Genomic relationships based on X chromosome markers and accuracy of genomic predictions with and without X chromosome markers

RESEARCH Open Access Genomic ela ionships based on X ch omosome ma ke s and accu acy o genomic p edic ions wi h and wi hou X ch omosome ma ke s Guosheng Su 1* , Be n Guldb and sen 1 , Ge P Aamand 2 , Ismo S andén 3 and Mogens S Lund 1 Abs ac Backg ound: Al hough he X ch omosome is he second la ges bo ine ch omosome, ma ke s on he X ch omosome a e no used o genomic p edic ion in some coun ies and popula ions. In his s udy, we p esen ed a me hod o compu ing genomic ela ionships using X ch omosome ma ke s, in es iga ed he accu acy o impu a ion om a low densi y (7K) o he 54K SNP (single nucleo ide polymo phism) panel, and compa ed he accu acy o genomic p edic ion wi h and wi hou using X ch omosome ma ke s. Me hods: The impac o conside ing X ch omosome ma ke s on p edic ion accu acy was assessed using da a om No dic Hols ein bulls and di e en se s o SNPs: (a) he 54K SNPs o e e ence and es animals, (b) SNPs impu ed om he 7K o he 54K SNP panel o es animals, (c) SNPs impu ed om he 7K o he 54K panel o hal o he e e ence animals, and (d) he 7K SNP panel o all animals. Beagle and Findhap we e used o impu a ion. GBLUP (genomic bes linea unbiased p edic ion) models wi h o wi hou X ch omosome ma ke s and wi h o wi hou a esidual polygenic e ec we e used o p edic genomic b eeding alues o 15 ai s. Resul s: A e aged o e he wo impu a ion da ase s, co ela ion coe icien s be ween impu ed and ue geno ypes o au osomal ma ke s, pseudo-au osomal ma ke s, and X-speci ic ma ke s we e 0.971, 0.831 and 0.935 when using Findhap, and 0.983, 0.856 and 0.937 when using Beagle. Es ima ed eliabili ies o genomic p edic ions based on he impu ed da ase s using Findhap o Beagle we e e y close o hose using he eal 54K da a. Genomic p edic ion using all ma ke s ga e sligh ly highe eliabili ies han p edic ions wi hou X ch omosome ma ke s. Based on ou da a which included only bulls, using a Gma ix ha accoun ed o sex-linked ela ionships did no imp o e p edic ion, compa ed wi h a Gma ix ha did no accoun o sex-linked ela ionships. A model ha included a polygenic e ec did no eco e he loss o p edic ion accu acy om exclusion o X ch omosome ma ke s. Conclusions: The esul s om his s udy sugges ha ma ke s on he X ch omosome con ibu e o accu acy o genomic p edic ions and should be used o ou ine genomic e alua ion. Backg ound Acco ding o he UMD 3.1 assembly, ch omosome X is he second la ges ch omosome in he bo ine genome [1]. A o al o 1128 anno a ed genes ha e been epo ed on he X ch omosome in he ENSEMBL e sion 72 [2]. Howe e , ma ke s on he X ch omosome a e no used o genomic p edic ion in some coun ies and popula ions. P e iously, No dic genomic e alua ions used X ch omo- some ma ke s o genomic p edic ions in No dic Red and Je sey popula ions bu no in he Hols ein popula ion be- cause ma ke s on he X ch omosome we e no included in he Eu oGenomics p ojec [3]. In mammals, inhe i ance o ch omosome X di e s om inhe i ance o au osomes. In ca le, a si e passes i s X ch omosome o all i s daugh e s bu ne e o i s sons. Consequen ly, a male inhe i s a copy o he X ch omo- some om i s mo he only, while a emale inhe i s one copy o he X ch omosome om i s a he and one copy om i s mo he . The e o e, he ela ionships caused by he X ch omosome a e di e en o males and emales. Fu he mo e, a small egion o he X ch omosome, called he pseudo-au osomal egion (PAR) is homologous o he * Co espondence: [email p o ec ed] 1 Cen e o Quan i a i e Gene ics and Genomics, Depa men o Molecula Biology and Gene ics, Aa hus Uni e si y, Tjele DK-8830, Denma k Full lis o au ho in o ma ion is a ailable a he end o he a icle Gene ics Selec ion E olu ion © 2014 Su e al.; licensee BioMed Cen al L d. This is an Open Access a icle dis ibu ed unde he e ms o he C ea i e Commons A ibu ion License (h p://c ea i ecommons.o g/licenses/by/2.0), which pe mi s un es ic ed use, dis ibu ion, and ep oduc ion in any medium, p o ided he o iginal wo k is p ope ly c edi ed. The C ea i e Commons Public Domain Dedica ion wai e (h p://c ea i ecommons.o g/publicdomain/ze o/1.0/) applies o he da a made a ailable in his a icle, unless o he wise s a ed. Su e al. Gene ics Selec ion E olu ion 2014, 46:47 h p://www.gsejou nal.o g/con en /46/1/47 Y ch omosome and is inhe i ed in an au osome-like ash- ion. This inc eases he complexi y o he gene ic ela ion- ships be ween indi iduals based on he X ch omosome. Mo eo e , in genomic p edic ion o dai y ca le, de eg- essed p oo s (DRP), daugh e yield de ia ions (DYD) and es ima ed b eeding alues (EBV) a e usually used as e- sponse a iables. These a iables a e p edic ed using a model in which a pedig ee-based ela ionship ma ix is cons uc ed based on inhe i ance o au osomes. In addi ion, he densi y o ma ke s on he X ch omosome is ma kedly lowe han ha on he au osomes in he cu en SNP (single nucleo ide polymo phism) chips [4,5]. These cha ac e is ics may educe he impac o X ch omosome ma ke s on accu acy o genomic p edic ion, and could be he eason why hey a e no used o genomic p edic ion in some coun ies and popula ions. Based on he cha ac e is ics o he X ch omosome, i can be hypo hesized ha X ch omosome ma ke s can con ibu e o he accu acy o genomic p edic ions, bu will gene ally ha e a smalle impac han au osomal ma ke s. Mo eo e , genomic p edic ion using a genomic ela ionship ma ix ha akes sex-linked inhe i ance o X-speci ic ma ke s in o accoun will p obably pe o m be e han using a genomic ela ionship ma ix ha does no dis inguish be ween au osomal and X-speci ic ma ke s. In addi ion, because ma ke densi y is lowe on he X ch omosome, impu a ion o X ch omosome ma ke s may be less accu a e han ha o au osomal ma ke s. When genomic p edic ions a e pe o med using da a om SNP chips wi h di e en densi ies, geno ypes o SNPs ab- sen om low-densi y chips a e usually in e ed (impu ed) om he highe densi y chips. The e o e, i is necessa y o in es iga e he accu acy o impu a ion o ma ke s on he X ch omosome in o de o pe o m genomic p edic- ion using hese ma ke s. Howe e , so a he e a e e y ew epo s on he impu a ion accu acy o X ch omosome ma ke s [6] and on hei con ibu ion o accu acy o gen- omic p edic ions [7]. The objec i es o his s udy we e (i) o in es iga e he accu acy o impu ing missing geno ypes on he X ch omosome, (ii) o demons a e a me hod o calcula e a genomic ela ionship ma ix which co ec ly accoun s o gene ic ela ionships wi h ega d o ma ke s on he X ch omosome, and (iii) o compa e he accu acy o gen- omic p edic ions wi h and wi hou X ch omosome in o - ma ion using di e en models and di e en scena ios. Da a om No dic Hols ein ca le we e used o add ess hese objec i es. Me hods Da a The da a used in his analysis consis ed o 5643 p ogeny- es ed No dic Hols ein bulls bo n om 1974 o 2010. The da a did no include cows since he numbe o No dic Hols ein cows a ailable as e e ence animals was insu i- cien o he p esen analysis. Animals we e geno yped wi h he Illumina Bo ine SNP50 BeadChip [4]. In o de o in es iga e he accu acy o impu a ion o ma ke s on he X ch omosome, low-densi y (LD) ma ke da a we e c ea ed om he SNP50 BeadChip ma ke da a by mask- ing ma ke s ha a e absen om he Illumina Bo ineLD BeadChip [5]. The Bo ine SNP50 BeadChip (abou 54K) and he Bo ineLD BeadChip (abou 7K) ma ke da a we e edi ed by emo ing ma ke s wi h a mino allele e- quency (MAF) lowe han 0.01, an a e age GenCall sco e lowe han 0.60, o an unknown loca ion in UMD 3.1 [1]. A e edi ing, 44 141 ma ke s emained in he 54K da a, and 6699 ma ke s in he LD da a. The numbe s o ma ke s a ailable on he au osomes and on he X ch omosome a e in Table 1. The bulls we e di ided in o a e e ence popula ion and a es popula ion acco ding o bi h da e, i.e., 3995 bulls bo n be o e Janua y 1 2005 cons i u ed he e e ence popula ion and he emaining 1648 bulls cons i u ed he es popula ion. Fou se s o da a we e used o alida e accu acies o geno ype impu a ion and genomic p edic ion: (1) 54K_ eal: all animals had ma ke da a om he 54K chip; (2) IMP_ es : o he es animals, he 54K ma ke da a we e impu ed om LD ma ke da a; (3) IMP_0.5 e : o hal ( andomly chosen) o he e e ence animals, he 54K ma ke da a we e impu ed om LD ma ke da a, and (4) LD_ eal: all animals had LD ma ke da a wi hou im- pu a ion o he 54K ma ke da a. The pheno ypic da a o genomic p edic ion we e DRP ha we e de i ed om he No dic gene ic e alua ions o Janua y 2013. Fi een ai s included in he No dic To al Me i index (h p://www.no diceb .in o) we e analyzed. DRP wi h eliabili ies lowe han 10% o animals in he e e ence da a and lowe han 20% o animals in he es da a we e dele ed. The numbe o animals wi h pheno- ypic in o ma ion di e ed be ween ai s because he numbe o bulls wi h published EBV di e ed be ween ai s. The numbe o animals a ailable o genomic p e- dic ion and he he i abili y (p o ided by No dic Ca le Gene ic E alua ion) o each ai a e in Table 2. Impu a ion me hods Fo da ase s IMP_ es and IMP_0.5 e , he LD ma ke da a we e impu ed o he 54K da a using wo p og ams: Table 1 Numbe o SNPs used a e edi ing (MAF > 0.01, a e age GC sco e > 0.60) Ma ke da a Au osomes X ch omosome PAR a X-speci ic 54K 43 314 133 694 LD (7K) 6458 25 188 a PAR: pseudo-au osomal egion on he X ch omosome. Su e al. Gene ics Selec ion E olu ion 2014, 46:47 Page 2 o 12 h p://www.gsejou nal.o g/con en /46/1/47 Beagle e sion 3.3.1 [8] and Findhap e sion 2 [9]. Beagle uses popula ion in o ma ion and a hidden Ma ko model o impu e missing geno ypes. Findhap is a as p og am ha impu es missing geno ypes using bo h amily and popula ion in o ma ion and akes he in- he i ance pa e n o he X ch omosome in o accoun . The e o e, when using Findhap, ma ke s on he PAR o he X ch omosome we e ea ed as au osomal ma ke s, while he es we e ea ed as X-speci ic ma ke s. The PAR was app oxima ely iden i ied based on he egion o he X ch omosome whe e ma ke s had a subs an- ial p opo ion o he e ozygous geno ypes (H%) in he geno yped bulls. The s a ing posi ion o he e- gion was de e mined wi h he c i e ia ha he H% a a SNP was highe han 5%, and a leas i e o he ollowing 10 SNPs wi h a MAF la ge han 0.05 had aH%highe han5%.ThePARs oppeda heendo he X ch omosome. Fo da ase s 54K_ eal and LD_ eal, spo adic missing geno ypes (4%) we e impu ed using Beagle. Geno ypes o he impu ed ma ke s (in da ase s IMP_ es and IMP_0.5 e ) we e compa ed o hei co esponding eal geno ypes in 54K_ eal. Accu acy o impu a ion was measu ed by he a io o he numbe o alsely impu ed alleles o o al numbe o impu ed alleles, which will be e e ed o as allele e o a e and he a io o he num- be o alsely impu ed geno ypes o he o al numbe o impu ed geno ypes, which will be e e ed o as geno- ype e o a e, as well as he co ela ion be ween im- pu ed and ue geno ypes. Genomic ela ionship ma ix (G ma ix) using ma ke da a including X-speci ic ma ke s As p esen ed by VanRaden [10] and Hayes e al. [11], a genomic ela ionship ma ix (G) can be calcula ed as: G¼MM0=X2pj1−pj  ; whe e elemen s in column j(m ij )o Ma e 0 - 2p j ,1-2p j and 2 - 2p j o SNP geno ypes A 1 A 1 ,A 1 A 2 and A 2 A 2 , espec i ely, p j is he equency o allele A 2 a SNP j. The Gma ix is calcula ed based on iden i y by s a e (IBS), wi h cen e ing and scaling. Consequen ly, elemen s o he Gma ix a e app oxima ions o ealized p opo - ions o he genome ha a e iden ical by descen (IBD) be ween pai s o indi iduals [11], which makes he G ma ix analogous o he con en ional nume a o ela- ionship ma ix [10]. The Gma ix desc ibes he ealized gene ic ela ion- ships be ween pai s o indi iduals a he au osomal ma ke s. Howe e , gene ic ela ionships be ween indi- iduals a ma ke s on he sex ch omosomes and he au osomes a e di e en . Fo example, o ma ke s on he X-speci ic egion o he X ch omosome, he gene ic ela- ionship is 0 be ween a he and son, 1ffiffi2 p .be ween mo he and son and be ween a he and daugh e , 0.50 be ween mo he and daugh e and be ween ull b o he s, 0.75 be- ween ull sis e s, and 1ffiffi2 p0:50 .be ween ull b o he and sis e . Fo au osomal loci, hese ela ionships all ha e an expec a ion o 0.50. The e o e, sex-linked inhe i ance should be conside ed when building a genomic ela ion- ship ma ix based on ma ke da a ha include X ch omo- some ma ke s. When X-speci ic ma ke s a e ea ed as au osomal ma ke s, he esul ing genomic ela ionship ma ix e- lec s sex-linked ela ionships, bu on an inco ec scale because males ha e one X ch omosome while emales ha e wo. Fo example, he ela ionship be ween si e and son is 0, bu he diagonal elemen o a male is 2, ins ead o 1. Consequen ly, he co a iance s uc u es o males, o emales, and be ween males and emales di e om each o he . Le A 1 O and A 2 O deno e geno ypes o an X-speci ic ma ke in males (O means null, since males ha e only one X ch omosome), and A 1 A 1 ,A 1 A 2 and A 2 A 2 deno e geno ypes in emales. Assuming ha A i O in males has he same e ec on he pe o mance o a ai as A i A i in emales, geno ypes o an X-speci ic ma ke can be coded in he same way as au osomal ma ke s. Thus, geno ypes A 1 OandA 2 O o males a e coded as 0 and 2, and geno- ypes A 1 A 1 ,A 1 A 2 and A 2 A 2 o emales a e coded as 0, 1 and 2. In addi ion, de ine γas he e ec o A 2 (i.e., allele e ec on pe o mance o a ai is exp essed as he Table 2 Numbe o animals in he e e ence da a and he es da a, and he i abili y o he ai s s udied T ai s Re e ence da a Tes da a He i abili y Milk 3943 1159 0.39 Fa 3943 1159 0.39 P o ein 3943 1159 0.39 G ow h 3451 1351 0.30 Fe ili y 3975 1158 0.04 Bi h index 3988 1642 0.06 Cal ing index 3986 1239 0.03 Udde heal h 3987 1204 0.04 O he diseases 3961 1050 0.02 Body con o ma ion 3823 1156 0.30 Fee and legs 3864 1150 0.10 Udde con o ma ion 3866 1156 0.25 Milking abili y 3832 1155 0.26 Tempe amen 3856 1142 0.13 Longe i y 3943 817 0.10 A e age 3891 1180 0.19 Su e al. Gene ics Selec ion E olu ion 2014, 46:47 Page 3 o 12 h p://www.gsejou nal.o g/con en /46/1/47 de ia ion om he e ec o A1, hus he e ec o A1 is ze o), pas he equency o A 2, and q=1-p.The expec a ion o he gene ic alue (μ) accoun ed o by an X-speci ic ma ke o a male is: μ¼q0þp2ðÞγ¼2pγ: Le xbe he geno ype code as de ined abo e and assume ha he allele e ec is independen o allele equency and is addi i e (i.e., absence o non-addi i e gene ic e ec ), hen he a iance o gene ic alue (σ 2 )a anX-speci iclocusin he popula ion o males is: σ2¼Va x−2pðÞγðÞ ¼Va x−2pðÞσ2 γ ¼q0−2pðÞ 2þp2−2pðÞ 2  σ2; γ ¼4pqσ2 γ whe e σ2 γis he a iance o he andom addi i e allele e ec γ. Fo emales, he expec a ion and a iance a e he same as hose o au osomal ma ke s, i.e. μ¼2pγ; and σ2¼2pqσ2 γ: Le m ij be he elemen o ma ix M o indi idual i and ma ke j, as de ined p e iously. The ela ionship coe icien be ween male kand male lcaused by he X-speci ic ma ke jcan hen be calcula ed as: kl ¼mkjmlj=4pjqj: The ela ionship coe icien be ween emale kand e- male lhas he same o m as o au osomal ma ke s, i.e. kl ¼mkjmlj=2pjqj: The ela ionship coe icien be ween male kand emale lis: kl ¼mkjmlj=ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4pjqj2pjqj q: Al e na i ely, i can be assumed ha geno ype A i Oin males has hal he e ec o geno ype A i A i in emales. Then, he geno ypes can be coded as he numbe o cop- ies o A 2 , i.e., 0 and 1 o geno ypes A 1 O and A 2 Oo males, 0, 1 and 2 o geno ypes A 1 A 1 ,A 1 A 2 and A 2 A 2 o emales, espec i ely. Fo emales, he expec a ion and a iance accoun ed o by an X-speci ic ma ke a e he same as he abo e. The expec a ion o he gene ic alue o a male is: μ¼q0þp1ðÞγ¼pγ; and he a iance o he gene ic alue o males is: σ2¼q0−pðÞ 2þp1−pðÞ 2  σ2 γ: ¼pqσ2 γ Le m *ij be he elemen o indi idual iand ma ke jin he co esponding Mma ix. De ine m *ij =0-p o geno- ype A 1 O and m *ij =1-p j o geno ype A 2 O o males, and m *ij =0-2p j ,1-2p j o 2-2p j o geno ypes A 1 A 1 ,A 1 A 2 , o A 2 A 2 o emales. Then, m *ij =m ij /2 o males, and m *ij =m ij o emales. Then, he ela ionship coe icien be ween male kand male lcaused by he X-speci ic ma ke jis: kl ¼mkjmlj=pjqj¼mkjmlj=4pjqj; he ela ionship coe icien be ween emale kand emale lis: kl ¼mkjmlj=2pjqj¼mkjmlj=2pjqj; and he ela ionship coe icien be ween male kand emale lis: kl ¼mkjmlj=ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pjqj2pjqj q¼mkjmlj=ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4pjqj2pjqj q: This demons a es ha he wo al e na e assump- ions o he e ec o he male geno ype o X-speci ic ma ke s lead o he same ela ionship coe icien . Thus, he Gma ix based on bo h au osomal and X ch omo- some ma ke s can be calcula ed as o au osomal ma ke s, bu elemen m ij o he Mma ix mus be di ided by ffiffiffi 2 p i ma ke jis a X-speci ic ma ke and indi idual iis a male, i.e. newmj¼mj∘δi jis an X‐speci ic ma ke mjelse ;  whe e ° is he Hadama d p oduc ope a ion, elemen i in ec o δis 1 i indi idual iis a emale, and 1ffiffi2 p .i indi idual iis a male. To cons uc he Mma ix, when he codes o A 1 A 1 ,A 1 A 2 and A 2 A 2 a e 0, 1 and 2, he X-speci ic geno ypes o A 1 OandA 2 Oa ecoded as 0 and 2. Genomic p edic ion models Genomic p edic ions based on ma ke da a wi h and wi hou ma ke s on he X ch omosome we e ca ied Su e al. Gene ics Selec ion E olu ion 2014, 46:47 Page 4 o 12 h p://www.gsejou nal.o g/con en /46/1/47 ou using he ollowing GBLUP models implemen ed in heDMUpackage[12]: (1) G(A): GBLUP wi h he Gma ix buil using au o- somal ma ke s (G a ) only: y¼μþZgaþe; (2) G(A + X): GBLUP wi h he Gma ix buil using all ma ke s and ea ing X-speci ic ma ke s as au osomal ma ke s (G 0 ): y¼μþZg0þe; (3) G c (A + X): GBLUP wi h he Gma ix buil using all ma ke s and accoun ing o he sex-linked inhe i - ance o X-speci ic ma ke s (G c ), y¼μþZgcþe; (4) G(A) + G(X): GBLUP using bo h he au osomal G ma ix and he X ch omosome Gma ix (G x ): y¼μþZgaþZgxþe; (5) G(A) + Pol: model G(A) plus a esidual polygenic e ec : y¼μþZgaþZuuþe; (6) G c (A + X) + Pol: model G c (A + X) plus a esidual polygenic e ec : y¼μþZgcþZuuþe: In he abo e models, yis he ec o o DRP, μis he in e cep , g a is he ec o o genomic b eeding alues accoun ed o by au osomes, g x is he ec o o genomic b eeding alues accoun ed o by he X ch omosome, g 0 is he ec o o o al genomic b eeding alues associa ed wi h he Gma ix ha ea s X-speci ic ma ke s as au o- somal ma ke s, g c is he ec o o o al genomic b eed- ing alues associa ed wi h he Gma ix ha accoun s o X-speci ic ma ke s as sex-linked ma ke s, Zis he in- cidence ma ix ela ing genomic b eeding alues o y,u is he ec o o esidual polygenic e ec s, Z u is he inci- dence ma ix ha associa es uwi h y, and eis he ec o o andom esiduals. Random e ec s a e assumed dis- ibu ed as ollows: gaeN0;Gaσ2 ga  ;g0eN0;G0σ2 g0  ;gceN0;Gcσ2 gc  ; gxeN0;Gxσ2 gx  ;ueN0;Aσ2 u  ; and eeN0;Rσ2 e  ; whe e Ais he pedig ee-based ela ionship ma ix, and R is a diagonal ma ix used o accoun o he e ogeneous esidual a iances due o di e en eliabili ies o DRP ( 2 DRP). The diagonal elemen io ma ix Rwas com- pu ed as Rii ¼1− 2 DRP 2 DRP . Reliabili y o DRP was calcula ed as 2 DRP ¼EDC EDCþλwhe e EDC is he equi alen daugh e con- ibu ion and λ¼4−he i abili y he i abili y [13]. All a iances (σ2 ga;σ2 gx; σ2 g0;σ2 gc;σ2 u;and σ2 e) we e es ima ed om he DRP da a used in he analyses, using he co esponding models. The allele equencies used o cons uc he G ma ix we e calcula ed om he cu en ma ke da a o he geno yped animals. In addi ion o he abo e analyses, genomic p edic- ions we e also pe o med using ou educed 54K ma ke da ase s. These da ase s we e: (1) Non-2: ma ke da a excluding he ma ke s on ch omosome 2 ha has a leng h simila o ha o he X ch omosome; (2) Non-10: ma ke da a excluding he ma ke s on ch omosome 10 which is simila o he X ch omosome in e ms o num- be o anno a ed genes; (3) Non-26: ma ke da a exclud- ing he ma ke s on ch omosome 26 which is simila o X ch omosome in e ms o numbe o ma ke s; (4) Non- an: ma ke da a excluding a andom sample o 827 ma ke s (equi alen o he numbe o ma ke s a ailable on he X ch omosome). Genomic p edic ions based on hese da ase s we e ca ied ou using he GBLUP model y=μ+Zg +e, whe e g is he ec o o genomic b eed- ing alues accoun ed o by he educed ma ke da a. The Gma ix used o he analyses conside ed sex-linked inhe i ance o X-speci ic ma ke s. Genomic p edic ions using di e en ma ke da ase s and di e en models we e alida ed by compa ing gen- omic es ima ed b eeding alues (GEBV) and DRP o an- imals in he es da a. GEBV we e calcula ed as he sum o he genomic e ec and he esidual polygenic e ec o models G(A) + Pol and G c (A + X) + Pol, and as he sum o he au osomal e ec and he X ch omosome e ec o model G(A) + G(X). Reliabili ies o genomic p edic ions we e es ima ed as he squa ed co ela ion be ween genomic p edic ions and DRP, and hen di ided by he a e age eliabili y o DRP, based on [14]: 2 GEBV ¼Co 2GEBV;DRPðÞ σ2 GEBVσ2 DRP 2 DRP ¼Co 2GEBV;TBV þ esidualðÞ σ2 GEBVσ2 TBV ; ¼Co 2GEBV;TBVðÞ σ2 GEBVσ2 TBV whe e TBV is ue b eeding alue. Bias o genomic p e- dic ions was assessed by eg ession o DRP on GEBV [15]. A necessa y condi ion o unbiased p edic ion is ha he eg ession coe icien does no de ia e signi i- can ly om 1. Su e al. Gene ics Selec ion E olu ion 2014, 46:47 Page 5 o 12 h p://www.gsejou nal.o g/con en /46/1/47 The log-likelihood a io s a is ic (−2lnLR) was used o es he di e ence in goodness o i be ween model G(A) + G(X) and model G(A), and be ween model G c (A+X)+PolandmodelG c (A + X). Taking G(A) + G(X) and G c (A + X) + Pol as al e na i e model while G(A) and G c (A + X) as null model, he log-likelihood a io s a is ic was calcula ed as -2lnLR = −2ln(likelihood o null model/ likelihood o al e na i e model). The P alue o -2lnLR was calcula ed assuming ha -2lnLR is asymp o ically χ2 d ¼1dis ibu ed [16], and calcula ed assuming ha he asymp o ic dis ibu ion o -2lnLR is a 50:50 mix u e o χ2 d ¼0and χ2 d ¼1;so ha P(−χ2 mix u e ) = 0.5P (χ2 d ¼1) [17]. Ho elling-Williams’ - es [18,19] was imple- men ed o es he equali y o wo dependen co ela- ions (Co (GEBV, DRP)) om wo models o he same ai . The log-likelihood a io es and Ho elling-Williams’ - es we e implemen ed in he ana- lysis using he 54K_ eal ma ke da a . Resul s The accu acy o impu a ion om he 7K o he 54K SNP panel was high (Table 3). Using Beagle, he allele e o a e o au osomal ma ke s a e aged o e he wo da ase s (IMP_ es and IMP_0.5 e ) was 1.1%. Com- pa ed wi h au osomal ma ke s, he allele e o a es o X-speci ic ma ke s and PAR ma ke s we e inc eased by 2.1 and 7.7%, espec i ely. The accu acy o impu a ion wi h Findhap was sligh ly lowe han ha wi h Beagle, wi h an inc ease o he allele e o a e o abou 0.7% o au osomes, 0.3% o X-speci ic ma ke s, and 1.5% o PAR ma ke s, a e aged o e he wo da ase s. Co el- a ion coe icien s be ween impu ed and ue geno ypes o au osomal ma ke s, pseudo-au osomal ma ke s, and X-speci ic ma ke s we e 0.983, 0.856 and 0.937 wi h Beagle, and 0.971, 0.831 and 0.935 wi h Finhap. Geno ype e o a e was nea ly wice as la ge as he al- lele e o a e o ma ke s on au osomes and PAR, bu almos he same o X-speci ic ma ke s (Table 3). This was because animals in he p esen da a we e all bulls, hus geno ype e o was in p inciple equi alen o he allele e o o X-speci ic ma ke s. The eason o a sligh ly highe geno ype e o a e han allele e o a e o X-speci ic ma ke s was ha some geno ypes we e he e ozygous in he eal 54K da a (due o yping e o ) and in he impu ed da a (due o impu a ion e o ). Al hough animals wi h LD geno ypes in he IMP_ es da ase had mo e ances o s wi h 54K geno ypes, while animals wi h LD geno ypes in he IMP_0.5 e da ase had mo e p ogeny wi h 54K geno ypes, hese wo da a- se s had simila accu acies o impu a ion (Table 3). Allele e o a es we e equal o 1.9% wi h Findhap and 1.2% wi h Beagle, a e aged o e he wo impu a ion da ase s and cal- cula ed om he da a pooled o e he au osomes and he Xch omosomema ke s. As shown in Table 4, o he ou da ase s, genomic p edic ions using all ma ke s ga e a sligh ly highe eliabili y han p edic ions wi hou ma ke s on he X ch omosome. A e aged o e he 15 ai s, he gain in eliabili y om using he X ch omosome ma ke s was 0.4 o 0.5% poin s when using models wi hou a esidual polygenic e ec , and 0.3 o 0.4% poin s when using models wi h a esidual polygenic e ec . Models G(A + X) and G c (A + X) esul ed in he same eliabili y o genomic p edic ions, which indica es ha a Gma ix ha ook sex-linked inhe i ance o X-speci ic ma ke s in o ac- coun did no imp o e genomic p edic ion mo e han a Gma ix ha deal wi h X-speci ic ma ke s as au osomal ma ke s, possibly because animals in he p esen da a we e all bulls. In addi ion, model G(A) + G(X) did no imp o e p edic ions compa ed o models G(A + X) and G c (A + X), which sugges s ha i is easonable o assume ha he e ec s o he ma ke s on he X ch omosome and he au osomes ha e he same dis ibu ion. A model ha included a esidual polygenic e ec im- p o ed he eliabili y o p edic ed b eeding alues, wi h an a e age inc ease o abou 0.8% poin s (Table 4). Fo all scena ios, he g ea es imp o emen in eliabili y by including a esidual polygenic e ec in he model was obse ed o he ai s longe i y and o he diseases. Reli- abili y o GEBV using he LD geno ypes was 5% poin s lowe han when using he eal 54K geno ypes and Table 3 Allele e o a e (ER A , %), geno ype e o a e (ER G , %) and co ela ion (COR) be ween impu ed and ue geno ypes o di e en se s o ma ke s a in wo da ase s b Da ase Me hod ALL AUTO PAR X ER A ER G COR ER A ER G COR ER A ER G COR ER A ER G COR IMP_ es Findhap 1.7 3.3 0.972 1.7 3.3 0.974 10.4 19.1 0.829 3.3 4.1 0.940 Beagle 1.1 2.2 0.982 1.1 2.1 0.983 8.8 15.9 0.858 3.0 3.0 0.941 IMP_0.5 e Findhap 2.0 3.9 0.967 2.0 3.8 0.968 10.3 18.7 0.833 3.8 4.4 0.930 Beagle 1.2 2.4 0.981 1.2 2.3 0.982 8.9 16.4 0.854 3.5 3.9 0.933 a ALL: all ma ke s; AUTO: ma ke s on he au osomes; PAR: ma ke s on he pseudo-au osomal egion; X: X-speci ic ma ke s on he X ch omosome; b IMP_ es : o he es animals in genomic p edic ion, he 54K ma ke da a we e impu ed om LD ma ke da a; IMP_0.5 e : o hal ( andomly chosen) o he e e ence animals, he 54K ma ke da a we e impu ed om LD ma ke da a. Su e al. Gene ics Selec ion E olu ion 2014, 46:47 Page 6 o 12 h p://www.gsejou nal.o g/con en /46/1/47 applying models wi hou a polygenic e ec , and 3.4% poin s lowe when applying models wi h a polygenic e ec . Fu he mo e, genomic p edic ions based on he impu ed da ase s o IMP_ es and IMP_0.5 e we e al- mos as accu a e as p edic ions based on he eal 54K da a. Reg ession coe icien s o DRP on genomic p edic ions based on he eal 54K o impu ed 54K geno ype da a anged om 0.782 o 1.064, excep o longe i y, o which he eg ession coe icien s anged om 0.631 o 0.685 (Table 5). A e aged o e he 15 ai s, he eg es- sion coe icien s we e sligh ly close o 1 wi h han wi h- ou using he X ch omosome ma ke s o p edic ion. Reg ession coe icien s we e he same when using eal e sus impu ed 54K geno ype da a. In addi ion, models ha included a esidual polygenic e ec esul ed in eg ession coe icien s conside ably close o 1 han models wi hou a polygenic e ec , which indica es a educ ion o p edic ion bias om including polygenic e ec s. Reg ession coe icien s de ia ed mo e om 1 o genomic p edic ions based on LD geno ype da a han o p edic ions using he 54K geno ype da a, which indica es a la ge p edic ion bias o he o me . Howe e , when using models wi h a esidual polygenic e ec , he eg es- sion coe icien s based on LD geno ypes we e e y close o hose based on he 54K geno ype da a. Table 6 shows he eliabili y o genomic p edic ions when excluding one o ou selec ed ch omosomes o when dele ing a andom sample o ma ke s. Compa ed o excluding he X ch omosome, excluding ch omosome 2 (simila o he X ch omosome in leng h), ch omosome 10 (simila o he X ch omosome in numbe o anno a ed genes), and ch omosome 26 (simila o he X ch omosome in numbe o ma ke s) led o la ge losses in eliabili y. Ex- cluding ch omosome 10 led o he la ges loss in eliabili y, while andomly dele ing 827 ma ke s (i.e. he same num- be o ma ke s as on he X ch omosome) led o no loss in eliabili y. The log likelihood a io es s a is ics in Table 7 indi- ca e ha model (G(A) + G(X)) using bo h au osomal and X ch omosome ma ke s had a signi ican ly be e goodness o i han model (G(A)) using only au osomal ma ke s o 13 o he 15 ai s, and ha model (G c (A + X) + Pol) wi h a esidual polygenic e ec was signi ican ly be e han model (G c (A + X)) wi hou a polygenic e ec o 12 ai s. As shown in Table 7, he a iance accoun ed o by he X ch omosome was signi ican ly di e en om 0 o 10 ai s, and he a iance accoun ed o by he esidual polygenic e ec was signi ican o 13 ai s. On a e age, he X ch omosome accoun ed o 1.7% o he o al addi i e gen- e ic a iance, and he esidual polygenic e ec o 17.2% o he o al addi i e gene ic a iance. Table 4 Reliabili y (%) o genomic p edic ions based on ou da ase s a wi h o wi hou X ch omosome ma ke s, using di e en models b and a e aged o e 15 ai s Da ase G(A) G(A + X) G c (A + X) G(A) + G(X) G(A) + Pol G c (A + X) + Pol 54K_ eal 38.0 38.5 38.5 38.5 38.9 39.3 IMP_ es 37.9 38.3 38.3 38.4 38.9 39.2 IMP_0.5 e 37.8 38.3 38.3 38.3 38.8 39.1 LD_ eal 33.0 33.5 33.6 33.6 35.5 35.9 a 54K_ eal: all animals wi h ma ke da a om he 54K chip; IMP_ es : o he es animals in genomic p edic ion, he 54K ma ke da a we e impu ed om LD ma ke da a; IMP_0.5 e : o hal ( andomly chosen) o he e e ence animals, he 54K ma ke da a we e impu ed om LD ma ke da a; LD_ eal: all animals had LD ma ke da a wi hou ex ension o he 54K ma ke da a; b G(A): model wi h a Gma ix buil using au osomal ma ke s only; G(A + X): model wi h a Gma ix buil using all ma ke s and ea ing X-speci ic ma ke s as au osomal ma ke s; G c (A + X): model wi h a Gma ix buil using all ma ke s and speci ying sex-linked inhe i ance o X-speci ic ma ke s; G(A) + G(X): model wi h an au osome Gma ix and an X ch omosome Gma ix; G(A) + Pol: model G(A) plus a esidual polygenic e ec ; G c (A + X) + Pol: model G c (A + X) plus a esidual polygenic e ec . Table 5 Reg ession coe icien s o de eg essed p oo s on genomic p edic ions based on ou da ase s a wi h o wi hou X ch omosome ma ke s, using di e en models b and a e aged o e 15 ai s Da ase s G(A) G(A + X) G c (A + X) G(A) + G(X) G(A) + Pol G c (A + X) + Pol 54K_ eal 0.881 0.885 0.885 0.885 0.918 0.919 IMP_ es 0.881 0.885 0.885 0.885 0.918 0.919 IMP_0.5 e 0.881 0.886 0.885 0.886 0.920 0.922 LD_ eal 0.834 0.835 0.837 0.838 0.914 0.915 a 54K_ eal: all animals wi h ma ke da a om he 54K chip; IMP_ es : o he es animals in genomic p edic ion, he 54K ma ke da a we e impu ed om LD ma ke da a; IMP_0.5 e : o hal ( andomly chosen) o he e e ence animals, he 54K ma ke da a we e impu ed om LD ma ke da a; LD_ eal: all animals had LD ma ke da a wi hou ex ension o he 54K ma ke da a; b G(A): model wi h a Gma ix buil using au osomal ma ke s only; G(A + X): model wi h a Gma ix buil using all ma ke s and ea ing X-speci ic ma ke s as au osomal ma ke s; G c (A + X): model wi h a Gma ix buil using all ma ke s and speci ying sex-linked inhe i ance o X-speci ic ma ke s; G(A) + G(X): model wi h an au osome Gma ix and an X ch omosome Gma ix; G(A) + Pol: model G(A) plus a esidual polygenic e ec ; G c (A + X) + Pol: model G c (A + X) plus a esidual polygenic e ec . Su e al. Gene ics Selec ion E olu ion 2014, 46:47 Page 7 o 12 h p://www.gsejou nal.o g/con en /46/1/47 Table 8 p esen s eliabili ies o genomic p edic ions o each ai using models G(A), G(A) + G(X) and G c (A + X) + Pol, based on he 54K_ eal da ase and shows ha he con ibu ion o X ch omosome ma ke s o he e- liabili y o genomic p edic ions di e ed be ween ai s. An inc ease in eliabili y o a ound 2% poin s was obse ed o e ili y and o he diseases. Co espondingly, he a i- ances explained by he X ch omosome we e much highe o hese wo ai s han o he o he ai s. Longe i y also showed a signi ican bene i o including X ch omosome ma ke s, al hough he a iance accoun ed o by he X ch omosome was small o his ai . A e aged o e he 15 ai s, including he X ch omosome imp o ed he p edic- ion eliabili y by 0.5% poin s. The bene i o including polygenic e ec s in o he model also di e ed among ai s (Table 8). A signi ican inc ease in he eliabili y o genomic p edic ions om including a esidual polygenic e ec was ob ained o ou ai s. The la ges imp o emen s we e o longe i y (3.6%) and o he diseases (3.7%). Fo hese wo ai s, he a iance accoun ed o by esidual polygenic e ec was mo e han 40% o he o al addi i e gene ic a iance (Table 7). Fo he o he ai s, he a e age imp o emen in p edic ion eliabili y was 0.3%. Table 6 Reliabili y (R 2 , %) o genomic p edic ions based on he 54K SNPs (54K_ eal) excluding one ch omosome o a andom sample o 827 ma ke s, a e aged o e 15 ai s Ch omosome excluded Ch leng h Numbe o genes Numbe o ma ke s on he map Numbe o ma ke s a e edi ing R 2 Di e ence om R 2 ull* X-Ch 147.8 1128 1176 827 38.0 0.5 Ch . 2 137.1 1021 2829 2289 37.6 0.9 Ch . 10 104.3 1074 2206 1800 37.4 1.1 Ch . 26 51.7 437 1116 921 37.8 0.7 Random - - - 827 38.5 0.0 * Di e ence om eliabili y (%) o genomic p edic ions ob ained wi h a model ha used a Gma ix buil wi h all ma ke s and speci ying sex-linked inhe i ance o X-speci ic ma ke s. Table 7 Log likelihood a io s a is ics be ween models and he a iance accoun ed o by he X ch omosome and by esidual polygenic e ec , based on he eal 54K da ase T ai s Log likelihood a io Va iance (SE) Va iance % e (A + X)/A a (AX + P)/AX b X-Ch c Pol d X-Ch c Pol d Milk 13.46 * 16.62 * 1.05 (0.48) * 14.34 (3.74) * 0.9 12.0 Fa 27.34 * 8.03 * 1.41 (0.53) * 9.27 (3.51) * 1.3 8.4 P o ein 27.07 * 34.62 * 1.80 (0.62) * 20.54 (3.74) * 1.5 17.3 G ow h 0.00 16.87 * 0.00 (0.28) 17.84 (4.67) * 0.0 13.5 Fe ili y 27.59 * 33.85 * 5.21 (1.66) * 42.81 (8.19) * 3.6 27.9 Bi h index 3.93 * 2.76 ¤ 0.93 (0.68) 9.09 (6.14) * 0.8 7.7 Cal ing index 0.66 0.80 0.73 (0.86) 6.51 (7.21) * 0.7 5.9 Udde heal h 21.96 * 18.6 * 2.44 (0.84) * 16.58 (4.17) * 2.7 17.6 O he diseases 26.05 * 47.93 * 6.13 (2.13) * 70.01 (11.21) * 4.1 40.4 Body con o ma ion 4.12 * 5.08 * 2.71 (1.42) * 15.82 (7.46) * 2.2 12.7 Fee and legs 3.62 ¤ 0.00 2.16 (1.60) 0.00 (9.97) 1.5 0.0 Udde con o ma ion 9.60 * 0.05 2.52 (1.10) * 1.34 (5.76) 1.8 1.2 Milking abili y 9.97 * 10.40 * 2.57 (1.28) * 23.66 (8.01) * 1.2 11.0 Tempe amen 5.23 * 22.22 * 3.36 (1.78) * 43.94 (10.30) * 2.5 29.8 Longe i y 3.87 * 118.57 * 1.07 (0.97) 87.50 (9.37) * 0.8 53.4 A e age 12.10 22.43 2.27 (1.08) 25.28 (6.90) 1.7 17.2 a Log likelihood a io o model G(A) + G(X) o model G(A), whe e G(A) was he model wi h an au osomal Gma ix and G(A) + G(X) was he model including an au osome Gma ix and an X ch omosome Gma ix; b Log likelihood a io o model G c (A + X) + Pol o model G c (A + X), whe e G c (A + X) was he model wi h a G ma ix buil using all ma ke s and G c (A + X) + Pol included also esidual polygenic e ec ; c Va iance accoun ed by he X ch omosome and es ima ed om model G (A) + G(X); d Va iance o esidual polygenic e ec and es ima ed om model G c (A + X) + Pol; e Va iance in p opo ion o o al addi i e gene ic a iance; * Signi ican a P < 0.05, whe e P was calcula ed as P(χ2 d ¼1); ¤ Signi ican a P m < 0.05, whe e P m was calcula ed as 0.5P(χ2 d ¼1), e.g., when P < 0.05, P m < 0.025. Su e al. Gene ics Selec ion E olu ion 2014, 46:47 Page 8 o 12 h p://www.gsejou nal.o g/con en /46/1/47 Discussion This s udy in es iga ed he accu acy o geno ype impu - a ion o ma ke s on he X ch omosome and he impac o including X ch omosome ma ke s on eliabili y o genomic p edic ions. The esul s showed ha a e aged o e he 15 ai s e alua ed, including X ch omosome ma ke s imp o ed he eliabili y o genomic p edic ion sligh ly, anging om 0.3 o 0.5% poin s in a ious da a- se s and using di e en models. The a iance accoun ed o by he X ch omosome was abou 1.7% o he o al addi i e gene ic a iance. Gains in eliabili y om in- cluding he X ch omosome we e smalle han obse ed in a p e ious s udy on USA Hols ein ca le by VanRaden e al. [7], who epo ed an inc ease in eliabili y o 1.5%, a e aged o e nine ai s, al hough he X ch omosome accoun ed o only 1% o he o al gene ic a iance in hei s udy. When he genomic model included a e- sidual polygenic e ec , b eeding alues p edic ed using ma ke da a ha included X ch omosome ma ke s we e s ill mo e accu a e han hose p edic ed wi hou X ch omosome ma ke s. This means ha a model ha in- cludes a esidual polygenic e ec does no eco e he loss o p edic ion accu acy om exclusion o X ch omo- some ma ke s. The loss o p edic ion accu acy om exclusion o he X ch omosome was smalle han when an au osome o simila size (ch omosome 2), o wi h an equi alen numbe o anno a ed genes (ch omosome 10), o wi h an equi alen numbe o ma ke s (ch omosome 26) was excluded. The e a e wo possible easons why ma ke s on he X ch omosome con ibu e less o he eliabili y o genomic p edic ions han hese h ee au osomes. One eason is ha he densi y o ma ke s on he X ch omo- some is much lowe han ha on au osomes; he a e age dis ance be ween adjacen ma ke s is abou 180 kb on he X ch omosome and 60 kb on he au osomes in he 54K ma ke da a. The second eason is ha ma ke s on he X ch omosome ep esen weake ela ionships be- ween indi iduals in he p esen da a, which consis ed only o males. The impac o gene ic ela ionships be- ween animals in he e e ence and es da ase s on eli- abili y o genomic p edic ions o es animals has been epo ed in many p e ious s udies [11,20-22]. Since he ela ionship be ween si es and sons is 0 o he X ch omosome, in o ma ion o a si e does no di ec ly in luence he son’s GEBV explained by he X ch omosome. On he con a y, in o ma ion o a si e di ec ly in luences he son’s GEBV explained by he au osomes, as epo ed in p e ious s udies ha showed ha eliabili y o GEBV is abou 5 o 10% highe o he es animals wi h han wi h- ou hei si es in he e e ence popula ion [23,24]. When a andom se o 827 ma ke s (i.e. he numbe o ma ke s on he X ch omosome) was excluded om he analysis, he e was no loss in eliabili y o genomic Table 8 Co ela ion be ween genomic p edic ions and de eg essed p oo s and eliabili y o genomic p edic ions o each ai , based on he eal 54K da ase T ai s Co ela ion Reliabili y % G(A) G(A) + G(X) G c (A + X) + Pol G(A) G(A) + G(X) G c (A + X) + Pol Milk 0.674 a 0.676 a 0.681 b 48.7 48.9 49.6 Fa 0.663 a 0.667 ab 0.670 b 47.1 47.6 48.0 P o ein 0.655 a 0.657 a 0.666 b 45.9 46.2 47.5 G ow h 0.665 a 0.665 a 0.668 a 47.2 47.2 47.6 Fe ili y 0.520 a 0.532 b 0.538 b 40.7 42.6 43.5 Bi h index 0.517 a 0.518 a 0.518 a 32.5 32.7 32.7 Cal ing index 0.452 a 0.454 a 0.452 a 30.3 30.5 30.2 Udde heal h 0.563 a 0.568 a 0.569 a 39.5 40.1 40.3 O he diseases 0.447 a 0.459 b 0.481 c 36.3 38.2 41.9 Body con o ma ion 0.480 a 0.478 a 0.480 a 27.6 27.4 27.6 Fee and legs 0.452 a 0.456 a 0.457 a 33.2 33.7 33.9 Udde con o ma ion 0.595 a 0.598 a 0.598 a 44.0 44.5 44.4 Milking abili y 0.642 a 0.644 a 0.644 a 47.1 47.4 47.3 Tempe amen 0.342 a 0.342 a 0.348 a 18.3 18.3 19.0 Longe i y 0.463 a 0.468 b 0.494 c 31.1 31.8 35.4 A e age 0.542 0.545 0.551 38.0 38.5 39.3 G(A): model wi h a Gma ix buil wi h au osomal ma ke s only; G(A) + G(X): model wi h an au osome Gma ix and an X ch omosome Gma ix; G c (A + X) + Pol: model wi h a Gma ix buil wi h all ma ke s plus a esidual polygenic e ec ; a,b,c Co ela ions wi hin a ai wi hou common supe sc ip di e ed signi ican ly (P < 0.05), acco ding o Ho elling-Williams’ - es . Su e al. Gene ics Selec ion E olu ion 2014, 46:47 Page 9 o 12 h p://www.gsejou nal.o g/con en /46/1/47