty of genotypng data were around.1 wth both 2 and 4 rossbred referene anmals. The orrespondng relabltes usng h 2.95 were around.27 and.43 wth 2 and 4 rossbred referene anmals respetvely. Correspondng dfferenes between relabltes predted wthout and wth avalablty of genotypng data were n the range.9;.6. Smlar dfferenes were observed wth unrelated breeds Fg. 5. The SD of relabltes aross replates were n the range.;.2 see ddtonal fle 4: Tables S3 S4. omparson of relabltes wth avalablty of genotypng data between SGM and BSM showed that SGM onsstently performed better than BSM. However relabltes for BSM nreased wth nreasng dstane between breeds whle relabltes for SGM were only slghtly affeted Fgs The nrease n relabltes wth nreasng dstane between breeds whh ompensates for the larger number of effets ftted n BSM ompared to SGM s n agreement wth prevous studes e.g. Ibanez-Esrhe et al. 4. CB + PB PB senaro The CB + PB PB senaro nluded both breed and rossbred anmals n the referene populaton. The number of breed referene anmals was always 4. The number of rossbred anmals was equal to 2 or 4. The CB + PB PB senaro also nluded both SGM and BSM. For related breeds relabltes wthout and wth avalablty of genotypng data are presented n Fg. 6 for r.3 and n Fg. 7 for r.7. Relabltes predted wthout and wth avalablty of genotypng data were of the same order of magntude for both SGM and BSM. Dfferenes between the two predted relabltes were n the range.9;.5. Smlar to prevous results these dfferenes nreased wth hertablty. Relabltes for BSM wth avalablty of genotypng data were about.3 to.4 lower than the orrespondng relabltes for SGM when hertabltes were assumed to be.2. Ths dfferene between relabltes for BSM and for SGM nreased wth nreasng hertablty and r and wth dereasng dstane between breeds. For example relabltes for BSM wth avalablty of genotypng data were between.7 and.12 ponts lower than the orrespondng relabltes for SGM when hertabltes were equal to.95. These lower relabltes for BSM an be attrbuted to the addtonal breed-spef effets ftted n the model for a gven number of reords. Smlar

14 Vandenplas et al. Genet Sel Evol :43 Page 14 of 19 Fg. 6 Relabltes wth a mxed referene populaton assumng two related breeds and a genet orrelaton of.3. Relabltes of genom estmated breedng values for rossbred performane wth W/ and wthout W/O avalablty of genotypng data based on an aross-breed SNP genotype model SGM or on a breed-spef allele substtuton effets model BSM. The referene populaton nluded 4 breed anmals and 2 or 4 rossbred anmals. Referene anmals were separated from breed seleton anddates by one G1 or three G3 generatons. Hertabltes of.2.4 and.95 were assumed. Results were averaged aross replates Fg. 8 Relabltes wth a mxed referene populaton assumng two unrelated breeds and a genet orrelaton of.3. Relabltes of genom estmated breedng values for rossbred performane wth W/ and wthout W/O avalablty of genotypng data based on an aross-breed SNP genotype model SGM or on a breed-spef allele substtuton effets model BSM. The referene populaton nluded 4 breed anmals and 2 or 4 rossbred anmals. Referene anmals were separated from breed seleton anddates by one G1 or three G3 generatons. Hertabltes of.2.4 and.95 were assumed. Results were averaged aross replates Fg. 7 Relabltes wth a mxed referene populaton assumng two related breeds and a genet orrelaton of.7. Relabltes of genom estmated breedng values for rossbred performane wth W/ and wthout W/O avalablty of genotypng data based on an aross-breed SNP genotype model SGM or on a breed-spef allele substtuton effets model BSM. The referene populaton nluded 4 breed anmals and 2 or 4 rossbred anmals. Referene anmals were separated from breed seleton anddates by one G1 or three G3 generatons. Hertabltes of.2.4 and.95 were assumed. Results were averaged aross replates Fg. 9 Relabltes wth a mxed referene populaton assumng two unrelated breeds and a genet orrelaton of.7. Relabltes of genom estmated breedng values for rossbred performane wth W/ and wthout W/O avalablty of genotypng data based on an aross-breed SNP genotype model SGM or on a breed-spef allele substtuton effets model BSM. The referene populaton nluded 4 breed anmals and 2 or 4 rossbred anmals. Referene anmals were separated from breed seleton anddates by one G1 or three G3 generatons. Hertabltes of.2.4 and.95 were assumed. Results were averaged aross replates trends were observed for relabltes wthout avalablty of genotypng data. Wth unrelated breeds the relabltes wthout and wth avalablty of genotypng data averaged aross replates are presented n Fg. 8 for r.3 and n Fg. 9 for r.7. Dfferenes between relabltes predted wthout and wth avalablty of genotypng data were n the range.4;.7 for all senaros wth hertabltes equal to.2 and to.4 and n the range.1;.5 for all senaros wth hertabltes equal to.95. Relabltes predted wth avalablty of genotypng data for BSM wth unrelated breeds were hgher by about.1 to.6 than the relabltes predted wth avalablty of genotypng data for BSM wth related breeds. Smlar trends were observed for relabltes predted

15 Vandenplas et al. Genet Sel Evol :43 Page 15 of 19 wthout avalablty of genotypng data showng a relable predton of relablty omputed wth avalablty of genotypng data. The SD of relabltes aross replates were n the range.;.6 see ddtonal fle 4: Tables S5 S6 S7 S8. Relabltes n a pg breedng program Predted relabltes for BSM when up to 1 rossbred anmals were added to a referene populaton of 1 breed anmals are n Fg. 1 showng that predted relabltes nreased when rossbred anmals were added to the referene populaton. The nrease n relabltes dereased wth nreasng r. The relabltes obtaned for SGM wth r.92 based on 1 breed referene anmals and no rossbred referene anmals.68 was the same as that for BSM based on only 1 rossbred referene anmals.e. wth r.. Therefore for r <.92 BSM wth only rossbred referene anmals an be at least as aurate as SGM wth a larger number of purebred referene anmals. Dsusson In ths study the term relablty refers to the preson of genom EBV obtaned by relatng ther PEV to the addtve genet varane of the base populaton.e. assumng absene of seleton. Equatons for predtng the relablty of genom EBV for rossbred performane are proposed for referene populatons that nlude purebred anmals rossbred anmals or both. Relabltes were predted for two models: SGM and BSM. For Fg. 1 Relabltes wth addtonal rossbred referene anmals and dfferent genet orrelatons. Relabltes predted wthout avalablty of genotypng data for genom estmated breedng values of rossbred performane usng a breed-spef allele substtuton effets model. The referene populaton nluded 1 purebred anmals and a number of rossbred anmals that vared from to 1. hertablty of.2 was assumed for both purebred and rossbred performane trats and the genet orrelaton between purebred and rossbred performane trats vared from. to 1.. ll the requred values of Me were assumed to be equal to the BSM we used the true breed-of-orgn of all alleles for the rossbred anmals whh would have to be estmated n prate whh may negatvely mpat the relablty obtaned. However we expet ths to have only a very mnor effet sne we showed n prevous studes that t s possble to aurately derve breed-of-orgn of alleles n three-breed rossbred pgs Relabltes of genom EBV an be predted when genotype data are already avalable.e. wth avalablty of genotypng data or wthout avalablty of genotypng data. For senaros wthout avalablty of genotypng data t s assumed that the requred genet parameters are omputed usng pedgree nstead of genom data or that estmates are avalable from the lterature. The results of ths study showed that the relabltes of genom EBV for rossbred performane predted wthout avalablty of genotypng data were of the same order of magntude as those predted wth avalablty of genotypng data. Therefore whle predton of relablty should preferably take the genotype data of seleton anddates nto aount when avalable both methods an predt the relablty of genom EBV for rossbred performane for dfferent referene populatons hertabltes and r. The derved equatons an therefore be useful to optmze the desgn of breedng programs. Relabltes predted wthout and wth avalablty of genotypng data The am of ths study was to predt the preson of genom EBV based on PEV n the absene of seleton. Thus the dervaton of our predton equatons wthout and wth avalablty of genotypng data was based on the SI and mxed model theores and assumed that phenotypes were orreted for all fxed and random effets other than the onsdered genet addtve effets. The equvalene between SI and mxed model theores under ertan ondtons suh as the use of the same estmates for the fxed effets has prevously been shown by several studes e.g Therefore relabltes predted wth avalablty of genotypng data would be expeted to be lose to relabltes omputed from PEV obtaned from genom best lnear unbased predton n the absene of seleton. Equatons for predtng the relablty of genom EBV wthout avalablty of genotypng data were valdated aganst the equatons for predtng relablty wth avalablty of genotypng data and not aganst the relablty of seleton.e. the squared orrelaton between estmated and true genom breedng values whh s often obtaned by ross-valdaton. Indeed the relablty of genom EBV s not equvalent to the relablty of seleton for populatons that are under seleton although they are equvalent for populatons wthout seleton Relablty of seleton