Identifying environmental variables explaining genotype-by-environment interaction for body weight of rainbow trout (Onchorynchus mykiss): reaction norm and factor analytic models

RESEARCH Open Access Iden i ying en i onmen al a iables explaining geno ype-by-en i onmen in e ac ion o body weigh o ainbow ou (Oncho ynchus mykiss): eac ion no m and ac o analy ic models Panya Sae-Lim 1,3* , Hans Komen 1 , An i Kause 2 and Han A Mulde 1 Abs ac Backg ound: Iden i ying he ele an en i onmen al a iables ha cause GxE in e ac ion is o en di icul when hey canno be expe imen ally manipula ed. Two s a is ical app oaches can be applied o add ess his ques ion. When da a on candida e en i onmen al a iables a e a ailable, GxE in e ac ion can be quan i ied as a unc ion o speci ic en i onmen al a iables using a eac ion no m model. Al e na i ely, a ac o analy ic model can be used o iden i y he la en common ac o ha explains GxE in e ac ion. This ac o can be co ela ed wi h known en i onmen al a iables o iden i y hose ha a e ele an . P e iously, we epo ed a signi ican GxE in e ac ion o body weigh a ha es in ainbow ou ea ed on h ee con inen s. He e we explo e hei possible causes. Me hods: Reac ion no m and ac o analy ic models we e used o iden i y which en i onmen al a iables (age a ha es , wa e empe a u e, oxygen, and pho ope iod) may ha e caused he obse ed GxE in e ac ion. Da a on body weigh a ha es was eco ded on 8976 o sp ing ea ed in a ious loca ions: (1) a b eeding en i onmen in he USA (nucleus), (2) a eci cula ing aquacul u e sys em in he F eshwa e Ins i u e in Wes Vi ginia, USA, (3) a high-al i ude a m in Pe u, and (4) a low-wa e empe a u e a m in Ge many. Akaike and Bayesian in o ma ion c i e ia we e used o compa e models. Resul s: The combina ion o days o ha es mul iplied wi h daily empe a u e (Day*Deg ee) and pho ope iod we e iden i ied by he eac ion no m model as he en i onmen al a iables esponsible o he GxE in e ac ion. The la en common ac o ha was iden i ied by he ac o analy ic model showed he highes co ela ion wi h Day*Deg ee. Day*Deg ee and pho ope iod we e he en i onmen al a iables ha di e ed mos be ween Pe u and o he en i onmen s. Akaike and Bayesian in o ma ion c i e ia indica ed ha he ac o analy ical model was mo e pa simonious han he eac ion no m model. Conclusions: Day*Deg ee and pho ope iod we e iden i ied as en i onmen al a iables esponsible o he s ong GxE in e ac ion o body weigh a ha es in ainbow ou ac oss ou en i onmen s. Bo h he eac ion no m and he ac o analy ic models can help iden i y he en i onmen al a iables esponsible o GxE in e ac ion. A ac o analy ic model is p e e ed o e a eac ion no m model when limi ed in o ma ion on di e ences in en i onmen al a iables be ween a ms is a ailable. * Co espondence: [email p o ec ed] 1 Animal B eeding and Genomics Cen e, Wageningen Uni e si y, P.O. Box 338, 6700, AH, Wageningen, The Ne he lands 3 Cu en add ess: No ima, Oslo eien 1, P.O. Box 210, NO-1431 Ås, No way 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 Sae-Lim 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. Sae-Lim e al. Gene ics Selec ion E olu ion 2014, 46:16 h p://www.gsejou nal.o g/con en /46/1/16 Backg ound Body weigh a ha es is an economically impo an ai in ainbow ou (Oncho ynchus mykiss) and o he a med ish species. Rainbow ou can be p oduced in a wide ange o a ming en i onmen s. When geno ype- by-en i onmen in e ac ion (GxE) is p esen and when selec ion is p ac iced only in a b eeding en i onmen , lowe - han-expec ed gene ic gains can be ob ained in o he p oduc ion en i onmen s. Op imiza ion o a b eed- ing p og am o accoun o GxE in e ac ion can inc ease gene ic gain ac oss en i onmen s [1-3]. Op imiza ion may be expensi e, o ins ance when en i onmen -speci ic b eeding p og ams need o be es ablished. Al e na i ely, i en i onmen al a iables (EV) a e changed so ha hey a e simila ac oss p oduc ion en i onmen s, GxE in e ac ion may dec ease. This equi es ha he EV ha cause GxE in e ac ion a e iden i ied, which can be done by using a eac ion no m model o quan i y GxE in e ac ion as he unc ion o speci ic EV [4-6]. Al e na i ely, in a wo-s ep ac o analysis, a la en common ac o esponsible o GxE in e ac ion is i s iden i ied and, subsequen ly, co e- la ions be ween he common ac o and EV a e calcula ed o iden i y he signi ican EV [7]. In his s udy, ou aim was o iden i y he EV ha cause a s ong GxE in e ac ion o body weigh a ha es in ainbow ou using a eac- ion no m model and a ac o analy ic model. Me hods Da a The da a used in his s udy we e om a GxE expe imen conduc ed in ou di e en en i onmen s on h ee con- inen s (No h Ame ica, Sou h Ame ica, and Eu ope as desc ibed by Sae-Lim e al. [8]). In Augus 2009, 100 ull-sib amilies we e p oduced om 58 si es and 100 dams (1 o 1.7 ma ing a io) a he T ou lodge b eeding company in Washing on S a e (nucleus: NUC). P oce- du es o he e hical ea men o animals a T ou lodge, Inc. ollowed he US and/o S a e guidelines o animal ca e and use including hose ou lined by “Guidelines o Use o Fishes in Field Resea ch”es ablished by he Ame ican Fishe ies Socie y (AFS), he Ame ican Socie y o Ich hyologis s and He pe ologis s (ASIH), and he Ame ican Ins i u e o Fishe ies Resea ch Biologis s (AIFRB). The same s anda d was applied o all animals in he s udy. Fe iliza ion ook place du ing a pe iod o ou weeks. Di e en wa e empe a u es we e used o synch onize emb yonic de elopmen and ha ching. A leas 25 eyed eggs pe amily we e shipped o each o he ollowing h ee loca ions: (1) he e-ci cula ing aquacul- u e sys em a he F eshwa e Ins i u e, Vi ginia, USA (FI); (2) a high al i ude a m wi h low oxygen dissol ed in wa e (Ti icaca Lake) in Pe u (PE); and (3) a low wa e empe a u e a m in Ge many (GE). A andom sample o 25 eyed eggs pe amily was main ained a NUC as a con ol. All ish we e measu ed o body weigh a ha es (BWH, in g ams), in June 2010 (NUC), in July 2010 (FI), in Augus 2010 (PE), and in Decembe 2010 (GE) (Table 1). Pedig ee econs uc ion The ish we e agged using passi e in eg a ed anspon- de s (PIT ag; All lex USA, Inc. o NUC, FI and PE, and DORSET Iden i ica ion b. ., he Ne he lands, o GE) and he PIT ag was scanned (scanne SF2001ISO: Des- on Fea ing, USA o NUC, FI and PE, and GR250: DORSET Iden i ica ion b. ., he Ne he lands, o GE) a an a e age size o 26.3 o 33.2 g ( i e o se en mon hs o age). Be o e agging, ish we e anes he ized wi h MS222 (150 mg/L) in he NUC, FI, and PE a ms and wi h clo e oil (10 mg/L) in he GE a m. Fin clips we e collec ed om all 158 pa en s and om he ish a agging om FI, PE and GE o DNA ex ac ion. In he NUC a m, in clips we e no collec ed, because ish we e kep in sepa - a e ull-sib amily anks un il agging, allowing he pedi- g ee o be eco ded. DNA was isola ed om in clips o econs uc pedi- g ees. Geno yping was done a h ee labo a o ies: Na ional Cen e o Cool and Cold Wa e Aquacul u e, USDA; T ou lodge, Inc.; and Animal B eeding and Genomics Cen e, Wageningen Uni e si y. The p o ocols o DNA isola ion and geno yping we e synch onized ac oss he h ee labo a o ies. DNA isola ion was done using he Nucleospin® 96 Tissue Co e Ki . Mul iplex PCR ampli ica- ion was as desc ibed in [9]. Nine mic osa elli e ma ke s we e used o PCR: OMM1008, OMM1051, OMM1088, OMM1097 [10], OMM5007, OMM5047 [11], OMM5233, OMM5177 [12], and OMM1325 [13]. Mul iplex PCR am- pli ica ions, i.e. quad oplex and pen aplex, we e as ollows [9]: an ini ial 5 min dena u a ion a 95°C, ollowed by 35 cycles o 30 s dena u a ion a 95°C, 45 s annealing a 55°C, and 90 s ex ension a 72°C, and a inal 10 min ex ension s ep a 72°C. F agmen analysis o he PCR p oduc s was done by se ing he agmen sizes o Genes- can LIZ 500 size s anda d (Applied Biosys em). Ou pu da a we e analysed using Genemappe so wa e e sion 4 (Applied Biosys em) [14]. Pa en al alloca ion was pe o med using PAPA so - wa e [15] based on he known ma ing da a o inc ease he accu acy o pa en al assignmen s [8]. In o al, 2142 ou o 2243 ish sampled in FI, 3106 ou o 3236 ish sampled in PE, and 2104 ou o 2235 ish sampled in GE we e success ully alloca ed o he 100 ull-sib amilies. The 362 ish ha we e no success ully alloca ed o a amily we e emo ed om he da ase . In o al, six gene a ions o pedig ee in o ma ion, one om he DNA econs uc ed pedig ee and i e om he p e ious gene - a ions o pedig ee in o ma ion, we e used in he gene ic analyses. Sae-Lim e al. Gene ics Selec ion E olu ion 2014, 46:16 Page 2 o 11 h p://www.gsejou nal.o g/con en /46/1/16 En i onmen al a iables Summa y s a is ics o he EV a e in Table 1. Tempe a u e The a e age wa e empe a u e (°C) was measu ed in he ank (NUC, FI), aceway (GE) o lake (PE) du ing he ea ing pe iod o he expe imen . In NUC, he a e - age ambien empe a u e was be ween 13 and 14°C h oughou he g owing season. In FI, PE, and GE, he wa e empe a u e ollowed he na u al (daily and sea- sonal) luc ua ions. Wa e empe a u e was eco ded e e y 15 min using a da a logging T ansmi e SC100 (Hach Lange, Ge many) in NUC and GE. In FI, empe a u e was measu ed once a day using ei he a Hach HQ40d hand held me e o a SC100 Uni e sal Con olle (Hach Company, Lo eland, CO). In PE, em- pe a u es we e measu ed wi h a s anda d me cu y he mome e in he Ti icaca Lake once a day o only a sho pe iod (Sep embe 3 o 16, 2010). Howe e , wa e empe a u e o he Ti icaca Lake does no luc ua e much h oughou he yea and a ies be ween 12 and 14°C. Age A e age age a ha es (in days) co esponded o he pe iod be ween ha ching and day o ha es . Di e ences in age a ha es we e caused by di e ences in p e e ed ma ke sizes ac oss en i onmen s. In NUC, ha es was done wice (a 2 week in e als). Day*Deg ee In salmonids, he g ow h a e depends on he wa e empe a u e. The p oduc o days o ha es and daily empe a u e is he e o e commonly used in salmonid a ming o compa e days o ha es ac oss empe a u e egimes. Day*Deg ee was calcula ed as: a e age wa e empe a u e du ing he g owing pe iod mul iplied by a e age age a ha es . Oxygen The amoun o oxygen dissol ed in he wa e du ing he ea ing pe iod, eco ded in mg/L o ppm, was calcula ed based on he a e age o daily measu emen s. In NUC, oxygen was measu ed daily in he mo ning (be ween 7:30 and 9:00 am) using a YSI model 550 (YSI, Yellow Sp ings, OH) a he inle and ou le o he ea ing anks. In FI, oxygen was measu ed a a single posi ion in he ci cula anks once a day be ween 8:00 and 9:30 am, using a Hach HQ40d wi h a Hach LDO p obe a ach- men , o a SC100 Uni e sal Con olle (Hach Company, Lo eland, CO). In PE, dissol ed oxygen was measu ed in he ne pens o Ti icaca Lake in he mo ning (be ween 9:00 and 10:00 am) o a sho pe iod o ime (same as empe a u e), using he Hach dissol ed oxygen es ki (Hach Company, Lo eland, CO). In GE, dissol ed oxy- gen le el was con olled o be abo e 10 mg/L. When he dissol ed oxygen dec eased, supplemen a y oxygen was au oma ically eleased un il he dissol ed oxygen was abo e 10 mg/L. Dissol ed oxygen was measu ed e e y 15 min using a da a logging T ansmi e SC100 (Hach Lange, Ge many). Pho ope iod Since he expe imen was conduc ed ac oss con inen s, changes in day leng h di e ed. “Pho ope iod”was de- ined as he di e ence be ween he maximum day leng h obse ed du ing he ea ing pe iod and a e age day leng h du ing he ea ing pe iod. This measu emen e- lec s he ampli ude o day leng h, which p o ides mo e in o ma ion han a e age day leng h. The loca ions ha we e used o calcula e pho ope iod we e: Sea le in Washing on S a e (NUC), Ma insbu g in Wes Vi ginia (FI), Juliaca in Pe u (PE), and Leipzig Schkeudi z in Ge many (GE). Da a on imes o sun ise and sunse each week in 2009 and 2010 we e ob ained om h p://www. wunde g ound.com/his o y/. A e age day leng h was calcula ed as he di e ence be ween sun ise and sunse in minu es, o each day o he week in he ea ing pe iod (Figu e 1). To accoun o di e ences be ween no he n and sou he n hemisphe es (NUC, FI and GE e sus PE), we used nega i e and posi i e signs o indi- ca e he di ec ions o change in he pho ope iod. S a is ical analysis In a p e ious s udy, we epo ed a signi ican GxE in e - ac ion o body weigh a ha es in ainbow ou ha Table 1 Means and s anda d de ia ions (SD) o body weigh a ha es (BWH) in ou en i onmen s and means o en i onmen al a iables du ing he ea ing pe iod En i onmen N BWH (g) SD (g) Age (day) Temp (°C) Day*Deg ee (day*°C) Oxygen (mg/L) Pho ope iod (min) NUC 2367 546.7 94.7 287.5 13.8 3940 7.3 223.1 FI 1893 395.2 75.8 294.0 12.5 3686 10.5 163.3 PE 2897 524.1 105.0 357.0 13.4 4805 6.6 −53.1 GE 1819 376.4 81.7 444.0 9.9 4439 12.0 292.9 N = numbe o obse a ions; NUC = b eeding en i onmen ; FI = F eshwa e Ins i u e; PE = Pe u; GE = Ge many; uni s a e indica ed be ween b acke s. Sae-Lim e al. Gene ics Selec ion E olu ion 2014, 46:16 Page 3 o 11 h p://www.gsejou nal.o g/con en /46/1/16 we e ea ed on h ee di e en con inen s [8]. Gene ic co ela ions (0.19 o 0.48) we e es ima ed using a mul i- a ia e model (mul i- ai mul i-en i onmen ) wi h co - ec ion o selec ion bias due o selec i e mo ali y. The same da a we e used o iden i y he EV ha con ibu ed o he GxE in e ac ion in his s udy. ASReml was used o all models in his s udy. Mul i a ia e model In his s udy, we compa ed eac ion no m and ac o analy ic models wi h he mul i a ia e model wi hou se- lec ion bias co ec ion. The mul i a ia e model wi hou he selec ion bias co ec ion was: Yhij ¼μþβhAGEhþFERThi þahj þehij; whe e Y hij is he obse a ion (body weigh a ha es ) o he j h indi idual in a gi en en i onmen (h=1: NUC, 2: FI, 3: PE, and 4: GE), μis he o e all mean. β h is he co- e icien o linea ixed eg ession on age a ha es (AGE h ) wi hin he h h en i onmen . The (AGE h ) was in- cluded in he model o co ec o di e en measu e- men da es, and co ec ed o he leng h o he ea ing pe iod om ha ching o he day o ai measu emen . The o hogonal polynomial o (AGE h ) was es ed o sig- ni icance up o he hi d o de bu he quad a ic and he cubic o de s we e no signi ican based on a Wald es . FERT hi is he e ec o he i h e iliza ion pe iod wi hin he h h en i onmen due o di e en g oups o a ailable e ile dams. a hj is he andom addi i e gene ic e ec , a∼MVN[0,A⊗G], o he j h animal, whe e MVN is he mul i a ia e no mal dis ibu ion, Ais he addi i e gen- e ic ela ionship ma ix among indi iduals and Gis he addi i e gene ic (co) a iance ma ix among body weigh in he di e en en i onmen s. Residual co a iances o he same ai measu ed in di e en en i onmen s we e se o ze o, because animals we e measu ed in only one en i onmen : VAR eðÞ¼ σ2 e1000 0σ2 e200 00σ2 e30 000σ2 e4 2 6 6 4 3 7 7 5 ; whe e σ2 ehis esidual a iance o body weigh in di e en hen i onmen s. Reac ion no m model The EV causing GxE in e ac ion can be iden i ied by i - ing each EV in a eac ion no m model. Random eg es- sion was used o es ima e (co) a iance componen s. The andom animal e ec was modelled as a unc ion o he EV. The andom eg ession model was: Yhij ¼μþηhþβhAGEhþFERThi þX m k¼0 αkjPkh þehij; whe e η h is ixed en i onmen al e ec (h=1: NUC, 2: FI, 3: PE, and 4: GE), accoun ing o di e en le els o en i onmen and α kj is andom eg ession coe i- cien k o animal j o he o hogonal polynomial P kh o anEVinen i onmen h, wi h mmaximum o de o he polynomial. The ma ix o andom eg ession coe icien s was assumed o be dis ibu ed mul i a ia e no mal: α0 ⋮ αm 2 43 5∼MVN 0;A⊗GRN ½, whe e MVN is he mul i a ia e no mal dis ibu ion, Ais headdi i egene ic ela ionship ma ix, and G RN is he n*ngene ic (co) a i- ance ma ix o pa ame e s o he eac ion no m model. The nis he highes o de o polynomial (m) + 1. Residual e ec s e hij o animal jin en i onmen hwe e assumed dis ibu ed e∼N0; Iσ2 e1000 0Iσ2 e200 00Iσ2 e30 000Iσ2 e4 2 6 6 4 3 7 7 5 0 B B @ 1 C C A , whe e Iis he iden i y ma ix. A hi d o de polynomial o he andom eac- ion no m model esul s in a 4×4 Gma ix, which is he same dimension as he o iginal mul i a ia e model wi h ou en i onmen s. When each en i onmen has jus one alue o he en i onmen al a iable, he mul i a i- a e model and he eac ion no m model yield iden ical gene ic co ela ions [16]. The e o e, e en meaningless EV would gi e he same esul s as he mul i a ia e model. Thus, o iden i y EV esponsible o he GxE in e ac ion, we decided o use a i s o de polynomial (m= 1), because i is he simples and has he la ges di - e ence in numbe o es ima ed pa ame e s. The addi i e gene ic a iance ^ VAo BWH o each le el o an EV Figu e 1 Day leng h p o iles in ou expe imen al en i onmen s. The x-axis ep esen s he ea ing pe iod in wo- mon h in e als (mon h-yea ); each obse a ion ep esen s he a e age day leng h du ing a wo-week in e al; he ea ing pe iod di e ed ac oss en i onmen s: NUC = b eeding en i onmen , FI = F eshwa e Ins i u e, PE = Pe u and GE = Ge many. Sae-Lim e al. Gene ics Selec ion E olu ion 2014, 46:16 Page 4 o 11 h p://www.gsejou nal.o g/con en /46/1/16 was calcula ed as ^ ϕ0^ GRN ^ ϕ,whe e ^ ϕis a n*1 ec o o polynomial coe icien s o each le el o he EV and ^ ϕ0is he ansposed ec o o ^ ϕ. The co a iance (COV) be- ween BWH a le els iand jo an EV was calcula ed as ^ ϕ0i ^ GRN ^ ϕj;i≠j. The gene ic co ela ion ( g ) be ween BWH a le els iand jo an EV was calcula ed as COV AEVi;AEVj  ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ^ VA;EVi ^ VA;EVj p. S anda d e o s o es ima es o gene ic co ela ions we e app oxima ed wi h ASReml [17]. The si e BLUP-es ima ed b eeding alue (EBV) o each le el o EV was calcula ed as ^ H ^ ϕ, whe e ^ His a 1*n ec o o si e BLUP-EBV o BWH.The si e BLUP-EBV o eigh andomly selec ed si es we e plo ed agains pho ope iod as an example o show he deg ee o he e ogenei y o addi i e gene ic a iance and e- anking o si es, de- pending on change ac oss le els o pho ope iod. Fac o -analy ic model The ac o analy ic (FA) model iden i ies la en common ac o s ha explain he a ia ion in he da a and can be used o es ima e GxE in e ac ion [18]. The FA animal mixed model was: Yhij ¼μþηhþβhAGEhþFERThi þACjþAShj þehij; whe e ACjis he andom gene ic e ec o he la en common ac o ac oss en i onmen s o animal jand AShj is he andom gene ic e ec speci ic o en i on- men h o animal j. The i e gene ic e ec s (one ac oss en i onmen s and ou speci ic o each en i on- men ) we e assumed dis ibu ed mul i a ia e no mal: Ac;As1;As2;As3;As4 ðÞ∼MNV 0;A⊗GFA ½,whe eAis he addi i e gene ic ela ionship ma ix and G FA is he gene ic (co) a iance ma ix o common and speci ic animal e ec s. The common animal e ec can be in e p e ed as he b eeding alue o he la en com- mon ac o whe eas he speci ic animal e ec s a e he en i onmen -speci ic emnan b eeding alue unex- plained by he common ac o . The e o e, each animal has i e b eeding alues. The gene ic (co) a iance ma ix G FA =ΓΓ '+Ψ,whe eΓis he ma ix o ac o loadings (coe icien ec o o he la en common ac- o ) and Ψis he diagonal ma ix o speci ic a iances (ψ h ) o each en i onmen h, accoun ing o addi ional a iance, i.e., a ia ion ha is no explained by la en common ac o s [18].The o al numbe o pa ame e s i ed in he FA model is n(k+1)-k(k-1)/2 and may no exceed n(n+1)/2, whe e nis hesizeo Gma ix om hemul i a ia emodel,andkis he numbe o la en common ac o s. When kis equal o 1, he numbe o pa ame e s i ed in FA is 4(1 + 1) -1(1-1)/2 = 8, com- pa ed o 4(4 + 1)/2 = 10 o he mul i a ia e model [19]. The eigh pa ame e s a e ou elemen s o es i- ma ed loading ^ γh  and ou es ima ed speci ic a i- ance ^ ψh ðÞ o each en i onmen h. The numbe o ac o s canno be highe han 1 in his s udy. In ASReml, di e en ypes o FA models can be im- plemen ed [19]. In his s udy, we used he ex ended FA (XFA) [18,19] model, which p o ides es ima es o he G FA ma ix, o loading pa ame e s, o co ela ions be ween gene ic e ec s in ou en i onmen s, and o he la en common ac o . The addi i e gene ic a i- ance ^ VA  o a ce ain en i onmen was es ima ed as: ^ VAh¼^ γ0 h ^ γhþ^ ψh. The squa e o he loading pa ame e indica es he amoun o addi i e gene ic e ec ex- plained by he la en common ac o . A high loading o an en i onmen indica es ha he la en common ac o explains a la ge amoun o he addi i e gene ic a iance in ha en i onmen . The pe cen age o addi- i e gene ic a iance explained by la en common ac- o s in a speci ic en i onmen was calcula ed as: %Expl ¼ ^ γ0 h ^ γh ^ VA100. The co a iance o BWH be ween en i onmen s iand jwas calcula ed as ^ γi 0^ γj.The g be ween BWH measu ed in di e en en i onmen s i and jwas es ima ed as: g¼ ^ γ0 i ^ γj ffiffiffiffiffiffiffiffiffiffiffiffiffiffi ^ VAi ^ VAj p. Ini ially, he en i onmen al e ec common o ull-sibs (caused by amily ea ing un il agging) was included in he model. Howe e , ASReml had di icul y in disen an- gling gene ic (co) a iance componen s om common en i onmen al (co) a iance componen s. The solu ion was no posi i e de ini e and he e o e we decided o ex- clude he common en i onmen al e ec om his and all o he models in his s udy. Model compa ison Reac ion no m and FA models we e compa ed using Akaike’s in o ma ion c i e ia (AIC: [20]) and Bayesian’s in o ma ion c i e ia (BIC: [21]). The model wi h he low- es AIC and BIC indica es he mos pa simonious model. All models we e kep he same wi h espec o ixed e - ec s so ha hey we e compa able in e ms o REML log likelihood. Iden i ica ion o EV Wi h a eac ion no m model, he EV ha p o ide he bes i o he da a will esul in he highes log likeli- hood o he model. In addi ion, he mean squa e de i- a ion (MSD) was calcula ed as he di e ence be ween es ima ed gene ic co ela ions ob ained om eac ion no m and mul i a ia e (MUV) models and was com- pu ed as MSD ¼Xn i¼1 gRN;i− gMUV ;i  2 n, whe e gRN;iand gMUV ;ia e he es ima ed gene ic co ela ions o BWH Sae-Lim e al. Gene ics Selec ion E olu ion 2014, 46:16 Page 5 o 11 h p://www.gsejou nal.o g/con en /46/1/16 be ween di e en en i onmen s ob ained om he eac- ion no m and mul i a ia e models, espec i ely. The i h gene ic co ela ion was om he same pai o en i on- men s o bo h models and nwas equal o six, because wi h ou en i onmen s he e a e six gene ic co ela- ions. The eac ion no m model wi h he lowes MSD is he model ha de ia es leas om he mul i a ia e model, which indica es ha he EV used in ha eac ion no m model is able o cap u e he GxE in e ac ion. The FA model was used as he i s s ep in a wo-s ep app oach. The second s ep consis ed o es ima ing co - ela ions be ween loadings and means o EV. Pea son (ρ EP,L ) and Kendall ank (τ EP,L ) co ela ions be ween loading o he la en common ac o and EV we e calcu- la ed o iden i y he EV ha shows he highes co el- a ion wi h he la en common ac o , which is he mos likely EV ha caused he GxE in e ac ion. Resul s Reac ion no m model Fo he eac ion no m model, es ima es o g o BWH be ween di e en en i onmen s a e in Table 2. Fo age a ha es , es ima es o g a ied be ween 0.57 and 0.99 (MSD = 0.17). Fo wa e empe a u e, es ima es o g a - ied be ween 0.61 and 0.99 (MSD = 0.19). Es ima es o g o Day*Deg ee we e lowe and a ied be ween 0.35 and 0.97 (MSD = 0.09). Fo dissol ed oxygen, es ima es o g anged om 0.60 o 0.99 (MSD = 0.14), which was simi- la o he ange o es ima es o g o wa e empe a u e. Fo pho ope iod, es ima es o g anged om 0.37 o 0.97 (MSD = 0.12). Reac ion no m models wi h day- deg ee and pho ope iod as EV esul ed in gene ic co e- la ions closes o he mul i a ia e model, which indica es ha day-deg ee and pho ope iod we e he mos impo - an EV ha explain he GxE in e ac ion. A plo o he EBV o eigh andomly selec ed si es agains pho o- pe iod shows ha he GxE in e ac ion was caused by bo h he e ogenei y o addi i e gene ic a iance and e- anking (Figu e 2). Fac o analy ic model Fo he FA model, es ima es o g o BWH be ween PE and NUC (0.36), be ween PE and FI (0.41), and be ween PE and GE (0.39) we e low, which indica e mode a e o Table 2 Es ima es o gene ic co ela ions o body weigh a ha es measu ed in di e en en i onmen s and mean squa e de ia ion (MSD*) be ween es ima es om eac ion no m and mul i a ia e models Model EV En i onmen FI PE GE MSD Reac ion no m Age NUC 0.99 ± 0.00 0.91 ± 0.03 0.57 ± 0.11 0.17 FI 0.94 ± 0.02 0.63 ± 0.10 PE 0.86 ± 0.04 Tempe a u e NUC 0.97 ± 0.01 0.99 ± 0.00 0.61 ± 0.11 0.19 FI 0.98 ± 0.01 0.79 ± 0.06 PE 0.65 ± 0.10 Day*Deg ee NUC 0.97 ± 0.01 0.56 ± 0.10 0.82 ± 0.05 0.09 FI 0.35 ± 0.13 0.66 ± 0.10 PE 0.93 ± 0.02 Oxygen NUC 0.75 ± 0.06 0.99 ± 0.00 0.45 ± 0.12 0.14 FI 0.68 ± 0.08 0.93 ± 0.02 PE 0.36 ± 0.13 Pho ope iod NUC 0.97 ± 0.01 0.60 ± 0.09 0.96 ± 0.01 0.12 FI 0.78 ± 0.06 0.87 ± 0.04 PE 0.37 ± 0.13 Fac o analy ic La en NUC 0.56 ± 0.06 0.36 ± 0.04 0.54 ± 0.06 N.A. FI 0.41 ± 0.05 0.61 ± 0.07 PE 0.39 ± 0.05 Mul i a ia e N. A. NUC 0.61 ± 0.10 0.25 ± 0.13 0.53 ±0.12 N.A. FI 0.40 ± 0.12 0.55 ± 0.12 PE 0.49 ± 0.12 EV = en i onmen al a iables; NUC = b eeding en i onmen ; FI = F eshwa e Ins i u e; PE = Pe u; GE = Ge many; EV = en i onmen al a iable; N.A. = no applicable. *MSD ¼Xn i¼1 gRN;i − gMUV;i  2 n, whe e gRN;iand gMUV;ia e he es ima ed gene ic co ela ion o BWH be ween di e en en i onmen s om eac ion no m (RN) and mul i a ia e (MUV) models. Sae-Lim e al. Gene ics Selec ion E olu ion 2014, 46:16 Page 6 o 11 h p://www.gsejou nal.o g/con en /46/1/16 s ong e- anking. The es ima e o g o BWH be ween NUC and FI was much lowe (0.56) han he es ima e ob ained h ough he eac ion no m model when he EV was pho ope iod (0.97) o Day*Deg ee (0.97). Fo pho o- pe iod, he co a iance be ween NUC and FI ob ained h ough he eac ion no m model was simila o ha ob- ained h ough he FA model (1524.3 and 1555.8, e- spec i ely), which indica es ha he highe es ima e o g ob ained wi h he eac ion no m model (pho ope iod) was mainly caused by a lowe V A (NUC: 1574 and FI: 1570), as shown in Table 3. In con as , o Day*Deg ee as he EV, he eac ion no m model ga e a high es ima e o g due o bo h a highe co a iance be ween NUC and FI (1931.7) and a lowe V A (NUC: 1774 and FI: 2221) compa ed o hose ob ained h ough he FA model. Ele- men s o he es ima ed loading ec o ^ γwe e equal o 40.34 o NUC, 38.57 o FI, 30.41 o PE, and 30.70 o GE, which means ha he la en common ac o ex- plained mos o he o V A in NUC and FI (Table 3). The p opo ion o gene ic a iance explained by he com- mon ac o was only 26.20% o PE and ^ ψwas high in PE (2606.73), which showed ha much o he addi i e gene ic a iance was no accoun ed o by he la en common ac o . Pea son co ela ions (ρ EP,L ) be ween he la en common ac o and he known EV we e nega i e and high o Day*Deg ee (-0.91), and o age a ha es (-0.86). The Kendall ank co ela ion (τ EP,L ) was in ag eemen wi h he (ρ EP,L ) bu lowe o bo h Day*Deg ee (τ EP,L =−0.67) and age a ha es (τ EP,L =−0.67) (Table 4). Wa e empe a u e was mode a ely co ela ed wi h he la en common ac o (ρ EP,L = 0.50). Dissol ed oxygen was weakly co ela ed (ρ EP,L =−0.14) o no co ela ed (τ EP,L =0.00) wi h he la en common ac o . Pho ope iod was posi i ely co ela ed wi h he la en common ac o (ρ EP,L = 0.32, τ EP, L = 0.33). These esul s indica e ha Day*Deg ee was he mos likely EV esponsible o he GxE in e ac ion in BWH. Model compa ison Wi h he eac ion no m model, he lowes AIC (87645.7) and BIC (87695.3) we e ob ained o pho ope iod, which indica ed ha i was he bes i ed EV, compa ed o he o he EV (Table 5). Howe e , Day*Deg ee (AIC = 87656.5, BIC = 87706.2) i ed he model simila ly well. The bes i was conco dan wi h a lowe a e age es ima e o g o ei he pho ope iod o Day*Deg ee. The AIC (87513.0) and BIC (87528.6) we e lowe wi h he FA model han wi h he eac ion no m model, which indica es ha he FA model is mo e pa simonious han he eac ion no m model. Discussion The aim o his s udy was o iden i y he en i onmen al a iables (EV) ha explain he GxE in e ac ion o body weigh a ha es (BWH) o ainbow ou using a eac- ion no m model and a ac o analy ic model. Iden i ica ion o en i onmen al a iables To ou knowledge, his is he i s s udy ha imple- men ed eac ion no m and ac o analy ic models o iden i y signi ican EV esponsible o GxE in e ac ion in aquacul u e. Ou indings show ha bo h me hods can be used o iden i y signi ican EV. Howe e , he eac ion no m and FA models iden i ied di e en signi ican EV. Based on AIC and BIC, pho ope iod ga e a sligh ly be - e i wi h he eac ion no m model han Day*Deg ee, which indica es ha pho ope iod may also be he mos signi ican EV. Howe e wi h he FA model, Day*Deg ee Figu e 2 Es ima ed b eeding alues o si es o body weigh (y-axis: in g ams) agains pho ope iod (min) using he eac ion no m model. Only eigh andomly chosen si es a e plo ed in his g aph o illus a e he deg ee o e- anking. Table 3 Es ima es o he o al gene ic a iance ( ^ VA), loadings (^ γ), speci ic gene ic a iances ( ^ ψ), and % gene ic a iance explained by he la en common ac o (%Expl) o each en i onmen En i onmen ^ VA , MUV ^ VA , RN, PP ^ VA , RN, DD ^ VA ,FA ^ γ ^ ψ%Expl NUC 3304 1574 1774 3283 40.3 1656 49.6 FI 2405 1570 2221 2362 38.6 874 63.0 PE 3558 3161 2455 3531 30.4 2607 26.2 GE 1638 1822 1713 1613 30.7 671 58.4 NUC = b eeding en i onmen ; FI = F eshwa e Ins i u e; PE = Pe u; GE = Ge many; MUV = mul i a ia e model; RN = eac ion no m model o pho ope iod (PP) and Day*Deg ee (DD); FA = ac o analy ic model. Sae-Lim e al. Gene ics Selec ion E olu ion 2014, 46:16 Page 7 o 11 h p://www.gsejou nal.o g/con en /46/1/16 was highly nega i ely co ela ed (Pea son co ela ion: ρ EP,L =−0.91) wi h loadings o he la en common ac- o , which sugges s ha Day*Deg ee was he mos sig- ni ican EV. Bo h he eac ion no m and FA models indica e ha Day*Deg ee is an impo an EV and ha i is less likely ha empe a u e is esponsible o he GxE in e ac ion. Howe e , he powe o iden i y EV is limi ed due o ha ing only ou en i onmen s. Iden i ica ion o en i onmen al a iables ha explain GxE in e ac ion has been s udied using di e en me hods. In Gue nsey cows om ou di e en coun ies, among he 15 en i onmen al a iables ha we e s udied using a andom eg ession model, nine indica ed he p esence o GxE in e ac ion (es ima es o g a ied be ween 0.85 and 0.98) [4]. By calcula ing gene ic co ela ions be ween ani- mals om opposi e ends o en i onmen al g adien s, Zwald e al. [6] epo ed ha se en o 13 EV caused gen- e ic co ela ions o de ia e om uni y ( g = 0.79 o 0.90). Iden i ica ion o signi ican EV ha cause GxE in e - ac ion is aluable because he in o ma ion can be used o educe GxE in e ac ion be o e op imiza ion o a b eeding p og am. Op imiza ion o a b eeding p og am may be mo e expensi e han changing he signi ican EV so ha hey a e simila ac oss en i onmen s, he eby e- ducing GxE in e ac ion, because o he possible need o es ablish mul iple sib- es ing s a ions o en i onmen - speci ic b eeding p og ams. Howe e , changing EV o be simila ac oss en i onmen s may be expensi e o impos- sible o some a me s o p oduce s, e.g. in he case o sea wa e empe a u e. I may be mo e easonable o manipula e EV in he b eeding en i onmen (NUC) a- he han ac oss all di e ging p oduc ion en i onmen s (FI, PE, and GE). Howe e , he decision on which EV o manipula e in he NUC will depend on he ela i e eco- nomic impo ance o he co esponding p oduc ion en- i onmen s o which his EV is ele an . A educ ion in geno ype e- anking ac oss en i onmen s would lead o an inc ease o gene ic gain o BWH in he p oduc ion en i onmen s bu he ex a p o i ha his gene a es may be o se by he ex a cos s o EV manipula ion. Finding he signi ican EV is also o biological in e es , because i p o ides e idence o en i onmen al sensi i - i y o g ow h in ainbow ou . A i icial selec ion will a ge hose ish ha pe o m bes in he s able and con- olled en i onmen in which selec ion is usually done. This could lead o inc eased en i onmen al sensi i i y ac oss mul iple en i onmen s [22,23]. The ele a ed sen- si i i y de elops as a logical consequence o e- anking GxE in e ac ion and/o when gene ic a ia ion in he se- lec ed en i onmen is highe han in he non-selec ed en i onmen s. Highe sensi i i y o en i onmen s may ha e nega i e consequences, such as educed i ness and poo animal heal h in challenging en i onmen s [24]. Al- e na i ely, selec ion o high g ow h pe o mance in a challenging en i onmen may lead o mo e obus and be e adap ed ish o comme cial p oduc ion en i on- men s, hus educing he de imen al side e ec s on, o e en imp o ing, su i al o disease esis ance [14,25]. P e ious s udies ha e shown ha pho ope iod is one o he majo ac o s ha in luence g ow h in ainbow ou [26-28]. In gene al, longe day leng h ends o in- c ease g ow h a e. Taylo e al. [27] ound ha ainbow ou exposed o a ligh o da k hou s (L:D) hy hm o 18:6 g ew signi ican ly as e han ainbow ou exposed o L:D = 8:16, and exp essed signi ican ly highe ci cula - ing le els o insulin-like g ow h ac o -I (IGF-I) ho - mone. This ho mone is posi i ely co ela ed wi h g ow h a e in ainbow ou [27]. These obse a ions suppo he idea ha pho ope iod may cause he signi ican GxE in e ac ion o g ow h i gene ic a ia ion in sensi i i y o pho ope iod exis s. The di ec ion o change in day leng h in Pe u is opposi e o ha in he o he loca ions. The ligh hy hm can be manipula ed in aquacul u e p oduc ion. Manipula ion o pho ope iod by placing lamps unde o abo e he wa e is becoming common p ac ice o enhance g ow h and delay sexual ma u a ion in A lan ic salmon and ainbow ou [28]. The e o e, i Table 4 Co ela ions be ween loadings* and en i onmen al a iables o body weigh a ha es En i onmen al a iable** Pea son Kendall ank Age −0.86 −0.67 Tempe a u e 0.50 0.33 Day*Deg ee −0.91 −0.67 Oxygen −0.14 0.00 Pho ope iod 0.32 0.33 *Ob ained om ac o analy ic model. **Mean o en i onmen al a iable (Table 1). Table 5 Model compa ison be ween i e di e en eac ion no m models, ac o analy ic model, and mul i a ia e model on body weigh a ha es Model EV LogL NPa AIC BIC Reac ion no m Age 0.0 7 87721.5 87735.1 Tempe a u e 3.1 7 87715.3 87728.9 Day*Deg ee 32.5 7 87656.5 87670.2 Oxygen 38.8 7 87643.8 87657.5 Pho ope iod 43.0 7 87635.4 87649.0 Fac o analy ic La en 105.2 12 87521.0 87544.4 Mul i a ia e N.A. 114.12 14 87507.2 87534.5 EV = en i onmen al a iable; LogL = na u al loga i hm o likelihood de ia ed om he smalles alue (Age: -43853.7); NPa = numbe o pa ame e s; AIC = Akaike’s in o ma ion c i e ion, BIC = Bayesian’s in o ma ion c i e ion; bold le e indica es he lowes AIC and BIC om bo h andom eg ession and ac o analy ic models; esidual deg ees o eedom a e equal o 8854 ( eac ion no m and ac o analy ic model) and 8853 (mul i a ia e model); N.A. = no applicable. Sae-Lim e al. Gene ics Selec ion E olu ion 2014, 46:16 Page 8 o 11 h p://www.gsejou nal.o g/con en /46/1/16 may be possible o educe he GxE in e ac ion due o di e en pho ope iods. Day*Deg ee is a combina ion o wo ac o s: days o ha es , which de e mine he leng h o he ea ing pe iod, and a e age wa e empe a u e. Di e ences in Day*Deg ee be ween en i onmen s may esul om di - e ences in age o empe a u e, o bo h. I is easy o adjus age a ha es so ha i is he same ac oss en i- onmen s, o educe he obse ed e- anking. Howe e , comme cial ma ke weigh s di e be ween coun ies, and hus he age di e ences mus be main ained. Mos o he p oduc ion o ainbow ou occu s in esh and sea wa e ne pens, ponds o aceways, in which empe a u e con ol is di icul . Model compa ison In his s udy, he mos signi ican EV was iden i ied using he ollowing c i e ia wi h he eac ion no m model: he EV ha bes i ed he da a based on AIC and BIC and he EV ha esul ed in he lowes mean squa e de ia ion (MSD) be ween es ima es o g om he eac ion no m and mul i a ia e models. Due o he lack o con inuous g adien s wi hin en i onmen s, he eac ion no m model esembled a model wi h ca ego - ical EV. The eac ion no m model would pinpoin he EV mo e e icien ly i he EV we e measu ed on a mo e con inuous scale (e.g. mo e en i onmen s o ea - men s). The ac o analy ic model is equen ly used in plan b eeding, o example in mul i-en i onmen ials o analyse da a on a ie y es ing [29]. The ac o ana- ly ic model is he andom e sion o a model wi h addi- i e main e ec s and mul iplica i e in e ac ion (AMMI) [30-32]. Recen ly, i was sugges ed ha he ac o ana- ly ic model was use ul o es ima e GxE in e ac ion in animal b eeding [18]. The ac o analy ic model was used in in e na ional si e e alua ions o educe he num- be o pa ame e s o be es ima ed, compa ed o es ima - ing he ull gene ic a iance-co a iance ma ix be ween coun ies [33]. Ou s udy used a wo-s ep ac o analy ic model o iden i y he en i onmen al a iable esponsible o he GxE in e ac ion. The ad an age o using a ac o analy ic model is he abili y o analyse la en common ac o s, which can be co ela ed o known EV [7], as shown in ou s udy. The la en common ac o can be ega ded as ei he a single ac o o a composi e o en- i onmen al ac o s, because se e al en i onmen al ac- o s may con ibu e o he GxE in e ac ion be ween en i onmen s. The la en common ac o in his s udy explained gen- e ic a iance in body weigh a ha es di e en ly be- ween en i onmen s. Fo ins ance, he la en common ac o explained only 26.2% o he o al addi i e gene ic a iance o BWH eco ded in PE bu 63% o BWH e- co ded in FI. These di e ences in he pe cen age o explained addi i e gene ic a iance indica es he p es- ence o GxE in e ac ion. In all en i onmen s, he pe - cen age o addi i e gene ic a iance was less han 100%, which indica es ha mo e han one la en common ac- o explained he GxE in e ac ion. Due o he limi ed di- mension o he Gma ix, he second la en common ac o could no be s udied, which would equi e, e.g., a 5×5 ma ix and ha he expe imen is conduc ed in a leas i e a ms o loca ions. The second la en common ac o is expec ed o explain mainly addi i e gene ic a iance in PE because common ac o s a e o hogonal and V A in he o he en i onmen s was mainly explained by he i s la en common ac o . Mo eo e , wi h a lim- i ed numbe o en i onmen s, he co ela ion be ween he la en common ac o and he EV may no be accu - a e and he e o e no solid conclusions can be made abou EV ha explain he GxE in e ac ion. The e o e, i is ecommended ha a highe numbe o en i onmen s a e in es iga ed in u u e esea ch on GxE in e ac ion. Based on AIC and BIC, he ac o analy ic model was mo e pa simonious han he eac ion no m model, which indica es ha he ac o analy ic model was he mos sui able o ou da a se . This model is sui able when he expe imen does no ha e mul iple a ms pe en i onmen , and o s udy la en common ac o s ac oss en i onmen s. Wi h mo e han i e en i onmen s, mul- iple la en common ac o s can be s udied [32]. As an al e na i e o he eac ion no m o ac o ana- ly ic models, a hyb id be ween hese wo models can be used o cap u e he GxE in e ac ion and o iden i y EV. By adding he en i onmen -speci ic andom e ec om he FA model o he i s o de eac ion no m model, we can quan i y how much o he GxE in e ac ion be ween en i onmen s is explained by he eac ion no m on he EV, wi hou he need o compa e o he mul i a ia e model. Fo Day*Deg ee, he p elimina y esul s om such a hyb id model indica ed a be e goodness o i (AIC = 87520.0 and BIC = 87598.0; esul s no shown) han he o iginal eac ion no m model (AIC = 87656.5 and BIC = 87670.2), as expec ed. The MSD om he hyb id model was equal o 0.005, which implies ha he hyb id model could cap u e all he GxE in e ac ion p esen be ween en i onmen s like he mul i a ia e model. This con as s wi h he eac ion no m model (MSD = 0.09), which de ia ed mo e om he mul i a i- a e model. Fo pho ope iod, he hyb id model also had a be e goodness o i (AIC = 87524.2 and BIC = 87539.8; esul s no shown) han he eac ion no m model (AIC = 87635.4 and BIC = 87649.0). Thus, he hyb id model is po en ially use ul o s udy GxE in e - ac ion and o iden i y EV. The common en i onmen al e ec was excluded om bo h eac ion no m and ac o analy ic models. In ou p e ious s udy wi h he same da a, his e ec explained Sae-Lim e al. Gene ics Selec ion E olu ion 2014, 46:16 Page 9 o 11 h p://www.gsejou nal.o g/con en /46/1/16