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
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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
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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
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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
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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.
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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.
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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
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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