Estimation of breeding values for uniformity of growth in Atlantic salmon (Salmo salar) using pedigree relationships or single‑step genomic evaluation

Sae‑Lim e al. Gene Sel E ol (2017) 49:33 DOI 10.1186/s12711‑017‑0308‑3 RESEARCH ARTICLE Es ima ion o b eeding alues o uni o mi y o g ow h inA lan ic salmon (Salmo sala ) using pedig ee ela ionships o single‑s ep genomic e alua ion Panya Sae‑Lim1*, An i Kause2, Ma ie Lillehamme 1 and Han A. Mulde 3 Abs ac Backg ound: In a med A lan ic salmon, he i abili y o uni o mi y o body weigh is low, indica ing ha he accu acy o es ima ed b eeding alues (EBV) may be low. The use o genomic in o ma ion could be one way o inc ease accu‑ acy and, hence, ob ain g ea e esponse o selec ion. Genomic in o ma ion can be me ged wi h pedig ee in o ma‑ ion o cons uc a combined ela ionship ma ix ( H ma ix) o a single‑s ep genomic e alua ion (ssGBLUP), allowing ealized ela ionships o he geno yped animals o be exploi ed, in addi ion o nume a o pedig ee ela ionships ( A ma ix). We compa ed he p edic i e abili y o EBV o uni o mi y o body weigh in A lan ic salmon, when implemen ‑ ing ei he he A o H ma ix in he gene ic e alua ion. We used double hie a chical gene alized linea models (DHGLM) based ei he on a si e‑dam (si e‑dam DHGLM) o an animal model (animal DHGLM) o bo h body weigh and i s uni o mi y. Resul s: Wi h he animal DHGLM, he use o H ins ead o A signi ican ly inc eased he co ela ion be ween he p e‑ dic ed EBV and adjus ed pheno ypes, which is a measu e o p edic i e abili y, o bo h body weigh and i s uni o mi y (41.1 o 78.1%). When log‑ ans o med body weigh s we e used o accoun o a scale e ec , he use o H ins ead o A p oduced a small and non‑signi ican inc ease (1.3 o 13.9%) in p edic i e abili y. The si e‑dam DHGLM had lowe p edic i e abili y o uni o mi y compa ed o he animal DHGLM. Conclusions: Use o he combined nume a o and genomic ela ionship ma ix ( H ) signi ican ly inc eased he p edic i e abili y o EBV o uni o mi y when using he animal DHGLM o un ans o med body weigh . The inc ease was only mino when using log‑ ans o med body weigh s, which may be due o he lowe he i abili y o scaled uni o mi y, he lowe gene ic co ela ion o ans o med body weigh wi h i s uni o mi y compa ed o he un ans‑ o med ai s, and he small numbe o geno yped animals in he e e ence popula ion. This s udy shows ha ssGB‑ LUP inc eases he accu acy o EBV o uni o mi y o body weigh and is expec ed o inc ease esponse o selec ion in uni o mi y. © The Au ho (s) 2017. This a icle is dis ibu ed unde he e ms o he C ea i e Commons A ibu ion 4.0 In e na ional License (h p://c ea i ecommons.o g/licenses/by/4.0/), which pe mi s un es ic ed use, dis ibu ion, and ep oduc ion in any medium, p o ided you gi e app op ia e c edi o he o iginal au ho (s) and he sou ce, p o ide a link o he C ea i e Commons license, and indica e i changes we e made. 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. Backg ound In aquacul u e, selec ion o inc ease economically impo - an ai s such as g ow h is one o he main b eeding goals. Howe e , ish p oduce s show in e es o imp o e no only he mean bu also he a iance o ai s [1]. Uni- o mi y o g ow h is p e e able because mo e uni o m g ow h allows a mo e uni o m p oduc , ha es o a la ge p opo ion o he popula ion a ma ke size, and educ ion o size g ading and mul iple ha es s [2–4]. Mo e uni o m g ow h may also educe compe i i e in e - ac ions be ween animals, which con ibu es o educe eed monopoliza ion and dominan beha iou , and hus imp o e well-being o ish [5]. Uni o mi y is also impo - an o ai s ha ha e an in e media e op imal ai alue [6], such as ille lipid%, body shape, and condi ion Open Access G ene ics S elec ion E olu ion *Co espondence: panya.sae‑[email p o ec ed] 1 No ima Ås, Oslo eien 1, P.O. Box 210, 1431 Ås, No way Full lis o au ho in o ma ion is a ailable a he end o he a icle Page 2 o 12 Sae‑Lim e al. Gene Sel E ol (2017) 49:33 ac o in he aquacul u e indus y. A ish whose g ow h is sensi i e o non-measu able en i onmen al ac o s, known as mic o-en i onmen s, shows mic o-en i on- men al sensi i i y, which esul s in high en i onmen- al a iance and consequen ly con ibu es o inc eased pheno ypic a ia ion, leading o inc eased size a ia ion wi hin a g oup o ish. A numbe o empi ical s udies in e es ial and aqua ic species show ha uni o mi y is pa ly de e mined by gene ic ac o s [4, 7–16]. Thus, selec i e b eeding can open up one a enue o imp o e uni o mi y o ish ai s. A lan ic salmon (Salmo sala L.) is a a med ish ha is o majo economic impo ance. He i abili y o uni- o mi y o body weigh has been es ima ed in A lan ic salmon [14], ainbow ou (Onco hynchus mykiss Wal- baum) [4, 8], and Nile ilapia (O eoch omis nilo icus) [15, 16]. In gene al, he i abili y o uni o mi y ( h2 ) is low in li es ock and aquacul u e species ( h2  < 0.05), indi- ca ing ha he p edic ion accu acy o b eeding alues o uni o mi y may be low [17, 18]. Howe e , he coe - icien o gene ic a ia ion ( GCV ) o uni o mi y o body weigh is high in ish species (median GCV = 34.0%: min=17.4% and max=64.0%), which indica es high po en ial o esponse o selec ion [4, 8, 14, 16, 19]. One way o inc ease esponse o selec ion o uni o mi y is o inc ease he accu acy o es ima ed b eeding alues (EBV) o uni o mi y [20]. In aquacul u e, ull- and hal -sib amily sizes a e usu- ally la ge and hus he accu acy o EBV based on ull- sibs, hal -sibs and own pe o mance is high o body weigh , bu no o uni o mi y due o i s low he i abili y [8]. One app oach o inc ease he accu acy o EBV is o use genomic in o ma ion [21]. Wi h genomic selec- ion, genomic es ima ed b eeding alues (GEBV) can be ob ained o he selec ion candida es ha a e geno- yped, e en when hey ha e no pheno ype eco ds. One eason why genomic selec ion esul s in highe accu acy o selec ion is he mo e accu a e es ima ion o he Men- delian sampling gene ic e ec s h ough ealized addi i e gene ic ela ionships among animals [22]. Consequen ly, indi idual squa ed esiduals, which is he pheno ype o uni o mi y in a double hie a chical gene alized linea model (DHGLM), may also be mo e accu a ely es ima ed when using genomic in o ma ion. In many cases, combining nume a o pedig ee and genomic in o ma ion in genomic e alua ions is imple- men ed in mul iple s eps, which may in oduce bias and need some calcula ions o combine wi h pedig ee-based EBV [23, 24]. Single s ep genomic bes linea unbiased p edic ion (ssGBLUP) a oids his, and genomic and pedi- g ee in o ma ion a e combined in one s ep [23], which may lead o less bias and is less p one o double coun ing o in o ma ion compa ed o genomic e alua ion me hods ha a e pe o med in mul iple s eps. The ssGBLUP aug- men s he nume a o ela ionship ( A ) ma ix by he genomic ela ionship ( G ) ma ix in con en ional gene ic e alua ion using BLUP [24]. This combined nume a- o and genomic ela ionship ma ix is known as he H ma ix [25]. In ish b eeding, combining pedig ee and genomic in o ma ion allows exploi ing he la ge ull- and hal -sib amilies and he mo e accu a e ela ionships o he geno yped animals, and may yield a highe accu acy o selec ion o uni o mi y han he use o he A ma ix. To da e, he use o ssGBLUP o uni o mi y has no been s udied. Fu he mo e, acco ding o a p e ious s udy, he si e-dam model, bu no he animal model, implemen ed wi hin he amewo k o DHGLM p o ided unbiased (co) a iance componen es ima es [14]. How- e e , an animal DHGLM is expec ed o pe o m be e han a si e-dam DHGLM o gene ic e alua ion because he animal DHGLM uses ull ela ionships be ween ani- mals a he han only among si es and dams. This is pa - icula ly impo an o uni o mi y, which is quan i ied by he esiduals o indi iduals, which in he animal model do no con ain he Mendelian sampling e m. Mo eo e , o gene ic e alua ion, he animal DHGLM uses all phe- no ypic in o ma ion and, o mos b eeding p og ams, a leas pa o he selec ion candida es, e.g. emales o sex-linked ai s, ha e pheno ypes a ailable a he ime o selec ion. Use o he animal DHGLM wi h ssGBLUP o uni o mi y has no been es ed. In his s udy, we implemen ed ssGBLUP o p edic ing GEBV o uni o mi y in A lan ic salmon. Speci ically, ou aim was o compa e he p edic i e abili y o EBV o uni- o mi y o body weigh when implemen ing ei he BLUP wi h he A ma ix o ssGBLUP wi h he H ma ix. The (co) a iance componen s we e es ima ed om he si e- dam DHGLM wi h ei he A o H and compa ed p io o gene ic e alua ion. Me hods Da a The da a used in his s udy o igina ed om he expe i- men conduc ed by No ima AS and he b eeding com- pany SalmoB eed in No way. The expe imen ollowed all he egula ions o animal e hical p ac ice and was app o ed by he No wegian Resea ch Animal Commi ee (ID 6489). In 2013, 234 ull-sib amilies we e es ablished om he ma ing o 131 si es o 234 dams (Table1) du - ing ou weeks. Fo y-se en pe cen o he pa en s we e om yea class 2009 and he es om yea class 2010. A e ha ching, inge lings om each amily we e held in a 180-L amily ank un il agging size (a mean body weigh o 50g). Each animal was agged using passi e in eg a ed ansponde (PIT) ags (Sa pos AS, No way). Du ing agging, a in sample o geno yping was collec ed Page 3 o 12 Sae‑Lim e al. Gene Sel E ol (2017) 49:33 om 21 o 38 sibs o each o 50 ull-sib amilies. The ea - e , all ish we e andomly alloca ed o h ee expe imen anks and g own o 11mon hs. A he a e age age o 16mon hs, all ish we e challenged wi h sea lice using a co-habi a challenge, and a he end o he challenge es , inal body weigh (g) was measu ed o all 3595 ish wi h an elec onic balance. A o al o 1416 o sp ing (39% o all o sp ing) and he 131 si es and 234 dams we e geno- yped using he 31K A yme ix single nucleo ide poly- mo phism (SNP) chip o A lan ic salmon de eloped by No ima. Quali y con ol o SNPs was pe o med in PLINK 1.9 [26] based on he ollowing c i e ia: SNPs we e emo ed i (1) hei call a e was lowe han 90%, (2) hey de ia ed om Ha dy–Weinbe g equilib ium wi h a P alue cu -o o 10−15, and (3) hei mino allele e- quency (MAF) was lowe han 0.01. A e quali y con ol, 921 o 31,013 SNPs we e emo ed (2.9%) and, hus 30,092 SNPs emained o c ea e he genomic ela ionship. Rela ionship ma ix The nume a o ela ionship ( A ) ma ix wi h 814 ances- o s in ou gene a ions was p epa ed based on pedig ee in o ma ion using ASReml [27]. The combined nume a- o and genomic ela ionship ( H ) ma ix was de ined as [23]: whe e A11 is he pedig ee ela ionship ma ix be ween non-geno yped animals, A12 and A21 a e pedig ee ela- ionship ma ices be ween geno yped and non-geno- yped animals, A22 is he pedig ee ela ionship ma ix be ween geno yped animals, and G is he genomic ela- ionship ma ix be ween geno yped animals. The G ma ix was compu ed as [28]: G = WW′ N , whe e W is he ma ix o he scaled SNP geno ypes o all loci and N is he o al numbe o SNPs (30,092). The elemen s o W we e calcula ed as: H =  A11 +A12 +A −1 22 (G−A22)A −1 22 A21 A12A −1 22 G GA−1 22 A 21 G , whe e xij is he SNP geno ype (coded 0, 1, o 2) o he i h indi idual a SNP j and pj is he allele equency o he homozygous geno ype coded as 2. Howe e , Aguila e al. [29] and Ch is ensen and Lund [30] showed ha he in e se o he H ma ix can be com- pu ed as: which is less compu a ional demanding and mo e simple han p epa ing and subsequen ly in e ing he H ma ix. The H−1 was p epa ed by using he Calc_g m compu e so wa e [31], which p epa es bo h A−1 and G−1 in e - nally be o e compu ing H−1 . S a is ical analysis Analysis o  esiduals Uni o mi y can be quan i ied by squa ed esiduals om a BLUP mixed model equa ion [32]. The use o genomic in o ma ion o cons uc ealised ela ionships be ween animals, especially o ull-sibs, is expec ed o inc ease he accu acy o esidual es ima es due o a g ea e accu- acy o EBV o body weigh . The e o e, we in es iga ed he e ec o ssGBLUP and adi ional BLUP on indi idual esidual es ima ion. Fu he mo e, we in es iga ed si e- dam and animal models because esidual es ima es om a si e-dam model con ain no only he unexplained en i- onmen al e ec s bu also Mendelian sampling gene ic e ec s. Residual es ima es om an animal model do no con ain he la e when EBV a e es ima ed wi h an accu- acy o 1. In o al, esiduals om ou models we e com- pa ed, i.e. he si e-dam o animal model wi h ei he A o H .The animal mixed model was: whe e yiklmn is he obse a ion (body weigh ) o he i h indi idual, µ is he o e all mean, age is he ixed co a ia e e ec due o di e en le els o age o he ish, calcula ed om he s a eeding da e un il he da e o measu emen (day), β is he ixed linea eg ession coe icien on age, is he l h ixed communal ank e ec , yc is he m h ixed e ec o yea class o he pa en s, ai is he andom addi- i e gene ic e ec , a ∼  0, Aσ 2 a , whe e A is he nume a- o ela ionship ma ix, o a ∼N  0, Hσ 2 a , whe e H is he combined genomic and pedig ee ela ionship ma ix, N is he no mal dis ibu ion, and σ2 a is he addi i e gene ic a iance o body weigh , cn is he andom common e ec o ull-sibs, c ∼N  0, Iσ 2 c, whe e I is he iden i y w ij =  xij −2pj   2pj  1−pj  , H −1=A−1+  00 0G −1−A−1 22 , (1) yiklmn =µ+βagek+ l+ycm+ai+cn+eiklmn, Table 1 Popula ion s uc u e o A lan ic salmon Popula ion s uc u e Si es, dams 131, 234 Si es pe dam, mean ( ange) 1.0 (1.0) Dams pe si e, mean ( ange) 1.78 (1–3) Full‑sib amilies 234 Fish pe ull‑sib amily, mean ( ange) 15.4 (4–54) Numbe o ish wi h eco ds 3595 Geno yped animals Full‑sib amilies 50 Fish pe ull‑sib amily, mean ( ange) 28.3 (21–38) Numbe o ish wi h eco ds 1416 Page 4 o 12 Sae‑Lim e al. Gene Sel E ol (2017) 49:33 ma ix and σ2 c is he common en i onmen al a iance o body weigh , and eiklmn is he andom esidual e ec , e ∼N  0, Iσ 2 e , whe e σ2 e is he esidual a iance o body weigh assumed o be homogeneous. Fo he si e-dam model, he e m ai in Eq.(1) was eplaced by he andom si e-dam ( ui ) e ec , u ∼N  0, Aσ 2 u o u ∼N  0, Hσ 2 u . The same A and H ma ices we e used o he si e-dam and he animal models. Es ima ion o gene ic pa ame e s o uni o mi y To es ima e gene ic pa ame e s o body weigh and i s uni o mi y, he si e-dam DHGLM was used [33, 34] because i is expec ed o p o ide unbiased (co) a iance componen s o uni o mi y [14]. Body weigh eco ds we e ea ed in wo di e en ways. Fi s , obse ed body weigh was s anda dized o a mean o 0 and a iance o 1, which acili a es con e gence o he DHGLM. Sec- ond, we used ei he he na u al log o he Box–Cox ans o ma ion o accoun o possible scale e ec s, because a iances ypically inc ease wi h inc easing ai means [35, 36]. Fo he Box–Cox ans o ma ion, each obse a ion was compu ed as y i − 1  , whe e  is he ans o ma ion pa ame e , which was es ima ed based on Eq. (1) wi hou he andom e ec s [37] by maxi- mum likelihood using he MASS package in R so wa e [38]. The es ima e o  was close o 0 (0.076), indica - ing ha he Box–Cox ans o ma ion is e y simila o log- ans o ma ion, which se s  equal o 0. The e o e, he Box–Cox ans o med body weigh was no used u he . The s anda dized body weigh and na u al loga- i hm body weigh a e abb e ia ed as s dWT and lnWT, espec i ely. To es ima e gene ic pa ame e s, s anda dized and ans o med body weigh s we e modelled using si e-dam DHGLM in ASReml [32]: whe e y is he ec o o s dWT o lnWT eco ds o he i h indi idual;  is he ec o o esponse a iables o he esidual a iance, whe e ψ i=log  ˆσ2 ei  + ˆe 2 i 1−hi−ˆσ2 ei ˆσ2 e i , which was linea ized using a Taylo se ies app oxima ion in ASReml [34], ˆ e2 i is he squa ed esidual o he i h body weigh eco d, hi is he diagonal elemen in he ha -ma ix o y [39], and ˆ σ2 ei is he es ima ed esidual a iance o he i h obse a ion in he p e ious i e a ion o ASReml; X and X a e incidence ma ices o he ixed e ec s desc ibed in Eq.(1) o he ai mean and i s uni o mi y, espec i ely; b ( b ) is he solu ion ec o o he co esponding ixed (2)  y   =  X0 0X  b b  +  (Zs+Zd)0 0(Zs+Zd)  ×  u u  +  Q0 0Q  c c  +  e e  , e ec s; Zs and Zd a e incidence ma ices o he andom si e (s) and dam (d) e ec s; u ( u ) is he ec o o addi- i e gene ic e ec s o si e-dam on he weigh (uni o m- i y), which was assumed o ollow a no mal dis ibu ion o he A ma ix: and o he H ma ix: whe e he 1 4 accoun s o he ac ha he si e and dam each explain only a qua e o he addi i e gene ic a i- ance; Q ( Q ) is he incidence ma ix o he andom com- mon e ec s o ull-sibs; c ( c ) is he ec o o common e ec s o ull-sibs: The esiduals o y ( e ) and  ( e ) we e assumed o be independen ly no mally dis ibu ed as ollows: whe e W = diag (ˆ  −1) and W =diag  1−h 2  , and σ2 ǫ ( σ2 ǫ ) is a scaled a iance ha was expec ed o be 1. The si e- dam DHGLM was i ed i e a i ely o upda e  , diag ( W) and diag ( W ) un il he log-likelihood con e ged [34]. Calcula ion o gene ic pa ame e s In he si e-dam DHGLM, he es ima ed a iance o si es was se equal o he es ima ed gene ic a iance o dams and equal o one qua e o he addi i e gene ic a iance. Hence, he addi i e gene ic a iance o body weigh ( σ2 a ) and i s uni o mi y ( σ2 a ,exp ) we e equal o 4 σ 2 u and 4 σ 2 u ,exp , espec i ely. Es ima es o σ2 u ,exp and σ2 c ,exp o uni o m- i y o body weigh we e on he exponen ial scale ( exp ) and we e con e ed o an addi i e scale ( σ2 u and σ2 c ) using he ex ension o he equa ions o Mulde e al. [17], as de i ed by Sae-Lim e al. [8]. The addi i e gene ic a iance o uni- o mi y o body weigh on he addi i e scale was equal o 4 σ 2 u . Pheno ypic a iance ( σ2 P ) o body weigh was equal o 2 σ 2 u +σ 2 c +σ 2 e , whe e σ2 c is he a iance componen o he e ec common o ull-sibs and σ2 e is he esidual a iance o body weigh . He i abili y o body weigh ( h2 ) was calcula ed as σ2 a /σ 2 P . He i abili y o uni o mi y o body weigh ( h2 ) on he addi i e scale was calcula ed as σ 2 a 2 σ4 P +3  σ2 a +σ2 c  [8, 40]. Simila ly, he common en i onmen- al e ec was calcula ed as c2 =σ 2 c /σ 2 P o body weigh and as c2 = σ 2 c 2 σ4 P +3  σ2 a +σ2 c  o uni o mi y o body weigh  u u ∼N0 0,1 4σ 2 aσa,a ,exp σa,a ,exp σ2 a ,exp ⊗A ,  u u ∼N0 0,1 4σ 2 aσa,a ,exp σa,a ,exp σ2 a ,exp ⊗H ,  c c ∼N0 0,σ 2 cσc,c ,exp σc,c ,exp σ2 c ,exp ⊗I .  e e  ∼N  0 0  ,  W −1 σ 2 ǫ0 0W −1 σ2 ǫ ⊖ , Page 5 o 12 Sae‑Lim e al. Gene Sel E ol (2017) 49:33 [8]. The gene ic coe icien o a ia ion o uni o mi y o body weigh ( GCV ) was calcula ed as  σ2 a , exp . S anda d e o s o h2 and GCV we e app oxima ed using he equa- ions p esen ed by Mulde e al. [41]. Gene ic e alua ion andc oss‑ alida ion Two gene ic e alua ions, i.e., BLUP wi h A and ssGBLUP wi h H , we e pe o med in a 10- old c oss- alida ion using he gene ic pa ame e s es ima ed based on he si e- dam DHGLM and !BLUP op ion in ASReml. In o al, ou models we e used in he 10- old c oss- alida ion, i.e. ani- mal DHGLM wi h ei he A o H on s dWT and lnWT. The 10- old c oss- alida ion was pe o med on s and- a dized and ans o med body weigh da a as ollows: 1. Adjus ed pheno ypes o body weigh ( y∗ i ) and i s uni o mi y ( ψ∗ i ) we e calcula ed as y∗ i = ˆ a i +ˆc i+ˆ e i and ψ∗ i = ˆ a i +ˆc i +ˆe i , using he solu ions om he analysis wi h Eq.(2) on he ull da ase . 2. In a modi ied da ase , app oxima ely 10% o obse ed pheno ypes ( yi ) o animals om each amily we e masked (=10% o he ull da ase ). All pheno ypes had an equal chance o be masked, bu he animals ha we e masked in he p e ious old we e no masked again in he nex old. 3. The gene ic analysis wi h Eq.(2) was un on he mod- i ied da ase using he A and H ma ices and EBV o body weigh and i s uni o mi y we e p edic ed o he masked animals. 4. Fo each old, wo measu emen s we e compu ed: (a) The p edic i e abili y o EBV was calcula ed as he Pea son co ela ion o adjus ed pheno ypes (s ep 1) wi h he co esponding EBV ( ˆ a∗ ) (s ep 3) o he masked animals ha we e geno yped, i.e., co ( y∗ i , ˆ a∗ i ) o body weigh and co ( ψ∗ i , ˆ a∗ i ) o uni o mi y. Kendall and Spea man co ela ions we e also calcula ed o uni o mi y because ψ∗ i was exponen ially a he han no mally dis ib- u ed. (b) To measu e he deg ee o bias and accu acy o EBV o GEBV o he masked eco ds, he mean squa e e o p edic ion (MSEP) was calcula ed as n i(ˆ a ∗ i−y ∗ i) 2 n o body weigh and  n iˆ a∗ i−ψ∗ i 2 n o uni o mi y o body weigh , whe e n is he numbe o masked eco ds in each old. The MSEP was scaled by he a iance o he adjus ed pheno ypes o he co esponding ai . 5. S eps (1) o (4) we e epea ed o each o he 10 olds. Finally, a e age Pea son, Kendall, and Spea man co e- la ions, MSEP and hei s anda d e o (SE) o e he 10 olds we e calcula ed. A 95% con idence in e al o he di - e ence ( d ) in he p edic i e abili y om di e en models wi h ei he A o H was cons uc ed using d±1.96 ×SEd , whe e he SE d=  SD2 animal DHGLM+SD2 si e-dam DHGLM numbe o olds . When 0 was no wi hin he 95% con idence in e al, he p edic- i e abili ies o wo models we e conside ed s a is ically di e en (P<0.05). Resul s Residual es ima es Indi idual esiduals es ima ed om using he A (BLUP) and H ma ices (ssGBLUP) we e plo ed agains each o he o examine hei ela ionship. As expec ed, he ange o esidual es ima es om he animal models was lowe han ha om he si e-dam model since esidual es ima es om he si e-dam model included he en i e Mendelian sampling e m (Fig.1). Fo he si e-dam model, he use o H ins ead o A did no a ec es ima ed esiduals o geno yped animals since he eg ession coe icien o he es ima ed esidu- als using H on he es ima ed esiduals using A and he Pea son co ela ion be ween he wo we e equal o 0.999, which was e y simila o he eg ession coe icien o non-geno yped animals (0.998). The Pea son co ela- ions be ween es ima ed esiduals using H and A we e he same as eg ession coe icien s o es ima ed esidu- als using A on es ima ed esiduals using H o geno yped animals (0.999) and non-geno yped animals (0.998). In con as , he use o H in he animal model a ec ed esidual es ima es o geno yped animals since hei dis- ibu ion was much mo e sca e ed (Fig.1). The slope o es ima ed esiduals using A on es ima ed esiduals using H was lowe han 1 and sligh ly s eepe o geno yped animals ( eg ession coe icien =0.7025) han o non- geno yped animals ( eg ession coe icien =0.6798). The Pea son co ela ions be ween es ima ed esiduals using H and A we e equal o 0.922 o geno yped animals and 0.966 o non-geno yped animals. When using he si e-dam model, he di e ence in es i- ma ed esiduals wi h H and A was small and anged om −10.8 o 10.0. When using he animal model, his di e - ence was la ge and anged om −95.3 o 104.5. Gene ic pa ame e s o body weigh andi s uni o mi y Fo body weigh , es ima es o addi i e gene ic a iances om he si e-dam DHGLM wi h ei he A o H we e simi- la (Table2). Likewise, es ima es o h2 we e simila wi h A and H o bo h ai s: 0.266 and 0.296, espec i ely o s dWT and 0.325 and 0.346, espec i ely o lnWT. When using A , he es ima e o h2 was highe o uni- o mi y o s dWT (0.036) han o uni o mi y o lnWT (0.015), while he use o H did no a ec he magni ude Page 6 o 12 Sae‑Lim e al. Gene Sel E ol (2017) 49:33 o h2 o uni o mi y. S anda d e o s o h2 es ima es we e, howe e , high (Table2). Al hough he es ima es o h2 we e low, es ima es o GCV we e high o uni o mi y o s dWT (48.0% o A and 52.3% o H ), which indica es subs an ial gene ic po en ial o esponse o selec ion. A e accoun ing o scale e ec s, es ima es o GCV o uni o mi y o lnWT we e educed o 30% ( o bo h A and H ), which suppo s he exis ence o gene ic a ia ion o uni o mi y beyond he scale e ec s. Es ima es o c2 o s dWT and lnWT we e mode a e and simila o A (0.103 o0.117) and H (0.103 o0.111), which sugges s ha pa o he pheno ypic a ia ion was explained by non-gene ic e ec s ha a e common o ull- sibs. Ins ead, he es ima es o c2 o uni o mi y o s dWT and lnWT we e e y low and anged om 0.001 o 0.022 o A and 0.002 o 0.019 o H (Table2). The es ima e o he gene ic co ela ion be ween s dWT and i s uni o mi y was close o 1, using ei he A (0.952) o H (0.951), which shows he high depend- ency be ween mean and a iance o body weigh . How- e e , he es ima e o he gene ic co ela ion be ween lnWT and i s uni o mi y was educed o −0.093 wi h A and o 0.024 wi h H , which sugges s ha a e accoun - ing o he scale e ec s, he mean and a iance became independen . C oss‑ alida ion The use o H ins ead o A wi h he animal DHGLM esul ed in mo e a ia ion o he wi hin- amily GEBV o s dWT and i s uni o mi y, compa ed o wi hin- am- ily EBV (Fig.2; Addi ional ile1: Figu e S1), o si e-dam DHGLM). The a e age co ela ion o adjus ed pheno ypes wi h p edic ed b eeding alues o s dWT and i s uni o mi y was signi ican ly highe wi h H (s dWT = 0.443; uni- o mi y=0.217 o0.317) han wi h A (s dWT=0.372; uni o mi y=0.128 o0.192). Howe e , a e accoun ing o scale e ec s using log- ans o ma ion, he a e age Pea son, Kendall and Spea man co ela ions o adjus ed pheno ypes wi h p edic ed b eeding alues o lnWT and hei uni o mi y we e only sligh ly highe wi h H han wi h A , and no signi ican ly di e en om each o he (P>0.05). Fig. 1 Sca e plo o esiduals o body weigh om he uni a ia e analysis wi h A ma ix (x‑axis) o H ma ix (y‑axis). Two models we e pe o med; si e‑dam uni a ia e model (le ) and animal uni a ia e model ( igh ). Red do s a e geno yped animals and g ey do s a e non‑geno yped animals Page 7 o 12 Sae‑Lim e al. Gene Sel E ol (2017) 49:33 The a e age MSEP o uni o mi y om he animal DHGLM (0.608 o0.944) we e lowe han hose om he si e-dam DHGLM (0.973 o1.112), sugges ing ha he use o an animal DHGLM inc eases he accu acy and may educe bias in p edic ing b eeding alues o uni- o mi y (Table3; Addi ional ile2: Table S1). Howe e , he a e age MSEP o uni o mi y o s dWT and lnWT ob ained wi h H (0.608 o0.944) we e no no ably di e - en om hose ob ained wi h A (0.625 o0.936). The p edic i e abili y o EBV o uni o mi y was sensi- i e o he ype o co ela ion used, i.e. Pea son, Kend- all and Spea man (Table3). Spea man co ela ions we e 39.1 o49.0% highe han Kendall co ela ions. P edic i e abili ies o EBV and GEBV o uni o mi y o lnWT di - e ed mo e om each o he based on Kendall and Spea - man co ela ions, albei no signi ican a P<0.05, han based on Pea son co ela ions. Howe e , he SE o Kendall co ela ions we e app oxima ely 50% lowe han he SE o Pea son and Spea man co ela ions, sugges ing ha Ken- dall co ela ions p o ide a mo e eliable es ima e o p e- dic i e abili y han Pea son and Spea man co ela ions. Discussion To he bes o ou knowledge, his is he i s s udy ha compa es he use o he nume a o ela ionship ( A ) and a combined genomics and nume a o ela ionship ( H ) ma ix o es ima ing gene ic pa ame e s and p edic ing b eeding alues o body weigh and i s uni o mi y. The use o he animal DHGLM wi h H signi ican ly imp o ed he p edic i e abili y o GEBV o uni o mi y o body weigh (s dWT) bu no o scale-adjus ed uni o mi y. Gene ic pa ame e s The es ima e o he i abili y o uni o mi y o s dWT om si e-dam DHGLM wi h A was low ( h2 = 0.036) bu highe han es ima es o h2 ob ained in p e ious s udies on ainbow ou [4, 8] and Nile ilapia [15, 16] ( ¯ h2 =0.016: min=0.010: max=0.024). Howe e , a e accoun ing o scale e ec s by loga i hm ans o ma ions, he es ima e o h2 dec eased o 0.014 o0.015, which is in line wi h he p e ious epo s ha also used ans o ma- ions [4, 8, 14–16]. Es ima es o h2 o s dWT and lnWT using he si e- dam DHGLM wi h H did no di e om hose wi h A , which is in line wi h es ima es o h2 o uni o mi y o pigle bi h weigh ob ained using ei he A o only he genomic ela ionship ma ix ( G ) [42], while lowe es i- ma es we e epo ed o en i onmen al a iance o soma ic cell sco e in dai y ca le when using G compa ed o A [43]. The simila i y o he es ima es o h2 ob ained by using A o H in his s udy can be explained by he e y simila es ima ed esiduals (p oxy o uni o mi y) be ween non-geno yped and geno yped animals when using he si e-dam model wi h A and H . The si e-dam model only exploi s ela ionships be ween si es and dams and does no exploi he ull po en ial o he geno ype-based ela ionships be ween animals, and especially be ween ull-sibs. In con as , esiduals o geno yped animals es ima ed by using he animal model we e mo e di e - en ia ed when ei he A o H was used, and likely mo e accu a e han es ima es o esiduals o non-geno yped animals. Howe e , in a DHGLM analysis, he si e-dam model p o ides less biased (co) a iance componen s han he animal model [14], likely because o he depend- ence be ween es ima es o he b eeding alue and esid- ual o an indi idual, which a e ob ained om he same pheno ype o body weigh . The use o genomic ela ion- ships combined wi h nume a o ela ionships is expec ed o educe he dependency be ween EBV and es ima ed esiduals because he EBV a e mo e accu a e. The e- o e, we pe o med he animal DHGLM wi h H bu he model did no con e ge when he a iance componen s we e es ima ed, which may be due o (1) he dependency be ween EBV and es ima ed esiduals o body weigh emaining high, o (2) he di icul y o disen angle gene ic Table 2 Es ima es o  a iance componen s and gene ic pa ame e s o  body weigh and i s uni o mi y based on he si e-dam double hie a chical gene alized linea model when using pedig ee ( A ) o combined pedig ee andgenomic ela ionships ( H ) ands anda d o log- ans- o med pheno ypes A =pedig ee based ela ionship ma ix; H =combined geno yped and non‑ geno yped ela ionship ma ix; σ2 P =pheno ypic a iance ( 2 σ 2 u +σ 2 c +σ 2 e ), whe e σ2 e is he esidual a iance o body weigh ; σ2 a and σ2 a =addi i e gene ic a iance o body weigh and i s uni o mi y, espec i ely; σ2 c =common en i onmen al a iance; GCV=coe icien o addi i e gene ic a iance o uni o mi y (  σ2 a , exp ); h2=he i abili y o body weigh ; c2 =common en i onmen al e ec due o ull‑sib anks; h2 =he i abili y o uni o mi y; c2 =same as c2 bu o uni o mi y o body weigh . Supe sc ip s a e SE o he es ima es T ai /pa ame e S anda diza ion Loga i hm A H A H Body weigh σ2 P 0.843 0.856 0.131 0.132 σ2 a 0.216 0.243 0.043 0.046 σ2 c 0.095 0.091 0.013 0.014 h20.2660.095 0.2960.102 0.3250.102 0.3460.107 c20.1170.037 0.1110.037 0.1030.038 0.1030.038 Uni o mi y o body weigh σ2 a , exp 0.23030.1094 0.27320.1211 0.08960.0569 0.08850.0598 σ2 a 0.0612 0.0677 0.0005 0.0005 σ2 c 0.0360 0.0306 0.0000 0.0001 GCV 0.4800.114 0.5230.116 0.2990.095 0.2980.100 h2 0.0360.019 0.0380.020 0.0150.014 0.0140.013 c2 0.022 0.019 0.001 0.002 Page 8 o 12 Sae‑Lim e al. Gene Sel E ol (2017) 49:33 e ec s om he common en i onmen al e ec s o uni- o mi y o body weigh . The s anda d e o s o h2 es ima es we e high, which may be due o he la ge a ia ion in amily size (4 o54). Acco ding o Hill and Mulde [30], la ge amily sizes o epea ed measu emen s a e ecommended o es ima ing he gene ic he e oscedas ici y o ai s. The op imal ull- sib amily size is 39 wi h a GCV o 39% and an h2 o 0.36 [18]. The use o H did no a ec he s anda d e o s o he h2 es ima es, which does no ag ee wi h p e ious s udies, o example Vee kamp e al. [44] epo ed lowe s anda d e o s o h2 es ima es o d y ma e in ake, milk yield, and body weigh o hei e s when using genomic ela ion- ships wi h an animal model. One possible explana ion could be ha he bene i o using he genomic ela ion- ship ma ix may be limi ed when he si e-dam DHGLM is applied, since he a iance o genomic ela ionships be ween si es (0.02) was e y simila o he a iance o nume a o ela ionships be ween si es (0.01). In con as , he a iance in genomic ela ionships be ween animals (0.01) was much la ge han he a iance o nume a- o ela ionships be ween animals (0.004). Hence, he Fig. 2 Boxplo s o es ima ed b eeding alues o s anda dized body weigh (s dWT) and i s uni o mi y om geno yped animals by amily. The b eeding alues we e es ima ed using he animal double hie a chical gene alized linea model. G een boxplo s a e es ima ed b eeding alues (EBV) using he A ma ix and ed boxplo s a e genomic es ima ed b eeding alues (GEBV) using he H ma ix. The x‑axis ep esen s amily iden i ica ion Table 3 A e age Pea son, Kendall andSpea man co ela ions andmean squa e e o p edic ion oma 10- old c oss- al- ida ion based on he si e-dam double hie a chical gene alized linea modela whenusing pedig ee ( A ) o combined pedi- g ee andgenomic ela ionships ( H ) ands anda d o log- ans o med pheno ypes a The a iance componen s om he si e‑dam double hie a chical gene alized linea model we e con e ed o he animal double hie a chical gene alized linea model and we e used in he 10‑ old c oss‑ alida ion. Rela ionship= ela ionship ma ix, whe e A e e s o pedig ee‑based ela ionship ma ix and H e e s o combined geno yped and non‑geno yped ela ionship ma ix. The p edic abili y was calcula ed as he Pea son, Kendall and Spea man co ela ions be ween ma ked pheno ype and p edic ed b eeding alue. MSEP was scaled by he pheno ypic a iance o co esponding ai s T ans o ma ion Rela ionship Body weigh Uni o mi y o body weigh Pea son MSEP Pea son Kendall Spea man MSEP S anda dized A ma ix 0.3720.013 0.7240.021 0.1920.033 0.1280.021 0.1780.030 0.6250.086 H ma ix 0.4430.017 0.6820.021 0.2710.018 0.2170.017 0.3170.025 0.6080.082 Loga i hm A ma ix 0.3960.019 0.8230.029 0.3780.032 0.1820.016 0.2630.023 0.9360.085 H ma ix 0.4400.016 0.8130.028 0.3830.026 0.2030.014 0.2940.020 0.9440.085 Page 9 o 12 Sae‑Lim e al. Gene Sel E ol (2017) 49:33 SE o h2 es ima es may be lowe when using an animal DHGLM wi h a genomic ela ionship ma ix, compa ed o he nume a o ela ionship ma ix. Ne e heless, in ou s udy, i was no possible o in es iga e his phenom- enon since he log-likelihood did no con e ge o he animal DHGLM wi h H . The GCV o uni o mi y o s dWT was subs an ial (48.0%), which indica es high po en ial o esponse o selec ion. This esul is in he uppe ange o p e ious indings in ish species (17.4 o64.0%) [4, 8, 14–16, 19] and in e es ial animals (10.0 o58.0%) [6, 9–13, 42]. A e accoun ing o scale e ec s by loga i hm ans- o ma ions, he GCV o uni o mi y was educed bu s ill subs an ial (29.5 o29.9%), which was also epo ed in p e ious s udies on A lan ic salmon [14], ainbow ou [8], abbi , and pig [45]. Thus, scale e ec s a ec es ima es o gene ic pa ame e s o uni o mi y o body weigh conside ably, bu he e is gene ic a ia ion o uni o mi y beyond he scale e ec . Genomic in o ma ion sligh ly inc eased he GCV o uni o mi y o s dWT ( om 48.0 o 52.3%). In con as , genomic in o ma ion did no in luence he GCV o uni- o mi y o lnWT (29.8%). Since es ima es o gene ic pa am- e e s ob ained wi h A and H we e simila , he GCV o body weigh emained simila , which is in ag eemen wi h he p e ious compa ison be ween A ( GCV =11.0 o12.0%) and G ( GCV =10.0 o11.0%) o uni o mi y o bi h weigh o pigle s using a dam model [42]. Gene ic andgenomic p edic ions In his s udy, we used he Pea son co ela ion o EBV and GEBV wi h adjus ed pheno ype as he measu e o p edic i e abili y. The use o H ins ead o A in he ani- mal DHGLM signi ican ly imp o ed he abili y o p e- dic b eeding alues o s dWT (19%) and i s uni o mi y (41.1 o 78.1%). Fu he mo e, he use o he animal DHGLM ins ead o he si e-dam DHGLM signi ican ly inc eased he p edic i e abili y o EBV and GEBV o uni- o mi y (see Addi ional ile2: Table S1), as expec ed. Ou indings indica e ha ssGBLUP wi h an animal DHGLM can inc ease he accu acy o EBV o uni o m- i y subs an ially compa ed o pedig ee-based BLUP. Howe e , a e accoun ing o scaling e ec s by using log ans o ma ions, he use o H compa ed o A only sligh ly imp o ed he co ela ion (1.6 o 13.9%) and MSEP be ween GEBV and adjus ed pheno ypes, and he imp o emen was no signi ican . The e a e wo main easons why hese esul s di e ed be ween uni o mi y o s dWT and lnWT. Fi s , log- ans o ma ion subs an- ially educed he gene ic co ela ion o s dWT wi h i s uni o mi y. As a esul , any inc eases in p edic i e abil- i y o GEBV o lnWT when using H ins ead o A (15.7%) did no posi i ely in luence he p edic i e abili y o GEBV o i s uni o mi y. Second, he lowe addi i e gene ic a iance and h2 o uni o mi y a e accoun ing o scale e ec s educes he accu acy o EBV o uni o mi y. Con- sequen ly, MSEP inc eased om 0.63 (s dWT) o 0.94 (lnWT) wi h A and om 0.61 (s dWT) o 0.94 (lnWT) wi h H in he animal DHGLM. The accu acy o genomic selec ion is expec ed o inc ease when he numbe o geno yped animals in he e e ence popula ion inc eases o any ai [46] bu in pa icula o lowly he i able ai s, such as uni o mi y as shown by Sell-Kubiak e al. [42] and soma ic cell sco e by Mulde e al. [43]. In his s udy, uni o mi y o lnWT had an e en lowe h2 han uni o mi y o s dWT. The numbe o geno yped animals in he e e ence popula ion used o c oss- alida ion was on a e age equal o 1274, which may ha e limi ed he bene i o using genomic in o ma- ion in ssGBLUP. A u u e empi ical s udy should in es- iga e he e ec o he numbe o geno yped animals in he e e ence popula ion on he abili y o p edic b eed- ing alues o uni o mi y o alida e ou indings and conclusions. Pea son o ank co ela ions? Squa ed esiduals o adjus ed pheno ype o uni o mi y ( ψ∗ i) a e exponen ially a he han no mally dis ibu ed, which may no jus i y quan i ying p edic i e abili y using a Pea son co ela ion. Thus, we also calcula ed dis ibu- ion- ee ank co ela ions (Kendall and Spea man) and indeed ound es ima ion o he p edic i e abili y o uni- o mi y o be sensi i e o he ype o co ela ion used. Al hough no signi ican ly di e en , Kendall and Spea - man co ela ions explained di e ences in p edic i e abili y o EBV and GEBV o uni o mi y o lnWT sligh ly be e han he Pea son co ela ion. Hence, he conclusion ha he bene i o using genomic ela ionship o compu ing EBV o uni o mi y o loga i hm ans o ma ions is lim- i ed emained he same when using Kendall and Spea - man co ela ions. Colwel and Gille [47] showed ha , in gene al, es ima es o Kendall co ela ions a e simila o es ima es o Spea man co ela ions, bu in some cases, he magni ude o Spea man co ela ions can be 50% g ea e han he magni ude o Kendall co ela ions [47]. This is in line wi h ou indings since Spea man co ela ions we e 42.2 o49.0% and 39.1 o46.1% g ea e han Kendall co - ela ions o he si e-dam DHGLM (see Addi ional ile2: Table S1) and he animal DHGLM, espec i ely. Ne e he- less, he SE o Kendall co ela ions we e no ably lowe by app oxima ely 50% han he SE o Pea son and Spea man co ela ions, which indica es ha he Kendall co ela ion may be a mo e eliable es ima e o p edic i e abili y han he Pea son and Spea man co ela ions. Hence, i is ec- ommended o use Kendall ins ead o Pea son co ela ions when s udying p edic i e abili y o uni o mi y.