Increased Prediction Ability in Norway Spruce Trials Using a Marker X Environment Interaction and Non-Additive Genomic Selection Model

Abstract

A genomic selection (GS) study of growth and wood quality traits is reported based on control-pollinated Norway spruce families established in two Northern Swedish trials at two locations using exome capture as a genotyping platform. Non-additive effects including dominance and first-order epistatic interactions (including additive-by-additive, dominance-by-dominance, and additive-by-dominance) and marker-by-environment interaction (M×E) effects were dissected in genomic and phenotypic selection models. GS models partitioned additive and non-additive genetic variances more precisely than pedigree-based models. In addition, predictive ability (PA) in GS was substantially increased by including dominance and slightly increased by including M×E effects when these effects are significant. For velocity, response to GS (RGS) per year increased 78.9/80.8%, 86.9/82.9%, and 91.3/88.2% compared with response to phenotypic selection (RPS) per year when GS was based on 1) main marker effects (M), 2) M + M×E effects (A), and 3) A + dominance effects (AD) for sites 1 and 2, respectively. This indicates that including M×E and dominance effects not only improves genetic parameter estimates but also when they are significant may improve the genetic gain. For tree height, Pilodyn, and modulus of elasticity (MOE), RGS per year improved up to 68.9%, 91.3%, and 92.6% compared with RPS per year, respectively.

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830
Journal of Heredity, 2019, 830–843
doi:10.1093/jhered/esz061
Original Article
Advance Access publication October 20, 2019
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/),
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© The American Genetic Association 2019.
Original Article
Increased Prediction Ability in Norway Spruce
Trials Using a Marker X Environment Interaction
and Non-Additive Genomic SelectionModel
Zhi-Qiang Chen, John Baison, Jin Pan, Johan Westin,
MariaRosarioGarcía Gil, and HarryX. Wu
From the Umeå Plant Science Centre, Department of Forest Genetics and Plant Physiology, Swedish University of
Agricultural Sciences, SE-90183 Umeå, Sweden (Chen, Baison, Pan, Gil and Wu); Skogforsk, Box 3, SE-918 21 Sävar,
Sweden (Westin); Beijing Advanced Innovation Centre for Tree Breeding by Molecular Design, Beijing Forestry
University, Beijing, China(Wu); CSIRO National Collection Research Australia, Black Mountain Laboratory, Canberra,
ACT 2601, Australia (Wu).
Address correspondence to Harry X.Wu at the address above, or e-mail: Harry.wu@slu.se and Harry.wu@csiro.au
Received December 28, 2018; First decision July 11, 2019; Accepted October 15, 2019.
Corresponding Editor: John R.Stommel
Abstract
A genomic selection study of growth and wood quality traits is reported based on control-
pollinated Norway spruce families established in 2 Northern Swedish trials at 2 locations using
exome capture as a genotyping platform. Nonadditive effects including dominance and first-order
epistatic interactions (including additive-by-additive, dominance-by-dominance, and additive-by-
dominance) and marker-by-environment interaction (M×E) effects were dissected in genomic and
phenotypic selection models. Genomic selection models partitioned additive and nonadditive
genetic variances more precisely than pedigree-based models. In addition, predictive ability in
GS was substantially increased by including dominance and slightly increased by including M×E
effects when these effects are significant. For velocity, response to genomic selection per year
increased up to 78.9/80.8%, 86.9/82.9%, and 91.3/88.2% compared with response to phenotypic
selection per year when genomic selection was based on 1)main marker effects (M), 2)M + M×E
effects (A), and 3)A + dominance effects (AD) for sites 1 and 2, respectively. This indicates that
including M×E and dominance effects not only improves genetic parameter estimates but also
when they are significant may improve the genetic gain. For tree height, Pilodyn, and modulus of
elasticity (MOE), response to genomic selection per year improved up to 68.9%, 91.3%, and 92.6%
compared with response to phenotypic selection per year, respectively.
Subject Area: Quantitative genetics and Mendelian inheritance
Keywords: dominance, epistasis, exome capture, Picea abies (L.) Karst
Genomic selection (GS) is a breeding method that uses a dense set of
genetic markers to accurately predict the genetic merit of individuals
(Meuwissen etal. 2001) and it has been incorporated into animal
breeding for many years (Van Eenennaam etal. 2014). Simulated
studies have also shown that including dominance could increase
the predictive ability (PA) (Nishio and Satoh 2014) and result in
a higher genetic gain in crossbred population when the dominance
variance and heterosis are large and over-dominance is present
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(Zeng etal. 2013). In livestock, accounting for dominance in GS has
improved genomic evaluations of dairy cows for fertility and milk
production traits (Aliloo etal. 2016). In tree species, GS studies have
been implemented in several breeding programs, but these studies
mostly focused on additive effects in several commercially important
conifer species, such as loblolly pine (Pinus taeda L.), maritime pine
(Pinus pinaster Ait.), Norway spruce (Picea abies (L.) Karst.), white
spruce (Picea glauca (Moench) Voss) and hardwood eucalypt species
(Resende etal. 2012a, 2012b; Tan etal. 2017; Chen etal. 2018). The
nonadditive contributions have also been estimated in several studies
(Muñoz etal. 2014; Bouvet etal. 2016; de Almeida Filho etal. 2016;
Gamal El-Dien etal. 2016; Tan etal. 2018).
Several recent studies show dominance and epistasis may be con-
founded with the additive effects in both pedigree-based relationship
matrix models (Gamal El-Dien et al. 2018) and genomic-based rela-
tionship matrix models (Tan etal. 2018). In the conventional pedigree-
based genetic analysis, estimates of different genetic components such as
additive, dominance, and epistatic variances need full-sib family struc-
ture or full-sib family structure plus clonally replicated tests (Mullin and
Park 1992). For most tree species, only a few reliable estimates for the
nonadditive variation have been reported based on pedigree-based rela-
tionship (Isik etal. 2003, 2005; Baltunis etal. 2007; Weng etal. 2008;
Wu etal. 2008), especially for wood quality traits (Wu 2018).
Signicant genotype-by-environment (G×E) interaction is com-
monly observed among the different deployment zones for growth
traits in Norway spruce (Kroon etal. 2011; Chen etal. 2014, 2017).
Literature also supports the importance of predicting nonadditive
effects including dominance and epistasis in tree breeding (Wu
etal. 2016) and in clonal forestry programs (Wu 2018). In a pre-
vious study (Chen et al. 2018), we used 2 full-sib family trials to
study GS efciency based on additive effects and different sampling
strategies. Here, we extend our study to examine nonadditive gen-
etic effects using the genomic matrix and to explore marker-by-
environment interaction (M×E) effects on GS. The aims of the study
were to 1)estimate and compare the nonadditive genetic variances
estimated from the average numerator relationship A-matrix (i.e. the
expected theoretical relationships) and the realized genomic rela-
tionship G-matrix (i.e. the observed relationships); 2)evaluate the
PA of different M×E models; 3)assess the PA of the models including
nonadditive effects; 4)evaluate change in the ranking of breeding
values when models include the nonadditive and M×E effects; and
5)assess genetic gain per year when M×E and dominance effects are
included in the GS and phenotypic selection (PS) models.
Materials and Methods
Sampling of Plant Material and Genotyping
In all, 1,370 individuals were selected from two 28-year-old control-
pollinated (full-sib) progeny trials. The progeny trials consist of the
same 128 families generated through a partial diallel mating design
involving 55 parents originating from Northern Sweden. Progenies
were raised in the nursery for 1year at Sävar, and the trials were
established in 1988 by Skogforsk in Vindeln (64.30°N, 19.67°E, alti-
tude: 325 m) and in Hädanberg (63.58°N, 18.19°E, altitude: 240m).
A completely randomized design without designed pre-blocking
was used in the Vindeln trial (site 1), which was divided into 44
post-blocks based on the terrain. Each rectangular block has 60 trees
(6×10) with expected 60 families at a spacing of 1.5 m × 2.0 m.The
same design was also used in the Hädanberg trial (site 2)with 44
post-blocks. But for the purpose of demonstration, there was an
extra block with 47 plots, each plot with 16 trees (4×4) planted in
site 2.Based on the spatial analysis, in the nal model, the 47 plots
were combined into 2 big post-blocks.
Phenotyping
The tree height was measured in 2003 at the age of 17years. Solid-
wood quality traits including Pilodyn penetration (Pilodyn) and
acoustic velocity (velocity) were measured in October 2016. Pilodyn
penetration, a surrogate for the trait of wood density, was meas-
ured using a Pilodyn 6J Forest (PROCEQ, Zurich, Switzerland)
with a 2.0mm diameter pin, without removing the bark. Velocity,
closely related to microbril angle (MFA) in Norway spruce (Chen
et al. 2015), was determined using a Hitman ST300 (Fiber-gen,
Christchurch, New Zealand). By combining the Pilodyn and velocity
data, indirect modulus of elasticity (MOE) was estimated using the
equation developed in the study by Chen etal. (2015).
Genotyping
Buds and the rst-year fresh needles from 1370 control-pollinated pro-
geny trees and their 46 unrelated parents were sampled and genotyped
using the Qiagen Plant DNA extraction protocol (Qiagen, Hilden,
Germany) and DNA quantication was undertaken using the Qubit®
ds DNA Broad Range Assay Kit (Oregon, USA). The 46 parents were
sampled in a grafted archive at Skogforsk, Sävar (63.89°N, 20.54°E)
and in a grafted seed orchard at Hjssjö (63.93°N, 20.15°E). Probe
design and evaluation are described by Vidalis etal. (2018). Sequence
capture was performed using the 40 018 probes previously designed
and evaluated for the material (Vidalis etal. 2018) and samples were
sequenced to an average depth of 15x on an Illumina HiSeq 2500
platform. The details of SNPs calling, ltering, quality control, and
imputation for these data can be found in Chen etal. (2018). Finally,
116,765 SNPs were kept for downstream analysis.
Variance Component and HeritabilityModels
The variance components and breeding values (BVs) for the geno-
types of each trait in the 2 trials were estimated by using the best
linear unbiased prediction (BLUP) method in 3 univariate models
that included either additive (A), both additive and dominance (AD)
or additive, dominance, and epistasis genetic effects (ADE) as men-
tioned below. In practice, pedigree-based models (ABLUP) had only
2 models because it is not possible to estimate the epistatic effect in
full-sib progeny trials without replicates for each genotype.
Pedigree-Based and Genomic-BasedModels
Five models were used to partition the genetic variance into additive,
dominance, and epistatic variances.
For the pedigree-based model with additive effect only (ABLUP-A):
y=Xβ+Wb+Za+ε
(1)
For the full pedigree-based model with both additive and dominance
effects (ABLUP-AD):
y=Xβ+Wb+Za+Z1d+ε
(2)
For the genomic-based model with additive effect only (GBLUP-A):
y=Xβ+fi+Wb+Z2a1+ε
(3)
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For the genomic-based model with both additive and dominance ef-
fects (GBLUP-AD):
y
=
X
β+
fi
+
Wb
+
Z2a1
+
Z3d1
+
ε
(4)
For the full genomic-based model with additive, dominance, and epi-
static effects (GBLUP-ADE):
y=Xβ+fi+Wb+Z2a1+Z3d1+Z4eaa +Z5ead +Z6edd +ε
(5)
where y is the vector of phenotypic observations of a single trait;
β
is the vector of xed effects, including a grand mean and site effects,
i is the inbreeding depression parameter per unit of inbreeding, b is
the vector of random post-block within site effects,
a
and
a1
are the
vectors of random additive effects in ABLUP and GBLUP models,
respectively, d and
d1
are the vectors of random dominance effects in
equations [2], [4], and [5], respectively,
eaa,ead ,and edd
are the vec-
tors of the random additive-by-additive epistatic effects, additive-by-
dominance epistatic effects, and dominance-by-dominance epistatic
effects in equation (5),
ε
is the random residual effect. X, W, Z, Z1,
Z2, Z3, Z4, Z1, and Z6 are the incidence matrices for
β
,
b
, a,
d
,
a1
,
d1
,
eaa
,
ead
, and
edd
, respectively. f is a vector of genomic inbreeding co-
efcients based on the proportion of homozygous SNPs. Although
Xiang etal. (2016) and Vitezica etal. (2013) proved that including
genomic inbreeding as a covariate is necessary to obtain correct es-
timates of dominance and epistatic variances, the inbreeding depres-
sion term () in equation (3–5) were excluded in the nal model
because it is not signicant for all the traits. The random post-block
effects (
b
) were assumed tofollow
b
∼N
Ç
0,
ñ
σ
2
b1
0
0σ2
b2ô
⊗I
å,
where I is the identity matrix,
σ2
b1
and
σ2
b1
are the variance compo-
nents of random post-block in site 1 and site 2, respectively, and
⊗
is
the Kronecker product operator. The random additive effects (
a
) in
equations (1) and (2) were assumed to follow
a∼N(0, VCOVa⊗A)
,
where A is the pedigree-based additive genetic relationship matrix
and
VCOVa
is the general case of additive variance and covariance
structure in Table 1. The random dominance effects (d) in equa-
tion [2] were assumed to follow
d∼N(0, VCOVd⊗D)
, where D
is the pedigree-based dominance relationship matrix and
VCOVd
is the general case of dominance variance and covariance struc-
ture. The
a1
in equations (3–5) is the vector of random additive ef-
fects in genomic-based models, following
a1∼N(0, VCOVa⊗Ga)
,
where
Ga
is the genomic-based additive genetic relationship matrix,
VCOVa
is the general case of additive variance and covariance
structure in Table 1. The
d1
in equations (4) and (5) is the vector
of random dominance effects following
d1∼N(0, VCOVd⊗Gd)
,
where
Gd
is the genomic-based dominance genetic relationship
matrix,
VCOVd
is the general case of dominance variance and co-
variance structure in Table 1. The
eaa,ead , and edd
are the vectors
of the random additive-by-additive epistatic effects, additive-by-
dominance epistatic effects, and dominance-by-dominance epi-
static effects following
eaa ∼N
(
0, Gaa
σ
2
aa)
,
e
ad
∼N
(
0, G
adσ
2
ad)
,
and
e
dd
∼N
(
0, G
ddσ
2
dd)
, respectively.
Gaa
,
Gad
, and
Gdd
are the
genomic-based additive-by-additive, additive-by-dominance, and
dominance-by-dominance epistatic relationship matrices, respect-
ively. The residual e was assumed to follow
ε∼N
Ç
0,
ñI
n1σ
2
e1
0
0I
n2σ2
e2ôå,
where
σ2
e1
and
σ2
e2
are the residual variances for site 1 and site 2,
respectively,
In1
and
In2
are identity matrices, and n1 and n2 are the
number of individuals at each site. In theory, all variance–covariance
structures in Table 1 could be used for additive, dominance, and epi-
static effects in equations (1)–(5).
The pedigree-based additive (A) and dominance (D) rela-
tionship matrices were constructed based on information from
pedigrees. The diagonal elements (i) of the A were calculated as
A
ii
=1+f
i
=1+Agh/2
, where
g
and
h
are the
i
th individual’s
parents, while the off-diagonal element is the relationship between
individuals
i
th and
j
th calculated as
A
ij
=A
ji
=(A
jg
+Ajh)/2
(Mrode and Thompson 2005). In the D matrix, the diagnonal
elements were all one (
Dii =1
), while the off-diagonal elem-
ents between the individual ith and jth can be calculated as
D
ij
=(Agk Ahl +AglAhk)/4
, where g and h are the parents of the
ith individual and k and l are the parents of the jth individual.
A relationship matrix was produced using ASReml 4.1 (Gilmour
etal. 2015) or ASReml-R package (Butler etal. 2009). AD rela-
tionship matrix was produced using kin function in the synbreed
package in R (Wimmer etal. 2012).
The genomic-based additive (
Ga
) and dominance (
Gd
) relation-
ship matrices were constructed based on genome-wide exome cap-
ture data as described by VanRaden (2008) for
Ga
and by Vitezica
etal. (2013) for
Gd
:
G
a=
ZZ

m
j=1
2piqi
G
d=
WW 

m
i=1(
2p
i
q
i)2
where
m
is the total number of SNPs; the elements of Z are equal
to
−2pi
,
qi−pi
, and
2qi
for aa, Aa, and AA genotypes, respectively,
with
pi
and
qi
being the allele frequency of A and a alleles at marker
i
in the population. For the dominance matrix
Gd
, aa, Aa, and AA
genotypes in
W
were coded as
−2p2
i
,
2piqi
, and
−2q2
i
, respectively.
Based on the paper of Vitezica etal. (2013), the method guarantees
Table 1. Six variance and covariance structures examined for the
additive, dominance, and epistatic effects in 2 pedigree-based
models and 3 genomic-based models.
Structure No. of
parameters
Description
IDEN 1 Identity
DIAG n Diagonal
CS 2 Compound symmetry
CS+DIAG 1+ nCompound symmetry with
heterogeneous variance
US n(n + 1)/2 Unstructured
FAMK 1+ (k + 1)nFactor analytic with the main
marker/genetic term and k factors
n is the number of sites. k is the number of factors.
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the absence of confounding between
Ga
and
Gd
and could be directly
compared to the pedigree-based A and D.
The relationship matrices due to the rst-order epistatic inter-
actions were computed using the Hadamard product (cell by cell
multiplication, denoted #) and trace (tr) (Vitezica etal. 2013). In
the pedigree-based model, the additive-by-additive terms are cal-
culated as
Paa = [(A#A)/(tr(A#A)/n)]
, additive-by-dominance
terms as
Pad = [(A#D)/(tr(A#D)/n)]
, and dominance-by-
dominance terms as
Pdd = [(D#D)/(tr(D#D)/n)]
. In genomic-
based relationship matrix models: additive-by-additive terms
are Gaa = [(Ga#Ga)/(tr(Ga#Ga)/n)]
, additive-by-dominance
terms are
Gad = [(Ga#Gd)/(tr(Ga#Gd)/n)]
, and dominance-by-
dominance terms are
Gdd = [(Gd#Gd)/(tr(Ga#Gd)/n)]
.
Different Variance–Covariance Structures
To partition, predict, and validate G×E interactions in additive (a),
dominance (d), epistatic effects (
eaa
,
ead
, and
edd)
, 6 types of the dif-
ferent variance and covariance structures (Table 1) including: 1)iden-
tity (IDEN), 2) diagonal (DIAG), 3) compound symmetry (CS),
4) compound symmetry with heterogeneous variance (CS+DIAG),
5)unstructured (US), and 6)factor analytic with the main marker/
genetic term and k factors (FAMK), could be tted for any of the
additive, dominance, and epistasis effects in equation (1)–(5). The
CS+DIAG, US, and FAMK structures are the same in any two-sites
multi-environment trial (MET) model (Oakey et al. 2016), except
that the models may have a slightly convergent difference. When
MET models with more than 2 sites were used, the models with
FAMK structure may be better than those with CS+DIAG and US
(Oakey etal. 2016). We therefore presented only the FAMK model
in the latter. The additive variance–covariance structures of IDEN,
DIAG, CS, and FAMK are, , respectively,
ñ
σ
2
a
0
0σ2
aô
,
ñ
σ
2
a1
0
0σ2
a2ô
,
ñ
σ
2
aσa12
σa21 σ2
aô
, and
ñ
σ
2
a1σa12
σa12 σ2
a2ô
The dominance variance structures of IDEN, DIAG, CS, and FAMK
are , respectively,
ñ
σ
2
d
0
0σ2
dô
,
ñ
σ
2
d1
0
0σ2
d2ô
,
ñ
σ
2
dσd12
σd21 σ2
dô
, and
ñ
σ
2
d1σd12
σd12 σ2
d2ô
In this study, the result of epistasis effects is shown only with the
variance and covariance structure IDEN because of the small
amount of the total genetic variance.
σ2
a
and
σ2
d
are the additive and
dominance variances if homogenous variance structures were used.
σ2
a1
,
σ2
a2
, and
σa12
are the additive variances for site 1, site 2 and the
additive covariance between sites 1 and 2, respectively.
σ2
d1
,
σ2
d2
, and
σd12
are dominance variances for site 1, site 2 and dominance covari-
ance between sites 1 and2.
Heritability
Under the above models, the narrow-sense heritability can
be estimated as
h2
=σ
2
a
/σ
2
p
, the dominance to total variance
ratio as
d2
=σ
2
d
/σ
2
p
, the epistatic to the total variance ratio as
i2
=σ
2
i
/σ
2
p
and the broad-sense heritability as
H2
=σ
2
g
/σ
2
p
, where
σ2
g=σ
2
a+σ
2
d
+σ
2
aa +σ
2
ad
+σ
2
dd
and
σ2
i=
σ2
aa
+σ
2
ad
+σ
2
dd
. Broad-
sense heritability for the ABLUP-AD model was estimated as
H2
=(σ
2
a
+σ
2
d
)/σ
2
p
as epistatic effects could not be estimated.
To partition and Predict Gxe Interaction and Dominance in
Cross-Validation
To compare the predictive ability of models with and without a G×E
interaction term in additive effects, a single-site model without speci-
fying the G×E interaction (i.e. ABLUP-AD and GBLUP-AD with DIAG
structure for additive + IDEN for dominance) and a MET model (i.e.
ABLUP-AD and GBLUP-AD with CS/FAMK for additive + IDEN for
dominance) were used. Based on the model comparison, CS were used
for additive effects of Pilodyn, velocity, and MOE and FAMK were
used for additive effects of tree height. In the MET models, additive
effect a/
a1
in all equations [1–5] could be described as
a=m+me
,
where m is the additive main marker/genetic effect (M), and me is
the additive main marker-by-environment effect. Therefore, with CS
and FAMK structures, the main marker effect (M), M + marker-by-
environment interaction effect (A), and A+ dominance effect (AD)
from the GBLUP-AD and ABLUP-AD models could be estimated. In
the CS model, m is the main term for markers and
me
is an interaction
term for the markers and trials. All trials have the same marker vari-
ance and all pairs of trials have the same marker covariance, so that
the
var(a)= var(m)+var(me)
. AFAMK model is equivalent to a
factor analytic model with (K+1) factors, where the rst set of load-
ings are constrained to equal.
Var (a)= var(m)+ΛΛ
T+Ψ
, where
Λ
is a matrix of loadings and Ψ is a diagonal matrix with diagonal elem-
ents referred to as specic variances. In two-trial analyses, K=0, then
var(a)= var(m)+ Ψ
, which is equivalent to the CS+DIAG model
(Table 1 and Oakey etal. (2016))
Model Comparison
To compare the relative quality of the goodness-of-t of the different
models, the Akaike Information Criterion (AIC) and the tted line
plot (graph of predicted
ˆ
y
vs. adjusted y values) were used for the
linear mixed-effects models (LMM) for all traits, while the standard
error of the predictions (SEPs) of the trait BVs was used to assess the
precision of the BVs.
Cross-validation
A 10-fold cross-validation scenario with 10 replications was used to
assess accuracy and prediction ability (PA).
Expected Performance of Genomic Selection
The expected performance of GS compared to standard phenotypic
selection (PS) was evaluated only for the GBLUP-AD model by cal-
culating the response to genomic selection (RGS) as a percentage of
the population average as follows:
RGS
(%)=
EGV
Gs −
EGV
o
EGVo
×
100
where
EGVGs
is the average of expected genetic values estimated
from the ABLUP-AD model (equation [2]) for the selected portion of
the population based on 1)main marker effects (M), 2)M + marker-
by-environment interaction effects (A), and 3)A+ dominance effects
(AD) for site 1/site 2 estimated from GBLUP-AD model (equation
[4]), respectively, and
EGVo
is the population average (Resende etal.
2017). Response to phenotypic selection (RPS) as a percentage of the
population average is as follows:
RPS
(%) =
EGV
As −
EGV
o
EGVo
×
100
Journal of Heredity, 2019, Vol. 110, No. 7 833
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where
EGVAs
is the average of expected genetic values estimated
from the ABLUP-AD model (equation [2]) for the selected portion
of the population based on AD effects from the ABLUP-AD model.
For different traits, ABLUP-AD and GBLUP-AD models with the
best-tting variance–covariance structures for additive and domin-
ance variances were used (Table 2), except for Pilodyn data with CS
for additive effects in order to permit comparison with ABLUP-AD
results. The main advantage of using GS is that it permits a shorter
breeding cycle. Thus, here we used RGS (%)/year and RPS (%)/year
to compare the expected performances of GS and PS. In the Swedish
Norway spruce breeding program, the traditional breeding cycle is
at least 25years long. If GS could be used as at a very early selection
stage, the breeding cycle could be reduced to ca. 12.5years (Chen
etal. 2018).
Results
Genetic Variance Components and Heritability
Estimates
The 6 variance and covariance structures examined for the addi-
tive, dominance, and epistatic effects are presented in Table 1. The
log-likelihood, Akaike Information Criterion (AIC), and Bayesian
Information Criterion (BIC) for the 5 models (ABLUP-A, ABLUP-AD,
GBLUP-A, GBLUP-AD, and GBLUP-ADE) under various vari-
ance structures are shown in the Supplementary Material, Table
S1. The models with the best tted variance–covariance structures
under ABLUP and GBLUP for additive variance only, additive plus
dominance variance or additive plus dominance and epistasis (e.g.
ABLUP-A, ABLUP-AD, GBLUP-A, GBLUP-AD, and GBLUP-ADE)
are listed in Table 2. These were used to estimate the variance com-
ponents (Table 3–5, Figure 1–2, except for Pilodyn with CS for
additive effects and IDEN for dominance effects from GBLUP-A,
GBLUP-AD, and GBLUP-ADE models). These models were included
because we wanted to use the same variance–covariance structure to
compare with the results from ABLUP-A and ABLUP-AD models for
Pilodyn data (Table 2).
M×E effects for the additive or nonadditive effects were con-
sidered signicant if the AIC values in MET analyses (e.g. under CS
and FAMK variance structures) were smaller than the corresponding
AIC values in single site (ST) analyses (e.g. under IDEN or DIAG
variance structure only) for the same trait or if the Log-likelihood
Ratio test (LRT) was signicant. All models with CS for additive gen-
etic effects were found performing best, except for the model with
FAMK for tree height additive genetic effects (Table 2). Based on this
criterion, all 4 traits showed signicant additive M×E effects, except
for the Pilodyn trait under GBLUP models. However, additive-by-
environment variance in site 1 from ABLUP-AD with FAMK was not
signicant (Table 3, 606.7) when assessed on the AIC. For the dom-
inance effect, however, only the tree height with IDEN and velocity
with DIAG structure had signicant effects: therefore, there was no
signicant M×E for a dominance effect of any trait. For epistasis,
there was no signicant effect on anytrait.
Estimates of variance components, their standard errors (SE),
and the variance proportion of each site for tree height and velocity
from the 5 genetic models tted (ABLUP-A, ABLUP-AD, GBLUP-A,
GBLUP-AD, and GBLUP-ADE) are shown in Table 3 and the re-
sults of Pilodyn and MOE are shown in Table S2. Block variance
components (
σ2
b
) for each site were almost consistent across the 5
models for all traits (Table 3 and Table S2). For example,
σ2
b
for
tree height accounted for 10.4%−12.9% and 14.9%−15.6% for
sites 1 and 2, respectively. For tree height, the main difference be-
tween the ABLUP-A and GBLUP-A models was the substantial
Table 2. Summary of 5 models (2 ABLUP and 3 GBLUP models) with various variance and covariance structures fitted to the full data set
for tree height, Pilodyn, velocity, andMOE
Trait Model Variance structure Log-likelihood AIC No.
Additive Dominance Epistasis
Height ABLUP-A FAMK −6873.47 13760.95 7
ABLUP-AD FAMK DIAG −6868.92 13755.85 9
GBLUP-A FAMK −6874.05 13762.10 7
GBLUP-AD FAMK IDEN −6870.21 13756.42 8
GBLUP-ADE FAMK IDEN IDEN-G3* −6870.21 13762.42 11
Pilodyn ABLUP-A CS −1727.77 3467.55 6
ABLUP-AD CS IDEN −1727.77 3469.55 7
GBLUP-A IDEN −1737.44 3484.88 5
GBLUP-AD IDEN DIAG −1735.87 3485.74 7
GBLUP-ADE IDEN IDEN IDEN-G3* −1736.77 3493.54 10
Velocity ABLUP-A CS 1192.66 −2373.33 6
ABLUP-AD CS IDEN 1194.59 −2375.19 7
GBLUP-A CS 1183.37 −2354.73 6
GBLUP-AD CS IDEN 1184.63 −2355.26 7
GBLUP-ADE CS IDEN IDEN-G3* 1184.66 −2349.32 10
MOE ABLUP-A CS −2347.46 4706.92 6
ABLUP-AD CS IDEN −2347.46 4708.92 7
GBLUP-A CS −2357.84 4727.67 6
GBLUP-AD CS IDEN −2357.84 4729.67 7
GBLUP-ADE CS IDEN IDEN-G3* −2357.84 4735.67 10
Variance and covariance structures: IDEN, identity; DIAG, diagonal; CS, compound symmetry; FAMK, factor analytic with the main marker/genetic term and
k factors. * G3 represents GBLUP-ADE model including 3 rst order epistatic effects (the random additive-by-additive epistatic effects, additive-by-dominance
epistatic effects, and dominance-by-dominance epistatic effects). No. is the number of variance parameters. Bold means the best model in GBLUP or ABLUP.
834 Journal of Heredity, 2019, Vol. 110, No. 7
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Table 3. Estimates of variance components (VC), their standard errors (SE) and the variance proportion of each site for tree height and velocity from the 5 genetic models fitted (ABLUP-A,
ABLUP-AD, GBLUP-A, GBLUP-AD, and GBLUP-ADE)
Trait VC ABLUP-A ABLUP-AD GBLUP-A GBLUP-AD GBLUP-ADE
Value (SE) % Value (SE) % Value (SE) % Value (SE) % Value (SE) %
Height
σ2
b1
815.5 (330.2) 12.1 804.0 (326.8) 11.9 772.4 (317.8) 11.5 703.1 (296.7) 10.4 703.1 (296.7) 10.4
σ2
b
2
1962.0 (655.8) 15.6 1863.3 (627.4) 14.9 1916.2 (643.0) 15.3 1918.6 (643.8) 15.3 1918.6 (643.8) 15.3
σ2
a1
690.8 (368.4) 10.2 606.7 (392.1) 9.0 902.2 (395.4) 13.4 778.0 (407.2) 11.5 778.0 (407.2) 11.5
σ2
a12
565.9 (374.6) 571.2 (368.5) 573.1 (406.4) 463.4 (409.6) 463.4 (409.6)
σ2
a2
2007.1 (717.5) 16.0 1371.5 (741.0) 11.0 2140.6 (736.4) 17.1 1858.7 (724.3) 14.8 1858.7 (724.3) 14.8
σ2
d1
572.2 (925.7) 8.5 1224.1 (566.7) 18.1 1224.1 (566.7) 18.1
σ2
d2
2881.9 (1443.9) 23.1 1224.1 (566.7) 9.8 1224.1 (566.7) 9.8
σ2
aa
0.00 (0.00) 0.0
σ2
ad
0.00 (0.00) 0.0
σ2
dd
0.00 (0.00) 0.0
σ2
e1
5260.5 (421.9) 77.7 4777.6 (862.6) 70.7 5064.1 (416.8) 75.1 4053.3 (572.4) 60.0 4053.28 (572.5) 60.0
σ2
e2
8604.5 (640.7) 68.4 6353.1 (1208.3) 50.9 8461.8 (679.1) 67.6 7523.9 (770.0) 60.1 7523.86 (770.1) 60.1
h2
1
0.12 (0.06) 0.10 (0.06) 0.15 (0.06) 0.13 (0.06) 0.13 (0.06)
h2
2
0.19 (0.06) 0.14 (0.07) 0.20 (0.06) 0.18 (0.06) 0.18 (0.06)
H2
1
0.20 (0.14) 0.33 (0.09) 0.33 (0.09)
H2
2
0.40 (0.12) 0.29 (0.07) 0.30 (0.07)
Velocity
σ2
b1
0.0018 (0.0013) 2.4 0.0019 (0.1355) 2.4 0.0013 (0.0011) 1.8 0.0014 (0.0011) 2.0 0.0014 (0.0011) 2.0
σ2
b
2
0.0036 (0.0018) 4.6 0.0034 (0.2356) 4.1 0.0033 (0.0017) 4.4 0.0034 (0.0017) 4.5 0.0034 (0.0017) 4.5
σ2
a1
0.0365 (0.0087) 48.1 0.0343 (0.0087) 42.0 0.0305 (0.0051) 42.4 0.0290 (0.0052) 40.3 0.0282 (0.0065) 39.1
σ2
a12
0.0320 (0.0086) 0.0293 (0.0087) 0.0241 (0.0051) 0.0224 (0.0052) 0.0215 (0.0066)
σ2
a2
0.0365 (0.0087) 46.8 0.0343 (0.0087) 40.9 0.0305 (0.0051) 40.3 0.0290 (0.0052) 38.3 0.0282 (0.0065) 37.2
σ2
d1
0.0081 (0.0051) 9.9 0.0067 (0.0046) 9.3 0.0051 (0.0071) 7.1
σ2
d2
0.0081 (0.0051) 9.6 0.0067 (0.0046) 8.8 0.0051 (0.0071) 6.8
σ2
aa
0.0030 (0.0152) 4.2/4.0
σ2
ad
0 (0) 0
σ2
dd
0.0005 (0.0108) 0.7/0.7
σ2
e1
0.0376 (0.0057) 49.5 0.0373 (0.0057) 45.7 0.0402 (0.0042) 55.8 0.0349 (0.0052) 48.4 0.0336 (0.0077) 46.7
σ2
e2
0.0379 (0.0053) 48.6 0.0381 (0.0053) 45.4 0.0418 (0.0040) 55.3 0.0367 (0.0050) 48.4 0.0355 (0.0079) 48.1
h2
1
0.43 (0.10) 0.40 (0.10) 0.34 (0.06) 0.32 (0.07) 0.31 (0.09)
h2
2
0.43 (0.09) 0.39 (0.10) 0.33 (0.06) 0.31 (0.07) 0.30 (0.09)
H2
1
0.51 (0.10) 0.41 (0.08) 0.43 (0.11)
H2
2
0.50 (0.10) 0.40 (0.08) 0.42 (0.11)
Note:
σ2
b1
and
σ2
b2
. are the block variance for site 1 and site 2.
σ2
a1
σ2
a2
, and
σa12
are the additive variances for site 1, site 2, and additive covariance between site 1 and site 2, respectively.
σ2
d1
σ2
d2
, and
σd12
are the dominance
variances for site 1, site 2, and dominance covariance between site 1 and site 2.
σ2
aa
,
σ2
ad
, and
σ2
dd
are the additive × additive epistatic variance, additive × dominance epistatic variance, and dominance × dominance epistatic
variances, respectively.
σ2
e1
and
σ2
e2
are the residual variances for site 1 and site 2, respectively.
h2
1
and
h2
2
are the narrow-sense heritability for site 1 and site 2, respectively.
H2
1
and
H2
2
are the broad-sense heritability for site
1 and site 2, respectively.
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increase of the additive variance (σ
2
a
) (Table 3), in contrast to re-
sults for wood quality traits. For example, tree height additive vari-
ances
σ2
a
s estimated from GBLUP-A were 130.6% and 106.7% of
the ABLUP-A
σ2
a
s at site 1 and site 2, respectively. However, Pilodyn
and velocity additive variances σ
2
a
s estimated from GBLUP-A aver-
aged 77.8% and 83.6% of the ABLUP-A
σ2
a
s for both sites. The tree
heights
σ2
a
s estimated from GBLUP-AD were also larger than those
from ABLUP-AD for both sites. In contrast, wood quality traits
σ2
a
s estimated from GBLUP-AD were also smaller than those from
ABLUP-AD for both sites. For tree height and velocity, the main dif-
ferences between ABLUP-A and ABLUP-AD and between GBLUP-A
and GBLUP-AD were the substantial decrease in
σ2
a
(Table 3). Pilodyn
and MOE had the same
σ2
a
s for the ABLUP-A and ABLUP-AD and
also for GBLUP-A and GBLUP-AD because dominance variances (
σ2
d
s) were zero for both traits (Table S3). For example, tree height
σ2
a
s
estimated from ABLUP-AD were 87.8% and 68.3% of the
σ2
a
s esti-
mated from ABLUP-A at site 1 and site 2, respectively.
In the ABLUP-AD model, tree height and velocity dominances
showed signicant effects based on the AIC (Tables 2 and 3). For
example, tree height dominance effects accounted for 8.5% and
23.1% of the phenotypic variation for site 1 and site 2, respectively.
In the GBLUP-AD model, tree height dominance effects accounted
for 18.1% and 9.8% of the phenotypic variation for site 1 and site
2, respectively. However, based on the AIC, the dominance variance
of 572.2 at site 1 was not signicant. In the GBLUP-ADE models,
rst-order epistatic effects were all zero for all the 4 traits, except for
velocity with nonsignicant additive × additive effects (4.2%) and
dominance × dominance effects (0.7%) (Table 3).
Estimates of tree height and velocity narrow-sense heritability
from ABLUP-A or GBLUP-A models were larger than those from
ABLUP-AD or GBLUP-AD. For example, tree height narrow-sense
heritability of 0.12 from ABLUP-A was larger than 0.10 from
ABLUP-AD at site 1. Broad-sense heritability estimates were sub-
stantially larger than narrow-sense heritability estimates from both
ABLUP-AD and GBLUP-AD at both sites for tree height and vel-
ocity. For example, tree height broad-sense heritability estimates
were 253.8% and 166.7% of the narrow-sense heritability estimates
from the GBLUP-AD model at site 1 and site 2, respectively. For
tree height, Pilodyn and MOE, GBLUP-ADE produced exactly the
same results as GBLUP-AD (Table 3 and Supplementary Material,
Table S2) because of the lack of epistasis. In this study, only vel-
ocity showed nonsignicant and nonzero epistatic effects. Moreover,
broad-sense heritability estimates from the GBLUP-ADE models
were slightly higher than those from GBLUP-AD (0.43 vs. 0.41 for
site 1 and 0.42 vs. 0.40 for site 2).
Comparison ofModels
We used 2 methods for model comparison, namely AIC
(Supplementary Material, Table S1 and Table 2) and the tted line
plots (represented by the graph of predicted values
ˆ
y
vs. observed
values y) (Figure 1). The tted line plot comparisons based on R2 re-
ected the goodness-of-t. For tree height and velocity, R2 increased
from GBLUP-A to GBLUP-AD (Tree height: 0.38 vs. 0.56 in site 1
and 0.56 vs 0.79 in site 2; velocity: 0.80 vs. 0.88 in site 1 and 0.78 vs.
0.87 in site 2)and from ABLUP-A to ABLUP-AD for both sites (Tree
height: 0.44 vs. 0.74 in site 1 and 0.58 vs 0.69 in site 2; velocity: 0.73
vs. 0.82 in site 1 and 0.73 vs. 0.82 in site 2). For Pilodyn and MOE,
R2 was the same from GBLUP-A to GBLUP-AD and from ABLUP-A
to ABLUP-AD, which was consistent with the zero estimates of dom-
inance variances for both traits (Supplementary Material, Table S2).
The difference of R2 for tree heights between site 1 and site 2 was
much larger than that of wood quality traits for all models.
A comparison of BVs’ precision using the standard errors for
the predictions (SEPs) between different models (GBLUP-AD vs.
GBLUP-A, GBLUP-AD vs. ABLUP-AD, GBLUP-AD vs. ABLUP-A,
GBLUP-A vs. ABLUP-AD, GBLUP-A vs. ABLUP-A, and ABLUP-AD
vs. ABLUP-A) is shown in Supplementary Material, Figure S1 for
all traits. For tree height, the SEPs of 21-year-old Norway spruce
breeding values between ABLUP-AD and ABLUP-A showed similar
values. GBLUP-AD for tree height had much lower SEPs than that
of GBLUP-A, but not for wood quality traits. GBLUP-AD for all
traits had much lower SEPs values than that from ABLUP-AD for
most SEPs values. ABLUP-AD for all traits had almost the same SEPs
as ABLUP-A, even for tree height. For all traits, GBLUP-AD and
GBLUP-A had more and lower SEPs than those from ABLUP-AD
and ABLUP-A, except the GBLUP-A for tree height had more and
larger SEPs than those from ABLUP-A and ABLUP-AD.
Cross-Validation of theModels
A random selection of 10% of the population was used as a valid-
ation set. To test the ranking difference of estimated breeding values
between 5 models, Spearman’s rank correlations were used (Table
4). Spearman’s rank correlations between breeding values estimated
by pedigree-based models (ABLUP-A and ABLUP-AD) and between
breeding values estimated by genomic-based models (GBLUP-A
and GBLUP-AD) in cross-validation were higher than between
pedigree-based and genomic-based models (Table 4). For example,
Spearman’s rank correlations between breeding values estimated
by pedigree-based and genomic-based models for tree height were
0.884. Spearman’s rank correlations between breeding values esti-
mated by within pedigree-based models or genomic-based models
were almost the same. For example, Spearman’s rank correlation
Table 4. Coefficients of Spearman’s rank correlations between
breeding values estimated by ABLUP-A, ABLUP-AD, GBLUP-A, and
GBLUP-AD in cross-validation for tree height, Pilodyn, velocity,
andMOE
Trait ABLUP-A ABLUP-AD GBLUP-A GBLUP-AD
Height
ABLUP-A 0.997 0.877 0.876
ABLUP_AD 0.998 0.873 0.873
GBLUP-A 0.884 0.878 0.995
GBLUP-AD 0.879 0.875 1
Pilodyn
ABLUP_A 1 0.818 0.819
ABLUP-AD 1 0.818 0.819
GBLUP-A 0.819 0.819 1
GBLUP-AD 0.820 0.820 1
Velocity
ABLUP_A 0.998 0.868 0.869
ABLUP-AD 0.998 0.868 0.868
GBLUP-A 0.869 0.869 1 0.999
GBLUP-AD 0.869 0.869 0.999 1
MOE
ABLUP_A 1 0.837 0.837
ABLUP-AD 1 0.837 0.837
GBLUP-A 0.837 0.837 1
GBLUP-AD 0.837 0.837 1
ABLUP-A, ABLUP-AD, GBLUP-A, and GBLUP-AD with the best variance
structure are based on AIC in Table 2.
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Table 5. Predictive abilities (PA) based on main marker effects (M), M + marker-by-environment interaction effects (A) and A+ dominance effects (AD) from GBLUP-AD and ABLUP-AD models
for tree height, Pilodyn, velocity, and MOE in the single trial (ST) and multi-environment trial (MET) model analysis in cross-validation
Trait Comparison Type StructureaTraining Validation GBLUP-AD ABLUP-AD
M A AD M A AD
Height 1 ST DIAG+IDEN Site 1 Site1 N/A 0.24 (0.04) 0.26 (0.03) N/A 0.21 (0.04) 0.20 (0.04)
2 ST DIAG+IDEN Site 1 Site2 N/A 0.09 (0.03) 0.16 (0.03) N/A 0.13 (0.03) 0.12 (0.03)
3 ST DIAG+IDEN Site 2 Site2 N/A 0.25 (0.03) 0.27 (0.03) N/A 0.26 (0.04) 0.29 (0.04)
4 ST DIAG+IDEN Site 2 Site1 N/A 0.07 (0.04) 0.12 (0.04) N/A 0.09 (0.03) 0.08 (0.03)
5 MET FAMK+IDEN Site 1 Site 1 0.22 (0.04) 0.23 (0.04) 0.26 (0.03) 0.19 (0.03) 0.19 (0.03) 0.20 (0.03)
6 MET FAMK+IDEN site 2 Site 2 0.22 (0.04) 0.25 (0.03) 0.27 (0.03) 0.21 (0.03) 0.24 (0.03) 0.29 (0.04)
Pilodyn 1 ST DIAG+IDEN Site 1 Site 1 N/A 0.26 (0.05) 0.27 (0.05) N/A 0.30 (0.05) 0.30 (0.05)
2 ST DIAG+IDEN Site 1 Site 2 N/A 0.23 (0.04) 0.23 (0.04) N/A 0.24 (0.03) 0.25 (0.03)
3 ST DIAG+IDEN Site 2 Site 2 N/A 0.23 (0.03) 0.31 (0.03) N/A 0.34 (0.02) 0.33 (0.02)
4 ST DIAG+IDEN Site 2 Site 1 N/A 0.23 (0.03) 0.23 (0.03) N/A 0.23 (0.03) 0.24 (0.03)
5 MET
CS
+ IDEN Site 1 Site 1 0.30 (0.04) 0.30 (0.04) 0.30 (0.04) 0.32 (0.03) 0.33 (0.04) 0.33 (0.04)
6 MET
CS
+IDEN Site 2 Site 2 0.32 (0.03) 0.32 (0.03)
(0.03)
0.32 (0.03) 0.34 (0.02) 0.35 (0.02) 0.35 (0.02)
Velocity 1 ST DIAG+IDEN Site 1 Site 1 N/A 0.44 (0.04) 0.45 (0.04) N/A 0.40(0.04) 0.42 (0.04)
2 ST DIAG+IDEN Site 1 Site 2 N/A 0.32 (0.03) 0.33 (0.02) N/A 0.35 (0.03) 0.36 (0.03)
3 ST DIAG+IDEN Site 2 Site 2 N/A 0.38 (0.02) 0.39 (0.02) N/A 0.40 (0.04) 0.41 (0.04)
4 ST DIAG+IDEN Site 2 Site 1 N/A 0.34 (0.06) 0.35 (0.06) N/A 0.36 (0.04) 0.38 (0.04)
5 MET CS+IDEN Site 1 Site 1 0.45 (0.05) 0.46 (0.04) 0.46 (0.04) 0.42 (0.04) 0.43 (0.04) 0.43 (0.04)
6 MET CS+IDEN Site 2 Site 2 0.39 (0.03) 0.39 (0.03) 0.39 (0.03) 0.42 (0.04) 0.43 (0.04) 0.43 (0.04)
MOE 1 ST DIAG+IDEN Site 1 Site 1 N/A 0.33 (0.03) 0.33 (0.03) N/A 0.34 (0.03) 0.35 (0.03)
2 ST DIAG+IDEN Site 1 Site 2 N/A 0.28 (0.04) 0.28 (0.04) N/A 0.31 (0.04) 0.32 (0.04)
3 ST DIAG+IDEN Site 2 Site 2 N/A 0.33 (0.03) 0.33 (0.04) N/A 0.36 (0.04) 0.36 (0.04)
4 ST DIAG+IDEN Site 2 Site 1 N/A 0.30 (0.04) 0.30 (0.04) N/A 0.32 (0.04) 0.32 (0.04)
5 MET CS+IDEN Site 1 Site 1 0.37 (0.04) 0.37 (0.04) 0.37 (0.04) 0.38 (0.03) 0.39 (0.03) 0.39 (0.03)
6 MET CS+IDEN Site 2 Site 2 0.35 (0.04) 0.35 (0.04) 0.35 (0.04) 0.38 (0.04) 0.38 (0.04) 0.38 (0.04)
Standard errors are in parentheses.
aIncluding additive structure plus dominance structure.
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Site1:R2= 0.38
Site2:R2= 0.56
Site1:R2= 0.56
Site2:R2= 0.79
Site1:R2= 0.44
Site2:R2= 0.58
Site1:R2= 0.74
Site2:R2= 0.69
Height: ABLUP−A Height: ABLUP−AD Height: GBLUP−A Height: GBLUP−AD
200 400 600 800 200 400 600 800 200400 600800 200400 600800
200
400
600
800
Phenotypic value (y)
Predicted value (y
^)
Site1:R2= 0.75
Site2:R2= 0.76
Site1:R2= 0.75
Site2:R2= 0.76
Site1:R2= 0.63
Site2:R2= 0.70
Site1:R2= 0.63
Site2:R2= 0.70
Pilodyn: ABLUP−A Pilodyn: ABLUP−AD Pilodyn: GBLUP−A Pilodyn: GBLUP−AD
10 15 20 25 30 10 15 20 25 30 10 15 20 25 30 10 15 20 25 30
10
15
20
25
30
Phenotypic value (y)
Predicted value (y
^)
Site1:R2= 0.80
Site2:R2= 0.78
Site1:R2= 0.88
Site2:R2= 0.87
Site1:R2= 0.73
Site2:R2= 0.73
Site1:R2= 0.82
Site2:R2= 0.82
Velocity: ABLUP−A Ve locity: ABLUP−AD Velocity: GBLUP−A Velocity: GBLUP−AD
345634563456
3456
3
4
5
6
Phenotypic value (y)
Predicted value (y
^)
Site1:R2= 0.75
Site2:R2= 0.81
Site1:R2= 0.75
Site2:R2= 0.81
Site1:R2= 0.64
Site2:R2= 0.75
Site1:R2= 0.64
Site2:R2= 0.75
MOE: ABLUP−A MOE: ABLUP−AD MOE: GBLUP−A MOE: GBLUP−AD
10 20 30 40 10 20 30 40 10 20 30 40 10 20 30 40
10
20
30
40
Phenotypic value (y)
Predicted value (y
^)
Site 1Site 2
Figure 1. Model comparisons using the fitted line plots (represented by the graph of predicted values
ˆ
y
vs observed values y) for tree height, Pilodyn, velocity,
and MOE.
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Site 1 Site 2
0.00 0.25 0.50 0.75 1.000.00 0.250.500.75 1.00
0.0
0.2
0.4
0.6
Proportion of individuals selected
Response to selection (%/year)
Effects (Model)
AD (ABLUP−AD, RPS)
AD (GBLUP−AD, RGS)
A (GBLUP−AD, RGS)
M (GBLUP−AD, RGS)
A) Tree height
Site 1 Site 2
0.00 0.25 0.50 0.75 1.000.00 0.250.500.75 1.00
0.0
0.5
1.0
Proportion of individuals selected
Response to selection (%/y
ear)
Effects (Model)
AD (ABLUP−AD, RPS)
AD (GBLUP−AD, RGS)
A (GBLUP−AD, RGS)
M (GBLUP−AD, RGS)
B) Pilodyn
Site 1 Site 2
0.00 0.25 0.50 0.75 1.000.00 0.25 0.50 0.75 1.00
0.0
0.2
0.4
0.6
Proportion of individuals selected
Response to selection (%/year)
Effects (Model)
AD (ABLUP−AD, RPS)
AD (GBLUP−AD, RGS)
A (GBLUP−AD, RGS)
M (GBLUP−AD, RGS)
C) Velocity
Site 1 Site 2
0.00 0.25 0.50 0.75 1.000.00 0.25 0.50 0.75 1.00
0.0
0.5
1.0
1.5
2.0
Proportion of individuals selected
Response to selection (%/y
ear)
Effects (Model)
AD (ABLUP−AD, RPS)
AD (GBLUP−AD, RGS)
A (GBLUP−AD, RGS)
M (GBLUP−AD, RGS)
D) MOE
Figure 2. Response to genomic selection (RGS), including three different selection scenarios based on 1)only main marker effects (M), 2)main marker effects
plus genotype-by-environment interaction effects (A), and 3)A + dominance (AD) from GBLUP-AD for A) tree height, B) Pilodyn, C) velocity, and D) MOE,
expressed as a percentage gain of the average population mean per year, compared with response to phenotypic selection (RPS) also including dominance
effects (ABLUP-AD) calculated for different proportions of individuals selected by GS.
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between breeding values estimated by ABLUP-A and ABLUP-AD for
tree height were1.00.
The cross-validation focused on comparing the predictive ability
(PA) between GBLUP-AD and ABLUP-AD models and between
MET and single-trial (ST) models for all traits; results are shown
in Table 5. We examined only the models with either CS or FAMK
for additive effects and either CS or IDEN for dominance effects
in the MET analysis. For a single trial (ST) analysis, the models
with DIAG for additive and IDEN or DIAG for dominance effects
based on Table 2 were used. Using the same site data as a training
set and a validation set showed higher PA. Tree height PA from the
ST analysis at site 2 was higher than that at site 1 for additive ef-
fects (A) from GBLUP-AD models (comparisons: 1 and 3, 0.25 vs.
0.24, Table 5) and ABLUP-AD models (comparisons: 1 and 3, 0.26
vs. 0.21, Table 5). The models with additive and dominance effects
(AD) showed results similar to those of the models with an additive
effect only (A) for tree height. If 1 site was used to build the model
and predict the breeding values (A) and genotype values (AD) for
the second site, then predicting for site 2 using the models from site
1 had a higher PA than the opposite for both GBLUP-AD (compari-
sons: 2 and 4, 0.09 vs. 0.07, Table 5) and ABLUP-AD (compari-
sons: 2 and 4, 0.13 vs. 0.09, Table 5). Ly etal. (2013) suggested that
G×E, which cannot be estimated for a single trial, reduced the ability
to make predictions. Our results proved that the site 2 tree height
might have a higher environmental component than that observed in
site 1, making the prediction of the BVs (additive) or genetic values
(GVs: additive and dominance) less accurate. PA of Pilodyn did not
change, or only slightly changed, using site 1 model for site 2 and
vice versa. This happened because there is almost no G×E in Pilodyn
measurements.
Generally, PA was higher in the MET analysis than that in ST
analysis for all traits, except for tree height (Table 5). For Pilodyn,
velocity, and MOE, PAs in MET analyses based on Aand AD effects
were higher than those from single site (ST) analyses (comparisons 1
and 5, comparisons 2 and 6, Table 5). For example, PAs for Pilodyn
based on Afrom GBLUP-AD showed an increase of 15.4% (com-
parisons 1 and 5, 0.26 vs. 0.30, Table 5) and 39.1% (comparisons 3
and 6, 0.23 vs. 0.32, Table 5) in sites 1 and 2, respectively.
Finally, we studied the additive M×E effects on the genomic-
based estimated breeding values (GEBVs). There was a reduction in
tree height PA if M×E was not included in calculating the GEBVs
for site 2 (comparison 6: 0.25 vs. 0.22, Table 5), and for site 1 (com-
parison 5: 0.23 vs. 0.22, Table 5). Including tree height dominance
in models in site 2, PA increased 8% from 0.25 to 0.27 and 20.8%
from 0.24 to 0.29 for GBLUP-AD and ABLUP-AD models, respect-
ively (Table 5). Including tree height dominance in models in site 1,
PA increased 13.0% from 0.23 to 0.26 and 5.3% from 0.19 to 0.20
for GBLUP-AD and ABLUP-AD models, respectively. For Pilodyn,
velocity, and MOE, PA including dominance in MET analysis was
not increased, even for velocity with a signicant dominance vari-
ance based onAIC.
Predictive ability (PA) for all traits from GBLUP-ADE is not
shown in Table 5 because their variance components were zero, ex-
cept for velocity. PA for velocity from the GBLUP-ADE model was
the same as the result from GBLUP-AD.
Expected Response to Genomic Selection(GS)
We compared the generation time of GS (ca. 12.5 years) with the
generation time of the phenotypic selection (ca. 25years), as in the
traditional breeding program in Northern Sweden (Chen etal. 2018).
Aconservative response of genomic selection per year (RGS%/year)
was calculated to compare with the response of phenotypic selec-
tion per year (RPS%/year) for variable proportions of individuals
selected by GS. We compared RGS per year with RPS per year for all
traits for variable proportions of individuals selected by GS (Figure
2). The results showed that RGS per year provided much larger
values than RPS per year for 3 genomic selection scenarios, including
selection based on 1)main marker effects (M), 2)M plus M×E ef-
fects (A), and 3)A plus dominance effects (AD) from GBLUP-AD
model for both sites (Figure 2). However, RGS per year for different
scenarios in both sites showed slight differences only for tree height,
not for wood quality traits. RGS per year for tree height based on
Aand AD was substantially higher than that based on M in site 2
(Figure 2). However, in site 1, RGS per year for tree height based on
Aand AD was slightly better than that based on M and showed only
at a low selection proportion. In the traditional Swedish breeding
program, 50 individuals were selected for each breeding popula-
tion. In Supplementary Material, Figure S2, the top 50 individuals
selected without considering relationships for selection based on M,
A, and AD for all traits were scaled to the total expected genetic
value (EGV) ranking of all individuals in sites 1 and 2.RGS per year
based on M, A, and AD for GBLUP-AD, and RPS per year based on
an AD for ABLUP-AD, are shown in Supplementary Material, Table
S3. For tree height, RGS per year based on AD in site 2 was 0.54
(%)/year, which was substantially higher than 0.45 and 0.46 (%)/
year based on Aand M, respectively. RGS per year based on AD in
site 1 was 0.43 (%)/year, which was slightly higher than 0.41 and
0.41 (%)/year based on Aand M, respectively. For wood quality
traits, RGS per year based on M, A, and AD were almost the same
(Figure 2), but they slightly increased when such effects were sig-
nicant (Supplementary Material, Table S3). If the top 50 velocity
individuals based on genomic-based expected genetic values were
selected, RGS per year from GBLUP-AD were 78.9%, 86.9%, and
91.3% in site 1, and 80.8%, 82.9%, and 88.2% in site 2, higher than
RPS (%)/year based on M, A, and AD effects, respectively. RGS per
year from GBLUP-AD for tree height, Pilodyn, and MOE were up to
68.9%, 91.3%, and 92.6%, respectively.
Discussion
Genetic Variance Components and Heritability
Estimates
In the traditional Norway spruce breeding program, estimates of
broad-sense heritability (H2) have previously been made in tests of
clones selected from commercial nurseries and with an unknown
family structure. For example, tree height H2 estimates vary from
0.12 to 0.40 for Norway spruce (Bentzer etal. 1989; Karlsson and
Högberg 1998), but it is not possible to compare with narrow-
sense heritability (h2), which requires a family structure. Using
a traditional pedigree-based model, epistasis estimation, on the
other hand, requires full-sib family structure plus the replication
of genotypes in clonal trials. Existing high-throughput single nu-
cleotide polymorphism (SNP) genotyping technology, such as SNP
arrays, re-sequencing, or genotyping-by-sequencing (GBS), allows
genotyping larger numbers of SNPs, and therefore is used to study
dominance and epistasis in populations without pedigree delineation
of full-sib family structure in both animals (Sun etal. 2013; Aliloo
etal. 2016) and plants (Gamal El-Dien etal. 2018).
In our study, tree height H2 estimated from ABLUP-AD (0.20–
0.40) was higher than h2 estimated from pedigree-based ABLUP-A
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and ABLUP-AD (0.10–0.19) (Table 3). In a previous study, it was
however observed that the average h2 of 0.29 (0.02–1.09) based on
170 eld tests with seedlings was higher than the average H2 of 0.18
(0.04–0.50) based on 123 eld tests with clonal material (Kroon etal.
2011), indicating that a valid comparison of relative genetic control
must use the datasets that come from the same trial with comparable
pedigree (Wu 2018). The ratio of tree height h2/H2 varies from 0.35–
0.50 (
σ2
D
/σ
2
A
=
2.10–0.94
) and from 0.39–0.60 (
σ2
D
/σ
2
A
=
1.60–0.67
) in ABLUP-AD and GBLUP-AD models, respectively. These gures
are lower than 0.60–0.84 (
σ2
D
/σ
2
A
=
0.67–0.19
) from 3 Norway
spruce progeny trials in the previous study (Kroon etal. 2011). The
usual range of the ratio h2/H2 has been reported to vary from 0.18
to 0.84 (
σ2
D
/σ
2
A
=
4.56–0.19
) for tree traits (Wu 2018). It is also
considered that signicant dominance could be utilized in advanced
Norway spruce breeding and deployment programs.
Our results show that the inclusion of dominance effects reduces
estimates of h2 from GBLUP-AD and ABLUP-AD when dominance
is not zero. For example, tree height h2 estimates decrease by 13%–
26%, less than the substantial decrease (50%–70%) reported in hy-
brid Eucalyptus by Tan etal. (2018). The situation is expected from a
theoretical standpoint as a substantial proportion of the nonadditive
variance can be inseparable from additive variance (Falconer and
Mackay 1996), that has been encountered in the several empirical
studies (Gamal El-Dien etal. 2016, 2018; Tan etal. 2018).
Comparison and Cross-Validation ofModels
AIC values for the GBLUP models were not signicantly higher than
those based on pedigree relationship matrices, which is consistent
with the results of Gamal El-Dien etal. (2016) in white spruce, but is
in contrast with the results from hybrid Eucalyptus (Tan etal. 2018).
In the latter, the signicant improvement from GBLUP models based
on AIC may result from a considerable number of uncorrected pedi-
grees including a labelling mistake. In our study, the SEPs of breeding
values in GBLUP-A models for tree height were higher than that in
pedigree-based ABLUP-A model (In Supplementary Material, Figure
S1), which is inconsistent with the results of Gamal El-Dien etal.
(2018). This seems reasonable in our study because the additive vari-
ance increases from ABLUP models to GBLUP models (Table 3). For
wood quality traits, the SEPs of breeding values in GBLUP-A models
are smaller than those in the pedigree-based ABLUP-A model. For all
traits, most SEPs of breeding values in GBLUP-AD model are smaller
than in GBLUP-A, ABLUP-AD, and ABLUP-A models, which indi-
cates that GBLUP-AD could produce more accurate breeding values,
even though the Spearman’s rank correlations between breeding
values estimated by GBLUP-AD and GBLUP-A are similar.
M×E for Genomic Selection in Multi-Environment
Trials(METs)
Gamal EL-Dien et al. (2018) showed that interior spruce (Picea
glauca x engelmannii) had substantially signicant additive M×E
and nonsignicant small dominance M×E terms for both height and
wood density. In our study, signicant but small M×E effects for all
traits were found only in additive genetic effects, not for domin-
ance. Gamal EL-Dien etal. (2018) did not use more comprehensive
models to dissect M×E, but used compound symmetry variance–co-
variance structures (CS). To more accurately dissect M×E in multi-
environment trials (METs), here we used 6 variance–covariance
matrices (Table 1) to model additive and dominance effects in GS
models for 4 traits. Asimilar approach was described by Burgueño
etal. (2012), Oakey etal. (2016) and Ventorim Eerrao etal. (2017).
Finally, we found that all 4 traits have signicant additive M×E
terms using CS for additive effects. For tree height, we also observed
a better goodness-of-t using FAMK in Supplementary Material,
Table S1. Here we should note that site 1 has a nonsignicant addi-
tive M×E term for tree height that resulted in a negligible increase
with the M×E term included in the GBLUP-AD model. Generally,
MET analysis shows slightly higher PA than does ST analysis, ex-
cept for tree height which has the same value. This may result from
the nonsignicant additive covariance (
σ2
a
12
) between 2 sites. In this
study, only tree height and velocity had slight increases for PA, which
also supports the previous study of Ly etal. (2013) that including the
G×E term could improve the PA.
Significant Dominance Effects Improve Predictive
Ability
Recent studies have shown that maximum PA can be reached when
the model is based on additive and nonadditive effects (Da et al.
2014; Muñoz etal. 2014; Aliloo etal. 2016; Tan etal. 2018). Ly etal.
(2013) considered that only the additive component may produce a
systematic underestimation of PA because only additive effects are
predicted. Here, the GBLUP-AD model for tree height shows homo-
genous dominance variances in both sites (Table 3, identity matrix
for dominance effect). However, the ABLUP-AD model shows a sig-
nicant dominance variance in site 2 (23.1%) and nonsignicant
dominance variance in site 1 (8.5%), indicating that the GBLUP-AD
model has higher efciency in separating the additive and dominance
genetic variances because it could account for the Mendelian sam-
pling within families for dominance.
It was found that including dominance could improve PA when
a considerable dominance variance in animal (Aliloo etal. 2016;
Esfandyari et al. 2016) and plant studies were observed (Wolfe
etal. 2016; Tan etal. 2018;). In this study, the improvement of tree
height and velocity PAs also agree with the previous observations.
However, including signicant dominance in this study may not
improve the Spearman’s rank correlations between breeding values
(Table 4).
A dominance effect has been used in several practical breeding
programs, such as loblolly pine (McKeand etal. 2003), Sitka spruce
(Picea sitchensis) (Thompson 2013), and eucalypts (Rezende etal.
2014). For instance, since 2000, the annual production of full-sib
seedlings in loblolly pine increased to 63.2 million in 2013, with a
total of over 325 million full-sib family seedlings planted over the
last 14 years (Steve Mckeand 2014, personal communication). In
Norway spruce, a dominance estimate was not widely included in
the breeding program, but we are commonly using full-sib family
material. Thus, it is important to estimate dominance effects in the
Norway spruce breeding program as more and more individuals will
be genotyped for selection and propagation.
EpistasisEffect
The full model (GBLUP-ADE), which was extended to include
3 rst-order interactions, shows almost the same results as
GBLUP-AD for all 4 traits based on AIC (Table 2). This indicates
the absence of 3 kinds of epistatic interactions even though addi-
tive × additive and dominance × dominance epistatic effects ex-
plained variations of 4.2% (4.0%) and 0.7% (0.2%) for velocity
in site 1 (site2), respectively. However, in several other forest tree
species, such as white spruce (Gamal El-Dien et al. 2016), lob-
lolly pine (de Almeida Filho etal. 2016), eucalypt (Bouvet et al.
2016; Resende etal. 2017; Tan et al. 2018), and interior spruce
Journal of Heredity, 2019, Vol. 110, No. 7 841
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(P.glauca x engelmannii) (Gamal El-Dien et al. 2018), signicant
epistatic effects have been reported for height or wood density. For
instance, Gamal El-Dien etal. (2016) showed a signicant addi-
tive × additive component and nonsignicant dominance for tree
height, while Gamal El-Dien etal. (2018) showed a considerable
dominance component (19.46% of total phenotypic variation) and
no epistatic effect. For wood density in spruce, Gamal El-Dien etal.
(2016, 2018) showed a signicant additive × additive interaction
that was absorbed from additive and residual variances. Tan etal.
(2018) showed no epistasis for wood density. The above results
agree with the suggestion by Tan etal. (2018) that the contribu-
tions of nonadditive effects, especially epistasis effects, are traits,
populations, and species-specic, or even site-specic as in this
study. However, including signicant nonadditive effects could im-
prove estimates of genetic parameters.
Expected Response to Genomic Selection
The main advantages of GS are to shorten the length of the breeding
cycle and reduce phenotypic evaluation costs in plant and animal
breeding (Grattapaglia and Resende 2011; de los Campos et al.
2013). In Northern Sweden, the length of the breeding cycle of
Norway spruce in GS could be ideally shortened from 25years to
12.5years (Chen etal. 2018) if we could complete owering induc-
tion and controlled pollinations within 12.5years. In our previous
paper (Chen et al. 2018), we calculated the RGS per year for GS
based on GBLUP-A using the same data set. Here we compared RPS
with RGS per year for GS based on a GBLUP-AD model and calcu-
lated the response to selection per year for PS and GS. We used EGVs
from an ABLUP-AD model as a benchmark for all traits. RGS per
year is considerably higher than RPS per year for all traits (Figure
2). RGS per year for wood quality traits has greater gain than those
for tree height when we select the top 50 individuals based on a
M, Aor AD effect, in contrast to the result reported by Resende
etal. (2017) for Eucalyptus. Thus, GS based on genomic-based ex-
pected genetic values is ideal for solid-wood quality improvement in
Norway spruce.
Conclusions
This is the rst paper to study M×E using a different covariance
structure for the additive and nonadditive effects and dominance
in GS for forestry trees species. We found that M×E and domin-
ance effects could improve PA when they are appreciably large.
In a GBLUP-AD model, M×E contributed 4.7% and 11.1% of
tree height phenotypic variation for sites 1 and 2, respectively.
Dominance contributed 18.1% and 9.8% of tree height pheno-
typic variation for sites 1 and 2, respectively. The higher PA of
the GBLUP-AD model for tree height compared to ABLUP-A and
GBLUP-A models suggests that dominance should be included in
GS models for genetic evaluations in forestry to improve the pre-
dictive accuracy or estimates of genetic parameters. Advanced M×E
models could improve PA and should be included in the model
tting. GBLUP-AD could be a more useful model in breeding and
propagation when tree breeders want to use the dominance using
full-sib family seedlings.
Supplementary Material
Supplementary data are available from the Journal of Heredity
online.
Funding
Financial support was received from Formas (grant number 230-2014-427),
the Swedish Foundation for Strategic Research (SSF, grant number RBP14-
0040), and from the European Union’s Horizon 2020 research and innovation
programme under grant agreement No 773383 (B4EST project).
Acknowledgements
The computations were performed on resources provided by the Swedish
National Infrastructure for Computing (SNIC) at UPPMAX and HPC2N. We
thank Dr Junjie Zhang, Tianyi Liu, Xinyu Chen, Ruiqi Pian, and Ms Linghua
Zhou for help in the DNA extraction and eld assistance, and Anders Fries
for eld work.
Data Archiving
The data is archived in the Dryad Data Repository https://doi.
org/10.5061/dryad.pk0p2nghn.
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