Application of single-step genomic evaluation for crossbred performance in pig 1

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1 Application of ingle-tep genomic evaluation for crobred performance in pig 1 T. Xiang* B. Nielen G. Su* A. Legarra and O. F. Chritenen* *Center for Quantitative Genetic and Genomic Department of Molecular Biology and Genetic Aarhu Univerity DK-8830 Tjele Denmark; INRA UR1388 GenPhye CS-567 F-3136 Catanet-Toloan France; and SEGES Pig Reearch Centre DK-1609 Copenhagen Denmark ABSTRACT: Crobreding i predominant and intenively ued in commercial meat production ytem epecially in poultry and wine. Genomic evaluation ha been uccefully applied for breeding within purebred but alo offer opportunitie of electing purebred for crobred performance by combining information from purebred with information from crobred. However it generally require that all relevant animal are genotyped which i cotly and preently doe not eem to be feaible in practice. Recently a novel ingle-tep BLUP method for genomic evaluation of both purebred and crobred performance ha been developed that can incorporate marker genotype into a traditional animal model. Thi new method ha not been validated in real data et. In thi tudy we applied thi ingle-tep method to analyze data for the maternal trait of total number of piglet INTRODUCTION Crobreding i predominant and intenively ued in meat production ytem (Wei 199) epecially in 936 born in Danih Landrace Yorkhire and two-way crobred pig in different cenario. The genetic correlation between purebred and crobred performance wa invetigated firt and then the impact of (crobred) genomic information on prediction reliability for crobred performance wa explored. The reult confirm the exitence of a moderate genetic correlation and it wa een that the tandard error on the etimate were reduced when including genomic information. Model with marker information epecially crobred genomic information improved model-baed reliabilitie for crobred performance of purebred boar and alo improved the predictive ability for crobred animal and to ome extent reduced the bia of prediction. We conclude that the new ingle-tep BLUP method i a good tool in the genetic evaluation for crobred performance in purebred animal. Key word: crobred performance genetic correlation genomic evaluation pig reliability ingle-tep method 016 American Society of Animal Science. All right reerved. J. Anim. Sci : doi:10.57/ja The project wa funded through the Green Development and Demontration Programme (grant number ) by the Danih Minitry of Food Agriculture and Fiherie the Pig Reearch Centre and Aarhu Univerity. The firt author benefited from a joint grant from the European Commiion and Aarhu Univerity within the framework of the Eramu-Mundu joint doctorate EGS-ABG. A.L. thank financing from INRA SelGen metaprogram project X-Gen and SelDir. The author alo thank for the valuable uggetion given by Per Maden from Center for Quantitative Genetic and Genomic Department of Molecular Biology and Genetic Aarhu Univerity. Correponding author: Tao.Xiang@mbg.au.dk Received October Accepted December Downloaded from on 10 January 018 wine and chicken. In two-way crobreding cheme election of purebred for their crobred performance i the ultimate goal (Wei 199; Bijma and Batiaanen 014). Becaue there exit genetic difference between breed and genotype environment interaction effect additive genetic effect etimated baed on purebred performance cannot be ued to perfectly predict the crobred performance (Lo et al. 1997). Ideally combined purebred and crobred information i required to implement the genetic evaluation for crobred performance (Wei and van der Werf 1994). However due to the difficulty and high cot of collection of data from crobred animal (Dekker 007) it i not common to have acce to crobred data. Genomic election ha been uccefully applied in purebred baed on data from purebred animal (Loberg and Dürr 009; Fulton 01) but it alo offer opportunitie for electing purebred for

2 GBLUP for crobred performance in pig 937 crobred performance by uing combined information from purebred and crobred (Ibáñez-Ecriche et al. 009; Zeng et al. 013) or by uing only purebred data (Efandyari et al. 015). However it generally require that all relevant animal are genotyped. Recently a novel ingle-tep BLUP method (Chritenen et al. 014) for genomic evaluation of both purebred and crobred performance in a two-way crobreding ytem wa developed that i an extenion of a ingle-tep BLUP method (Legarra et al. 009; Chritenen and Lund 010) from purebred performance to combined purebred and crobred performance. The aim of thi tudy i to implement the new ingle-tep BLUP method by uing both purebred and crobred data of total number of piglet born (TNB) in different cenario etimate the genetic correlation between purebred and crobred performance and then explore the impact of (crobred) genomic information on prediction reliability for crobred performance. MATERIALS AND METHODS Data For thi tudy all data et were provided by Danih Pig Reearch Centre. Three population were imultaneouly analyzed: Danih Landrace (LL) Danih Yorkhire (YY) and two-way crobred Danih Landrace Yorkhire. Crobred animal that had a Landrace ire and a Yorkhire dam were termed Landrace_Yorkhire () wherea Yorkhire_Landrace (YL) repreented crobred with Yorkhire ire and Landrace dam. The TNB data in thi tudy compried the record of the firt parity in all three population. Altogether TNB wa recorded in LL YY and crobred animal. Thi data et i termed the full population throughout the whole paper. Among the crobred 7407 were and 3567 were YL. All of the purebred animal had firt farrowing date between 003 and 013 and the crobred animal firt farrowed between 010 and 013. The pedigree for both purebred and crobred animal wa available and all the crobred were traced back to their purebred ancetor until 1994 by the DMU Trace program (Maden 01). Conequently 3399 LL YY and crobred were in the pedigree. Among thoe animal 773 LL and 7785 YY were genotyped with an Illumina PorcineSNP60 Genotyping BeadChip (Ramo et al. 009). Two-third of purebred genotyped animal were boar. For the crobred 503 animal (4077 and 116 YL) were genotyped with a 8.5K GGP-Porcine Low Denity Illumina Bead SNP Chip (GeneSeek 01). Single nucleotide polymorphim quality control were applied on the ame data et in a previou tudy (Xiang et al. 015) where more detail can be found. Finally SNP and 7916 SNP in autoome chromoome were acceible in purebred and crobred repectively. Imputation wa implemented in crobred from 7916 SNP to SNP with oftware Beagle (Browning 008) which output phaed SNP for both reference and imputed population by uing a joint reference panel of the two pure breed (Xiang et al. 015). A a reult phaed genotyped SNP were available for the genotyped animal in both purebred and crobred for the current tudy. Single-Step BLUP Model for Purebred and Crobred Performance The new ingle-tep BLUP method of evaluating both purebred and crobred performance wa developed by Chritenen et al. (014). The model reformulate the full Wei and van der Werf (1994) A1 model and incorporate genomic information by uing two breed-pecific combined relationhip matrice which extend the marker-baed relationhip matrice to the non-genotyped animal. The Wei and van der Werf model i a trivariate model: y L = X L β L + Z L a L + e L y Y = X Y β Y + Z Y a Y + e Y and y = X β + Z c + e in which y L y Y and y contain phenotype for purebred Landrace (L) purebred Yorkhire (Y) and crobred animal repectively; X L β L X Y β Y and X β repreent fixed effect; e L e Y and e were overall random reidual effect aumed to be independently normally ditributed with mean 0 and variance I e I L e and I Y e repectively; a L and a Y contain breeding value for breed L and breed Y for their purebred performance (mating within each own breed); c tand for the additive genetic effect of crobred animal; and Z L Z Y and Z are the repective incidence matrice. Note that the c animal additive genetic effect are actually formed a the um of two additive gametic effect one from L and another from Y. In other word a crobred diploid genome decompoe into two purebred haploid genome. The Chritenen et al. (014) method firt aume that effect of marker acro the different origin (Yorkhire and Landrace in thi cae) are unrelated. Under thi aumption the additive effect of the genome of an F 1 crobred animal can be plit into Downloaded from on 10 January 018

3 938 Xiang et al. the um of two additive gametic effect one gamete from each breed where the two gametic effect are uncorrelated by aumption of the model. Therefore eparate matrice of pedigree-baed or genomicbaed relationhip can be et up within each breed and then be combined according to purebred theory for the ingle tep (Legarra et al. 009; Chritenen and Lund 010). The analyi proceed by etimating olution to two different breed-pecific random effect. The key to dientangle the breed of origin for the genetic effect of the F 1 individual i the ability to contruct pedigree-baed partial relationhip matrice (García-Corté and Toro 006) or eparate (by origin) genomic matrice which in turn require acertainment of breed origin of the marker genotype. More pecifically there are three tep: Step 1). Reformulate the Wei and van der Werf model by plitting additive genetic effect for crobred animal () into breed of origin pecific genetic effect that i plit the additive genetic value of the ith F1 crobred in two additive genetic value one from each origin (LL or YY): c i = c L i + cy i. It ha to be undertood that neither of thee i a breeding value enu tricto; intead they are additive effect in the tatitical ene a regreion of value on gene doage a explained by Falconer et al. (1985) who clarifie the variou definition of average effect of gene in abence of random mating. Note that the new ingle-tep model (Chritenen et al. 014) i not the animal model ued by Lo et al. (1997) and Lutaaya et al. (001). Actually the new ingle-tep model i a reformulation of the full model from Wei and van der Werf (1994; equation A1) wherea Lo et al. (1997) and Lutaaya et al. (001) refer to the reduced animal model from Wei and van der Werf (1994; equation A). In the preence of only pedigree information the full and the reduced animal model are equivalent but in the preence of crobred genomic information thi i no longer the cae. In the paper of Lo et al. (1997) and Lutaaya et al. (001) the additive genetic value of the ith F 1 crobred i u i = (u L p(i L) + Φ Li ) + (uy p(i Y) + Φ Yi ). Here u L p(i L) and uy p(i Y) are half the additive genetic value of the purebred parent p(i Y) and p(i L) which are common to all the offpring of the ame ire or dam and Φ Li and Φ Yi are the repective Mendelian ampling which are different for each offpring. In the reduced animal model both Mendelian ampling term are included in the reidual effect of the crobred animal and only u L p(i L) and uy p(i Y) are etimated. Thi i for two reaon: firt with only pedigree information thi term cannot be etimated; econd etting up matrice of additive relationhip (and their invere) for crobred animal at the animal model i not traightforward (Lo et al. 1993; García-Corté and Toro 006). Therefore in the work of Lo et al. (1997) and Lutaaya et al. (001) the additive genetic value of the ith F 1 crobred u i i replaced by u L p(i L) + uy p(i Y). With genomic relationhip and in the model of Chritenen et al. (014) thee Mendelian ampling term are embedded into a genomic relationhip matrix (relationhip acro animal for purebred and gamete for crobred) and they are no longer uncorrelated. Therefore the aborption of thi term into the reidual error term i not uitable. In the current tudy c L i = ul p(i L) + ΦL i and c Y i = u Y p(i Y) + ΦL i. The additive genetic value of the ith F 1 crobred c i i not identical to u L p(i L) + u Y p(i Y) in Lo et al. (1997) and Lutaaya et al. (001). Therefore our model (which i a gametic model at the level of crobred) i not a ingle-tep model equivalent of Lo et al. (1997) and Lutaaya et al. (001) which at the level of crobred are reduced animal model. Step ). Contruct breed-pecific partial relationhip matrice for each breed of origin genetic effect. Conidering pedigree relationhip the variance and covariance between additive genetic purebred (a) and crobred (c) effect of breed LL i decribed a a a a c L L L var = H. c c a c L L L Thi i a two-trait repreentation. For better undertanding the genetic effect can be plit into animal effect belonging to purebred animal (a L and c L ) and gametic effect belonging to crobred animal ( a ( L and c ) ): al a a a c L L L var = H c L c a c L L L c a a c H H L L L LL L = c a c L L L L H H in which matrix H (L) i a matrix of partial relationhip that contain 4 block 1 for within purebred animal (H L L ) for purebred with crobred animal ( H L ) and vice vera ( H L ) and 1 for within crobred animal ( H ). If there are nl pure Landrace animal and n crobred animal the ize of H (L) i (nl + n) (nl + n). The nl purebred animal have additive effect which are breeding value a L (when mated within breed) and c L (when mated to the other breed). The n purebred gamete of crobred animal have additive effect c (within the cro itelf). The covariance tructure include for eae of repreentation a ) ( L which are Downloaded from on 10 January 018

4 GBLUP for crobred performance in pig 939 effect of crobred gamete in purebred performance; thee effect are merely conceptual but they implify the repreentation and computation. The covariance tructure for breed YY i imilar: ay ( Y) a a a c Y Y Y var = H c Y c a c Y Y Y ( Y) c ( Y) ( Y) a a c H H Y Y Y YY Y = ( Y) ( Y) c a c Y Y Y Y H H with the ize of H (Y) equal to (n Y + n ) (n Y + n ) and both tructure are aumed independent that i there i no covariance between LL effect and YY effect. A in Wei and van der Werf (1994) there are ix genetic variance or covariance component three for each breed. Matrix H (L) can be contructed baed on available information (pedigree and marker) a follow. The pedigree-baed and marker-baed breed LL partial relationhip matrice are ( L ) ALL AL A = êë AL A é ù úû é ù GLL GL and G = repectively in which êë GL G úû the partition divide purebred animal from purebred gamete in crobred animal. Becaue of the plit into breed-pecific gamete the pedigree-baed partial relationhip matrice A (L) and A (Y) mut be computed a in García-Corté and Toro (006). Contruction of the breed-pecific marker-baed relationhip matrice aume that the breed of origin of phaed allele in crobred animal i known. In other word it i known which phaed allele in a crobred animal i from breed LL and which one i from breed YY. Then the marker-baed partial relationhip matrix contain cro product of centered genotype: G L L = (m L p L 1 )(m L p L 1 ) G L G = (m L p L 1 )(q p L 1 ) and = (q p L 1 )(q p L 1 ) in which m L and q contain breed-pecific allele content of the econd allele for purebred LL (coded a 0 1 or ) and crobred animal (coded a 0 or 1) repectively and vector p L are breed LL pecific allele frequencie baed on marker genotype for purebred and crobred animal. Later matrix G (L) i adjuted to be compatible with A (L) : G (L) a = G(L) β + Kα in which K = é J J/ù ê ëj/ J /4ú û and J denote a matrix of one partitioned a G (L). Scalar α and β are etimated through olving the following equation: A = G + K and b a da = dg b+ dk a for example equating the average of the full matrice and equating the average of the diagonal of pedigree and genomic relationhip for genotyped individual ( L (Chritenen et al. 01). Matrix A ) contain pedigree relationhip for genotyped LL individual. The procedure i identical for breed YY. Step 3). Combine the pedigree-baed and adjuted marker-baed partial relationhip matrice to a combined partial relationhip matrix H (L) which i imilar to the H matrix ued in the ingle-tep method for purebred animal (Legarra et al. 009; Chritenen and Lund 010). The invere of H (L) i 0 0 ( ) 1 H = + ( ) A 0 ( Gw ) ( A ) ( L in which G w = (1 ω) A + ωa ). Parameter ω i the relative weight on the reidual polygenic effect. Many other tudie have invetigated the weighting factor between the pedigree-baed and markerbaed relationhip matrice (Chritenen and Lund 010; Chritenen et al. 01; Gao et al. 01; Su et al. 01; Guo et al. 015) and commonly they put forward that the weighting factor hould be determined by the pecific trait and the data et analyzed. We invetigated weighting factor from 0.1 to 0.5. Preliminary analyi (reult not hown) for different weighing factor howed that ω = 0.4 wa appropriate in term of balance between predictive abilitie and biae for crobred animal. The procedure i identical for breed YY. The pare invere partial relationhip matrice (H (L) ) 1 and (H (Y) ) 1 are ued a input to olve the mixed model equation of the model. Step 4). Therefore the complete repreentation of the final model for genetic evaluation i y L = X L β L + Z L a L + e L y Y = X Y β Y + Z Y a Y + e Y Downloaded from on 10 January 018

5 940 Xiang et al. y = X β + c ( Y) + c al a a a c L L L var = H c L c a c L L L c + e ay ( Y) a a a c Y Y Y var = H c Y c a c Y Y Y ( Y) c var (e L ) = I e var(e Y ) = I e L ( Y) Y and var(e ) = I e. Thi i a three oberved trait model (performance in LL YY and ) but with two genetic effect (LL and YY) each with two genetic trait: purebred and crobred performance. Etimation of genetic parameter by REML and BLUP prediction were done uing the DMU oftware (Maden and Jenen 013). Crobred Allele Tracing Software Beagle which wa ued to impute and phae genotype in crobred animal doe not give breed allele origin a an output. Therefore to infer the allele origin in crobred animal we proceeded a follow. The allele tracing wa proceed eparately on each chromoome per individual. Among the 503 genotyped crobred animal ire of 450 crobred were genotyped wherea neither parent of the other 683 crobred wa genotyped. When the ire wa genotyped total difference between the two et of phaed imputed allele of a croed animal and two et of phaed allele of it correponding purebred ire were compared. Comparion between crobred and purebred phaed allele were made on each SNP along the chromoome. For a pecific comparion if a crobred allele wa different from the correponding purebred allele that SNP wa counted a one difference. Along the chromoome if the um of difference between one et of crobred phaed allele and one et of pecific purebred phaed allele wa lowet among the 4 comparion then thi et of pecific crobred phaed allele wa conidered a originating from the breed of the ire. Logically the other et of crobred phaed allele wa aigned to the other breed. When neither parent wa genotyped one of the two et of phaed imputed crobred allele wa tudied egment by egment. Each crobred phaed chromoome wa plit into everal mall egment which conited of 50 conecutive SNP marker. Thee were compared with the correponding collection of egment from phaed chromoome of two purebred reference population LL and YY which were ued for imputing crobred genotype. Each mall egment in the crobred animal hould exactly match at leat one egment in the reference panel becaue each crobred egment wa imputed by the purebred reference population. Copie of that pecific egment being detected in the reference population of LL and YY were counted eparately and were divided by the total number of egment in the ame poition in the reference panel of LL and YY to get proportion of the matched egment. If the proportion wa higher in one breed the crobred egment wa conidered to originate from thi breed. Throughout all the egment within a crobred phaed chromoome if the vat majority of egment were conidered a originating from one pecific breed then the crobred phaed chromoome wa aigned to that breed. Conequently 503 crobred phaed allele were traced to either breed LL or YY. Statitical Model For Landrace and Yorkhire the tatitical model wa a follow: y ijklmn = μ + hy i + month j + hybrid k + b 1 age ijklmn + b age ijklmn + a m + b n + e ijlkmn in which the dependent variable y ijklmn repreented TNB in the firt parity in breed LL or YY; μ wa the general mean; hy i month j and hybrid k repreented fixed effect of herd year eaon month at farrowing and hybrid indicator of ervice ire (ame or different breed a ow); age ijklmn and age ijklmn were covariate for the age of farrowing and it quared value with regreion coefficient b 1 and b repectively; a m wa the random additive genetic effect of ow; b n wa a random ervice ire effect; and e ijklmn wa the random reidual effect. Random effect were aumed to be independently normally ditributed a ~ N(0 H (L) a ) or a ~ N(0 H (Y) a ) depending L Y on pure breed; b ~ N(0 Iσ b ) and e ~ N(0 Iσ e ) in which H (L) and H (Y) were previouly defined; I wa the identify matrix; and a L a were additive genetic variance for breed LL and YY Y for purebred performance repectively; and σ b and σ e were the variance of ervice boar effect and the variance of the reidual effect repectively. The model for crobred record wa y ijlm = μ + hy i + month j + b 1 age ijlm + b age ijlm + c(l) m + c(y) m + e ijlm Downloaded from on 10 January 018

6 Table 1. Scenario for model-baed reliability GBLUP for crobred performance in pig 941 Scenario 1 Genotype Phenotype Nogen_SC No genotype Full data: Genpure_SC 773 LL and 7785 YY LL YY Genall_SC 773 LL 7785 YY and 503 crobred and crobred animal 1 Nogen_SC = only pedigree information; Genpure_SC = pedigree information and purebred genotype; Genall_SC = pedigree information and all purebred and crobred genotype. LL = Danih Landrace; YY = Danih Yorkhire. in which the dependent variable y ijlm repreented TNB in the firt parity in crobred animal; μ hy i month j age ijlm and e ilmn repreented the ame effect a in the model for purebred record; and c (L) m and c (Y) m were breed LL and YY origin additive genetic effect repectively. The two additive genetic effect were aumed to be independently normally ditributed c (L) ~ N(0 H (L) c ) and c (Y) ~ N(0 H (Y) L c ) Y in which H (L) and H (Y) were breed LL or YY pecific c and L c Y partial additive genetic relationhip and were additive genetic variance for crobred performance of breed LL and YY repectively. Scenario Variance component heritabilitie and genetic correlation between purebred and crobred performance (r pc ) were firt invetigated in the full population. Heritability for purebred performance wa defined a the ratio of additive genetic variance for purebred performance (σ a ) to phenotypic variance (σ p = σ a + σ b + σ e ) wherea heritability for crobred animal wa defined a the ratio of total additive genetic variance of crobred performance for two breed-pecific gamete (0.5( + c L c )) to phenotypic variance (0.5( Y c + L c Y ) + e ). To explore the effect of different genotyping trategie on genetic evaluation for crobred performance the breed-pecific partial relationhip matrice were contructed baed on three different cenario (SC): 1) Nogen_SC only pedigree information which repreented the traditional BLUP method; ) Genpure_SC pedigree information and purebred genotype (773 LL and 7785 YY) repreenting genotyping only purebred; and 3) Genall_SC pedigree information and all purebred and crobred genotype (773 LL 7785 YY and 503 crobred). The purpoe of tudying Genall_SC were to check the neceity of including crobred genomic information which i normally not available and to tudy the improvement of genomic prediction of purebred animal for crobred performance. Information on each cenario i hown in Table 1. To make the reult comparable acro all tudie pecific relationhip matrice for breed LL and YY were calculated uing allelic frequencie etimated from old purebred population (born before January 1 011) which were 10 LL and 161 YY repectively. For each cenario the variance component for purebred and crobred performance were etimated and the genetic correlation between them wa obtained. Second model-baed reliabilitie of crobred performance for purebred boar were calculated in the 3 different cenario mentioned. According to pedigree 7407 and 3567 YL were offpring of 765 LL and 465 YY ire repectively. Thee ire were divided into ubgroup of genotyped and non-genotyped animal and mean model-baed reliabilitie were computed in each ubgroup. Mean model-baed reliability wa calculated a (Mrode and Thompon 005): ( i c) = n i= r 1 SEP / / n in which SEP 1 i wa the SE of prediction for animal i σ c wa the variance of additive genetic effect for crobred performance and n wa the number of purebred boar that were tudied. In addition the proportion of animal that have higher model-baed reliabilitie in one cenario compared with another cenario in each ubgroup wa alo invetigated. Finally the predictive ability for crobred animal in the validation population (4195 crobred) wa invetigated in different cenario. The farrowing date of January 1 01 wa ued a the cut-off date to divide recorded ow in the full population into training and validation population. For purebred genotyped boar only birth date were acceible not day of farrowing. Therefore for genotyped animal the birth date of January wa intead ued a the cut-off date. A a reult LL YY and 6779 crobred were contained in training population with 10 genotyped LL 161 genotyped YY and 357 genotyped crobred being included a well. The validation population for crobred performance included 4195 crobred among which 846 were genotyped. Phenotype of crobred animal in the validation population were corrected for fixed and random effect other than additive genetic effect (Y c = c (L) m + c(y) m + e). Y c were obtained by uing full population data with partial relationhip matrice contructed in Genall_SC. Breed-pecific partial relationhip matrice were contructed baed on cenario concerning genotype of animal in the training population: Nogen_T i the cenario in which relationhip matrice H contained only pedigree information (i.e. H (L) = A (L) and H (Y) = A (Y) ); Downloaded from on 10 January 018

7 94 Xiang et al. Table. Scenario for predictive ability Scenario 1 Genotype Phenotype Nogen_T No genotype Training: LL YY Genpure_T 10 LL and 161 YY and 6779 crobred animal Genpc_T 10 LL 161 YY and.357 crobred Validation: 5796 LL 4044 YY and 4195 crobred animal Genall_T 10 LL 161 YY and 503 crobred 1 Nogen_T = the cenario in which relationhip matrice H contained only pedigree information; Genpure_T = the cenario in which relationhip matrice H contained pedigree information and purebred genotype of 10 LL and 161 YY; Genpc_T = the cenario in which relationhip matrice H contained pedigree information and genotype of the 10 LL 161 YY and 357 crobred that were involved in the training data et; Genall_T = the cenario in which relationhip matrice H compried all information in Genpc_T plu extra genomic information (but not the phenotypic information) of the 846 crobred in the validation population. LL = Danih Landrace; YY = Danih Yorkhire. Genpure_T i the cenario in which relationhip matrice H contained pedigree information and purebred genotype of 10 LL and 161 YY; Genpc_T i the cenario in which relationhip matrice H contained pedigree information and genotype of the 10 LL 161 YY and 357 crobred that were involved in the training data et; and Genall_T i the cenario in which relationhip matrice H compried all information in Genpc_T plu extra genomic information (but not the phenotypic information) of the 846 crobred in the validation population. Detailed information on each cenario i hown in Table. Variance component were etimated baed on phenotype from the training population in each cenario being only lightly different from thoe baed on phenotype from the full population. The predictive ability of crobred wa meaured by validation correlation cor( ĉ Y c ) in each cenario in which ĉ were the etimated additive genetic effect for crobred (ĉ = c (L) m + c(y) m ) in the validation population from different cenario. For Genall_T the validation population wa divided into ubgroup of genotyped and non-genotyped animal and the validation correlation were made in the ubgroup a well a in the whole validation population. A Hotelling William t tet at a 5% confidence level wa applied to evaluate the ignificance for the difference of validation correlation in each cenario. Moreover to detect the poible inflation or deflation of prediction the regreion coefficient of Y c on ĉ were explored to check whether they were cloe to 1. In addition to meaure uncertainty aociated with reult boottrap ampling (Mäntyaari and Koivula 01; Cuyabano et al. 015) wa ued in the tet population to etimate mean and SE of correlation. Reult were imilar to the Hotelling William tet above and are not hown. To check the poible impact of different genotyping cenario on the ranking and election of purebred animal for their crobred performance Spearman rank correlation (Spearman 1904) between breeding value of purebred ire (765 LL and 465 YY) for crobred performance were calculated acro different cenario. In addition the breeding value for crobred performance were ranked from highet to lowet in different cenario and then the conitency of the purebred boar in the top 5% highet breeding value wa checked acro different cenario. Furthermore to invetigate re-ranking in a ituation cloer to the way election for crobred performance could be implemented in practice for uch a ow trait the Spearman rank correlation and the top 5% tudie were alo made on the young ow that were included in the validation population (5796 LL and 4044 YY) that i purebred animal without their own record. Among thee young ow 1103 LL and 1085 YY were genotyped. Thee two tudie were eparately proceed on the genotyped and non-genotyped young ow. The new ingle-tep BLUP method for crobred i complex and therefore we tried a impler ingletrait ingle-tep BLUP method (Legarra et al. 009; Chritenen and Lund 010). Thi method aumed that all animal belonged to a ingle population uing a ingle relationhip matrix where the compatibility adjutment of G to A wa done a in Chritenen et al. (01). Predictive abilitie for crobred animal in the validation population were alo meaured a cor(ĉ Y c ). RESULTS e Variance Component Heritabilitie and Genetic Correlation Etimate of variance component and genetic correlation between purebred and crobred performance for Landrace and Yorkhire in each cenario are hown in Table 3 together with calculated heritabilitie. For each cenario both pure breed howed higher additive genetic variance for purebred performance (σ a ) than for crobred performance (σ c ). Reidual variance for purebred animal (σ e ) were larger than thoe for crobred animal ( ). For all cenario the etimated heritabilitie for purebred performance (h ) were alway 0.11 and 0.09 for Landrace and Yorkhire repectively. Heritabilitie for crobred animal (h ) were around Downloaded from on 10 January 018

8 GBLUP for crobred performance in pig 943 Table 3. Variance component 1 heritabilitie for purebred performance genetic correlation between purebred and crobred performance for Landrace and Yorkhire 3 and heritabilitie for crobred animal 4 Scenario 5 Breed σ a σ a c σ c σ b σ e r pc (SE) h e h Nogen_SC Landrace (0.1) 0.11 Yorkhire (0.13) 0.09 Genpure_SC Landrace (0.11) 0.11 Yorkhire (0.1) 0.09 Genall_SC Landrace (0.09) 0.11 Yorkhire (0.10) σ a = additive genetic variance for purebred performance; σ a c = genetic covariance between purebred and crobred performance; σ c = additive genetic variance for crobred performance; σ b = variance of ervice-boar effect; σ e = reidual variance for purebred performance; e = reidual variance for crobred animal. h = heritability for purebred performance (σ a /(σ a + σ b + σ e ). 3 r pc = genetic correlation between purebred and crobred performance. 4 h = heritability for crobred animal (0.5( c + L c )/[0.5( Y c + L c ) + Y e ]). 5 Nogen_SC = only pedigree information; Genpure_SC = pedigree information and purebred genotype; Genall_SC = pedigree information and all purebred and crobred genotype in the different cenario. The etimated genetic correlation between purebred and crobred ranged from 0.70 in Nogen_SC to 0.78 in Genall_SC for the Landrace breed and ranged from 0.57 in Nogen_SC to 0.68 in Genall_SC for the Yorkhire breed. Standard error were generally large but kept decreaing from around 0.1 (Nogen_SC) to 0.1 (Genall_SC) for both breed. Slight difference of the etimated genetic correlation were oberved between the two breed. The Landrace breed howed lightly higher genetic correlation between purebred and crobred performance than that for the Yorkhire breed. Model-Baed Reliability Table 4 compare the mean model-baed reliabilitie for purebred ire for their crobred performance in different cenario acro all boar and for genotyped and non-genotyped ubgroup. The genotyped ubgroup alway had higher model-baed reliabilitie than the nongenotyped group and for the group of all boar modelbaed reliabilitie were in between thoe of the ubgroup of genotyped and non-genotyped animal in each cenario. Model-baed reliabilitie increaed from about 0.8 to 0.39 for the Landrace breed and from about 0. to 0.37 for the Yorkhire breed from Nogen_SC to Genall_SC. From Nogen_SC to Genall_SC model-baed reliabilitie kept increaing in all three group. Overall method with marker information (Genpure_SC and Genall_SC) preented higher model-baed reliabilitie than the pedigree-baed cenario (Nogen_SC). In addition proportion of purebred boar that have larger model-baed reliabilitie between pairwie cenario were alo tudied. Reult how that 100% of LL and YY boar had larger model-baed reliabilitie in the Genall_SC compared with the Nogen_SC and Genpure_SC (reult not hown). Concerning the ingle-trait ingle-tep BLUP model model-baed reliabilitie for purebred LL and YY in Genall_SC were 0.70 ± 0.1 and 0.69 ± 0.1 repectively. Although thee value are much higher than reult hown in Table 4 they cannot be directly compared becaue they repreent the reliability of animal drawn from a breed that would be a mixture of YY and LL which i not the cae. In fact thi ingle-trait model ha lower predictive abilitie than Chritenen model a will be hown next. Predictive Abilitie Predictive abilitie for crobred pig in the validation group for different cenario are hown in Table 5. The Pearon correlation between the corrected phenotype and the EBV (cor(ĉ Y c )) range from in Nogen_T to 0.10 in Genall_T a hown in the econd row of Table 5. No tatitically ignificant difference between Genpure_T and Nogen_T were found but Genpc_T and Genall_T were tatitically ignificantly more accurate than thoe two cenario. For the Genall_T the ubgroup of 846 genotyped crobred pig reveal larger correlation coefficient than that in the ubgroup of non-genotyped pig. Furthermore the ubgroup of non-genotyped pig in Genall_T how larger correlation coefficient than thoe in other cenario. Regreion coefficient of corrected phenotype on the EBV are hown in Table 5. In general regreion coefficient were a little bit larger than 1 for all the cenario. Regreion coefficient for cenario with marker information (Genpure_T Genpc_T and Genall_T) were cloer to 1 than that for pedigreebaed cenario (Nogen_T). Among cenario with marker information in term of unbiaedne there wa no clear trend howing which cenario performed better but none wa clearly biaed. For the Genall_T Downloaded from on 10 January 018

9 944 Xiang et al. Table 4. Mean model-baed reliabilitie of purebred boar for their crobred performance Breed 1 Nogen_SC Genpure_SC Genall_SC Nogen_SC Genpure_SC Genall_SC Nogen_SC Genpure_SC Genall_SC All Genotyped 3 Non-genotyped 4 LL YY LL = Danih Landrace; YY = Danih Yorkhire. All = all the ire of crobred animal coniting of 765 Landrace and 465 Yorkhire. Nogen_SC = only pedigree information; Genpure_SC = pedigree information and purebred genotype; Genall_SC = pedigree information and all purebred and crobred genotype. 3 Genotyped = genotyped ire of crobred animal coniting of 656 Landrace and 443 Yorkhire. 4 Non-genotyped = Non-genotyped ire of crobred animal coniting of 109 Landrace and Yorkhire. the ubgroup of genotyped animal had le bia than the ubgroup of non-genotyped animal. Single-Trait Single-Step BLUP Predictive Abilitie Predictive abilitie by a ingle-trait ingle-tep BLUP method for crobred animal in the validation population are hown in lat row in Table 5. They increae from 0.08 in Nogen_T to in Genall_T. It can alo be een that the predictive abilitie calculated baed on the ingle-trait model how trend imilar to thoe calculated from the three-trait model but are maller than in each correponding cenario. Regreion coefficient increae lightly from 0.61 in Nogen_T to 0.71 in Genall_T but are further from 1 when compared with regreion coefficient calculated baed on the three-trait model. For Genall_T the genotyped ubgroup alo had higher predictive abilitie than that in non-genotyped ubgroup. Re-ranking of Purebred Animal acro Scenario The Spearman rank correlation between etimated crobred breeding value of purebred boar (765 LL and 465 YY) in pairwie cenario are hown in Table 6. For both breed it can be een that the pairwie correlation are alway maller than 1. In term of the top 5% tudy from 60% to 8% of purebred boar (either LL or YY) were hared from one cenario to another in the top 5% highet breeding value (reult not hown). Similar reult were oberved in young purebred ow (reult not hown). DISCUSSION Thi tudy implemented the ingle-tep BLUP method of Chritenen et al. (014) by uing both purebred and crobred data from LL and Yorkhire in everal cenario with regard to different amount of genomic information. Reult indicated that the model wa applicable. The genetic correlation between purebred and crobred performance for TNB wa uccefully etimated. Method with marker information were powerful for genetic evaluation for crobred performance with regard to the predictive ability and unbiaedne. In addition thi tudy demontrated that to implement genetic evaluation for crobred performance crobred genomic information i ueful in addition to purebred genotype. In the model a key aumption wa that breed origin of phaed marker genotype for crobred animal were known. In thi tudy 60K crobred genotype were imputed from a 8K crobred panel. Although Xiang et al. (015) concluded that the imputation accuracie would be larger than 99% in term of allele correct rate and 95% in term of correlation coefficient between imputed genotype and true genotype the uncertainty of crobred genotype cannot be totally eliminated. The algorithm of tracing allele in the current tudy wa conidered to be working efficiently becaue the difference between two purebred reference panel were coniderably large in everal ampled chromoome. However error of tracing allele probably till appeared if the imilarity of two phaed crobred egment were high. All in all a hidden rik of uing incorrect allele may till exit when building the breedpecific partial relationhip matrix. Thi need further reearch. The additive genetic variance for purebred performance (σ a ) were larger than thoe for crobred performance (σ c ) implying that the phenotype of purebred animal could be more divere than for the crobred animal which wa in line with the phenotypic variance for purebred animal (15.1 and for LL and YY repectively) being larger than thoe for crobred animal (9.49). The heritabilitie for crobred animal (h ) were not dramatically different from heritabilitie for purebred performance (h ) which wa oppoite to reult in Wei and van der Werf (1995) and i due to the fact that in the current tudy variance of environmental effect for crobred ( ) were only e two-third of thoe for purebred (σ e ) which could be a conequence of heteroi and phenotypic platicity (better fitne) to the multiple herd for crobred than for purebred (Miztal and Løvendahl 01) or could Downloaded from on 10 January 018

10 GBLUP for crobred performance in pig 945 Table 5. Predictive abilitie for crobred animal in the validation population in different cenario Perdiction Nogen_T 1 Genpure_T 1 Genpc_T 1 All Genotyped Non-genotyped Genall_T 1 cor( ĉ Y c ) a a b 0.10 c Regreion coefficient Single-trait cor( ĉ Y c ) Single-trait regreion coefficient a c Different upercript of mall letter among cenario indicate ignificant difference (P < 0.05) by a Hotelling William t tet. 1 Nogen_T = the cenario in which relationhip matrice H contained only pedigree information; Genpure_T = the cenario in which relationhip matrice H contained pedigree information and purebred genotype of 10 LL and 161 YY; Genpc_T = the cenario in which relationhip matrice H contained pedigree information and genotype of the 10 LL 161 YY and 357 crobred that were involved in the training data et; Genall_T = the cenario in which relationhip matrice H compried all information in Genpc_T plu extra genomic information (but not the phenotypic information) of the 846 crobred in the validation population. cor( ĉ Y c ) i correlation coefficient between corrected phenotype and EBV. 3 Regreion coefficient of corrected phenotype on EBV. 4 Single-trait cor( ĉ Y c ) i correlation coefficient between corrected phenotype and EBV baed on the ingle trait ingle-tep BLUP method. 5 Single-trait regreion coefficient i regreion coefficient of corrected phenotype on EBV baed on the ingle trait ingle-tep BLUP method. alternatively be due to fact that only three different herd were ued for crobred. Crobreding capitalize on heteroi effect and complementarity between breed and reult in an increaed performance of crobred compared with purebred (Dekker 007). When election i baed on purebred performance the genetic correlation between purebred and crobred performance (r pc ) i a key genetic parameter in crobreding cheme (Bell 198; Bijma and Batiaanen 014). The genetic correlation between purebred and crobred performance for TNB were around 0.75 and 0.63 for Landrace and Yorkhire repectively which confirmed the exitence of a moderate correlation. The r pc i maller than 1 which i due to different environment for purebred and crobred (Lutaaya et al. 001) and the preence of dominant gene action combined with different allele frequencie in the two breed (Lo et al. 1997; Chritenen et al. 014). Thi reult wa in line with Wong et al. (1971) who reported that the r pc for litter ize wa However Wei (199) reviewed ome other tudie that reported low or even negative genetic correlation between purebred and crobred performance for litter ize. A change of r pc over time wa reported to be caued by long-term purebred election (Pirchner and VonKroigk 1973) and therefore it need to be etimated regularly. The SE on the etimated genetic correlation were generally large in the current tudy which implie that the ample ize wa not large enough epecially for crobred. Taking the SE into account the etimated correlation in different cenario were not very different. Neverthele the light decreae of SE with an increaed amount of genomic information indicated that genotype epecially crobred genotype would reduce the uncertainty of r pc. The decreaing SE demontrated the better performance of the new ingle-tep model incorporating crobred marker information compared with the pedigree-baed election of purebred animal for crobred performance. Bijma and Batiaanen (014) howed that when uing pedigree relationhip the SE of r pc wa determined by number of ire familie and reliabilitie of EBV and uggeted that the SE hould not exceed In the current tudy the TNB wa a low heritable trait (around 0.1) and only 1018 ire of the 130 ire of crobred animal were genotyped which wa alo low. Therefore large SE were expected. Reult in the current tudy howed that the r pc for Landrace wa lightly larger than that for Yorkhire although the SE were large. Genetic correlation (r pc ) alo conitently increae with number of genotype ued. One poible explanation could be that there are till ome dicordance between the definition of bae population in genomic and pedigree relationhip. Concerning heritabilitie for purebred performance our etimate confirmed the reult of Guo et al. (015) who etimated heritabilitie of 0.11 and 0.09 for TNB in Landrace and Yorkhire repectively. The model-baed reliabilitie for purebred boar for their crobred performance were generally low in the current tudy. The magnitude of thee reliabilitie i a direct function of the prediction error variance which in thi cae are motly determined by the number of offpring per boar (Dufrane et al. 011). In the current tudy the number of crobred offpring for each boar ranged from 1 to 11 with an average of 5 which were low and led to a high uncertainty of prediction. According to Table 4 model-baed reliabilitie tended to increae a the amount of genomic information increaed for both breed. The cenario with marker information preented larger model-baed reliabilitie than the pedigree-baed cenario which may be due to Downloaded from on 10 January 018

11 946 Xiang et al. Table 6. Spearman rank correlation between crobred breeding value for 765 Landrace boar (above the diagonal) and 465 Yorkhire boar (below the diagonal) of crobred animal in pairwie cenario Nogen_SC 1 Genpure_SC 1 Genall_SC 1 Nogen_SC Genpure_SC Genall_SC Nogen_SC = only pedigree information; Genpure_SC = pedigree information and purebred genotype; Genall_SC = pedigree information and all purebred and crobred genotype. the additional marker information. Reliabilitie for the ubgroup of genotyped animal were larger than that for the ubgroup of non-genotyped animal in each cenario but non-genotyped animal alo benefitted from the genomic information of genotyped animal a the reliabilitie for the non-genotyped ubgroup kept increaing from Nogen_SC to Genall_SC. Thee reult are in line with Lourenco et al. (015). Reliabilitie for non-genotyped animal in Genall_SC were even larger than thoe in Nogen_SC and Genpure_SC for genotyped animal implying the benefit of genotyping crobred animal. In addition 100% of purebred boar had larger model-baed reliabilitie in Genall_SC than that in the other two cenario which alo provided evidence that the model incorporating crobred marker information wa ueful for genetic evaluation for crobred performance in purebred boar. We concluded that crobred genomic information play a role in improving reliabilitie for crobred performance in purebred boar. Neverthele it ha been reported that the model-baed reliabilitie overetimated the true reliabilitie (VanRaden et al. 009) becaue the marker may overfit the data et (Su et al. 01). Therefore further invetigation on true reliabilitie i needed potentially by a imulation tudy. Correlation coefficient between corrected phenotype and EBV for TNB in crobred animal were lower than reult for daily gain and feed converion ratio in Chritenen et al. (01). Thi may be related to the fact that the heritability wa higher for the trait of daily gain and feed converion ratio than for the TNB in the current tudy. Moreover the additive genetic effect for crobred animal required etimating breed of origin genetic effect c (L) and c (Y) which may lead to more uncertainty for crobred animal than tudie for purebred animal in Chritenen et al. (01). The cor(ĉ Y c ) in different cenario confirmed that the method with marker information would enhance the predictive ability. The crobred genomic information wa ueful to improve the prediction becaue cenario with only purebred genotype did not how ignificant improvement compared with the pedigree-baed cenario but ignificantly improved when crobred genomic information wa alo involved. Reult howed that genotyped animal had larger cor(ĉ Y c ) than nongenotyped animal which wa oppoite to tudie by Guo et al. (015). Thi could be becaue in the current tudy the validation group conited of crobred animal among which the genotyped ubet wa a random ample without biae for prediction (Su et al. 01) wherea in Guo et al. (015) the validation group conited of purebred animal among which the genotyped ubet wa a preelected group. Pre-election reduce accuracie of EBV (Bijma 01; Lourenco et al. 015). The non-genotyped ubgroup of crobred animal in Genall_T had larger accuracie than thoe in other cenario indicating that non-genotyped validated animal benefited from crobred genotyped animal in the validation population. Therefore we ugget genotyping crobred animal a well a purebred animal when implementing genomic election for crobred animal. Regreion coefficient of corrected phenotype on EBV did not how a clear preference for a pecific cenario but coefficient in all cenario with marker information were cloer to 1 than in the pedigree-baed cenario. All the regreion coefficient were larger than 1 uggeting the underetimation (deflation) of variation of the etimated genomic breeding value (Gao et al. 01). Both the value of Spearman rank correlation lower than 1 and the top 5% tudy indicated that ranking of purebred animal breeding value for crobred performance were not conitent acro different cenario. The elected purebred candidate for crobred performance will be different with the availability of (crobred) genomic information. In term of the predictive abilitie and bia the ingle-trait model wa le robut than the three-trait model although it wa eaier to implement. With crobred genomic information the three-trait model howed up to 13% higher predictive abilitie than the ingle-trait model which eem an intereting gain for thi low heritable trait. Concluion The new ingle-tep model work well for genetic evaluation for crobred performance in pig. A moderate poitive genetic correlation between purebred and crobred performance (r pc ranged from 0.57 to 0.78) for TNB in purebred Landrace and Yorkhire i confirmed. Crobred genomic information reduce the SE on the etimate of thi genetic correlation. Model with marker information epecially crobred genomic information improve model-baed reliabilitie for crobred performance of purebred boar and alo improve the predictive ability for validated crobred animal and omehow reduce the bia of prediction. The ingle- Downloaded from on 10 January 018