RESEARCH ARTICLE Open Access
Gene ic (co) a iance o ainbow ou
(Onco hynchus mykiss) body weigh and i s
uni o mi y ac oss p oduc ion en i onmen s
Panya Sae-Lim
1,2*
, An i Kause
2
, Ma i Janhunen
2
, Ha i Veh iläinen
2
, Heikki Koskinen
3
, Bja ne Gje de
1
,
Ma ie Lillehamme
1
and Han A Mulde
4
Abs ac
Backg ound: When ainbow ou om a single b eeding p og am a e in oduced in o a ious p oduc ion
en i onmen s, geno ype-by-en i onmen (GxE) in e ac ion may occu . Al hough g ow h and i s uni o mi y a e wo
o he mos impo an ai s o ou p oduce s wo ldwide, GxE in e ac ion on uni o mi y o g ow h has no been
s udied. Ou objec i es we e o quan i y he gene ic a iance in body weigh (BW) and i s uni o mi y and he
gene ic co ela ion (
g
) be ween hese ai s, and o in es iga e he deg ee o GxE in e ac ion on uni o mi y o
BW in b eeding (BE) and p oduc ion (PE) en i onmen s using double hie a chical gene alized linea models.
Log- ans o med da a we e also used o in es iga e whe he he gene ic a iance in uni o mi y o BW, GxE
in e ac ion on uni o mi y o BW, and
g
be ween BW and i s uni o mi y we e in luenced by a scale e ec .
Resul s: Al hough he i abili y es ima es o uni o mi y o BW we e low and o simila magni ude in BE (0.014) and
PE (0.012), he co esponding coe icien s o gene ic a ia ion eached 19 and 21%, which indica ed a high po en ial
o esponse o selec ion. The gene ic e- anking o uni o mi y o BW (
g
= 0.56) be ween BE and PE was mode a e
bu g ea e a e log- ans o ma ion, as exp essed by he low
g
(-0.08) be ween uni o mi y in BE and PE, which
indica ed independen gene ic ankings o uni o mi y in he wo en i onmen s when he scale e ec was accoun ed
o . The
g
be ween BW and i s uni o mi y we e 0.30 o BE and 0.79 o PE bu wi h log- ans o med BW, hese alues
swi ched o -0.83 and -0.62, espec i ely.
Conclusions: Gene ic a iance exis s o uni o mi y o BW in bo h en i onmen s bu i s low he i abili y implies ha a
la ge numbe o ela i es a e needed o each e en mode a e accu acy o selec ion. GxE in e ac ion on uni o mi y is
p esen o bo h en i onmen s and sib- es ing in PE is ecommended when he aim is o imp o e uni o mi y ac oss
en i onmen s. Posi i e and nega i e
g
be ween BW and i s uni o mi y es ima ed wi h o iginal and log- ans o med
BW da a, espec i ely, indica e ha inc eased BW is gene ically associa ed wi h inc eased a iance in BW bu wi h a
dec ease in he coe icien o a ia ion. Thus, he scale e ec subs an ially in luences he gene ic pa ame e s o
uni o mi y, especially he sign and magni ude o i s
g
.
Backg ound
Uni o mi y o ai s depends on an indi idual’s sensi i i y
o pe u ba ions in i s in e nal en i onmen and o un-
known local mic o-en i onmen al ac o s [1-3]. Addi i e
gene ic a iance in uni o mi y is de ined as he gene ic
he e ogenei y o he esidual a iance o a ai [4-6].
Acco dingly, less sensi i e geno ypes ha e o sp ing ha
a e mo e uni o m and show a smalle wi hin- amily
esidual a iance. In animal p oduc ion, uni o mi y is
o en a desi ed cha ac e because: (1) i indica es pheno-
ypic obus ness and (2) i aids in p oducing homogeneous
animal s ocks and uni o m ood p oduc s. Gene ally,
aqua ic animals exhibi conside able he e ogenei y in
g ow h pe o mance. La ge a ia ion in body weigh (BW)
among indi iduals educes ish wel a e and dec eases he
sus ainabili y o he aquacul u e indus y [7]. A common
p ac ice o educe he e ogenei y in g ow h pe o mance is
* Co espondence: [email p o ec ed]
1
No ima Ås, Oslo eien 1 P.O. Box 210, NO-1431 Ås, No way
2
Na u al Resou ces Ins i u e Finland (LUKE), Biome ical Gene ics, FI-31600
Jokioinen, Finland
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
© 2015 Sae-Lim e al.; licensee BioMed Cen al. 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/4.0), which pe mi s un es ic ed use, dis ibu ion, and
ep oduc ion in any medium, p o ided he o iginal wo k is p ope ly c edi ed. The C ea i e Commons Public Domain
Dedica ion wai e (h p://c ea i ecommons.o g/publicdomain/ze o/1.0/) applies o he da a made a ailable in his a icle,
unless o he wise s a ed.
Sae-Lim e al. Gene ics Selec ion E olu ion (2015) 47:46
DOI 10.1186/s12711-015-0122-8
egula g ading du ing ea ing, whe e he e ogeneous ish
schools a e size-so ed in o mo e homogeneous g oups
ha a e ha es ed a di e en imes. Howe e , hese p o-
cedu es educe o e all p o i a he a m scale because
labo and a ming cos s inc ease and he p ice o small-
sized ish is lowe . Ano he solu ion would be o selec
animals o uni o mi y o g ow h pe o mance, p o ided
ha some gene ic a iance exis s o his ai .
Rainbow ou , Onco hynchus mykiss (Walbaum 1792),
is an economically impo an aquacul u e species, and
b eeding p og ams dis ibu e imp o ed ma e ial ac oss
con inen s [8]. P oduce s wo ldwide o ainbow ou
ega d g ow h pe o mance and i s uni o mi y as wo o
he mos impo an ai s o be imp o ed by selec i e
b eeding [9]. When ainbow ou om a single b eeding
p og am a e in oduced in o a ious p oduc ion en i-
onmen s, a geno ype by en i onmen (GxE) in e ac ion
on g ow h pe o mance and i s uni o mi y may occu ,
which hampe s gene ic imp o emen o hese ai s ac oss
mul iple en i onmen s. Howe e , o ou knowledge, GxE
in e ac ion on uni o mi y o g ow h pe o mance in ain-
bow ou has no been s udied.
In Finland, ainbow ou is a med in sea and in inland
eshwa e en i onmen s. The nucleus o he Finnish na-
ional b eeding p og am is loca ed inland, whe e b eeding
candida es a e kep in esh wa e , while hei sibs a e
pe o mance- es ed in he Bal ic Sea, whe e mos la ge-
scale comme cial p oduc ion akes place. To educe he
isk o disease in ec ions, sea- es ed indi iduals and hei
eggs o mil a e no anspo ed om he sea es s a ion
back o he nucleus. Gene ic pa ame e s o uni o mi y
o BW in ainbow ou ha e been s udied only in he
nucleus en i onmen [10], using he addi i e model
desc ibed by Mulde e al. [11]. The s a is ical me hods
applied o gene ic analysis o uni o mi y o BW ha e,
howe e , e ol ed apidly in ecen yea s. Rönnegå d e al.
[12] in oduced a double hie a chical gene alized linea
model (DHGLM), which has he ad an age o accoun -
ing o he non-no mal dis ibu ion o squa ed esiduals.
The e o e, in his s udy, gene ic pa ame e s o uni o mi y
o BW ha we e p e iously es ima ed in he nucleus en-
i onmen we e con i med by using mul i a ia e DHGLM,
and uni o mi y o BW was s udied on ish om bo h he
eshwa e nucleus and sea es s a ions. Fo many mo -
phological ai s, a posi i e co ela ion be ween mean and
a iance is expec ed, i.e. he a iance inc eases wi h he
mean, which is e e ed o as a scale e ec [13]. When
ai a ia ion is scaled by he mean ai alue, e.g. by log-
ans o ming he da a, he esul ing log- ans o med a i-
ance quan i ies he a ia ion ha does no depend on he
scale e ec [13,14].
Thus, he aims o his s udy we e: (1) o quan i y he
gene ic a iance o ha es BW and i s uni o mi y and he
gene ic co ela ion be ween hese ai s o sibs ea ed in
he eshwa e b eeding nucleus and in he seawa e p o-
duc ion en i onmen , and (2) o in es iga e he deg ee o
GxE in e ac ion on uni o mi y o BW o hese wo en i-
onmen s. Finally, we also log- ans o med he da a o
in es iga e whe he gene ic a iance in uni o mi y o BW,
GxE in e ac ion on uni o mi y o BW, and he gene ic
co ela ion be ween BW and i s uni o mi y we e in lu-
enced by he scale e ec , mic o-en i onmen al sensi i i y,
o bo h.
Me hods
Da a
The da a used in his s udy o igina ed om he Finnish
na ional b eeding p og am [15,16]. All p ocedu es ha
in ol ed animals we e app o ed by he animal ca e
commi ee o he Finnish Game and Fishe ies Resea ch
Ins i u e (FGFRI). The b eeding nucleus (de ined as he
b eeding en i onmen o BE) was loca ed on he FGFRI
ish a m loca ed in Te o (Cen al Finland). Siblings o
he b eeding candida es we e es ed in comme cial sea
cages (de ined as he p oduc ion en i onmen o PE)
loca ed in he Bal ic Sea. Pheno ypic da a comp ised 53
638 eco ds on BW a agging om ou yea classes
and belonged o wo subpopula ions, i.e., 1996/1999 and
1997/2000, which we e measu ed o bo h en i onmen s.
Fo each yea class, he numbe o si es and dams and he
numbe o eco ded o sp ing a e in Table 1. Bo h subpop-
ula ions we e es ablished om he pa en s o yea class
1993. Si es and dams we e ma ed using ei he pa e nal
nes ed o pa ial ac o ial ma ing designs. Each yea class
consis ed o 94 o 197 ull-sib amilies es ablished om
he ma ing o 37 o 95 si es wi h 79 o 129 dams. A e
ha ching, inge lings om he same ull-sib amily we e
main ained in one o mo e amily anks un il hey eached
a body size sui able o indi idual passi e in eg a ed
Table 1 Popula ion s uc u e o ainbow ou
Subpopula ion I Subpopula ion II
1996 1999 1997 2000
Numbe o pa en s and amilies
Si es, dams 57, 129 37, 94 65, 79 95, 121
Si es pe dam,
mean ( ange)
1.00 (1-1) 1.00 (1-1) 2.41 (1-3) 1.63 (1-3)
Dams pe si e,
mean ( ange)
2.26 (1-4) 2.54 (1-4) 2.93 (1-5) 2.06 (1-5)
Full-sib amilies,
amily anks
129, 129 94, 135 191, 259 197, 197
Numbe o ish wi h eco ds
F eshwa e
nucleus s a ion
4994 3084 8099 5998
Fish pe ull-sib amily 38.7 32.8 42.4 30.4
Seawa e s a ion 2573 2442 8351 7499
Fish pe ull-sib amily 19.9 26.0 43.7 38.1
Sae-Lim e al. Gene ics Selec ion E olu ion (2015) 47:46 Page 2 o 10
ansponde (PIT) agging (i.e. a a mean BW o app oxi-
ma ely 50 g). Du ing agging, ull-sibs om each amily
we e andomly sampled and di ided in o wo o h ee
ba ches ha we e ea ed ei he in BE o PE. When he ish
we e 2 yea s old, hey we e indi idually weighed, deno ed
by BW
BE
in g o BE and BW
PE
o PE. Fo BE, sex and
sexual ma u i y s a us we e eco ded based on ex e nal
sex cha ac e s, whe eas o PE, since ish we e slaugh-
e ed, sex and ma u i y we e iden i ied based on he
mo phology o he gonads.
In o al, 22 175 and 20 865 indi idual eco ds we e
a ailable o BW
BE
and BW
PE
, espec i ely (Table 1).
A e age BW
BE
and BW
PE
(s anda d de ia ion, SD) es i-
ma ed om he aw da a we e equal o 1094 (364) and
1050 (335) g, espec i ely.
S a is ical analysis
We used DHGLM o s a is ical analysis [12,14,17],
which uses a log-link unc ion o accoun o he non-
no mal dis ibu ion o squa ed esiduals. The models
we e un o wo ans o ma ions o he da a. Fi s ,
obse ed BW we e s anda dized o a mean o 0 and
a iance o 1 o escale he o iginal da a, which acili a es
con e gence. Second, obse ed BW we e log- ans o med
o accoun o he scale e ec . Log- ans o ma ion is one
way o educedependencyo a ianceonmean,since he
log- a iance ep esen s a pa ame e ha is simila o he
coe icien o a ia ion [13]. Bo h s anda dized and log-
ans o med da a we e modelled using he ollowing
mul i a ia e si e-dam DHGLM in ASReml [18,19]:
yE1
ΨE1
yE2
ΨE2
2
6
6
43
7
7
5¼
XE1
sym
0
X ;E1
0
0
XE2
0
0
0
X ;E2
2
6
6
43
7
7
5
bE1
b ;E1
bE2
b ;E2
2
6
6
43
7
7
5þ
ZsþZd
ðÞ
E1000
ZsþZd
ðÞ
;E100
sym ZsþZd
ðÞ
E20
ZsþZd
ðÞ
;E2
2
6
6
43
7
7
5
uE1
u ;E1
uE2
u ;E2
2
6
6
43
7
7
5þ
QE1000
Q ;E100
sym QE20
Q ;E2
2
6
6
43
7
7
5
cE1
c ;E1
cE2
c ;E2
2
6
6
43
7
7
5þ
eE1
e ;E1
eE1
e ;E2
2
6
6
43
7
7
5;
whe e y
Ej
is he ec o o BW pheno ypes o y
ij
o
he i
h
indi idual measu ed in he j
h
en i onmen (E
j
=
BE o PE). ψis he ec o o he esidual a iances
ϕij ¼
^
e2
ij
1−hij

, which was linea ized using a Taylo se ies
app oxima ion in ASReml, whe e ^
e2
ij is he squa ed e-
sidual es ima e o BW
,
and h
ij
is he diagonal elemen in
he ha -ma ix (p edic ed alue ma ix) o y
Ej
co e-
sponding o y
ij
.X(X
) is he incidence ma ix o ixed
in e ac ion e ec s o yea class, si e ( eshwa e and
seawa e ), sex (male, emale, o unknown), and ma u i y
(ma u i y a 2 o 3 yea s o age, o unknown). Wi hin-
amily addi i e gene ic a iance can be in luenced by
pa en al inb eeding [3], bu in ou da a, pa en al a e age
inb eeding coe icien s we e equal o 0 [15], and hus
his coe icien was excluded om he model. b(b
)is
he solu ion ec o o ixed in e ac ion e ec s. Z
S
and
Z
d
a e he incidence ma ices o andom si e (s)and
dam (d) e ec s, and u(u
) is he ec o o addi i e gen-
e ic e ec s o si es and dams on BW (uni o mi y) and
was assumed o ha e he ollowing dis ibu ion:
uE1
u ;E1
uE2
u ;E2
2
6
6
43
7
7
5∼N0;1
4G⊗A

;
whe e Gis 4×4 si e-dam (co) a iance ma ix, and Ais
he nume a o ela ionship ma ix. Q(Q
) is he inci-
dence ma ix o andom e ec s common o ull-sibs
( amily ank p io o communal ea ing and non-addi i e
gene ic e ec s) o he han addi i e gene ic e ec s, and
c(c
) is he ec o o solu ions o he e ec common o
ull-sibs,
cE1
c ;E1
cE2
c ;E2
2
6
6
43
7
7
5∼N0;C⊗IðÞ,whe eCis 4×4 (co) a iance
ma ix o he e ec common o ull-sibs and Iis an
iden i y ma ix. The esidual o y(e)andψ(e
)we e
assumed independen ly no mally dis ibu ed:
eE1
e ;E1
eE2
e ;E2
2
6
6
43
7
7
5∼N
0
0
0
0
;
W−1
E1σ2
∈000
W−1
;E1σ2
∈ 00
sym W−1
E2σ2
∈0
W−1
;E2σ2
∈
2
6
6
6
4
3
7
7
7
5
0
B
B
B
@
1
C
C
C
A;
whe e WEj ¼diag b
ψ−1
Ej

,W ;Ej ¼diag 1−hj
2

,andσ2
∈σ2
∈

is a scaling a iance ha was expec ed o be 1, since W
con ains he ecip ocal o he indi idual esidual a iances.
The mul i a ia e si e-dam DHGLM was i ed i e a i ely,
wi h upda ing o ψand he diagonal elemen s o W
Ej
and W
,Ej
un il he log-likelihood con e ged [19].
Calcula ion o es ima es o gene ic pa ame e s
The es ima ed addi i e gene ic si e-dam a iance com-
ponen σ2
u ;exp

o uni o mi y o BW was on he expo-
nen ial scale (exp) and was consequen ly con e ed o
an addi i e scale σ2
u

using he equa ions de i ed by
Mulde e al. [5]. The es ima ed a iance componen o
he e ec common o ull-sibs σ2
c;
exp

o uni o mi y o
Sae-Lim e al. Gene ics Selec ion E olu ion (2015) 47:46 Page 3 o 10
BW was con e ed o an addi i e scale σ2
c

using he
equa ion de i ed in he Appendix.
In he si e-dam model, he es ima ed a iance compo-
nen o si es was se equal o he a iance componen
o dams and equal o one qua e o he addi i e gene ic
a iance σ2
s¼σ2
d¼σ2
u¼1
4σ2
a

, and he es ima ed a i-
ance componen o uni o mi y o BW σ2
u

was equal
o one qua e o he gene ic a iance o uni o mi y o
BW. The e o e, addi i e gene ic a iance componen s
es ima ed o BW σ2
a

and o uni o mi y o BW σ2
a

we e equal o 4σ2
uand 4σ2
u , espec i ely. Pheno ypic
a iance σ2
p

o BW was equal o 2σ2
uþσ2
cþσ2
e, whe e
σ2
cis he a iance componen o he e ec common o
ull-sibs and σ2
eis he esidual a iance o BW, which in
a si e-dam model includes one hal o he addi i e gene ic
a iance plus he andom en i onmen al a iance. The e-
o e, σ2
uwas mul iplied by 2 o calcula e σ2
p.He i abili y
o BW (h
2
) was calcula ed as σ2
a=σ2
pand o uni o mi y o
BW h2

as σ2
a
2σ4
pþ3σ2
a þσ2
c
ðÞ
(see [20] and Appendix). Simi-
la ly, he common en i onmen al e ec o BW (c
2
)
was calcula ed as σ2
c=σ2
pand o uni o mi y o BW c2

as σ2
c
2σ4
pþ3σ2
a þσ2
c
ðÞ
(see Appendix).
The gene ic coe icien o a ia ion o uni o mi y o
BW (CVa ) was calcula ed as σa =σ2
E,whe eσ2
E¼σ2
e−2σ2
u
. Th ee gene ic co ela ions (
g
) we e calcula ed based
on he addi i e gene ic co a iance di ided by he p od-
uc o he wo co esponding addi i e gene ic s anda d
de ia ions: (1) be ween BW and i s uni o mi y wi hin an
en i onmen , (2) o one ai (BW o i s uni o mi y) in
BE e sus PE, i.e. o quan i y gene ic e- anking be ween
en i onmen s, and (3) be ween BW in one en i onmen
and i s uni o mi y in he o he en i onmen .
App oxima e s anda d e o s o a iance componen
es ima es we e calcula ed wi h ASReml ollowing Fishe
e al. [21]. App oxima ed s anda d e o s o h2
and c2
a e
no a ailable in ASReml and o ou knowledge ha e no
been de i ed.
Compa ison wi h an addi i e model
We also used an addi i e model ha e e s o he “i e a-
i e bi a ia e model”desc ibed in Mulde e al. [11], o
analyze pa o he da a o BW and i s uni o mi y using
he log-squa ed esiduals, as desc ibed in [10,11]. In ha
analysis, we included only he da a om BE and we
epo only he gene ic co ela ion be ween BW and i s
uni o mi y. Ou aim was o e i y whe he o no he
gene ic co ela ion es ima ed by he addi i e model was
consis en wi h ha es ima ed by he DHGLM when he
scale e ec on uni o mi y o BW was accoun ed o by
log- ans o ma ion o BW.
Resul s
Gene ic a ia ion o BW and i s uni o mi y
Using s anda dized da a, addi i e gene ic a iances o
BW we e simila o BE and PE (0.140 o 0.143). He i -
abili y es ima es o BW (h
2
) we e also simila and mod-
e a e o BE (0.258) and PE (0.221) (Table 2). He i abili y
es ima es o uni o mi y o BW h2
we e low and o
simila magni ude o BE (0.011) and PE (0.010). Using
log- ans o med da a, addi i e gene ic a iances in BW
we e p opo ionally lowe o bo h en i onmen s (0.013
o 0.015) han wi h s anda dized da a. All es ima es o
gene ic a iance o uni o mi y o BW we e g ea e han
hei s anda d e o s (SE). Using log- ans o med da a,
es ima es o h
2
o BW in BE and PE we e sligh ly lowe
(0.12 o 0.17) han wi h s anda dized da a, and he es i-
ma e o h2
 o uni o mi y o BW in BE (0.024) was
sligh ly highe han wi h s anda dized da a, whe eas
h2
in PE (0.010) was simila o ha ob ained wi h
s anda dized da a.
While es ima es o h2

we e low, gene ic coe icien s
o a ia ion CVa o uni o mi y o BW es ima ed wi h
s anda dized da a we e equal o 21.1% o BE and 19.0%
o PE, which indica ed a high gene ic po en ial o e-
sponse o selec ion ela i e o he mean. The CVa o
uni o mi y o BW es ima ed wi h log- ans o med da a
was equal o 29.6% and 17.4% o BE and PE, espec -
i ely, which suppo s he exis ence o gene ic di e ences
o uni o mi y o BW beyond he scale e ec .
Es ima es o common en i onmen al e ec s on BW, c
2
,
anged om o 0.02 o 0.03 o bo h en i onmen s, which
sugges s ha a small amoun o pheno ypic a ia ion was
due o sepa a e ull-sib anks be o e communal ea ing
and o non-addi i e gene ic e ec s. The es ima e o c2
o
uni o mi y o BW anged om 0.004 o 0.005 when es i-
ma ed based on s anda dized da a and om 0.019 o
0.021 when es ima ed wi h log- ans o med da a.
Geno ype by en i onmen in e ac ion
Using s anda dized da a, he es ima e o
g
o BW be-
ween BE and PE was equal o 0.70 ± 0.06, which
means ha a low deg ee o e- anking occu ed be ween
en i onmen s (Table 3), while sligh ly g ea e e- anking
(
g
= 0.56 ± 0.20) was ound o uni o mi y o BW be ween
BE and PE. Using log- ans o med da a, he es ima e o
g
o BW be ween BE and PE was equal o 0.66 ± 0.06, which
was simila o ha ob ained wi h s anda dized da a. In
con as , he es ima e o
g
o uni o mi y o BW be ween
BE and PE was close o 0 (-0.08 ± 0.33), which indica es
ha , a e accoun ing o he scale e ec , he anking o
Sae-Lim e al. Gene ics Selec ion E olu ion (2015) 47:46 Page 4 o 10
b eeding alues o uni o mi y o BW be ween BE and PE
was independen .
Gene ic co ela ion be ween BW and i s uni o mi y
Wi h s anda dized da a, he es ima e o
g
be ween BW
and uni o mi y o BW was lowe in BE (0.30) han in PE
(0.79). Howe e , wi h log- ans o med da a, he es i-
ma es o
g
be ween BW and uni o mi y o BW in he
wo en i onmen s we e simila bu nega i e (-0.83 in BE
and -0.62 in PE). Fo ans o med da a, he magni ude o
hese es ima es was g ea e han he es ima es o
g
be ween BW
BE
and i s log-squa ed esiduals om he
addi i e model (-0.40 ± 0.05).
As o gene ic co ela ions wi hin one en i onmen ,
es ima es o
g
be ween ai s measu ed in di e en
en i onmen s depended on whe he s anda dized o log-
ans o med da a we e used (Table 3). Wi h s anda dized
da a, he es ima es o
g
be ween BW
BE
and uni o mi y
PE
(0.49) and be ween BW
PE
and uni o mi y
BE
(0.46) we e
simila . Con e sely,
g
es ima ed wi h log- ans o med
da a was nega i e bu o simila magni ude be ween
BW
BE
and uni o mi y
PE
(-0.42) and be ween BW
PE
and
uni o mi y
BE
(-0.31).
Discussion
Gene ic a ia ion o uni o mi y o body weigh
He i abili y o uni o mi y o BW es ima ed wi h s an-
da dized da a was low o bo h en i onmen s (<0.02).
A e log- ans o ma ion, es ima es o h
2
and c
2
o BW
we e lowe in bo h en i onmen s, whe eas es ima es o
h2
and c2
o uni o mi y o BW we e highe in BE bu
lowe in PE. The es ima es o h2
o uni o mi y o BW
ob ained in his s udy a e in line wi h hose p e iously
epo ed o ainbow ou h2
¼0:024

[10] and o
e es ial animals such as snail [22], b oile chickens
[11,23,24], mice [25], and pigs [26] (

h2
¼0:028 : min =
0.006 and max = 0.047; e iewed by Hill and Mulde [6]).
These h2
es ima es a e low pa ly because he
Table 2 Es ima es o a iance componen s and gene ic pa ame e s o body weigh a ha es and i s uni o mi y
measu ed unde b eeding and p oduc ion en i onmen s, wi h o wi hou log- ans o ma ion o he da a
T ai /Pa ame e En i onmen
S anda dized Log- ans o med
B eeding P oduc ion B eeding P oduc ion
Body weigh
σ2
p0.543 0.646 0.089 0.109
σ2
a0.140 0.143 0.015 0.013
σ2
c0.019 0.024 0.003 0.003
h
2
(SE) 0.258 (0.031) 0.221 (0.028) 0.170 (0.023) 0.120 (0.017)
c
2
(SE) 0.036 (0.007) 0.038 (0.006) 0.031 (0.005) 0.026 (0.004)
Uni o mi y o body weigh
σ2
a ;exp (SE) 0.0433 (0.014) 0.0354 (0.012) 0.0814 (0.030) 0.0289 (0.020)
σ2
a 0.0068 0.0085 0.0004 0.0003
σ2
c 0.0032 0.0031 0.0004 0.0005
CVa 0.211 0.190 0.296 0.174
h2
0.011 0.010 0.024 0.010
c2
0.005 0.004 0.021 0.019
σ2
p= pheno ypic a iance 2σ2
uþσ2
cþσ2
e

, whe e σ2
eis he esidual a iance o body weigh ; σ2
aand 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; CVa = coe icien o addi i e gene ic a iance o uni o mi y σa =σ2
E

, whe e σ2
E¼σ2
e
−2σ2
u;
h
2
= he i abili y o body weigh ; c
2
= 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 c
2
bu o uni o mi y o
body weigh .
Table 3 Es ima es o he gene ic co ela ion (
g
) and
s anda d e o s be ween body weigh a ha es (BW)
and i s uni o mi y, wi hin and be ween en i onmen s
and wi h o wi hou log- ans o ma ion o he da a
T ai
g
(SE)
S anda dized Log- ans o med
Wi hin en i onmen
BW
BE
–uni o mi y
BE
0.30 (0.15) −0.83 (0.10)
BW
PE
–uni o mi y
PE
0.79 (0.13) −0.62 (0.21)
GxE in e ac ion
BW
BE
–BW
PE
0.70 (0.06) 0.66 (0.06)
uni o mi y
BE
–uni o mi y
PE
0.56 (0.20) −0.08 (0.33)
Di e en ai - di e en
en i onmen
BW
BE
–uni o mi y
PE
0.49 (0.14) −0.42 (0.25)
BW
PE
–uni o mi y
BE
0.46 (0.15) −0.31 (0.16)
BE = b eeding en i onmen ; PE = p oduc ion en i onmen .
Sae-Lim e al. Gene ics Selec ion E olu ion (2015) 47:46 Page 5 o 10

he i abili y is de ined a he le el o a single obse a ion
and es ima ing a b eeding alue o a iance based on a
single obse a ion will be inaccu a e. In addi ion,
uni o mi y o BW can be a ec ed by mul iple en i-
onmen al ac o s ha educe he i abili y es ima es [27].
In ac , inding low he i abili ies wi h high CV
a
seems o
be a gene al obse a ion o ai s ha a e closely
ela ed o i ness, such as ecundi y and age a sexual
ma u i y [27].
Al hough we ound low es ima es o h2
o uni o mi y
o BW, i s CVa was high in bo h en i onmen s (21.1%
in BE and 19.0% in PE), which indica es a high po en ial
o gene ic gain in esponse o selec ion o inc eased
uni o mi y ela i e o he mean [5,27,28]. The CVa
es ima ed in his s udy a e in he lowe ange o hose e-
po ed p e iously o uni o mi y o BW in ainbow ou
(0.374) [10], A lan ic salmon (0.417) [14], and e es ial
animals ( CVa = 40.6%; min = 30.0% and max = 58.0%)
[6,11,22-26].
The CVa es ima ed wi h s anda dized BW da a can be
explained by bo h he scale e ec and addi i e gene ic e -
ec s o mic o-en i onmen al sensi i i y. As expec ed, when
he scale e ec was accoun ed o by log- ans o ma ion o
BW, he addi i e gene ic a iance o uni o mi y o BW de-
c eased. Ye , a e log- ans o ma ion, CVa es ima es
emained high, which indica es ha gene ic a ia ion
o uni o mi y o BW is scale independen . P e ious
s udies ha e epo ed a simila phenomenon by compa -
ing ans o med and un ans o med da a o BW in A -
lan ic salmon [14] and o li e size in abbi s and pigs
[29]. S udies on uni o mi y commonly use ans o med
da a o educe non-no mali y o he da a. Fo example,
squa ed esiduals we e log- ans o med in he addi i e
model applied in [10,11], and a Box-Cox ans o ma ion
was used in he Bayesian app oach o [10,23,28,29]. I is
likely ha such ans o ma ions also emo ed pa o
he scale e ec om he da a, which in luences he gen-
e ic pa ame e s o uni o mi y, as e idenced by he
cu en and p e ious s udies [14,29].
The de ini ion o uni o mi y be o e and a e log-
ans o ma ion is no he same. F om a biological
poin o iew, uni o mi y o log- ans o med BW may
be mo e ele an because he scale e ec is accoun ed
o and hus he ac ual gene ic a ia ion o en i on-
men al canaliza ion can be quan i ied. Howe e , o a
ish a me , uni o mi y a he obse ed scale may be
mo e ele an because i co esponds o he eal
ange o ish sizes ha a e p ocessed by he indus y.
Va iance a he obse ed scale can be selec ed o di -
ec ly, whe eas log- ans o med a iance can be con-
olled ei he by di ec selec ion, o by selec ing on
an index wi h app op ia e weigh s on mean BW and
obse ed a iance.
In he si e-dam mixed DHGLM ha we applied, he
squa ed esiduals ha we e used as pheno ypic obse a-
ions o uni o mi y included bo h he Mendelian sampling
e m and he ue esidual ha emained unexplained by
he sys ema ic ixed e ec s, he andom addi i e gene ic
e ec s, and he non-gene ic andom e ec s. The animal
mixed DHGLM, assumes ha he esidual is ee o
Mendelian sampling a iance [14]. Howe e , applying
his model may c ea e biased gene ic pa ame e s o
uni o mi y [30] and hus equi es ha epea ed eco ds
om he same indi iduals a e used o minimise he bias
o gene ic pa ame e s [12].
A educ ion in pheno ypic a ia ion o animal ai s is
bene icial o animal p oduc ion. Howe e , selec ion o
uni o mi y in li es ock is in i s ini ial phase o de elop-
men . In abbi s, selec ion o uni o mi y o bi h weigh
was implemen ed success ully and esul ed in imp o ed
su i al a e o baby abbi s wi hou educing mean
bi h weigh [31]. To ou knowledge, selec ion o uni-
o mi y has no been implemen ed ye in ish b eeding.
I has been s a ed ha selec ion o uni o mi y is no
ele an when he p o i unc ion based on mean alues
o a ai is linea [28], which is he case o g ow h
pe o mance o body weigh . Howe e , i is a guable ha
uni o mi y pe se has bo h an economic and a non-
economic alue [32]. In aquacul u e, a mo e uni o m
g ow h pa e n educes he mo ali y o smalle ish [33].
Du ing he g ow-ou pe iod, he size o eed pelle s is
inc eased as he mean BW o a ish school inc eases.
Thus, a uni o m g ow h pa e n allows mos ish o
adap o changes in pelle size. Uni o mi y o g ow h
may also pa ially educe nega i e social in e ac ions
be ween ish and hus he de elopmen o beha iou al
dominance hie a chies [34,35], which u he imp o es
ish wel a e. Mo eo e , i has been sugges ed ha uni-
o mi y o g ow h pe o mance educes he need o
size-g ading and hus, imp o es he e iciency o ish
p oduc ion [36]. The e o e, while he economic alue o
uni o mi y emains o be calcula ed, simul aneous selec-
ion o BW and i s uni o mi y is expec ed o yield di ec
and indi ec p o i able p ospec s. Di ec selec ion o
uni o mi y o a ai should be ca ied ou i his ai is
economically impo an and can be eco ded a an ac-
cep able cos .
The me hods in es iga ed in his s udy can also be ex-
ended o o he ai ypes. Fo example, educing he
a ia ion in ca cass quali y ai s ha ha e in e media e
op imum alues such as ille colo , ille lipid con en
and body shape, has economic alue, i.e. ille colo and
ille lipid con en should no be oo low o oo high,
and body shape should no be oo hin o oo ound.
Conside ing he b eede s equa ion ΔG=i
IH
σ
a
[3],
esponse o selec ion is de e mined by h ee ac o s: se-
lec ion in ensi y (i), accu acy o selec ion (
IH
), and he
Sae-Lim e al. Gene ics Selec ion E olu ion (2015) 47:46 Page 6 o 10
gene ic s anda d de ia ion (σ
a
)o CV
a
when ΔGis ela-
i e o a ai mean. We ound ha he CVa o uni-
o mi y o BW was high, which indica es ha subs an ial
gene ic esponse o selec ion ela i e o he mean can be
expec ed. To minimize sampling a iance o he es i-
ma es o σa , pheno ypes on a la ge numbe o ela i es
a e equi ed. Based on he equa ion in Hill and Mulde
[6], he op imal amily size o es ima e a iance compo-
nen s o uni o mi y o BW is 85 o ull-sibs when using
a e age h
2
es ima es o 0.145 o log- ans o med BW
and a CVa o 23.5% o log- ans o med uni o mi y o
BW (Table 2). In li es ock, e.g., o dai y ca le, in o -
ma ion is mainly a ailable om hal -sibs, o which
he op imal design is 190 hal -sibs o he same inpu
pa ame e s.
Wi h espec o he
IH
, accu acies o sib selec ion o
a ai wi h a h2
o 0.014 and c2
o 0.012 (a e age alues
om Table 2) a e equal o 0.234, 0.300, 0.364, and 0.412
o ull-sib amily sizes o 40, 80, 160, and 300, espec -
i ely. When he alues o h2
and c2
epo ed by Janhunen
e al. [10] a e used, accu acies inc ease sligh ly and he
equi ed amily sizes dec ease. Wi h he accu acies o
sib selec ion abo e, i is possible o calcula e expec ed
changes in uni o mi y o BW. Using a p opo ion o
10% o selec ed animals (selec ion in ensi y = -1.755), a
CVa o 0.211 in BE (Table 2), gene ic gain was calcu-
la ed ollowing Mulde e al. [5]. Residual a iance o
BW (as a pe cen o he ai mean) dec eased by -9%,
-11%, -13%, and -15%, o ull-sib amily sizes o 40, 80,
160, and 300, espec i ely.
Fo many aquacul u e species, i is possible o ha e
la ge amilies. Howe e , he challenge is ha b eeding
candida es a e om he o sp ing gene a ion and hei
selec ion accu acy is lowe han ha o hei pa en s.
P ogeny- es ing schemes a e e ec i e o inc ease he ac-
cu acy o selec ion o ai s wi h low he i abili y, includ-
ing uni o mi y [5,28], bu ha e no gained popula i y in
aquacul u e b eeding. In aquacul u e b eeding schemes,
sib- es ing is conside ed o be mo e easible because
la ge sib g oups inc ease selec ion accu acy and gene a ion
in e als a e sho e han in p ogeny- es ing schemes. The
mos sui able designs o imp o e uni o mi y in aquacul u e
a e s ill o be de eloped. Ano he app oach o inc ease he
accu acy o sib selec ion is o use genomic selec ion
[37,38], which can heo e ically inc ease accu acy o selec-
ion wi hou p ogeny es ing.
Geno ype by en i onmen in e ac ion
To he bes o ou knowledge, his is he i s s udy on
GxE in e ac ion on uni o mi y o BW in ainbow ou .
The main p oduc ion en i onmen o Finnish ainbow
ou is in he Bal ic Sea. PE and BE di e conside ably in
e ms o wa e empe a u e, salini y, leng h o g owing
season, eeding p ac ice, and ype o cage cul u e (sea
cages s. ea h-bo omed aceways). Wi h s anda dized
da a, mode a e e- anking o amilies o uni o mi y o
BW was ound (
g
= 0.56), which indica es ha uni o mi y
o BW sha es a ce ain deg ee o gene ic backg ound
in each en i onmen . When scale e ec s and mic o-
en i onmen al sensi i i y simul aneously in luence uni-
o mi y o BW, he magni ude o e- anking o uni o mi y
o BW is only sligh ly smalle han o BW (0.62 o 0.70).
This was su p ising, gi en ha he wo en i onmen s ana-
lyzed di e ed g ea ly, and ha s anda d de ia ions o indi-
idual BW, measu ed as squa ed esiduals, a e in luenced
by many unspeci ic abio ic and bio ic en i onmen al ac-
o s, as well as by de elopmen al pe u ba ions du ing he
wo yea s o g ow h. Howe e , when he scale e ec was
accoun ed o by log- ans o ma ion, he gene ic co el-
a ion be ween uni o mi y o BW in BE and PE dec eased
o -0.08. This shows ha he scale e ec may be he main
ac o ha causes he mode a e posi i e co ela ion
be ween uni o mi y o BW in he wo en i onmen s,
and ha uni o mi ies es ima ed wi h s anda dized e -
sus log- ans o med da a a e gene ically dis inc ai s.
Log- ans o med uni o mi y is mo e g ea ly in luenced
by mic o-en i onmen al sensi i i y han by scale e ec s.
The gene ic co ela ion o -0.08 be ween uni o mi ies o
BW in BE and PE was he lowes gene ic co ela ion
epo ed o any ai ac oss hese wo en i onmen s, bu
had a high s anda d e o (0.33). The high sampling a i-
ance o he
g
may be explained by he low h2
o uni o m-
i y o BW in bo h en i onmen s, bu also by he ac ha
s anda d e o s o gene ic co ela ions end o inc ease
wi h dec easing magni ude o gene ic co ela ions [39].
I he aim is o inc ease gene ic esponse in uni o mi y
o BW in bo h en i onmen s, an op imized selec ion
s a egy ha accoun s o he GxE in e ac ion on uni-
o mi y and uses sib pe o mances in bo h en i onmen s
is ecommended [40-42]. Uni o mi y o BW in he nu-
cleus en i onmen and in he p oduc ion en i onmen
should be conside ed as wo di e en ai s and should
be included sepa a ely in a selec ion index. In a si ua ion
whe e wo o mo e en i onmen s a e equally impo an ,
i migh bepossible oes ablishasepa a eb eedingp o-
g am o each en i onmen o maximize esponse o selec-
ion o uni o mi y in each en i onmen [43]. Ne e heless,
es ablishing an addi ional b eeding p og am is e y cos ly
and may no be possible in many cases.
Gene ic co ela ion be ween body weigh and uni o mi y
In addi ion o he deg ee o e- anking o amilies o
uni o mi y in he wo en i onmen s, he scale e ec
d as ically a ec ed he gene ic co ela ion be ween BW
and i s uni o mi y. Gene ic co ela ions o 0.30 and 0.79
we e ound be ween BW and i s uni o mi y in BE and
Sae-Lim e al. Gene ics Selec ion E olu ion (2015) 47:46 Page 7 o 10
PE, espec i ely, bu hese alues swi ched o -0.83 and
-0.62 a e he scale e ec was accoun ed o by log-
ans o ma ion. A simila change in sign was obse ed
o co ela ions be ween BW in one en i onmen and i s
uni o mi y in he o he en i onmen .
The da a ob ained o BE we e also analyzed using he
addi i e model, which used log-squa ed esiduals [11].
This esul ed in a gene ic co ela ion o -0.40 be ween
BW and i s uni o mi y, which is close o he gene ic
co ela ion es ima ed a e log- ans o ma ion in he
DHGLM. On he whole, he gene ic co ela ion es i-
ma ed be ween BW and i s uni o mi y was un a ou able
when un ans o med BW da a we e used bu a ou able
when log- ans o med BW da a we e used. Hence, selec-
ion o BW inc eases he a iance o BW, bu dec eases
he coe icien o a ia ion (CV) o BW because he
inc ease in a iance o BW is smalle han expec ed i
he CV o BW emains cons an o dec eases. I may be
a gued ha due o inc eased g ow h a e, a me s can
ha es ish ea lie a he han a an inc eased BW.
Hence, he gene ic gain in BW o g ow h (e.g. g/day) is
exp essed as lowe age a he han highe weigh a
slaugh e . In ha case, i is s ill unknown whe he gen-
e ic a ia ion in uni o mi y o BW changes since ish a e
slaugh e ed a a younge age.
We obse ed a change in he magni ude and sign o
gene ic co ela ions be ween BW and i s uni o mi y a e
da a ans o ma ion, which ag ees wi h o he s udies.
Sonesson e al. [14] epo ed ha he Pea son co el-
a ion be ween es ima ed b eeding alues o BW and i s
uni o mi y in A lan ic salmon changed om 0.42 wi h
un ans o med da a o -0.17 wi h log- ans o med da a.
Se e al s udies on li es ock species ha e epo ed nega-
i e gene ic co ela ions be ween BW and i s uni o mi y
(
g= -0.36: min = -0.81 and max = -0.11) [6,11,22-24].
Yang e al. [29] es ima ed he gene ic co ela ion be-
ween he mean and a iance o li e size in abbi s and
pigs using a model wi h Ma ko chain Mon e Ca lo
(MCMC) sampling, which simul aneously es ima ed he
model pa ame e s and he Box-Cox ans o ma ion pa-
ame e s. They compa ed gene ic co ela ions be o e
and a e Box-Cox ans o ma ion and ound ha hey
changed om -0.73 o 0.28 o abbi da a and om
-0.64 o 0.70 o pig da a. Mo eo e , while he gene ic
ends ac oss ou successi e gene a ions showed ha
g ow h a e inc eased ac oss gene a ions by selec ion, no
co ela ed gene ic change in uni o mi y o g ow h a e
was ound du ing he same pe iod, when uni o mi y was
es ima ed based on log- ans o med da a ( esidual a i-
a ion scaled by he ai mean). Es ima es o gene ic co -
ela ions be ween BW and i s uni o mi y ob ained in ou
s udy using he DHGLM and an addi i e model we e o
he same sign (-0.157) as in Janhunen e al. [10] bu
mo e nega i e. Thus, i is likely ha selec ion o
inc eased BW based on he gene ic pa ame e s es ima ed
he e, will esul in a a ou able co ela ed end o log-
ans o med uni o mi y. O iginally, i was sugges ed ha
mass selec ion o an inc ease in he mean o a ai
may esul in inc eased en i onmen al a iance be-
cause he selec ed ex eme indi iduals may also ha e
he highes mic o-en i onmen al sensi i i y, e en i
he e is no gene ic co ela ion be ween he mean o he
ai and i s uni o mi y [4,5]. Howe e , o es his hypo h-
esis, i is necessa y o conside whe he he da a on he
ai is log- ans o med o no . In o he wo ds, i is im-
po an o be explici whe he analysis o uni o mi y (o
mic o-en i onmen al sensi i i y) conce ns he combined
e ec o scale and ue mic o-en i onmen al sensi i i y, o
only he la e .
Conclusions
We ound a high po en ial o esponse o selec ion o
uni o mi y o BW in ainbow ou ela i e o he mean
and ha uni o mi y o BW is a gene ically di e en ai
in b eeding and p oduc ion en i onmen s. We ecom-
mend ha , in p ac ice, aquacul u e b eeding p og ams
use sib es ing when he aim is o imp o e uni o mi y
ac oss en i onmen s. A la ge numbe o ela i es will
aid in ob aining a su icien ly high accu acy o selec ion
o uni o mi y o BW. When using log- ans o med ha -
es BW, we ound a nega i e gene ic co ela ion be ween
BW and i s uni o mi y, which indica es ha selec ing o
inc eased BW and mo e uni o m ish is possible. The scale
e ec subs an ially in luences he gene ic pa ame e s o
uni o mi y o BW, especially he sign and magni ude o
he gene ic co ela ions be ween BW and i s uni o mi y
and uni o mi y be ween en i onmen s.
Appendix
The aim he e is o show he ex ension o equa ion 16 in
Mulde e al. [5] o mul iple andom e ec s and how
o he pa ame e s such as c
2
can be calcula ed. Felleki
and Lundeheim [20] showed de i a ions o es ima e he
he i abili y o en i onmen al a iance. Fo comple eness,
hey a e p o ided he e. In addi ion, we gi e equa ions
o c2
, he p opo ion o a ia ion in squa ed pheno ypic
de ia ions explained by common en i onmen al e ec s.
Fi s , he esidual a iance in he exponen ial model is
calcula ed as:
σ2
e;exp ¼σ2
E=exp 1
2σ2
a ;exp

exp 1
2σ2
c ;exp

;ð1Þ
whe e σ2
Eis he esidual a iance om he mean model,
assuming homogenous esidual a iance and assuming
he use o an animal model.
Subsequen ly, as an analogy o equa ion 17 in Mulde
e al. [5], he sum o he gene ic a iance and common
Sae-Lim e al. Gene ics Selec ion E olu ion (2015) 47:46 Page 8 o 10
en i onmen al a iance o he addi i e model can be
calcula ed as:
σ2
a þσ2
c ¼σ4
e;exp exp 2σ2
a ;exp

exp 2σ2
c ;exp

−σ4
E:
ð2Þ
The p oduc o equa ion (2) is a combina ion o σ2
a
and σ2
c . Unde he assump ion ha he a io o σ2
a
σ2
a þσ2
c
is
equal on bo h he addi i e and exponen ial scales, subse-
quen ly σ2
a is calcula ed as:
σ2
a ¼σ2
a þσ2
c

σ2
a ;exp
σ2
a ;exp þσ2
c ;exp
;ð3Þ
and o common en i onmen al e ec s:
σ2
c ¼σ2
a þσ2
c

σ2
c ;exp
σ2
a ;exp þσ2
c ;exp
:ð4Þ
The he i abili y o en i onmen al a iance h2
can
be calcula ed as:
h2
¼σ2
a
2σ4
pþ3σ2
a þσ2
c

:ð5Þ
Simila ly, he a io be ween common en i onmen al
e ec s c2

can be calcula ed as:
c2
¼σ2
c
2σ4
pþ3σ2
a þσ2
c

:ð6Þ
Fo hese equa ions, i is assumed ha gene ic and
common en i onmen al co ela ions be ween mean and
a iance a e 0; o he wise he denomina o would be
sligh ly highe wi h he exponen ial model (no shown).
Howe e , he e ec o his simpli ying assump ion is
negligible. The equa ions we e e i ied wi h Mon e Ca lo
simula ion and ollowing he same assump ions as in
Mulde e al. [5].
Compe ing in e es s
The au ho s decla e ha hey ha e no compe ing in e es s.
Au ho s’con ibu ions
PSL, BG, ML, HAM, and AK planned he s udy. HK con ibu ed o he da a
collec ion. PSL pe o med da a analysis. Fo compa ison, MJ and HV
pe o med he analysis wi h he addi i e model using he same da ase .
HAM con ibu ed o he heo y and o he da a analysis using DHGLM.
HAM also de i ed he equa ions shown in he Appendix. AK, HAM, MJ, HV,
HK, BG and ML con ibu ed o discussion o he da a analysis and he esul s.
PSL d a ed he manusc ip and all au ho s con ibu ed o discussion o he
esul s and imp o ed he manusc ip o he inal e sion. All au ho s ead
and app o e he inal e sion o he manusc ip .
Acknowledgemen s
This s udy is a pa o he pos doc o al esea ch p ojec STABLEFISH
(NRC: 234144/E40) unded by No wegian Resea ch Council. PSL and AK
would like o acknowledge Timo Pi känen (LUKE) o his use ul cons uc i e
discussion. PSL would like o hank A hu Gilmou ega ding his commen s
on mul i a ia e DHGLM in ASReml 4.0.
Au ho de ails
1
No ima Ås, Oslo eien 1 P.O. Box 210, NO-1431 Ås, No way.
2
Na u al
Resou ces Ins i u e Finland (LUKE), Biome ical Gene ics, FI-31600 Jokioinen,
Finland.
3
Na u al Resou ces Ins i u e Finland (LUKE), Aquacul u e Uni ,
FI-72210 Te o, Finland.
4
Animal B eeding and Genomics Cen e,
Wageningen Uni e si y, P.O. Box 338, 6700 AH Wageningen, he Ne he lands.
Recei ed: 7 No embe 2014 Accep ed: 21 Ap il 2015
Re e ences
1. Wadding on CH, Robe son E. Selec ion o de elopmen al canalisa ion.
Gene Res. 1966;7:303–12.
2. Le ne IM. Gene ic Homeos asis. London: Oli e & Boyd; 1954.
3. Falcone DS, Mackay TFC. In oduc ion o quan i a i e gene ics. 4 h ed.
Essex: Longman; 1996. p. 464.
4. Hill WG, Zhang XS. E ec s on pheno ypic a iabili y o di ec ional selec ion
a ising h ough gene ic di e ences in esidual a iabili y. Gene Res.
2004;83:121–32.
5. Mulde HA, Bijma P, Hill WG. P edic ion o b eeding alues and selec ion
esponse wi h gene ic he e ogenei y o en i onmen al a iance. Gene ics.
2007;175:1895–910.
6. Hill WG, Mulde HA. Gene ic analysis o en i onmen al a ia ion. Gene Res.
2010;92:381–95.
7. Gilmou KM, DiBa is a JD, Thomas JB. Physiological causes and
consequences o social s a us in Salmonid ish. In eg Comp Biol.
2005;45:263–73.
8. Sae-Lim P, Kause A, Mulde HA, Ma in K, Ba oo A, Pa sons J, e al.
Geno ype-by-en i onmen in e ac ion o g ow h ai s in ainbow ou
(Onco hynchus mykiss): a con inen al scale s udy. J Anim Sci. 2013;91:5572–81.
9. Sae-Lim P, Komen H, Kause A, an A endonk JAM, Ba oo AJ, Ma in KE,
e al. De ining desi ed gene ic gains o ainbow ou b eeding objec i e
using analy ic hie a chy p ocess. J Anim Sci. 2012;90:1766–76.
10. Janhunen M, Kause A, Veh iläinen H, Jä isalo O. Gene ics o
mic oen i onmen al sensi i i y o body weigh in ainbow ou
(Onco hynchus mykiss) selec ed o imp o ed g ow h. PLoS ONE.
2012;7, e38766.
11. Mulde HA, Hill WG, Ve eijken A, Vee kamp RF. Es ima ion o gene ic
a ia ion in esidual a iance in emale and male b oile chickens.
Animal. 2009;3:1673–80.
12. Rönnegå d L, Felleki M, Fikse F, Mulde HA, S andbe g E. Gene ic
he e ogenei y o esidual a iance - es ima ion o a iance componen s
using double hie a chical gene alized linea models. Gene Sel E ol.
2010;42:8.
13. Lande R. On compa ing coe icien s o a ia ion. Sys Zool. 1977;26:214–7.
14. Sonesson AK, Ødegå d J, Rönnegå d L. Gene ic he e ogenei y o
wi hin- amily a iance o body weigh in A lan ic salmon (Salmo sala ).
Gene Sel E ol. 2013;45:41.
15. Kause A, Ri ola O, Paananen T, Wahl oos H, Män ysaa i EA. Gene ic ends
in g ow h, sexual ma u i y and skele al de o ma ions, and a e o inb eeding
in a b eeding p og amme o ainbow ou (Onco hynchus mykiss).
Aquacul u e. 2005;247:177–87.
16. Kause A, Ri ola O, Paananen T, Män ysaa i E, Eskelinen U. Selec ion agains
ea ly ma u i y in la ge ainbow ou Onco hynchus mykiss: he quan i a i e
gene ics o sexual dimo phism and geno ype-by-en i onmen in e ac ions.
Aquacul u e. 2003;228:53–68.
17. Mulde HA, Rönnegå d L, Fikse WF, Vee kamp RF, S andbe g E.
Es ima ion o gene ic a iance o mac o- and mic o-en i onmen al
sensi i i y using double hie a chical gene alized linea models.
Gene Sel E ol. 2013;45:23.
18. Gilmou AR, Gogel BJ, Cullis BR, Thompson R. ASReml Use Guide Release
4.0. Hemel Hemps ead: VSM In e na ional L d; 2012.
19. Felleki M, Lee D, Lee Y, Gilmou AR, Rönnegå d L. Es ima ion o b eeding
alues o mean and dispe sion, hei a iance and co ela ion using double
hie a chical gene alized linea models. Gene Res. 2012;94:307–17.
20. Felleki M, Lundeheim N. Gene ic con ol o esidual a iance o ea
numbe in pigs. P oc Assoc Ad m Anim B eed Gene . 2013;20:538–41.
Sae-Lim e al. Gene ics Selec ion E olu ion (2015) 47:46 Page 9 o 10