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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/),

which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.

© The American Genetic Association 2019.

Original Article

Increased Prediction Ability in Norway Spruce

Trials Using a Marker X Environment Interaction

and Non-Additive Genomic SelectionModel

Zhi-Qiang Chen, John Baison, Jin Pan, Johan Westin,

MariaRosarioGarcía Gil, and HarryX. 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 etal. 2001) and it has been incorporated into animal

breeding for many years (Van Eenennaam etal. 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

Downloaded from https://academic.oup.com/jhered/article-abstract/110/7/830/5601174 by guest on 07 February 2020

(Zeng etal. 2013). In livestock, accounting for dominance in GS has

improved genomic evaluations of dairy cows for fertility and milk

production traits (Aliloo etal. 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 etal. 2012a, 2012b; Tan etal. 2017; Chen etal. 2018). The

nonadditive contributions have also been estimated in several studies

(Muñoz etal. 2014; Bouvet etal. 2016; de Almeida Filho etal. 2016;

Gamal El-Dien etal. 2016; Tan etal. 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 etal. 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 etal. 2003, 2005; Baltunis etal. 2007; Weng etal. 2008;

Wu etal. 2008), especially for wood quality traits (Wu 2018).

Signicant genotype-by-environment (G×E) interaction is com-

monly observed among the different deployment zones for growth

traits in Norway spruce (Kroon etal. 2011; Chen etal. 2014, 2017).

Literature also supports the importance of predicting nonadditive

effects including dominance and epistasis in tree breeding (Wu

etal. 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 efciency 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 1year 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: 240m).

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 17years. 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 2.0mm diameter pin, without removing the bark. Velocity,

closely related to microbril 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 etal. (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 quantication 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 etal. (2018). Sequence

capture was performed using the 40 018 probes previously designed

and evaluated for the material (Vidalis etal. 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 etal. (2018). Finally,

116,765 SNPs were kept for downstream analysis.

Variance Component and HeritabilityModels

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-BasedModels

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)

Journal of Heredity, 2019, Vol. 110, No. 7 831

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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-

efcients based on the proportion of homozygous SNPs. Although

Xiang etal. (2016) and Vitezica etal. (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 signicant for all the traits. The random post-block

effects (

b

) were assumed tofollow

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

etal. 2015) or ASReml-R package (Butler etal. 2009). AD rela-

tionship matrix was produced using kin function in the synbreed

package in R (Wimmer etal. 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

etal. (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 etal. (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.

832 Journal of Heredity, 2019, Vol. 110, No. 7

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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 etal. 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 etal. 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 and2.

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)

. AFAMK 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 specic 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 etal. (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 etal.

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

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 25years long. If GS could be used as at a very early selection

stage, the breeding cycle could be reduced to ca. 12.5years (Chen

etal. 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 signicant 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 signicant. 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 signicant 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

signicant (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 signicant effects: therefore, there was no

signicant M×E for a dominance effect of any trait. For epistasis,

there was no signicant effect on anytrait.

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, andMOE

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

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.

Journal of Heredity, 2019, Vol. 110, No. 7 835

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 signicant 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 signicant. In the GBLUP-ADE models,

rst-order epistatic effects were all zero for all the 4 traits, except for

velocity with nonsignicant 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 nonsignicant 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 ofModels

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 theModels

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,

andMOE

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.

836 Journal of Heredity, 2019, Vol. 110, No. 7

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.

Journal of Heredity, 2019, Vol. 110, No. 7 837

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.

838 Journal of Heredity, 2019, Vol. 110, No. 7

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.

Journal of Heredity, 2019, Vol. 110, No. 7 839

between breeding values estimated by ABLUP-A and ABLUP-AD for

tree height were1.00.

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 etal. (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 Aand 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 Afrom 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 signicant dominance vari-

ance based onAIC.

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. 25years), as in the

traditional breeding program in Northern Sweden (Chen etal. 2018).

Aconservative 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

Aand 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

Aand 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 Aand 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 Aand 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-

nicant (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 etal. 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 etal. 2013; Aliloo

etal. 2016) and plants (Gamal El-Dien etal. 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

840 Journal of Heredity, 2019, Vol. 110, No. 7

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 etal.

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 etal. 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 signicant 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 etal. (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 etal. 2016, 2018; Tan etal. 2018).

Comparison and Cross-Validation ofModels

AIC values for the GBLUP models were not signicantly higher than

those based on pedigree relationship matrices, which is consistent

with the results of Gamal El-Dien etal. (2016) in white spruce, but is

in contrast with the results from hybrid Eucalyptus (Tan etal. 2018).

In the latter, the signicant 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 etal.

(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 signicant additive M×E

and nonsignicant small dominance M×E terms for both height and

wood density. In our study, signicant but small M×E effects for all

traits were found only in additive genetic effects, not for domin-

ance. Gamal EL-Dien etal. (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. Asimilar approach was described by Burgueño

etal. (2012), Oakey etal. (2016) and Ventorim Eerrao etal. (2017).

Finally, we found that all 4 traits have signicant 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 nonsignicant 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 nonsignicant 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 etal. (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 etal. 2014; Aliloo etal. 2016; Tan etal. 2018). Ly etal.

(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-

nicant dominance variance in site 2 (23.1%) and nonsignicant

dominance variance in site 1 (8.5%), indicating that the GBLUP-AD

model has higher efciency 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 etal. 2016;

Esfandyari et al. 2016) and plant studies were observed (Wolfe

etal. 2016; Tan etal. 2018;). In this study, the improvement of tree

height and velocity PAs also agree with the previous observations.

However, including signicant 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 etal. 2003), Sitka spruce

(Picea sitchensis) (Thompson 2013), and eucalypts (Rezende etal.

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.

EpistasisEffect

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 etal. 2016), eucalypt (Bouvet et al.

2016; Resende etal. 2017; Tan et al. 2018), and interior spruce

Journal of Heredity, 2019, Vol. 110, No. 7 841

(P.glauca x engelmannii) (Gamal El-Dien et al. 2018), signicant

epistatic effects have been reported for height or wood density. For

instance, Gamal El-Dien etal. (2016) showed a signicant addi-

tive × additive component and nonsignicant dominance for tree

height, while Gamal El-Dien etal. (2018) showed a considerable

dominance component (19.46% of total phenotypic variation) and

no epistatic effect. For wood density in spruce, Gamal El-Dien etal.

(2016, 2018) showed a signicant additive × additive interaction

that was absorbed from additive and residual variances. Tan etal.

(2018) showed no epistasis for wood density. The above results

agree with the suggestion by Tan etal. (2018) that the contribu-

tions of nonadditive effects, especially epistasis effects, are traits,

populations, and species-specic, or even site-specic as in this

study. However, including signicant 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 25years to

12.5years (Chen etal. 2018) if we could complete owering induc-

tion and controlled pollinations within 12.5years. 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, Aor AD effect, in contrast to the result reported by Resende

etal. (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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