Sae‑Lim e al. Gene Sel E ol (2017) 49:33
DOI 10.1186/s12711‑017‑0308‑3
RESEARCH ARTICLE
Es ima ion o b eeding alues
o uni o mi y o g ow h inA lan ic salmon
(Salmo sala ) using pedig ee ela ionships o
single‑s ep genomic e alua ion
Panya Sae‑Lim1*, An i Kause2, Ma ie Lillehamme 1 and Han A. Mulde 3
Abs ac
Backg ound: In a med A lan ic salmon, he i abili y o uni o mi y o body weigh is low, indica ing ha he accu acy
o es ima ed b eeding alues (EBV) may be low. The use o genomic in o ma ion could be one way o inc ease accu‑
acy and, hence, ob ain g ea e esponse o selec ion. Genomic in o ma ion can be me ged wi h pedig ee in o ma‑
ion o cons uc a combined ela ionship ma ix (
H
ma ix) o a single‑s ep genomic e alua ion (ssGBLUP), allowing
ealized ela ionships o he geno yped animals o be exploi ed, in addi ion o nume a o pedig ee ela ionships (
A
ma ix). We compa ed he p edic i e abili y o EBV o uni o mi y o body weigh in A lan ic salmon, when implemen ‑
ing ei he he
A
o
H
ma ix in he gene ic e alua ion. We used double hie a chical gene alized linea models (DHGLM)
based ei he on a si e‑dam (si e‑dam DHGLM) o an animal model (animal DHGLM) o bo h body weigh and i s
uni o mi y.
Resul s: Wi h he animal DHGLM, he use o
H
ins ead o
A
signi ican ly inc eased he co ela ion be ween he p e‑
dic ed EBV and adjus ed pheno ypes, which is a measu e o p edic i e abili y, o bo h body weigh and i s uni o mi y
(41.1 o 78.1%). When log‑ ans o med body weigh s we e used o accoun o a scale e ec , he use o
H
ins ead o
A
p oduced a small and non‑signi ican inc ease (1.3 o 13.9%) in p edic i e abili y. The si e‑dam DHGLM had lowe
p edic i e abili y o uni o mi y compa ed o he animal DHGLM.
Conclusions: Use o he combined nume a o and genomic ela ionship ma ix (
H
) signi ican ly inc eased he
p edic i e abili y o EBV o uni o mi y when using he animal DHGLM o un ans o med body weigh . The inc ease
was only mino when using log‑ ans o med body weigh s, which may be due o he lowe he i abili y o scaled
uni o mi y, he lowe gene ic co ela ion o ans o med body weigh wi h i s uni o mi y compa ed o he un ans‑
o med ai s, and he small numbe o geno yped animals in he e e ence popula ion. This s udy shows ha ssGB‑
LUP inc eases he accu acy o EBV o uni o mi y o body weigh and is expec ed o inc ease esponse o selec ion in
uni o mi y.
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Backg ound
In aquacul u e, selec ion o inc ease economically impo -
an ai s such as g ow h is one o he main b eeding
goals. Howe e , ish p oduce s show in e es o imp o e
no only he mean bu also he a iance o ai s [1]. Uni-
o mi y o g ow h is p e e able because mo e uni o m
g ow h allows a mo e uni o m p oduc , ha es o a
la ge p opo ion o he popula ion a ma ke size, and
educ ion o size g ading and mul iple ha es s [2–4].
Mo e uni o m g ow h may also educe compe i i e in e -
ac ions be ween animals, which con ibu es o educe
eed monopoliza ion and dominan beha iou , and hus
imp o e well-being o ish [5]. Uni o mi y is also impo -
an o ai s ha ha e an in e media e op imal ai
alue [6], such as ille lipid%, body shape, and condi ion
Open Access
G
ene ics
S
elec ion
E olu ion
*Co espondence: panya.sae‑[email p o ec ed]
1 No ima Ås, Oslo eien 1, P.O. Box 210, 1431 Ås, No way
Full lis o au ho in o ma ion is a ailable a he end o he a icle
Page 2 o 12
Sae‑Lim e al. Gene Sel E ol (2017) 49:33
ac o in he aquacul u e indus y. A ish whose g ow h
is sensi i e o non-measu able en i onmen al ac o s,
known as mic o-en i onmen s, shows mic o-en i on-
men al sensi i i y, which esul s in high en i onmen-
al a iance and consequen ly con ibu es o inc eased
pheno ypic a ia ion, leading o inc eased size a ia ion
wi hin a g oup o ish. A numbe o empi ical s udies
in e es ial and aqua ic species show ha uni o mi y
is pa ly de e mined by gene ic ac o s [4, 7–16]. Thus,
selec i e b eeding can open up one a enue o imp o e
uni o mi y o ish ai s.
A lan ic salmon (Salmo sala L.) is a a med ish ha
is o majo economic impo ance. He i abili y o uni-
o mi y o body weigh has been es ima ed in A lan ic
salmon [14], ainbow ou (Onco hynchus mykiss Wal-
baum) [4, 8], and Nile ilapia (O eoch omis nilo icus)
[15, 16]. In gene al, he i abili y o uni o mi y (
h2
) is low
in li es ock and aquacul u e species (
h2
 < 0.05), indi-
ca ing ha he p edic ion accu acy o b eeding alues
o uni o mi y may be low [17, 18]. Howe e , he coe -
icien o gene ic a ia ion (
GCV
) o uni o mi y o body
weigh is high in ish species (median
GCV
= 34.0%:
min=17.4% and max=64.0%), which indica es high
po en ial o esponse o selec ion [4, 8, 14, 16, 19]. One
way o inc ease esponse o selec ion o uni o mi y is o
inc ease he accu acy o es ima ed b eeding alues (EBV)
o uni o mi y [20].
In aquacul u e, ull- and hal -sib amily sizes a e usu-
ally la ge and hus he accu acy o EBV based on ull-
sibs, hal -sibs and own pe o mance is high o body
weigh , bu no o uni o mi y due o i s low he i abili y
[8]. One app oach o inc ease he accu acy o EBV is
o use genomic in o ma ion [21]. Wi h genomic selec-
ion, genomic es ima ed b eeding alues (GEBV) can
be ob ained o he selec ion candida es ha a e geno-
yped, e en when hey ha e no pheno ype eco ds. One
eason why genomic selec ion esul s in highe accu acy
o selec ion is he mo e accu a e es ima ion o he Men-
delian sampling gene ic e ec s h ough ealized addi i e
gene ic ela ionships among animals [22]. Consequen ly,
indi idual squa ed esiduals, which is he pheno ype o
uni o mi y in a double hie a chical gene alized linea
model (DHGLM), may also be mo e accu a ely es ima ed
when using genomic in o ma ion.
In many cases, combining nume a o pedig ee and
genomic in o ma ion in genomic e alua ions is imple-
men ed in mul iple s eps, which may in oduce bias and
need some calcula ions o combine wi h pedig ee-based
EBV [23, 24]. Single s ep genomic bes linea unbiased
p edic ion (ssGBLUP) a oids his, and genomic and pedi-
g ee in o ma ion a e combined in one s ep [23], which
may lead o less bias and is less p one o double coun ing
o in o ma ion compa ed o genomic e alua ion me hods
ha a e pe o med in mul iple s eps. The ssGBLUP aug-
men s he nume a o ela ionship (
A
) ma ix by he
genomic ela ionship (
G
) ma ix in con en ional gene ic
e alua ion using BLUP [24]. This combined nume a-
o and genomic ela ionship ma ix is known as he
H
ma ix [25]. In ish b eeding, combining pedig ee and
genomic in o ma ion allows exploi ing he la ge ull- and
hal -sib amilies and he mo e accu a e ela ionships o
he geno yped animals, and may yield a highe accu acy
o selec ion o uni o mi y han he use o he
A
ma ix.
To da e, he use o ssGBLUP o uni o mi y has no
been s udied. Fu he mo e, acco ding o a p e ious
s udy, he si e-dam model, bu no he animal model,
implemen ed wi hin he amewo k o DHGLM p o ided
unbiased (co) a iance componen es ima es [14]. How-
e e , an animal DHGLM is expec ed o pe o m be e
han a si e-dam DHGLM o gene ic e alua ion because
he animal DHGLM uses ull ela ionships be ween ani-
mals a he han only among si es and dams. This is pa -
icula ly impo an o uni o mi y, which is quan i ied by
he esiduals o indi iduals, which in he animal model
do no con ain he Mendelian sampling e m. Mo eo e ,
o gene ic e alua ion, he animal DHGLM uses all phe-
no ypic in o ma ion and, o mos b eeding p og ams,
a leas pa o he selec ion candida es, e.g. emales o
sex-linked ai s, ha e pheno ypes a ailable a he ime o
selec ion. Use o he animal DHGLM wi h ssGBLUP o
uni o mi y has no been es ed.
In his s udy, we implemen ed ssGBLUP o p edic ing
GEBV o uni o mi y in A lan ic salmon. Speci ically, ou
aim was o compa e he p edic i e abili y o EBV o uni-
o mi y o body weigh when implemen ing ei he BLUP
wi h he
A
ma ix o ssGBLUP wi h he
H
ma ix. The
(co) a iance componen s we e es ima ed om he si e-
dam DHGLM wi h ei he
A
o
H
and compa ed p io o
gene ic e alua ion.
Me hods
Da a
The da a used in his s udy o igina ed om he expe i-
men conduc ed by No ima AS and he b eeding com-
pany SalmoB eed in No way. The expe imen ollowed
all he egula ions o animal e hical p ac ice and was
app o ed by he No wegian Resea ch Animal Commi ee
(ID 6489). In 2013, 234 ull-sib amilies we e es ablished
om he ma ing o 131 si es o 234 dams (Table1) du -
ing ou weeks. Fo y-se en pe cen o he pa en s we e
om yea class 2009 and he es om yea class 2010.
A e ha ching, inge lings om each amily we e held
in a 180-L amily ank un il agging size (a mean body
weigh o 50g). Each animal was agged using passi e
in eg a ed ansponde (PIT) ags (Sa pos AS, No way).
Du ing agging, a in sample o geno yping was collec ed
Page 3 o 12
Sae‑Lim e al. Gene Sel E ol (2017) 49:33
om 21 o 38 sibs o each o 50 ull-sib amilies. The ea -
e , all ish we e andomly alloca ed o h ee expe imen
anks and g own o 11mon hs. A he a e age age o
16mon hs, all ish we e challenged wi h sea lice using a
co-habi a challenge, and a he end o he challenge es ,
inal body weigh (g) was measu ed o all 3595 ish wi h
an elec onic balance. A o al o 1416 o sp ing (39% o
all o sp ing) and he 131 si es and 234 dams we e geno-
yped using he 31K A yme ix single nucleo ide poly-
mo phism (SNP) chip o A lan ic salmon de eloped
by No ima. Quali y con ol o SNPs was pe o med in
PLINK 1.9 [26] based on he ollowing c i e ia: SNPs
we e emo ed i (1) hei call a e was lowe han 90%, (2)
hey de ia ed om Ha dy–Weinbe g equilib ium wi h
a P alue cu -o o 10−15, and (3) hei mino allele e-
quency (MAF) was lowe han 0.01. A e quali y con ol,
921 o 31,013 SNPs we e emo ed (2.9%) and, hus 30,092
SNPs emained o c ea e he genomic ela ionship.
Rela ionship ma ix
The nume a o ela ionship (
A
) ma ix wi h 814 ances-
o s in ou gene a ions was p epa ed based on pedig ee
in o ma ion using ASReml [27]. The combined nume a-
o and genomic ela ionship (
H
) ma ix was de ined as
[23]:
whe e
A11
is he pedig ee ela ionship ma ix be ween
non-geno yped animals,
A12
and
A21
a e pedig ee ela-
ionship ma ices be ween geno yped and non-geno-
yped animals,
A22
is he pedig ee ela ionship ma ix
be ween geno yped animals, and
G
is he genomic ela-
ionship ma ix be ween geno yped animals. The
G
ma ix was compu ed as [28]:
G
=
WW′
N
, whe e
W
is he
ma ix o he scaled SNP geno ypes o all loci and
N
is
he o al numbe o SNPs (30,092). The elemen s o
W
we e calcula ed as:
H
=

A11 +A12 +A
−1
22 (G−A22)A
−1
22 A21 A12A
−1
22 G
GA−1
22
A
21
G
,
whe e
xij
is he SNP geno ype (coded 0, 1, o 2) o he
i
h indi idual a SNP
j
and
pj
is he allele equency o he
homozygous geno ype coded as 2.
Howe e , Aguila e al. [29] and Ch is ensen and Lund
[30] showed ha he in e se o he
H
ma ix can be com-
pu ed as:
which is less compu a ional demanding and mo e simple
han p epa ing and subsequen ly in e ing he
H
ma ix.
The
H−1
was p epa ed by using he Calc_g m compu e
so wa e [31], which p epa es bo h
A−1
and
G−1
in e -
nally be o e compu ing
H−1
.
S a is ical analysis
Analysis o  esiduals
Uni o mi y can be quan i ied by squa ed esiduals om
a BLUP mixed model equa ion [32]. The use o genomic
in o ma ion o cons uc ealised ela ionships be ween
animals, especially o ull-sibs, is expec ed o inc ease
he accu acy o esidual es ima es due o a g ea e accu-
acy o EBV o body weigh . The e o e, we in es iga ed
he e ec o ssGBLUP and adi ional BLUP on indi idual
esidual es ima ion. Fu he mo e, we in es iga ed si e-
dam and animal models because esidual es ima es om
a si e-dam model con ain no only he unexplained en i-
onmen al e ec s bu also Mendelian sampling gene ic
e ec s. Residual es ima es om an animal model do no
con ain he la e when EBV a e es ima ed wi h an accu-
acy o 1. In o al, esiduals om ou models we e com-
pa ed, i.e. he si e-dam o animal model wi h ei he
A
o
H
.The animal mixed model was:
whe e
yiklmn
is he obse a ion (body weigh ) o he i h
indi idual,
µ
is he o e all mean,
age
is he ixed co a ia e
e ec due o di e en le els o age o he ish, calcula ed
om he s a eeding da e un il he da e o measu emen
(day),
β
is he ixed linea eg ession coe icien on age,
is he
l
h ixed communal ank e ec ,
yc
is he
m
h ixed
e ec o yea class o he pa en s,
ai
is he andom addi-
i e gene ic e ec ,
a
∼

0, Aσ
2
a
, whe e
A
is he nume a-
o ela ionship ma ix, o
a
∼N

0, Hσ
2
a
, whe e
H
is he
combined genomic and pedig ee ela ionship ma ix,
N
is he no mal dis ibu ion, and
σ2
a
is he addi i e gene ic
a iance o body weigh ,
cn
is he andom common
e ec o ull-sibs,
c
∼N

0, Iσ
2
c,
whe e
I
is he iden i y
w
ij =

xij −2pj


2pj

1−pj

,
H
−1=A−1+

00
0G
−1−A−1
22 ,
(1)
yiklmn =µ+βagek+ l+ycm+ai+cn+eiklmn,
Table 1 Popula ion s uc u e o A lan ic salmon
Popula ion s uc u e
Si es, dams 131, 234
Si es pe dam, mean ( ange) 1.0 (1.0)
Dams pe si e, mean ( ange) 1.78 (1–3)
Full‑sib amilies 234
Fish pe ull‑sib amily, mean ( ange) 15.4 (4–54)
Numbe o ish wi h eco ds 3595
Geno yped animals
Full‑sib amilies 50
Fish pe ull‑sib amily, mean ( ange) 28.3 (21–38)
Numbe o ish wi h eco ds 1416
Page 4 o 12
Sae‑Lim e al. Gene Sel E ol (2017) 49:33
ma ix and
σ2
c
is he common en i onmen al a iance
o body weigh , and
eiklmn
is he andom esidual e ec ,
e
∼N

0, Iσ
2
e
, whe e
σ2
e
is he esidual a iance o body
weigh assumed o be homogeneous. Fo he si e-dam
model, he e m
ai
in Eq.(1) was eplaced by he andom
si e-dam (
ui
) e ec ,
u
∼N

0, Aσ
2
u
o
u
∼N

0, Hσ
2
u
.
The same
A
and
H
ma ices we e used o he si e-dam
and he animal models.
Es ima ion o gene ic pa ame e s o uni o mi y
To es ima e gene ic pa ame e s o body weigh and
i s uni o mi y, he si e-dam DHGLM was used [33, 34]
because i is expec ed o p o ide unbiased (co) a iance
componen s o uni o mi y [14]. Body weigh eco ds
we e ea ed in wo di e en ways. Fi s , obse ed body
weigh was s anda dized o a mean o 0 and a iance o
1, which acili a es con e gence o he DHGLM. Sec-
ond, we used ei he he na u al log o he Box–Cox
ans o ma ion o accoun o possible scale e ec s,
because a iances ypically inc ease wi h inc easing
ai means [35, 36]. Fo he Box–Cox ans o ma ion,
each obse a ion was compu ed as
y
i
−
1

, whe e

is he
ans o ma ion pa ame e , which was es ima ed based
on Eq. (1) wi hou he andom e ec s [37] by maxi-
mum likelihood using he MASS package in R so wa e
[38]. The es ima e o

was close o 0 (0.076), indica -
ing ha he Box–Cox ans o ma ion is e y simila o
log- ans o ma ion, which se s

equal o 0. The e o e,
he Box–Cox ans o med body weigh was no used
u he . The s anda dized body weigh and na u al loga-
i hm body weigh a e abb e ia ed as s dWT and lnWT,
espec i ely.
To es ima e gene ic pa ame e s, s anda dized and
ans o med body weigh s we e modelled using si e-dam
DHGLM in ASReml [32]:
whe e
y
is he ec o o s dWT o lnWT eco ds o he
i
h indi idual;

is he ec o o esponse a iables o he
esidual a iance, whe e
ψ
i=log

ˆσ2
ei

+
ˆe
2
i
1−hi−ˆσ2
ei
ˆσ2
e
i
, which
was linea ized using a Taylo se ies app oxima ion in
ASReml [34], ˆ
e2
i
is he squa ed esidual o he
i
h body
weigh eco d,
hi
is he diagonal elemen in he ha -ma ix
o
y
[39], and ˆ
σ2
ei
is he es ima ed esidual a iance o he
i
h obse a ion in he p e ious i e a ion o ASReml;
X
and
X
a e incidence ma ices o he ixed e ec s desc ibed in
Eq.(1) o he ai mean and i s uni o mi y, espec i ely;
b
(
b
) is he solu ion ec o o he co esponding ixed
(2)

y


=

X0
0X

b
b

+

(Zs+Zd)0
0(Zs+Zd)

×

u
u

+

Q0
0Q

c
c

+

e
e

,
e ec s;
Zs
and
Zd
a e incidence ma ices o he andom
si e (s) and dam (d) e ec s;
u
(
u
) is he ec o o addi-
i e gene ic e ec s o si e-dam on he weigh (uni o m-
i y), which was assumed o ollow a no mal dis ibu ion
o he
A
ma ix:
and o he
H
ma ix:
whe e he
1
4
accoun s o he ac ha he si e and dam
each explain only a qua e o he addi i e gene ic a i-
ance;
Q
(
Q
) is he incidence ma ix o he andom com-
mon e ec s o ull-sibs;
c
(
c
) is he ec o o common
e ec s o ull-sibs:
The esiduals o
y
(
e
) and

(
e
) we e assumed o be
independen ly no mally dis ibu ed as ollows:
whe e
W
=
diag
(ˆ

−1)
and
W
=diag

1−h
2

, and
σ2
ǫ
(
σ2
ǫ
)
is a scaled a iance ha was expec ed o be 1. The si e-
dam DHGLM was i ed i e a i ely o upda e

,
diag
(
W)
and
diag
(
W )
un il he log-likelihood con e ged [34].
Calcula ion o gene ic pa ame e s
In he si e-dam DHGLM, he es ima ed a iance o si es
was se equal o he es ima ed gene ic a iance o dams
and equal o one qua e o he addi i e gene ic a iance.
Hence, he addi i e gene ic a iance o body weigh (
σ2
a
)
and i s uni o mi y (
σ2
a ,exp
) we e equal o
4
σ
2
u
and
4
σ
2
u ,exp
,
espec i ely. Es ima es o
σ2
u ,exp
and
σ2
c ,exp
o uni o m-
i y o body weigh we e on he exponen ial scale (
exp
) and
we e con e ed o an addi i e scale (
σ2
u
and
σ2
c
) using he
ex ension o he equa ions o Mulde e al. [17], as de i ed
by Sae-Lim e al. [8]. The addi i e gene ic a iance o uni-
o mi y o body weigh on he addi i e scale was equal o
4
σ
2
u
. Pheno ypic a iance (
σ2
P
) o body weigh was equal
o
2
σ
2
u
+σ
2
c
+σ
2
e
, whe e
σ2
c
is he a iance componen
o he e ec common o ull-sibs and
σ2
e
is he esidual
a iance o body weigh . He i abili y o body weigh (
h2
)
was calcula ed as
σ2
a
/σ
2
P
. He i abili y o uni o mi y o
body weigh (
h2
) on he addi i e scale was calcula ed as
σ
2
a
2
σ4
P
+3

σ2
a
+σ2
c 
[8, 40]. Simila ly, he common en i onmen-
al e ec was calcula ed as
c2
=σ
2
c
/σ
2
P
o body weigh
and as
c2
=
σ
2
c
2
σ4
P
+3

σ2
a
+σ2
c 
o uni o mi y o body weigh

u
u ∼N0
0,1
4σ
2
aσa,a ,exp
σa,a
,exp σ2
a ,exp
⊗A
,

u
u ∼N0
0,1
4σ
2
aσa,a ,exp
σa,a
,exp σ2
a ,exp
⊗H
,

c
c ∼N0
0,σ
2
cσc,c ,exp
σc,c
,exp σ2
c ,exp
⊗I
.

e
e

∼N

0
0

,

W
−1
σ
2
ǫ0
0W
−1
σ2
ǫ
⊖
,
Page 5 o 12
Sae‑Lim e al. Gene Sel E ol (2017) 49:33
[8]. The gene ic coe icien o a ia ion o uni o mi y o
body weigh (
GCV
) was calcula ed as

σ2
a ,
exp
. S anda d
e o s o
h2
and
GCV
we e app oxima ed using he equa-
ions p esen ed by Mulde e al. [41].
Gene ic e alua ion andc oss‑ alida ion
Two gene ic e alua ions, i.e., BLUP wi h
A
and ssGBLUP
wi h
H
, we e pe o med in a 10- old c oss- alida ion
using he gene ic pa ame e s es ima ed based on he si e-
dam DHGLM and !BLUP op ion in ASReml. In o al, ou
models we e used in he 10- old c oss- alida ion, i.e. ani-
mal DHGLM wi h ei he
A
o
H
on s dWT and lnWT.
The 10- old c oss- alida ion was pe o med on s and-
a dized and ans o med body weigh da a as ollows:
1. Adjus ed pheno ypes o body weigh (
y∗
i
) and i s
uni o mi y (
ψ∗
i
) we e calcula ed as
y∗
i
=
ˆ
a
i
+ˆc
i+ˆ
e
i
and
ψ∗
i
=
ˆ
a
i
+ˆc
i
+ˆe
i
, using he solu ions om he
analysis wi h Eq.(2) on he ull da ase .
2. In a modi ied da ase , app oxima ely 10% o obse ed
pheno ypes (
yi
) o animals om each amily we e
masked (=10% o he ull da ase ). All pheno ypes
had an equal chance o be masked, bu he animals
ha we e masked in he p e ious old we e no
masked again in he nex old.
3. The gene ic analysis wi h Eq.(2) was un on he mod-
i ied da ase using he
A
and
H
ma ices and EBV o
body weigh and i s uni o mi y we e p edic ed o he
masked animals.
4. Fo each old, wo measu emen s we e compu ed:
(a) The p edic i e abili y o EBV was calcula ed as
he Pea son co ela ion o adjus ed pheno ypes
(s ep 1) wi h he co esponding EBV (
ˆ
a∗
) (s ep 3)
o he masked animals ha we e geno yped, i.e.,
co (
y∗
i
,
ˆ
a∗
i
) o body weigh and co (
ψ∗
i
,
ˆ
a∗
i
) o
uni o mi y. Kendall and Spea man co ela ions
we e also calcula ed o uni o mi y because
ψ∗
i
was exponen ially a he han no mally dis ib-
u ed.
(b) To measu e he deg ee o bias and accu acy o
EBV o GEBV o he masked eco ds, he mean
squa e e o p edic ion (MSEP) was calcula ed
as
n
i(ˆ
a
∗
i−y
∗
i)
2
n
o body weigh and

n
iˆ
a∗
i−ψ∗
i
2
n
o uni o mi y o body weigh , whe e
n
is he
numbe o masked eco ds in each old. The
MSEP was scaled by he a iance o he adjus ed
pheno ypes o he co esponding ai .
5. S eps (1) o (4) we e epea ed o each o he 10 olds.
Finally, a e age Pea son, Kendall, and Spea man co e-
la ions, MSEP and hei s anda d e o (SE) o e he 10
olds we e calcula ed. A 95% con idence in e al o he di -
e ence (
d
) in he p edic i e abili y om di e en models
wi h ei he
A
o
H
was cons uc ed using
d±1.96 ×SEd
,
whe e he
SE
d=

SD2
animal DHGLM+SD2
si e-dam DHGLM
numbe o olds . When 0
was no wi hin he 95% con idence in e al, he p edic-
i e abili ies o wo models we e conside ed s a is ically
di e en (P<0.05).
Resul s
Residual es ima es
Indi idual esiduals es ima ed om using he
A
(BLUP)
and
H
ma ices (ssGBLUP) we e plo ed agains each
o he o examine hei ela ionship. As expec ed, he
ange o esidual es ima es om he animal models was
lowe han ha om he si e-dam model since esidual
es ima es om he si e-dam model included he en i e
Mendelian sampling e m (Fig.1).
Fo he si e-dam model, he use o
H
ins ead o
A
did
no a ec es ima ed esiduals o geno yped animals
since he eg ession coe icien o he es ima ed esidu-
als using
H
on he es ima ed esiduals using
A
and he
Pea son co ela ion be ween he wo we e equal o 0.999,
which was e y simila o he eg ession coe icien o
non-geno yped animals (0.998). The Pea son co ela-
ions be ween es ima ed esiduals using
H
and
A
we e
he same as eg ession coe icien s o es ima ed esidu-
als using A on es ima ed esiduals using H o geno yped
animals (0.999) and non-geno yped animals (0.998).
In con as , he use o
H
in he animal model a ec ed
esidual es ima es o geno yped animals since hei dis-
ibu ion was much mo e sca e ed (Fig.1). The slope o
es ima ed esiduals using A on es ima ed esiduals using
H was lowe han 1 and sligh ly s eepe o geno yped
animals ( eg ession coe icien =0.7025) han o non-
geno yped animals ( eg ession coe icien =0.6798). The
Pea son co ela ions be ween es ima ed esiduals using
H
and
A
we e equal o 0.922 o geno yped animals and
0.966 o non-geno yped animals.
When using he si e-dam model, he di e ence in es i-
ma ed esiduals wi h
H
and
A
was small and anged om
−10.8 o 10.0. When using he animal model, his di e -
ence was la ge and anged om −95.3 o 104.5.
Gene ic pa ame e s o body weigh andi s uni o mi y
Fo body weigh , es ima es o addi i e gene ic a iances
om he si e-dam DHGLM wi h ei he
A
o
H
we e simi-
la (Table2). Likewise, es ima es o
h2
we e simila wi h
A
and
H
o bo h ai s: 0.266 and 0.296, espec i ely o
s dWT and 0.325 and 0.346, espec i ely o lnWT.
When using
A
, he es ima e o
h2
was highe o uni-
o mi y o s dWT (0.036) han o uni o mi y o lnWT
(0.015), while he use o
H
did no a ec he magni ude

Page 6 o 12
Sae‑Lim e al. Gene Sel E ol (2017) 49:33
o
h2
o uni o mi y. S anda d e o s o
h2
es ima es we e,
howe e , high (Table2).
Al hough he es ima es o
h2
we e low, es ima es o
GCV
we e high o uni o mi y o s dWT (48.0% o
A
and 52.3% o
H
), which indica es subs an ial gene ic
po en ial o esponse o selec ion. A e accoun ing o
scale e ec s, es ima es o
GCV
o uni o mi y o lnWT
we e educed o 30% ( o bo h
A
and
H
), which suppo s
he exis ence o gene ic a ia ion o uni o mi y beyond
he scale e ec s.
Es ima es o
c2
o s dWT and lnWT we e mode a e
and simila o
A
(0.103 o0.117) and
H
(0.103 o0.111),
which sugges s ha pa o he pheno ypic a ia ion was
explained by non-gene ic e ec s ha a e common o ull-
sibs. Ins ead, he es ima es o
c2
o uni o mi y o s dWT
and lnWT we e e y low and anged om 0.001 o 0.022
o
A
and 0.002 o 0.019 o
H
(Table2).
The es ima e o he gene ic co ela ion be ween
s dWT and i s uni o mi y was close o 1, using ei he
A
(0.952) o
H
(0.951), which shows he high depend-
ency be ween mean and a iance o body weigh . How-
e e , he es ima e o he gene ic co ela ion be ween
lnWT and i s uni o mi y was educed o −0.093 wi h
A
and o 0.024 wi h
H
, which sugges s ha a e accoun -
ing o he scale e ec s, he mean and a iance became
independen .
C oss‑ alida ion
The use o
H
ins ead o
A
wi h he animal DHGLM
esul ed in mo e a ia ion o he wi hin- amily GEBV
o s dWT and i s uni o mi y, compa ed o wi hin- am-
ily EBV (Fig.2; Addi ional ile1: Figu e S1), o si e-dam
DHGLM).
The a e age co ela ion o adjus ed pheno ypes wi h
p edic ed b eeding alues o s dWT and i s uni o mi y
was signi ican ly highe wi h
H
(s dWT = 0.443; uni-
o mi y=0.217 o0.317) han wi h
A
(s dWT=0.372;
uni o mi y=0.128 o0.192). Howe e , a e accoun ing
o scale e ec s using log- ans o ma ion, he a e age
Pea son, Kendall and Spea man co ela ions o adjus ed
pheno ypes wi h p edic ed b eeding alues o lnWT and
hei uni o mi y we e only sligh ly highe wi h
H
han
wi h
A
, and no signi ican ly di e en om each o he
(P>0.05).
Fig. 1 Sca e plo o esiduals o body weigh om he uni a ia e analysis wi h
A
ma ix (x‑axis) o
H
ma ix (y‑axis). Two models we e pe o med;
si e‑dam uni a ia e model (le ) and animal uni a ia e model ( igh ). Red do s a e geno yped animals and g ey do s a e non‑geno yped animals
Page 7 o 12
Sae‑Lim e al. Gene Sel E ol (2017) 49:33
The a e age MSEP o uni o mi y om he animal
DHGLM (0.608 o0.944) we e lowe han hose om
he si e-dam DHGLM (0.973 o1.112), sugges ing ha
he use o an animal DHGLM inc eases he accu acy and
may educe bias in p edic ing b eeding alues o uni-
o mi y (Table3; Addi ional ile2: Table S1). Howe e ,
he a e age MSEP o uni o mi y o s dWT and lnWT
ob ained wi h
H
(0.608 o0.944) we e no no ably di e -
en om hose ob ained wi h
A
(0.625 o0.936).
The p edic i e abili y o EBV o uni o mi y was sensi-
i e o he ype o co ela ion used, i.e. Pea son, Kend-
all and Spea man (Table3). Spea man co ela ions we e
39.1 o49.0% highe han Kendall co ela ions. P edic i e
abili ies o EBV and GEBV o uni o mi y o lnWT di -
e ed mo e om each o he based on Kendall and Spea -
man co ela ions, albei no signi ican a P<0.05, han
based on Pea son co ela ions. Howe e , he SE o Kendall
co ela ions we e app oxima ely 50% lowe han he SE o
Pea son and Spea man co ela ions, sugges ing ha Ken-
dall co ela ions p o ide a mo e eliable es ima e o p e-
dic i e abili y han Pea son and Spea man co ela ions.
Discussion
To he bes o ou knowledge, his is he i s s udy ha
compa es he use o he nume a o ela ionship (
A
) and
a combined genomics and nume a o ela ionship (
H
)
ma ix o es ima ing gene ic pa ame e s and p edic ing
b eeding alues o body weigh and i s uni o mi y. The
use o he animal DHGLM wi h
H
signi ican ly imp o ed
he p edic i e abili y o GEBV o uni o mi y o body
weigh (s dWT) bu no o scale-adjus ed uni o mi y.
Gene ic pa ame e s
The es ima e o he i abili y o uni o mi y o s dWT
om si e-dam DHGLM wi h
A
was low (
h2
= 0.036)
bu highe han es ima es o
h2
ob ained in p e ious
s udies on ainbow ou [4, 8] and Nile ilapia [15, 16]
(
¯
h2
=0.016: min=0.010: max=0.024). Howe e , a e
accoun ing o scale e ec s by loga i hm ans o ma ions,
he es ima e o
h2
dec eased o 0.014 o0.015, which is in
line wi h he p e ious epo s ha also used ans o ma-
ions [4, 8, 14–16].
Es ima es o
h2
o s dWT and lnWT using he si e-
dam DHGLM wi h
H
did no di e om hose wi h
A
,
which is in line wi h es ima es o
h2
o uni o mi y o
pigle bi h weigh ob ained using ei he
A
o only he
genomic ela ionship ma ix (
G
) [42], while lowe es i-
ma es we e epo ed o en i onmen al a iance o
soma ic cell sco e in dai y ca le when using
G
compa ed
o
A
[43]. The simila i y o he es ima es o
h2
ob ained
by using
A
o
H
in his s udy can be explained by he e y
simila es ima ed esiduals (p oxy o uni o mi y) be ween
non-geno yped and geno yped animals when using
he si e-dam model wi h
A
and
H
. The si e-dam model
only exploi s ela ionships be ween si es and dams and
does no exploi he ull po en ial o he geno ype-based
ela ionships be ween animals, and especially be ween
ull-sibs. In con as , esiduals o geno yped animals
es ima ed by using he animal model we e mo e di e -
en ia ed when ei he
A
o
H
was used, and likely mo e
accu a e han es ima es o esiduals o non-geno yped
animals. Howe e , in a DHGLM analysis, he si e-dam
model p o ides less biased (co) a iance componen s
han he animal model [14], likely because o he depend-
ence be ween es ima es o he b eeding alue and esid-
ual o an indi idual, which a e ob ained om he same
pheno ype o body weigh . The use o genomic ela ion-
ships combined wi h nume a o ela ionships is expec ed
o educe he dependency be ween EBV and es ima ed
esiduals because he EBV a e mo e accu a e. The e-
o e, we pe o med he animal DHGLM wi h
H
bu he
model did no con e ge when he a iance componen s
we e es ima ed, which may be due o (1) he dependency
be ween EBV and es ima ed esiduals o body weigh
emaining high, o (2) he di icul y o disen angle gene ic
Table 2 Es ima es o  a iance componen s and gene ic
pa ame e s o  body weigh and i s uni o mi y based
on he si e-dam double hie a chical gene alized linea
model when using pedig ee (
A
) o combined pedig ee
andgenomic ela ionships (
H
) ands anda d o log- ans-
o med pheno ypes
A
=pedig ee based ela ionship ma ix;
H
=combined geno yped and non‑
geno yped ela ionship ma ix;
σ2
P
=pheno ypic a iance (
2
σ
2
u
+σ
2
c
+σ
2
e
), whe e
σ2
e
is he esidual a iance o body weigh ;
σ2
a
and
σ2
a
=addi i e
gene ic a iance o body weigh and i s uni o mi y, espec i ely;
σ2
c
=common
en i onmen al a iance; GCV=coe icien o addi i e gene ic a iance
o uni o mi y (

σ2
a ,
exp
); h2=he i abili y o body weigh ;
c2
=common
en i onmen al e ec due o ull‑sib anks;
h2
=he i abili y o uni o mi y;
c2
=same as
c2
bu o uni o mi y o body weigh . Supe sc ip s a e SE o he
es ima es
T ai /pa ame e S anda diza ion Loga i hm
A
H
A
H
Body weigh
σ2
P
0.843 0.856 0.131 0.132
σ2
a
0.216 0.243 0.043 0.046
σ2
c
0.095 0.091 0.013 0.014
h20.2660.095 0.2960.102 0.3250.102 0.3460.107
c20.1170.037 0.1110.037 0.1030.038 0.1030.038
Uni o mi y o body weigh
σ2
a
,
exp
0.23030.1094 0.27320.1211 0.08960.0569 0.08850.0598
σ2
a
0.0612 0.0677 0.0005 0.0005
σ2
c
0.0360 0.0306 0.0000 0.0001
GCV
0.4800.114 0.5230.116 0.2990.095 0.2980.100
h2
0.0360.019 0.0380.020 0.0150.014 0.0140.013
c2
0.022 0.019 0.001 0.002
Page 8 o 12
Sae‑Lim e al. Gene Sel E ol (2017) 49:33
e ec s om he common en i onmen al e ec s o uni-
o mi y o body weigh .
The s anda d e o s o
h2
es ima es we e high, which
may be due o he la ge a ia ion in amily size (4 o54).
Acco ding o Hill and Mulde [30], la ge amily sizes o
epea ed measu emen s a e ecommended o es ima ing
he gene ic he e oscedas ici y o ai s. The op imal ull-
sib amily size is 39 wi h a
GCV
o 39% and an
h2
o 0.36
[18]. The use o
H
did no a ec he s anda d e o s o he
h2
es ima es, which does no ag ee wi h p e ious s udies,
o example Vee kamp e al. [44] epo ed lowe s anda d
e o s o
h2
es ima es o d y ma e in ake, milk yield,
and body weigh o hei e s when using genomic ela ion-
ships wi h an animal model. One possible explana ion
could be ha he bene i o using he genomic ela ion-
ship ma ix may be limi ed when he si e-dam DHGLM
is applied, since he a iance o genomic ela ionships
be ween si es (0.02) was e y simila o he a iance o
nume a o ela ionships be ween si es (0.01). In con as ,
he a iance in genomic ela ionships be ween animals
(0.01) was much la ge han he a iance o nume a-
o ela ionships be ween animals (0.004). Hence, he
Fig. 2 Boxplo s o es ima ed b eeding alues o s anda dized body weigh (s dWT) and i s uni o mi y om geno yped animals by amily. The
b eeding alues we e es ima ed using he animal double hie a chical gene alized linea model. G een boxplo s a e es ima ed b eeding alues (EBV)
using he
A
ma ix and ed boxplo s a e genomic es ima ed b eeding alues (GEBV) using he
H
ma ix. The x‑axis ep esen s amily iden i ica ion
Table 3 A e age Pea son, Kendall andSpea man co ela ions andmean squa e e o p edic ion oma 10- old c oss- al-
ida ion based on he si e-dam double hie a chical gene alized linea modela whenusing pedig ee (
A
) o combined pedi-
g ee andgenomic ela ionships (
H
) ands anda d o log- ans o med pheno ypes
a The a iance componen s om he si e‑dam double hie a chical gene alized linea model we e con e ed o he animal double hie a chical gene alized linea
model and we e used in he 10‑ old c oss‑ alida ion. Rela ionship= ela ionship ma ix, whe e
A
e e s o pedig ee‑based ela ionship ma ix and
H
e e s o
combined geno yped and non‑geno yped ela ionship ma ix. The p edic abili y was calcula ed as he Pea son, Kendall and Spea man co ela ions be ween ma ked
pheno ype and p edic ed b eeding alue. MSEP was scaled by he pheno ypic a iance o co esponding ai s
T ans o ma ion Rela ionship Body weigh Uni o mi y o body weigh
Pea son MSEP Pea son Kendall Spea man MSEP
S anda dized
A
ma ix 0.3720.013 0.7240.021 0.1920.033 0.1280.021 0.1780.030 0.6250.086
H
ma ix 0.4430.017 0.6820.021 0.2710.018 0.2170.017 0.3170.025 0.6080.082
Loga i hm
A
ma ix 0.3960.019 0.8230.029 0.3780.032 0.1820.016 0.2630.023 0.9360.085
H
ma ix 0.4400.016 0.8130.028 0.3830.026 0.2030.014 0.2940.020 0.9440.085
Page 9 o 12
Sae‑Lim e al. Gene Sel E ol (2017) 49:33
SE o
h2
es ima es may be lowe when using an animal
DHGLM wi h a genomic ela ionship ma ix, compa ed
o he nume a o ela ionship ma ix. Ne e heless, in
ou s udy, i was no possible o in es iga e his phenom-
enon since he log-likelihood did no con e ge o he
animal DHGLM wi h
H
.
The
GCV
o uni o mi y o s dWT was subs an ial
(48.0%), which indica es high po en ial o esponse o
selec ion. This esul is in he uppe ange o p e ious
indings in ish species (17.4 o64.0%) [4, 8, 14–16, 19]
and in e es ial animals (10.0 o58.0%) [6, 9–13, 42].
A e accoun ing o scale e ec s by loga i hm ans-
o ma ions, he
GCV
o uni o mi y was educed bu
s ill subs an ial (29.5 o29.9%), which was also epo ed
in p e ious s udies on A lan ic salmon [14], ainbow
ou [8], abbi , and pig [45]. Thus, scale e ec s a ec
es ima es o gene ic pa ame e s o uni o mi y o body
weigh conside ably, bu he e is gene ic a ia ion o
uni o mi y beyond he scale e ec .
Genomic in o ma ion sligh ly inc eased he
GCV
o
uni o mi y o s dWT ( om 48.0 o 52.3%). In con as ,
genomic in o ma ion did no in luence he
GCV
o uni-
o mi y o lnWT (29.8%). Since es ima es o gene ic pa am-
e e s ob ained wi h
A
and
H
we e simila , he
GCV
o body
weigh emained simila , which is in ag eemen wi h he
p e ious compa ison be ween
A
(
GCV
=11.0 o12.0%)
and
G
(
GCV
=10.0 o11.0%) o uni o mi y o bi h weigh
o pigle s using a dam model [42].
Gene ic andgenomic p edic ions
In his s udy, we used he Pea son co ela ion o EBV
and GEBV wi h adjus ed pheno ype as he measu e o
p edic i e abili y. The use o
H
ins ead o
A
in he ani-
mal DHGLM signi ican ly imp o ed he abili y o p e-
dic b eeding alues o s dWT (19%) and i s uni o mi y
(41.1 o 78.1%). Fu he mo e, he use o he animal
DHGLM ins ead o he si e-dam DHGLM signi ican ly
inc eased he p edic i e abili y o EBV and GEBV o uni-
o mi y (see Addi ional ile2: Table S1), as expec ed.
Ou indings indica e ha ssGBLUP wi h an animal
DHGLM can inc ease he accu acy o EBV o uni o m-
i y subs an ially compa ed o pedig ee-based BLUP.
Howe e , a e accoun ing o scaling e ec s by using
log ans o ma ions, he use o
H
compa ed o
A
only
sligh ly imp o ed he co ela ion (1.6 o 13.9%) and
MSEP be ween GEBV and adjus ed pheno ypes, and he
imp o emen was no signi ican . The e a e wo main
easons why hese esul s di e ed be ween uni o mi y
o s dWT and lnWT. Fi s , log- ans o ma ion subs an-
ially educed he gene ic co ela ion o s dWT wi h i s
uni o mi y. As a esul , any inc eases in p edic i e abil-
i y o GEBV o lnWT when using
H
ins ead o
A
(15.7%)
did no posi i ely in luence he p edic i e abili y o GEBV
o i s uni o mi y. Second, he lowe addi i e gene ic
a iance and
h2
o uni o mi y a e accoun ing o scale
e ec s educes he accu acy o EBV o uni o mi y. Con-
sequen ly, MSEP inc eased om 0.63 (s dWT) o 0.94
(lnWT) wi h
A
and om 0.61 (s dWT) o 0.94 (lnWT)
wi h
H
in he animal DHGLM.
The accu acy o genomic selec ion is expec ed o
inc ease when he numbe o geno yped animals in he
e e ence popula ion inc eases o any ai [46] bu in
pa icula o lowly he i able ai s, such as uni o mi y as
shown by Sell-Kubiak e al. [42] and soma ic cell sco e by
Mulde e al. [43]. In his s udy, uni o mi y o lnWT had
an e en lowe
h2
han uni o mi y o s dWT. The numbe
o geno yped animals in he e e ence popula ion used
o c oss- alida ion was on a e age equal o 1274, which
may ha e limi ed he bene i o using genomic in o ma-
ion in ssGBLUP. A u u e empi ical s udy should in es-
iga e he e ec o he numbe o geno yped animals in
he e e ence popula ion on he abili y o p edic b eed-
ing alues o uni o mi y o alida e ou indings and
conclusions.
Pea son o ank co ela ions?
Squa ed esiduals o adjus ed pheno ype o uni o mi y
(
ψ∗
i)
a e exponen ially a he han no mally dis ibu ed,
which may no jus i y quan i ying p edic i e abili y using
a Pea son co ela ion. Thus, we also calcula ed dis ibu-
ion- ee ank co ela ions (Kendall and Spea man) and
indeed ound es ima ion o he p edic i e abili y o uni-
o mi y o be sensi i e o he ype o co ela ion used.
Al hough no signi ican ly di e en , Kendall and Spea -
man co ela ions explained di e ences in p edic i e abili y
o EBV and GEBV o uni o mi y o lnWT sligh ly be e
han he Pea son co ela ion. Hence, he conclusion ha
he bene i o using genomic ela ionship o compu ing
EBV o uni o mi y o loga i hm ans o ma ions is lim-
i ed emained he same when using Kendall and Spea -
man co ela ions. Colwel and Gille [47] showed ha , in
gene al, es ima es o Kendall co ela ions a e simila o
es ima es o Spea man co ela ions, bu in some cases, he
magni ude o Spea man co ela ions can be 50% g ea e
han he magni ude o Kendall co ela ions [47]. This is in
line wi h ou indings since Spea man co ela ions we e
42.2 o49.0% and 39.1 o46.1% g ea e han Kendall co -
ela ions o he si e-dam DHGLM (see Addi ional ile2:
Table S1) and he animal DHGLM, espec i ely. Ne e he-
less, he SE o Kendall co ela ions we e no ably lowe by
app oxima ely 50% han he SE o Pea son and Spea man
co ela ions, which indica es ha he Kendall co ela ion
may be a mo e eliable es ima e o p edic i e abili y han
he Pea son and Spea man co ela ions. Hence, i is ec-
ommended o use Kendall ins ead o Pea son co ela ions
when s udying p edic i e abili y o uni o mi y.