Estimates of Additive, Dominance and
Epistatic Genetic Variances from a
Clonally Replicated Test of Loblolly Pine
Fikret Isik, Bailian Li, and John Frampton
ABSTRACT. Nine full-sib families were generated using a factorial mating design consisting
of three female and three male loblolly pine (Pinus taeda L.) parents. Full-sib seedlings and
clones of the same families were planted in two test sites in Alabama and Florida. Additive,
dominance, and epistatic genetic variances were estimated for growth traits and for fusiform
rust incidence for ages 1 through 6. Epistatic variances did not have a significant role in growth
traits, but additive gene actions were the major source of genetic variance in loblolly pine.
Dominance variance for height, diameter, and volume was negligible at early ages, but it was
considerable at age 6, particularly for volume. Fusiform rust incidence appeared to be partially
under additive and epistatic gene actions and genetic differences among the clones within
families accounted for 48.6% of the total variance. Within-plot variance for clones was always
smaller than that within-plot variance for seedlings of the same full-sib families. Clonally
replicated progeny tests may provide special advantages for loblolly pine tree improvement
programs, as they would substantially increase the efficiency of testing by reducing the
microenvironmental variance and better estimation of genetic parameters. This may provide
greater genetic gains, particularly for fusiform rust incidence. Potential effects of the small
parental size and violations of the assumptions of the genetic model are discussed. Negative
additive and nonadditive genetic correlations between the growth traits and fusiform rust
incidence are encouraging for rapid and simultaneous improvement of the traits during the
same cycle selection. FOR. SCI. 49(1):77–88.
Key Words: Pinus taeda, additive, dominance and epistatic gene actions, nonadditive genetic
correlations.
G
ENETIC VARIANCE CAN BE PARTITIONED into additive,
dominance, and epistatic variances (Falconer and
Mackay 1996, p. 122–131). Additive effects of
genes are cumulative over generations and are the main
source of genetic variation exploited by most plant breeding programs. Quantitative geneticists have generally ignored the interactions between alleles at a locus (dominance), and particularly the interactions of alleles between
loci (epistasis) (Lynch and Walsh 1998, p. 82–92). Igno-
rance of epistasis is particularly common in forest trees
because of substantial limitations in the statistical power
and experimental methods required to partition the nonadditive variance into its components (Foster and Shaw
1988). However, depending on the gene frequencies involved, epistatic interactions could greatly inflate the
additive and/or dominance component estimates of genetic variance (Lynch and Walsh 1998, p. 82–92). A
considerable number of theoretical and empirical studies
Fikret Isik, North Carolina State University College of Natural Resources, Campus Box 8002, Raleigh, NC 27695—Phone:
(919) 515-5029; Fax: (919) 515-3169, E-mail: [email protected]. Bailian Li, North Carolina State University, College of
Natural Resource, Campus Box 8002, Raleigh, NC 27695; E-mail: [email protected]. John Frampton, North Carolina
State University, College of Natural Resources, Campus Box 8002, Raleigh, NC 27695—E-mail: [email protected].
Acknowledgments: Funding for this study was initiated by the industrial supporters of the North Carolina State University
Project on Tissue Culture and continued by the NCSU-Industry Cooperative Tree Improvement Program, the Christmas
Tree Genetics Program and the North Carolina Agricultural Research Service. We would like to thank Dr. Tim Mullin and
three anonymous reviewers for their careful and constructive criticisms of the paper.
Manuscript received, February 26, 2001, accepted December 12, 2001.Copyright © 2003 by the Society of American Foresters
Forest Science 49(1) 2003
77
have shown that epistasis plays a central role in evolution
and speciation, heterosis, and polymorphism (Weller 1976,
Wright 1980, Minvielle 1987, Lynch and Walsh 1998, p.
86–92). Two estimation methods based on the level of
gene interactions have been proposed to isolate epistatic
variance from other genetic variance components in forest
tree species. Foster and Shaw (1988) estimated epistatic
variance from a clonally replicated experiment using the
expected covariances among relatives. Their model assumed that epistasis arises mainly from higher level loci
interactions. In contrast, the model proposed by Wu (1996)
was based on the assumption that epistasis for a quantitative trait is limited to interactions between a pair of
quantitative-trait loci (QTLs). If low-order gene interactions have a major influence, the additive variance is
inflated mainly by second and third order additive epistatic genetic variances. Similarly, dominance variance is
partially contaminated with part of epistatic genetic variance (Foster 1990, Mullin and Park 1992, Wu 1996). On
the other hand, total epistatic variance will be underestimated when low-order interactions are relatively large
(Mullin et al. 1992, Wu 1996). Each model has its own
advantage in precision depending on the assumptions and
the number of major genes involved in the epistasis.
However, Foster and Shaw’s method is easier to apply
compared to Wu’s method. The latter method requires
testing of the parents with siblings and clones in the same
genetic test.
In the literature there are considerable numbers of
studies reporting contrasting results regarding a few QTLs
(e.g., Doabley and Stec 1991, Paterson et al. 1991,
Bradshaw and Stettler 1995, Wilcox et al. 1996) versus
many QTLs (e.g., Paterson et al. 1988, Paterson et al.
1990, Long et al. 1995, Amerson et al. 1997, Kao et al.
1999, Kaya et al. 1999) affecting quantitative traits in
laboratory animals and crops. When the number of QTLs
affecting the trait is not known or is difficult to determine,
then both methods may be used (Wu 1996). When height
and diameter growth of forest trees are considered poly
genic traits, the assumption of estimates of the genetic
variance components can be relaxed (Mullin et al. 1992).
There are numerous studies on plants and laboratory animals showing that quantitative traits are controlled by
genes at many loci (Falconer and Mackay 1996, p. 100–
104, Miklas et al. 1999, Frewen et al. 2000). Marques et al.
(1999) hypothesized three QTLs for mortality, nine for
adventitious rooting, four for petrification (surviving
unrooted cuttings), one for sprouting ability, and four for
the stability of adventitious rooting. In loblolly pine, 13
different height-increment and 8 different diameter-increment QTLs were detected (Kaya et al. 1999).
Very little is known about the contribution of epistatic
variance to total genetic variance and its effect on growth
of loblolly pine. Using two 4 × 4 factorial mating designs
and replicated clonal test of loblolly pine, Paul et al.
(1997) reported epistatic genetic variance at age 1 but not
ages 2 to 5 in one of the factorials. In the same study,
epistatic genetic variance was detected at two ages out of
78
Forest Science 49(1) 2003
five in the other factorial. Foster (1990) reported very high
additive genetic control and no epistatic gene effects in
rooting of loblolly pine cuttings. However, in black spruce
(Picea mariana) 36% of the genetic variance for height
growth at age 5 was due to epistatic variance, and genetic
gain from clonal selection was much higher by capturing
the epistatic variance (Mullin et al. 1992). In the same
study, the additive genetic variance for height decreased from 66% to 38% between ages 5 and 10, while
the dominance and epistatic genetic portions increased
from 3% to 13% and 31% to 49%, respectively (Mullin
and Park 1994).
The levels of the additive and nonadditive genetic
variance in traits important for tree breeding programs
have a great impact on the determination of the breeding
strategies (Stonecypher and McCullough 1986, Foster and
Shaw 1987). Also, it is very important for designing
efficient deployment strategies. For example, deployment
of controlled pollinated families as seedlings or rooted
cuttings would be sufficient to use additive genetic variance, but to more fully exploit dominance and epistatic
genetic variance, clonal deployment would be required.
Loblolly pine is the most economically important forest
tree species in the southern United States, where its propagation by rooted cuttings has been studied during the last
two decades. The technology to root loblolly pine has
progressed such that several forestry organizations in the
southern United States have initiated pilot-scale rootedcutting production (Goldfarb et al. 1998, Frampton et al.
2000). Many potential benefits of rooted cutting material
have been reported, including uniformity, lower incidence
of fusiform rust disease (Cronartium quercuum sp.
fusiforme) and greater genetic gain (Foster and Anderson
1989, Frampton et al. 2000, McRae et al. 1993). A tree
improvement program based on clonally replicated genetic tests was proposed to improve fusiform rust resistance (Foster and Shaw 1987). Rooted-cutting technology
will also make it feasible to partition the genetic variance
into its components and to exploit nonadditive genetic
variance in deployment programs to increase the gain from
tree improvement programs (Foster and Shaw 1988). For
loblolly pine, there is still a lack of information regarding
the contribution of nonadditive genetic variance, particularly epistatic genetic variance to growth and fusiform rust
disease. A few studies have reported considerable variation among clones within families for growth traits, fusiform rust resistance, and root collar diameter in loblolly
pine (Foster et al. 1985, Foster 1988, Paul et al. 1997).
However, to our knowledge, comparison of genetic variances estimated from seedlings and clones of the same
families has not been done in the literature, which could
give further insight into the genetic basis of economically
important traits. Estimation of nonadditive genetic variances for loblolly pine may help to develop more efficient
breeding strategies to maximize gain (McKeand et al.
1986). Using full-sib seedlings and clones deployed in the
same field tests derived from a factorial mating design, the
objectives of this study were:
1. to compare observed variance components from cuttings
and seedlings of the same families,
2. to partition genetic variance into additive, dominant, and
epistatic components and examine the time trends and
differences among traits, and
3. to estimate additive and nonadditive genetic correlations
among fusiform rust incidence and growth traits.
Material and Methods
Genetic Material
A factorial mating design consisting of three unrelated
individuals as females (2, 3, 6) and three others as males (1,
4, 5) was implemented to produce nine full-sib families of
loblolly pine. The seeds from the full-sib families were
utilized to grow hedges in greenhouse containers in December 1988 (Anderson et al. 1999). One harvest of cuttings was
rooted to produce planting material in 1990, and vegetative
propagation continued through five sequential harvests in
1991. Containerized cuttings were rooted under mist in a
greenhouse and transferred outdoors for hardening. Approximately 4 months prior to establishment, cold stratified seeds
of the same nine families were sown and then cultured in the
greenhouse. One month prior to field planting, the seedlings
were moved outdoors for hardening. Rooted cuttings propagated from hedges and seedlings were used to establish one
study site in Monroe County, Alabama, in spring of 1990.
Cuttings from subsequent harvests and seedlings were used
to establish the second study site in Nassau Co., Florida, in
spring of 1991 (Anderson et al. 1999, Frampton et al. 2000).
The reason for inclusion of the seedlings was to compare the
growth of seedlings and cuttings of the same families, which
has been reported by Frampton et al. (2000).
Field Experimental Design
A randomized block design with six replications (blocks)
was installed at two locations. To avoid complications associated with possible differences between the initial growth
rates of the rooted cuttings and seedlings, a split plot design
was employed as suggested by Frampton and Foster (1993).
Each block was split into two main plots, one for seedlings
and one for rooted cuttings (Figure 1). Each main plot was
Figure 1. Experimental field design used for clonally replicated loblolly pine. Each block was split into
two main plots, one for seedlings and one for rooted cuttings. Seedlings of a full-sib family (S1) were
randomly allocated to the two-seedling subplots. Similarly, clones (C1 to C6) produced for each fullsib family were randomly distributed within the main plot. The main plots were buffered with border
trees (S and C) of the same propagule type (seedlings or rooted cuttings).
Forest Science 49(1) 2003
79
Table 1. Field experimental design, traits studied, and observation ages for loblolly pine clonally replicated
experiment.
Experimental design
Test sites and measurement ages
(split plot design)
Traits
Florida site
Alabama site
2 sites
Height
1, 2, 4, 5, 6
1, 2, 3, 4, 6
6 reps/site
Dbh
4, 5, 6
4, 6
3 males, 3 females/9 full-sib families
Volume
4, 5, 6
4, 6
5 to 9 clones/full-sib family/ main plot
Rust incidence
4, 5, 6
3, 4, 6
3 subplots of seedlings/family/main plot
surrounded by one row of border trees of the same propagule
type. Subplots of rooted cuttings were composed of two
ramets of a clone while those of seedlings had two full-sibs.
Each full-sib family was represented by three seedling subplots and five to nine rooted cutting subplots per main plot.
The design was balanced at the family level but was unbalanced at the clonal level across the blocks and sites. The
analyses included all clones in order to have a larger sample
size. The total number of (nonborder) trees planted in the
Florida and Alabama sites was approximately 1,056 and
1,152, respectively. About 324 trees per site were seedlings.
Both were established at a spacing of about 2.5 × 2.5 m
(Frampton et al. 2000).
Data Collection
Total height of each tree was measured annually for years 1
through 6 at both sites, except for age 3 at the Florida site and
age 5 at the Alabama site (Table 1). Diameter at breast height
(dbh) was measured at ages 4 through 6 at both sites (except
at age 5 at the Alabama site). Height was measured to the
nearest 3.0 cm (1/10 ft) at ages 1 and 2, to the nearest 14.2 cm
(1/2 ft) at ages 4 and 6. Diameter was measured to the nearest
2.5 mm (1/10 in.) at ages 4 and 6. Volume was estimated
according to Goebel and Warner (1966). The presence or
absence of one or more fusiform rust gall(s) was recorded for
each tree from years 3 to 6 at both sites, except for age 5 at the
Alabama site and for age 3 at the Florida site.
Statistical Analysis
Analyses of variance were conducted to detect differences
among families and within families using the model given in
Table 2a for rooted cuttings data and the model given in Table
2b for the seedling data. Fusiform rust incidence (as a
percentage of all trees infected) was analyzed on a clone-site
mean basis. The trait was transformed using the arcsine
function to satisfy the assumptions of analysis of variance.
Clone means for fusiform rust incidence were based on
approximately 12 trees per site. Thus, a reduced analysis of
variance model was applied for the fusiform rust incidence,
i.e., dropping the replication and its interactions terms from
the model (Table 3a). For the seedling data, fusiform rust
incidence plot means were calculated as a percentage of
infected trees out of six trees in a block. The linear model was
the same as growth traits for the seedling data, except for
dropping the replication × female × male interaction and
plot-to-plot terms (Table 3b). In the analyses, a split-plot field
layout design was not used because one of the main objectives of the study was to compare genetic variances estimated
from seedlings and rooted cuttings of the same full-sib
families. Instead, a factorial mating design was used to
Table 2a. Analysis of variance and expected mean squares for loblolly pine factorial mating design using rooted
cuttings.
Source†*
Expected mean squares
DF
Fp
VE + nVCL(FM)*R(S) + cnVR(S)*F*M + mcnVR(S)*F + bcnVS*F*M + bnVS*CL(FM) + bmcnVS*F +
f-1
sbnVCL(FM) + sbcnVF*M + sbmcnVF
Mq
VE + nVCL(FM)*R(S) + cnVR(S)*F*M + fcnVR(S)*M + bcnVS*F*M + bnVS*CL(FM) + bfcnVS*M +
m-1
sbnVCL(FM) + sbcnVF*M + sbfcnVM
FMpq
VE + nVCL(FM)*R(S) + cnVR(S)*F*M + bcnVS*F*M + bnVS*CL(FM) + sbnVCL(FM) + sbcnVF*M
(m-1)(f-1)
C(FM)k(pq)
VE + nVCL(FM)*R(S) + bnVS*CL(FM) + sbnVCL(FM)
(c-1)fm
Si
VE + nVCL(FM)*R(S) + cnVR(S)*F*M + fcnVR(S)*M + mcnVR(S)*F + fmcnVR(S) + bcnVS*F*M +
s-1
bnVS*CL(FM) + bfcnVS*M + bmcnVS*F + bfmcnVS
R(S)j(i)
VE + nVCL(FM)*R(S) + cnVR(S)*F*M + fcnVR(S)*M + mcnVR(S)*F + bmcnVR(S)
(b-1)s
SFip
VE + nVCL(FM)*R(S) + cnVR(S)*F*M + bnVS*CL(FM) + bcnVS*F*M + mcnVR(S)*F + bmcnVS*F
(s-1)(f-1)
SMiq
VE + nVCL(FM)*R(S) + cnVR(S)*F*M + bnVS*CL(FM) + bcnVS*F*M + fcnVR(S)*M + bfcnVS*M
(s-1)(m-1)
SFMipq
VE + nVCL(FM)*R(S) + bnVS*CL(FM) + bcnVS*F*M
(s-1)(f-1)(m-1)
SC(FM)ik(pq)
VE + nVCL(FM)*R(S) + bnVS*CL(FM)
(s-1)(c-1)fm
R(S)Fj(i)p
VE + nVCL(FM)*R(S) + cnVR(S)*F*M + mcnVR(S)*F
(r-1)s(f-1)
R(S)Mj(i)q
VE + nVCL(FM)*R(S) + cnVR(S)*F*M + fcnVR(S)*M
(r-1)s(m-1)
R(S)FMj(i)pq
(r-1)s(f-1)(m-1) VE + nVCL(FM)*R(S) + cnVR(S)*F*M
VE + nVCL(FM)*R(S)
R(S)C(FM)k(pq)j(i)
(r-1)s(c-1)fm
El(k(j)(i))
VE
srfmc(n-1)
* Linear model y = u + Fp + Mq + FMpq + C(FM)k(pq) + Si + SFip + SMiq + SFMipq + SC(FM)ik(pq) + R(S)j(i) + R(S)Fj(i)p + R(S)Mj(i)q + R(S)FMj(i)pq +
R(S)C(FM)k(pq)j(i) + El(k(j)(i)). Fp female, Mq male, FMpq female male interaction, C(FM)k(pq) clone within female male, Si site, R(S)j(i) block within site,
SFip site female, SMiq site male, SFMipq site female male, SC(FM)ik(pq) site clone, R(S)Fj(i)p block female, R(S)Mj(i)q block male, R(S)FMj(i)pq block female
male, R(S)C(FM)j(i)k(pq) plot to plot, El(ijpqk) within plot effect. Coefficients are for demonstration purposes only and assume complete balance design.
The actual analysis was done with SAS GLM with fraction. c number of clones per family (c = 5 to 9), n number of ramets per clone per plot (n = 2), b
number of blocks (b = 6), m number of males (m = 3), f number of females (f = 3), s number of sites (s = 2).
80
Forest Science 49(1) 2003
Table 2b. Analysis of variance and expected mean squares
seedlings.
Source*
DF
Fp
VE + nVR(S)*T(FM) + tnVR(S)*F*M
f-1
Mq
VE + nVR(S)*T(FM) + tnVR(S)*F*M
m-1
FMpq
VE + nVR(S)*T(FM) + tnVR(S)*F*M
(m-1)(f-1)
Si
VE + nVR(S)*T(FM) + tnVR(S)*F*M
s-1
+ bftnVS*M + bfmtnVS
SFip
VE + nVR(S)*T(FM) + tnVR(S)*F*M
(s-1)(f-1)
SMiq
VE + nVR(S)*T(FM) + tnVR(S)*F*M
(s-1)(m-1)
SFMipq
(s-1)(f-1)(m-1) VE + nVR(S)*T(FM) + tnVR(S)*F*M
R(S)j(i)
VE + nVR(S)*T(FM) + tnVR(S)*F*M
s (b-1)
R(S)Fj(i)p
VE + nVR(S)*T(FM) + tnVR(S)*F*M
(r-1)s(f-1)
R(S)Mj(i)q
VE + nVR(S)*T(FM) + tnVR(S)*F*M
(r-1)s(m-1)
R(S)FMj(i)pq
VE + nVR(S)*T(FM) + tnVR(S)*F*M
(r-1)s(f-1)(m-
for loblolly pine factorial mating design using full-sib
+
+
+
+
Expected mean squares
mtnVR(S)*F + btnVS*F*M + sbtnVF*M + bmtnVS*F + sbmtnVF
ftnVR(S)*M + btnVS*F*M + sbtnVF*M + bftnVS*M + sbftnVM
btnVS*F*M + sbtnVF*M
mtnVR(S)*F + ftnVR(S)*M + fmtnVR(S) + btnVS*F*M + bmtnVS*F
+
+
+
+
+
+
mtnVR(S)*F + btnVS*F*M + bmtnVS*F
ftnVR(S)*M + btnVS*F*M + bftnVS*M
btnVS*F*M
mtnVR(S)*F + ftnVR(S)*M + fmtnVR(S)
mtnVR(S)*F
ftnVR(S)*M
1)
TFM(RS)t(j(i)pq)
Et(j(i)pq))
(r-1)s(t-1)fm
srfm(n-1)
VE + nVR(S)*T(FM)
VE
* Linear model y = u + Fp + Mq + FMpq + Si + SFip + SMiq + SFMipq + R(S)j(i) + R(S)Fj(i)p + R(S)Mj(i)q + R(S)FMj(i)pq + TFM(RS)j(i)t(fm) + El(ijpqt). Where
TFM(RS) is plot to plot effect within blocks families and sites, E is within plot variance. See Table 2a for the definition of other codes. Coefficients are for
demonstration purposes only and assume complete balance design. The actual analysis was done with SAS GLM with fraction. n number of seedlings per
family per block per plot (n = 2), t is number of plots per family within each replication (t = 3), b number of blocks (b = 6), m number of males (m = 3), f
number of females (f = 3), s number of sites (s = 2).
analyze seedlings and rooted cuttings separately. For all
analyses, variance components were estimated by equating
the mean squares to the expected mean squares (Table 2a,
Table 2b). The equations were then solved using the REML
option of the VARCOMP procedure of SAS (SAS/STAT
1989). All terms in the models were considered random when
estimating the variance components. Standard errors of variance components were estimated according to Becker (1984,
p. 44–45).
Estimation of Genetic Variances
Additive (σ2A), dominance (σ2D) and epistatic (σ2I) genetic variances were estimated according to the Foster and
Shaw (1988) model:
Estimate of additive genetic variance for seedlings and
rooted cuttings:
ˆ 2A = 2( σ2M + σ2F ) = σ2A +
σ
1
4
σ2AA +
1 σ2
16 AAA
+ ...
(2a)
SE ( σ2A ) = Var ( σ2A ) = Var (2( σ2M + σ2F ))
= 4[Var ( σ2M ) + Var ( σ2F ) + 2Cov (( σ2M σ2F )]
(2b)
Table 3a. Variance components for each entry in the model, their standard errors and percentages of the variance
components for height, diameter, volume, and fusiform rust incidence estimated from rooted cuttings at age 6.
Variance
Height
Diameter
Volume
Rust
components
Estimate ± SE
%
Estimate ± SE
%
Estimate ± SE
%
Estimate ± SE
%
0.0 ± 0.0
0.0
0.1061 ± 0.1139
5.5
0.0738 ± 0.0863
6.1
0.0531 ± 0.0815
5.1
σ 2F
σ 2M
0.1129 ± 0.1257
2.3
0.0327 ± 0.0542
1.7
0.0657 ± 0.0913
5.5
0.2155 ± 0.2520
20.6
σ 2FM
σ 2C ( FM )
0.0021 ± 0.0138
0.1
0.0020 ± 0.0159
0.1
0.0107 ± 0.0233
0.9
0.0 ± 0.0
0.0
0.0564 ± 0.0277
1.2
0.0604 ± 0.0329
3.1
0.0833 ± 0.0360
6.9
0.5082 ± 0.1235
48.6
σS2
2
σSF
2
σSM
2
σSC
( FM )
3.970 ± 5.671
79.7
0.9264 ± 1.350
47.9
0.1144 ± 0.2147
9.5
0.0274 ± 0.0539
2.6
0.0 ± 0.0
0.0
0.0 ± 0.0
0.0
0.0015 ± 0.0095
0.1
0.0003 ± 0.0150
0.0
0.0087 ± 0.0191
0.2
0.0224 ± 0.0315
1.2
0.0258 ± 0.0335
2.1
0.0146 ± 0.0296
1.4
—*
—
0.0753 ± 0.0278
1.4
0.1015 ± 0.0326
5.3
0.0774 ± 0.0300
0.0
2
σSFM
σ 2R (S )
0.0019 ± 0.0138
0.0
0.0 ± 0.0
0.0
0.0 ± 0.0
6.4
0.2034 ± 0.0973
4.1
0.1041 ± 0.0504
5.4
0.1514 ± 0.0711
σ 2R (S )F
0.0101 ± 0.0081
0.1
0.0031 ± 0.0064
0.2
σ 2R (S )M
0.0155 ± 0.0100
0.2
0.0044 ± 0.0069
0.0 ± 0.0
0.0
0.0 ± 0.0
σ 2R (S )FM
0.0 ± 0.0
0.0
12.6
—
—
0.0012 ± 0.0073
0.1
—
—
0.2
0.0 ± 0.0
0.0
—
—
0.0
0.0 ± 0.0
0.0
—
—
σ 2R (S )*C ( FM )
0.0885 ± 0.0260
1.7
0.0720 ± 0.0282
3.7
0.1131 ± 0.0278
9.4
—
—
σ 2E
0.4460 ± 0.0269
8.8
0.5092 ± 0.0306
25.8
0.4829 ± 0.0268
40.2
0.2891 ± 0.0571
27.7
* These terms were not included in the analysis of variance for rust incidence due to using a reduced model based on clone means at each test site.
Forest Science 49(1) 2003
81
Table 3b. Variance components for each entry in the model, their standard errors and percentages of the variance
components for height, diameter, volume, and fusiform rust incidence using full-sib seedlings at age 6.
Variance
Height
Diameter
Volume
Rust
components
Estimate ± SE
%
Estimate ± SE
%
Estimate ± SE
%
Estimate ± SE
%
2
0.0
±
0.0
0.0
0.0342
±
0.0522
1.3
0.0185
±
0.0277
1.3
0.1432
±
0.2098
11.6
σF
σ 2M
0.0375 ± 0.0605
0.6
0.0 ± 0.0
0.0
0.0065 ± 0.0526
0.5
0.4693 ± 0.5409
37.9
σ 2FM
σS2
2
σSF
2
σSM
2
σSFM
σ 2R (S )
0.0143 ± 0.0153
0.2
0.0190 ± 0.0221
0.7
0.0113 ± 0.0158
0.8
0.1016 ± 0.0930
8.2
4.995 ± 7.147
80.8
1.492 ± 2.187
55.0
0.3393 ± 0.5402
24.5
0.0 ± 0.0
0.0
0.0 ± 0.0
0.0
0.0109 ± 0.0206
0.4
0.0 ± 0.0
0.0
0.0347 ± 0.0501
2.8
0.0121 ± 0.0331
0.2
0.0350 ± 0.0420
1.3
0.0489 ± 0.0640
3.5
0.0511 ± 0.0635
4.1
0.0 ± 0.0
0.0
0.0 ± 0.0
0.0
0.0 ± 0.0
0.0
0.0 ± 0.0
0.0
0.2833 ± 0.1467
4.6
0.1963 ± 0.1045
7.2
0.2055 ± 0.1075
14.8
0.0692 ± 0.0519
5.6
σ 2R (S )F
0.0114 ± 0.0178
0.2
0.0025 ± 0.0188
0.1
0.0152 ± 0.0183
1.1
0.0094 ± 0.0324
0.7
σ 2R (S )M
0.0744 ± 0.0383
1.21
0.0544 ± 0.0337
2.0
0.0448 ± 0.0279
3.2
0.0025 ± 0.0295
0.2
σ 2R (S )FM
0.0 ± 0.0
0.0
0.0 ± 0.0
0.0
0.0 ± 0.0
0.0
—*
—
σ 2TFM ( RS )
0.0047 ± 0.0496
0.1
0.0 ± 0.0
0.0
0.0 ± 0.0
0.0
—
—
σ 2E
0.7506 ± 0.0466
12.1
0.8689 ± 0.0539
32.0
0.7721 ± 0.0480
50.2
0.3569 ± 0.0622
28.8
* These terms were not included in the analysis of variance for rust incidence due to using a reduced model based on clone means at each test site.
Estimate of dominance genetic variance for seedlings and
rooted cuttings:
2
2
ˆ 2D = 4 σMF
σ
= σD
+
1
2
σ2AA +
1
2
σ2AD +
1
4
σ2DD + ...
(3a)
SE ( σ2D ) = Var ( σ2D ) = Var ( 4 σ2FM ) = 16Var ( σ2FM )
(3b)
estimates, as suggested by Snyder and Namkoong (1978).
Additive and nonadditive genetic correlations for seedlings
and rooted cuttings were estimated among growth traits
(height, diameter at breast height, volume) and fusiform rust
incidence at age 4 and at age 6. Approximate standard errors
of additive genetic correlations were estimated according to
Falconer and Mackay (1996, p. 316), and standard errors of
nonadditive genetic correlations according to Stuart and Ord
(1991, p. 980–981).
Estimate of epistatic genetic variance for rooted cuttings:
Results
2
2
σˆ 2I = σ C2 ( FM ) − (σ M
+ σ 2F ) − 3σ MF
=
1
2
4 σ AA
+
1
2
2 σ AD
+
3
2
4 σ DD
+ ...
(4a)
Var (σ 2I ) = Var (σ C2 ( FM ) − (σ 2M + σ 2F ) − 3σ 2MF
= Var (σ C2 ( FM ) + Var (σ 2M ) + Var (σ 2F )
2
2
+9Var (σ MF
) − 2Cov(σ C2 ( FM )σ M
)
2
−2Cov(σ C2 ( FM )σ 2F ) − 6Cov(σ C2 ( FM )σ MF
)
(4b)
2
2
+2Cov(σ M
σ 2F ) + 6Cov(σ 2FM σ M
)
+6Cov(σ 2FM σ 2F )
SE (σ I2 ) = Var (σ I2 )
Frampton et al. (2000) reported the differences in growth
and fusiform rust incidence of the seedlings and rooted
cuttings included in this study. Briefly, seedlings and
rooted cuttings did not differ significantly for height,
diameter, and volume at both sites for all ages, except age
1 for height. Least squares means for clones and seedlings
were 6.0 m and 5.6 m for height at the Florida site; they
were 7.8 m and 7.8 m at the Alabama site at age 6.
Similarly, least squares means of clones and seedlings for
volume were 16.7 dm3 and 15.0 dm3 for the Florida site
and 39.9 and 41.9 dm3 for the Alabama site, respectively.
However, seedlings of the same full-sib families had a
significantly greater fusiform rust incidence than the rooted
cuttings in both the Florida (22.3 versus 15.6%) and
Alabama (51.0 versus 46.0%) sites at age 6 (Frampton et
al. 2000).
Observed Variance Components
Epistatic genetic variance is approximate and always less
than the actual value. Additive and dominance genetic variances are biased upward due to contamination of a part of the
epistatic variance. Coefficients of variation (CV) were estimated to compare additive, dominance and epistatic variances to remove scale effects of different traits and different
ages. We considered variance components to be important if
the standard errors were less than half of the component
82
Forest Science 49(1) 2003
Variance components for the traits studied and distribution of the variance components among entries in the
models at age 6 are given in Table 3. Variance due to
female and male parents varied for the traits studied. For
both rooted cuttings and seedlings, the female component
was higher for some traits, whereas the male component
was higher for other traits. However, when the total genetic variance explained by female, male, and their inter-
actions is considered, rooted cuttings of the same families
explained much higher percentages than did seedlings for
all the growth traits. For example, σ2F, σ2M and σ2FM
together made up 12.5% of the total genetic variance for
volume from rooted cuttings versus 2.6% from seedlings.
This was reversed for fusiform rust incidence. Female ×
male interaction variance was not statistically significant
for any trait and accounted for less than 1% of the total
variance for both rooted cuttings and seedlings, except for
fusiform rust incidence estimated from seedlings. Female
× male interaction variance components from seedlings
were in general greater than those from rooted cuttings.
Variances due to genetic differences among the clones
within families for height, diameter, volume, and fusiform
rust incidence were statistically significant at age 6 (Table
3a). The clone component explained 6.9% of the total variance for volume (Table 3). A very high percentage (48.6%)
of the total variance for rust incidence was because of
variation among clones within families.
For all the growth traits studied, site and within plot
variances made up the greater proportion of the total observed variance (Table 3). Within plot variance from rooted
cuttings was always smaller than that of seedlings. For
example, this component for height was 8.8% from rooted
cuttings whereas it was 12.1% from seedlings. For diameter,
the within plot variance was 25.8 vs 32.0% from rooted
cuttings and seedlings, respectively (Table 3a, 3b).
Casual (Genetic) Variance Components
Additive, dominance, and epistatic genetic variances as
well as their standard errors estimated from rooted cuttings
and seedlings are given in Table 4. Coefficients of genetic
variation were used to avoid scale effect when comparing
different traits or the same trait at different ages (Steel et al.
1997, p. 26–27). Variances due to additive effects estimated
from rooted cuttings were always greater than the estimates
from seedlings for growth traits. Additive CVs for height
estimated from rooted cuttings were 0.1 to 3.5% greater than
the CVs estimated from seedlings. For diameter and volume,
the differences between CVA estimated from cuttings and
seedlings were even greater. CVA of cuttings for volume at
age 6 was two times that of the seedlings. Additive genetic
variance coefficients (CVA) decreased with age for all growth
traits. For instance, CVA from rooted cuttings decreased from
9.4 to 6.8, whereas CVA from seedlings dropped from 9.3 to
4.0 for height. Similar to growth traits, fusiform rust incidence had greater CVA from rooted cuttings at age six;
however, this relationship was reversed at age 4.
Dominance genetic variance estimated from seedlings
(CVD(s)) was greater than that from rooted cuttings for all the
growth traits (Table 4). For volume, CVD was considerably
higher, both from rooted cuttings (8.9) and seedlings (9.6) at
age 6 compared to height and diameter. There was an increasing trend of CVD estimated from rooted cuttings and seedlings for growth traits, particularly for height. Dominance
Table 4. Additive, dominance, epistatic genetic variances, their standard errors, and coefficients of genetic variances for
height (HT), diameter (DBH), volume (VOL), and fusiform rust incidence in loblolly pine at various ages.
HT1
HT2
HT4
HT6
DBH4
DBH6
A (rc)
0.132 ± 0.142
0.162 ± 0.146
0.121 ± 0.138
0.229 ± 0.255
0.166 ± 0.161
0.277 ± 0.252
A (s)
0.107 ± 0.120
0.082 ± 0.086
0.069 ± 0.088
0.075 ± 0.121
0.075 ± 0.127
0.068 ± 0.104
D (rc)
0.0 ± 0.0
0.0 ± 0.0
0.0 ± 0.0
0.011 ± 0.057
0.0 ± 0.0
0.009 ± 0.054
NA (s)
0.0 ± 0.0
0.0 ± 0.0
0.011 ± 0.051
0.057 ± 0.061
0.008 ± 0.055
0.076 ± 0.088
I (rc)
–0.052 ± 0.081
–0.050 ± 0.078
–0.006 ± 0.076
–0.064 ± 0.141
–0.058 ± 0.085
–0.082 ± 0.143
D/A (rc)
0.0
0.0
0.0
0.04
0.0
0.03
D/A (s)
0.0
0.0
0.16
0.76
0.11
1.12
I/A (rc)
0.0
0.0
0.0
0.0
0.0
0.0
CVA (rc)
9.4
11.2
6.9
6.8
11.3
10.9
CVA (s)
9.3
7.7
5.4
4.0
7.6
5.5
CVD (rc)
0.0
0.0
0.0
1.4
0.0
2.0
CVD (s)
0.0
0.0
2.2
35
2.5
5.8
CVI (rc)
0.0
0.0
0.0
0.0
0.0
0.0
A (rc)
A (s)
D (rc)
NA (s)
I (rc)
D/A (rc)
D/A (s)
I/A (rc)
CVA (rc)
CVA (s)
CVD (rc)
CVD (s)
CVI (rc)
VOL4
0.279 ± 0.252
0.082 ± 0.120
0.0 ± 0.0
0.0 ± 0.0
–0.056 ± 0.098
0.0
0.0
0.0
26.1
14.6
0.0
0.0
0.0
VOL6
0.310 ± 0.281
0.050 ± 0.120
0.042 ± 0.093
0.045 ± 0.063
–0.088 ± 0.149
0.14
0.82
0.0
24.2
10.6
8.9
9.6
9.6
Rust4
0.304 ± 0. 365
1.08 ± 1.07
0.0 ± 0.0
0.298 ± 0.396
0.368 ± 0.228
0.0
0.28
1.21
53.6
59.3
0.0
31.2
58.9
Rust6
0.537 ± 0.527
1.23 ± 1.16
0.0 ± 0.0
0.421 ± 0.372
0.240 ± 0.295
0.0
0.33
0.45
66.6
62.1
0.0
36.4
44.5
NOTE: A = additive genetic variance estimated from rooted cuttings (rc) and seedlings (s), D = dominant genetic variance estimated from rooted cuttings
(rc) and seedlings (s), I = epistatic genetic variance estimated from rooted cuttings, NA = nonadditive genetic variance estimated from seedlings.
CVA = coefficient of additive genetic variance, CVI = coefficient of epistatic genetic variance, CVD = coefficient of dominance genetic variance,
D/A = dominance to additive variance ratio, I/A = epistatic to additive variance ratio. Coefficients of genetic variances were estimated as CV =
sqrt(genetic variance)/mean × 100. Standardized or transformed means from the combined site analyses were used in the estimation.
Forest Science 49(1) 2003
83
genetic variance for fusiform rust incidence estimated from
rooted cuttings was essentially zero at both ages. In contrast,
CVD estimated from seedling was considerably high at age 4
(31.2) and at age 6 (36.4).
Epistatic genetic variances estimated from rooted cutting
data were negative for all growth traits at all ages (Table 4).
We assumed negative epistatic genetic variances were zero.
In contrast to growth traits, epistatic genetic variance (CVI)
for the rust incidence was considerable; the coefficients of
variation were 58.9 at age 4 and 44.5 at age 6.The ratio of
epistatic and dominance variance to additive variance may be
taken as an indicator of the importance of nonadditive variance. The ratio of dominance to additive genetic variance
from rooted cuttings for all traits was very small, varying
from 0.0 to 0.14 (Table 4). However, this ratio estimated from
the seedlings was greater compared to the ratio of rooted
cuttings, varying from 0.0 to 1.12 for growth traits. As
expected, the ratio increased for all growth traits because of
an increasing and decreasing trend of additive and dominance genetic variances, respectively, by age. For example,
the ratio of dominance to additive genetic variance increased
to 1.12 for diameter and to 0.82 for volume at age 6. For
fusiform rust incidence, dominance genetic variance was
about one-third of the additive genetic variance at both ages,
except for seedlings at age 4.The ratio of epistatic variance to
additive genetic variance was not different from zero for all
the growth traits. The importance of epistatic genetic variance for rust incidence was more apparent when compared to
additive genetic variance. It was about 20% greater than the
additive genetic variance (ratio = 1.21) at age 4 and was about
one-half of the additive variance at age 6.
Additive and Nonadditive Genetic Correlations
Additive genetic correlation between height and fusiform
rust incidence was positive and moderate (0.29) at age 4, but
weak at age 6 based on cuttings (Table 5). Additive genetic
correlations estimated from seedlings were weak (0.02 –
0.07) at both ages. Diameter had moderate and negative
additive genetic correlations with fusiform rust at age 4 and
at age 6; coefficients varied from –0.25 to –0.47 and were
similar in magnitude for seedlings and rooted cuttings. Similarly, volume had negative and moderate additive genetic
correlations with fusiform rust incidence at both ages. Most
correlation coefficients, particularly those based on seedlings, were associated with high standard errors.
Nonadditive genetic correlations were estimated only
from the seedlings and not from the rooted cuttings as
dominance and epistatic genetic variances were almost zero
for rooted cuttings. Nonadditive genetic correlations between height and fusiform rust incidence were weak. Diameter had also weak (0.07) nonadditive genetic correlation
with fusiform rust at age 4; however, the nonadditive genetic
relationship was negative and moderate (–0.43) at age 6.
Nonadditive genetic relations between volume and fusiform
rust incidence were negative and moderate at age 4 (–0.36),
and moderately high (–0.65) at age 6.
Discussion
Distribution of variances for seedlings and cuttings
The uniqueness of this study was to compare rooted
cuttings and seedlings of the same full-sib loblolly pine
families under the same environmental conditions. This
experimental design revealed important information on the
genetic basis of growth traits and fusiform rust incidence
between the two material types. The results clearly showed
that clonally replicated families yielded higher estimates of
variance components for genetic effects than those based on
seedlings with relatively lower standard errors. Better control
of environmental noise and further decomposition of the
within family variance may have contributed to this (Libby
and Jund 1962). Although variances due to clones accounted
for only 1.2 to 6% of the total variance for growth traits, they
were estimated with rather low standard errors. Anderson et
al. (1999) reported a significant clonal variance for rooting
percentage, and clonal differences within families accounted
for 24% of the total variation. In another study on loblolly
pine, the clonal effect was also significant for height, diameter, and volume, and accounted for 14 to 23% of the total
variation (McRae et al. 1993). We found a very high percentage of variance (48.6%) due to clones within families for rust
incidence. Clonal variance may be utilized in loblolly pine
tree breeding strategies to achieve greater gain, particularly
for the reduction of rust incidence. Since there are no marked
differences between seedlings and clones for growth performance in loblolly pine, tree improvement programs based on
GCA can increase gain by replication of seedlings within
superior families. Stonecypher and McCullough (1986) reported a significant improvement in Douglas-fir (Pseudotsuga
menziessii [Mirb] Franco) using this approach; as did Mullin
et al. (1992) for black spruce (Picea mariana [Mill.] B.S.P).
In this study, within plot error variances estimated for clones
were considerably smaller than the within plot variances of
seedlings of the same families. This is not surprising, since in
Table 5. Additive and nonadditive genetic correlations between fusiform rust incidence and growth traits (height,
diameter and volume) at age four and six in loblolly pine.
Additive genetic correlations
Nonadditive genetic correlations
Rust at age 4
Rust at age 6
Rust at age 4
Rust at age 6
Height (rc)*
0.29 ± 0.09
–0.08 ± 0.22
—†
—
Height (s)††
0.07 ± 0.65
–0.07 ± 0.78
0.02 ± 0.09
0.04 ± 0.09
DBH (rc)
–0.31 ± 0.08
–0.35 ± 0.15
—
—
DBH (s)
–0.25 ± 0.54
–0.47 ± 0.56
0.07 ± 0.09
–0.43 ± 0.07
Volume (rc)
–0.24 ± 0.08
–0.29 ± 0.16
—
—
Volume (s)
–0.13 ± 0.63
–0.28 ± 0.63
–0.36 ± 0.08
–0.65 ± 0.05
* (rc)—Estimation was based on rooted cuttings.
†
Dominance or epistatic genetic variances were not estimated due to zero or negative estimates.
††
(s)—Estimation was based on seedlings.
84
Forest Science 49(1) 2003
addition to all the environmental noise, within plot variance
of seedlings includes genetic differences within full-sib families, whereas within plot variance among the ramets of clones
is theoretically only environmental as the ramets are genetic
replicates. However, within plot variance for rooted cuttings
might have been biased upward due to propagation effects
and the small two-tree plot size. Partitioning the error variance into plot-to-plot and within plot variance for rooted
cuttings and seedlings revealed that clonally replicated progeny tests would substantially increase the efficiency of testing by reducing the microenvironmental variance.
Most variance components in this study were accompanied by high standard errors. This is expected since there was
a limited number of parents (3 males, 3 females) used in the
experiment. In the study, the parent trees were not randomly
sampled from the population, but were selected for their
superior performance (Frampton et al. 2000). This violated
the assumptions such as “there is no selection among parents
or progeny” and “the reference population is noninbred
random mating population and may have affected the genetic
variance components (Lynch and Walsh 1998, p. 69–78).
Additive, Dominance and Epistatic Effects
Almost all the genetic variance for height was due to the
additive genetic effects in early ages with a slight increase of
non-additive variance at age six. Similarly, additive effects
were the major source of genetic variance for diameter and
volume. Parallel results were reported by Byram and Lowe
(1986) in loblolly pine for growth traits from ages 5 to 20.
Higher additive genetic variances were estimated from rooted
cuttings than seedlings of the same families for all the traits,
except for fusiform rust incidence at age 4 (Table 4). The
difference between the two propagule types for additive
genetic variance implies the efficiency of clonal testing in
estimation of genetic parameters and increasing genetic gain
(Libby 1962, Libby 1964).
There was an increasing trend for dominance variance and
decreasing trend for additive variance for growth traits,
particularly for the seedling data set. It may be speculated that
dominance variance may have more importance if the selection is applied in the mature ages for certain traits. However,
this needs to be further tested before any clear conclusions are
drawn as our results were based on four age measurements for
height and on two age measurements for diameter and for
volume. The importance of epistatic variance was not detected for any growth traits. Our results were not parallel with
Franklin (1979), Foster (1986), and Paul et al. (1997) who
reported an increase in additive genetic variance by age in
loblolly pine. The discrepancy between studies could originate from scale effect as well as sampling effect. Also,
different genes involved at different ages may cause differences between studies (Lynch and Walsh 1998, p. 60). There
are strong indications suggesting that fusiform rust incidence
is partly controlled by additive and epistatic genetic effects.
Although dominance genetic variance was considerable for
fusiform rust incidence from seedlings, this could be due to
the confounding effect of epistatic variance within dominance variance, which was not separated for the seedling
data. The results indicated that epistatic genetic interactions
have a strong control on the fusiform rust incidence on
loblolly pine, together with additive gene effects. Clonally
replicated tests should be considered more efficient than
seedling based family tests to select for the fusiform rust
resistance.
Foster (1978, 1990) and Anderson et al. (1999) reported a
dominance/additive variance ratio of less than 1.0 for shoot
production and rooting ability while epistatic variances were
zero in loblolly pine. McKeand et al. (1986) reported that
nonadditive genetic variance ratios ranged from 0.0 to 0.25
for height at age 1 through 5 in loblolly pine. In a more recent
study by Paul et al. (1997), inconsistent ratios of additive to
nonadditive genetic variances were reported for height from
two factorials in loblolly pine. In the same study, dominance
genetic variance for diameter and volume was about equal,
and even exceeded the additive genetic variance at age 5. In
this study, the ratios of nonadditive to additive genetic
variances for growth traits were in general less than 1.0 and
were in close agreement with previous studies (Table 4).
The Foster and Shaw model (1988) used in this study
cannot separate additive × additive from higher epistatic
gene interactions. If limited numbers of QTLs are controlling
fusiform rust incidence and growth traits in loblolly pine,
additive genetic variance may be biased upward by the
additive × additive genetic interactions. However, the low
epistatic variances for growth traits estimated in this study
indicated that the estimated additive variances are probably
free from epistatic gene interactions and not contaminated by
two or higher level gene interactions. At least six genes have
been linked to molecular markers for fusiform rust incidence
for loblolly pine and more likely exist (Wilcox et al. 1996,
Amerson et al. 1997). Thus, additive genetic variances estimated for fusiform rust incidence in this study are probably
not contaminated by low-level gene interactions (Wu 1996).
C Effects
C effects were not accounted for in the estimation of
genetic parameters in this study. Clonal variance estimates
may be influenced by the “c” effects such as common
environmental factors associated with the rooting and location of the cutting on the tree (Stonecypher and McCullough
1986). Environmental variation common to specific clones
could be significant in the early stages of the cloning for some
traits (i.e., rooting ability), and may bias genetic parameters
(Libby and Jund 1962, Foster et al. 1985). Rooted cuttings
from the same clone may perform differently in the field due
to effects of nongenetic factors such as topophysis and
cyclophsis (Frampton and Foster 1993). C effects may have
a significant effect on the estimation of genetic parameters in
early ages. Foster et al. (1985) reported considerable C
effects on the rooting ability traits of western hemlock (Tsuga
heterophylla (Raf.) Sarg.). However, nonsignificant C effects were reported for height for Populus balsamifera L.
(Farmer et al. 1988), for western hemlock (Paul et al. 1993),
for Pinus contorta Dougl. and for Picea sitchensis (Bong.)
Carr. (Cannel et al. 1988), and C effects diminished with age.
In this study, epistatic genetic variance was negligible for
growth traits. However, considerable epistatic genetic variance was observed for fusiform rust incidence. The observed
Forest Science 49(1) 2003
85
mean differences between seedlings and rooted cuttings of
the same families used in this study were not statistically
significant for growth traits, but these two propagule types
differed for fusiform rust infection (Frampton et al. 2000).
Very high epistatic variance observed for fusiform rust incidence could be partly due to common rooting procedures
biasing specific clonal estimates. Also, the physiological age
of the cuttings is generally higher than the seedlings of the
same families. Younger planting material such as seedlings
may be more prone to disease. Loblolly pine tissue culture
propagules exhibited mature shoot morphology relative to
seedlings and had less fusiform rust infection (Frampton
1986, Amerson et al. 1988). Rooted cuttings had lower
fusiform rust incidence than seedlings from the same families
of loblolly pine (Foster and Anderson 1989, Frampton et al.
2000). Even if the epistatic genetic variance is biased with C
effects, clonal deployment can exploit this effect and offer
greater resistance.
Genetic Correlations
Negative additive genetic correlations between fusiform
rust incidence and volume suggest that selection for growth
traits would decrease fusiform rust incidence, which is desirable. Additive genetic correlations estimated from seedlings
and clones of the same families were not always comparable
in this study. Results from simulation and empirical studies
have suggested that propagation effects common to specific
clones (c effects) might affect the correspondence between
genetically related clones and seedlings (Frampton and Foster 1993, Borralho and Kanowski 1995).In estimation of
genetic parameters, several assumptions were made. Some of
the assumptions such as “the reference population is a
noninbred random mating population, no common environmental effect associated with specific clones, no selection
among the parent trees, the population is in genetic equilibrium” might have been violated and biased the estimation of
genetic parameters (Libby and Jund 1962, Lynch and Walsh
1998, pp 69-78). The weakness of this experiment is the
limited number of parent trees used in the mating design and
is reflected in the standard error of the estimates.
Conclusions
The results in this study revealed certain important
points for loblolly pine tree improvement strategies. First,
epistatic and dominant gene interactions seemed to have
no significant role in growth traits particularly in early
ages, while additive genetic effects are the major source of
genetic variance for growth traits in loblolly pine. Second,
dominance variance for growth traits tends to increase
with age. Third, fusiform rust incidence appears to be
partially under additive and epistatic genetic control. Genetic differences among clones within families accounted
for about 50% of the total variance for disease incidence.
A tree improvement strategy based on general combining
ability of parent trees selection based on clone means
might substantially increase genetic gain both in growth
and especially in fusiform rust incidence. Also, using
clonally replicated trials would increase selection efficiency and gain substantially, since environmental noise
86
Forest Science 49(1) 2003
is better controlled by the clones within families. Negative
additive and nonadditive genetic correlations between the
growth traits and fusiform rust incidence are also encouraging for rapid simultaneous genetic improvement of
these traits during the same selection cycle.
Literature Cited
AMERSON, H.V., L.J. FRAMPTON, JR., R.L. MOTT, AND P.C. SPAINE.
1988. Tissue culture of conifers using loblolly pine as a model. P.
117–137 in Genetic manipulation of woody plants. Hanover, J.,
and D. Keathley (eds.). Plenum, New York.
AMERSON , H.V., A.P. JORDAN , E.G. KUHLMAN, D.M. O’MALLEY,
AND R.R. S EDEROFF . 1997. Genetic basis of fusiform rust
disease resistance in loblolly pine. Abstract. P. 403 in Proc.
of 24th Bienn. South. For. Tree Improv. Conf., Nat. Tech. Inf.
Serv., Springfield, VA.
ANDERSON, H.V., L.J. FRAMPTON, JR., AND R.J. WEIR. 1999. Shoot
production and rooting ability of cuttings from juvenile greenhouse loblolly pine hedges. Trans. IL State Acad. Sci. 92:1–14.
BECKER, W.A. 1984. Manual of quantitative genetics. Ed. 4. Academic Enterprises, Pullman, WA. 1988 p.
BORRALHO, N.M.G., AND P.J. KANOWSKI. 1995. Correspondence of
performance between genetically related clones and seedlings.
Can. J. For. Res. 25:500–506.
BRADSHAW, H.D., JR., AND R.F. STETTLER. 1995. Molecular genetics
of growth and development in populus IV. Mapping QTLs with
large effects on growth, form and phenology traits in forest trees.
Genetics 139:963–973.
BYRAM, T., AND B. LOW. 1986. General and specific combining ability
estimates for growth in loblolly pine. P. 352–360 in Proc. Joint
meet. of working parties on breeding theory, progeny testing and
seed orchards. North Carolina State Univ.–Industry Tree Improve. Prog., Coll. of Natur. Resour., Raleigh, NC.
CANNEL, M.G.R., L.J. SHEPPARD, AND C.M. CALAHAN. 1988. C effects
and second generation clone performance in Picea sitchensis and
Pinus contorta. Silvae Genetica 37:15–19.
DOABLEY, J., AND A. STEC. 1991. Genetic analysis of the morphological differences between maize and teosinte. Genetics
129:285–295.
FALCONER, F.S., AND T.F.C. MACKAY. 1996. Introduction to
quantitative genetics. Ed. 4. Longman Group Ltd., Edinburgh,
U.K. 464 p.
FARMER, R.E., JR., K. GARLICK, AND S.R. WATSON. 1988. Heritability
and C effects in a 3-year old balsam poplar clonal test. Can. J. For.
Res. 18:1059–1062.
FOSTER, G.S. 1978. Genetic variation in rooting stem cuttings from
four-year-old loblolly pine. Weyerhauser Co., Hot Springs, AR.
Tech Rep. No. 042-3204/78/97.
FOSTER, G.S. 1986. Trends in genetic parameters with development
and their influence on early selection for volume growth in
loblolly pine. For. Sci. 32:944–959.
FOSTER , G.S. 1988. Growth and morphology of rooted cuttings
and seedlings of loblolly pine and their genetic analysis. P.
67–78 in 10th North Am. For. Biol. Workshop, Univ. of B.C.,
Vancouver, Canada.
FOSTER, G.S. 1990. Genetic control of rooting ability of stem cuttings
from loblolly pine. Can. J. For. Res. 20:1361–1368.
FOSTER, G.S., AND R.L. ANDERSON. 1989. Indirect selection and clonal
propagation of loblolly pine seedlings enhance resistance to
fusiform rust. Can. J. For. Res. 19:534–537.
FOSTER, G.S., AND D.V. SHAW. 1987. A tree improvement program to
develop clonal of loblolly pine for reforestation. P. 17–21 in Proc.
19th South. For. Tree Improv. Conf., Nat. Tech. Inf. Serv.,
Springfield, VA.
FOSTER, G.S., AND D.V. SHAW. 1988. Using clonal replicates to
explore genetic variation in a perennial plant species. Theo. Appl.
Genet. 76:788–794.
FOSTER, G.S., R.K. CAMPBELL, AND W.T. ADAMS. 1985. Clonal selection prospects in western hemlock combining rooting traits with
juvenile height growth. Can. J. For. Res.15:488–493.
FRAMPTON, L.J., JR. 1986. Field performance of loblolly pine tissue
culture plantlets. P. 547–533 in IUFRO Conf. Proc. Joint Meet. of
Working Parties on breeding theory, progeny testing and seed
orchards. N.C. State Univ.-Industry Coop. Tree Improv. Progr.,
Raleigh, NC.
FRAMPTON, L.J., JR., AND G.S. FOSTER. 1993. Field testing vegetative
propagules. P. 110–134 in Clonal Forestry I. Genetic and Biotechnology, Ahuja, M.H., and W.J. Libby (eds.). Springer-Verlag,
Berlin, Germany.
FRAMPTON, L.J., JR., B. LI, AND B. GOLDFARB. 2000. Early field growth
of loblolly pine rooted cuttings and seedlings. South. J. Appl. For.
24:98–105.
FRANKLIN, E.C. 1979. Model relating levels of genetic variance to
stand development of four North American conifers. Silvae
Genet. 28:207–212.
FREWEN, B.E., T.H.H. CHEN, G.T. HOWE, J. DAVIS, A. ROHDE, W.
BOERJAN, AND H.D. BRADSHAW, JR. 2000. Quantitative trait loci
and candidate gene mapping of bud set and bud flush in Populus.
Genetics 154:837–845.
GOEBEL, N.B., AND J.R. WARNER. 1966. Volume tables for small
diameter loblolly, short leaf and Virginia pine in the upper South
Carolina Piedmont. For. Res. Serv. No. 7, Clemson University,
Clemson, SC.
GOLDFARB, B., S.E. SURLES, M. THETFORD, AND F.A. BLAZICH. 1998.
Effects of root morphology of rooted stem cuttings of loblolly
pine on growth in a nursery and the first year in the field. South.
J. Appl. For. 22:231–234.
KAO, C.H., Z.B. ZENG, AND R.D. TEASDALE. 1999. Multiple interval
mapping for quantitative trait loci. Genetics 152:1203–1216.
KAYA, Z., M.M. SEWELL, AND D.B. NEALE. 1999. Identification of
quantitative trait loci influencing annual height- and diameterincrement growth in loblolly pine (Pinus taeda L.). Theor. Appl.
Genet. 98:586–592.
LIBBY, W.J. 1962. Estimation of variance components of inter-node
length in a cloned population of Mimulus guttatus. Genetics
47:769–777.
LONG, A.D., S.L. MULLANEY, L.A. REID, J.D. FRY, C.H. LANGLEY, AND
T.F.C. MACKAY. 1995. High resolution mapping of genetic factors affecting abdominal bristle number in Drosophila
melanogaster. Genetics 139:1273–1291.
LYNCH, M., AND B. WALSH. 1998. Genetics and analysis of quantitative traits. Sinauer Associates, Inc., Sunderland, MN. 980 p.
MARQUES, C.M., K.J. VASQUEZ, V.J. CAROCHA, J.G. FERREIRA, D.M.
O’MALLEY, B.H. LIU, AND R.R. SEDEROFF. 1999. Genetic dissection of vegetative propagation traits in Eucalyptus tereticornis
and E. globulus. Theor. Appl. Genet. 99:936–946.
MCKEAND, S.E., G.S. FOSTER, AND F.E. BRIDGWATER. 1986. Breeding
controlled production populations of loblolly pines. P. 53–61 in
Advanced generation breeding of forest trees. Louisiana Agric.
Exp. Sta. South. Coop. Series Bull. 309.
MCRAE, J.B., H.E. STELTZER, G.S. FOSTER, AND T. CALDWELL. 1993.
Genetic test results from a tree improvement program to develop
clones of loblolly pine for reforestation. P. 424–433 in 22nd
South. For. Tree Improve. Conf., Nat. Tech. Inf. Serv., Springfield, VA.
MIKLAS, P.N., V. STONE, C.A. URREA, U.E. JOHNSON, AND J.S. BEAVER.
1999. Inheritance and QTL analysis of field resistance to ashy
stem blight in common bean. Crop Sci. 38:916–921.
MINVIELLE, F. 1987. Dominance is not necessary for heterosis: A twolocus model. Genet. Res 49:245–247.
MULLIN, T.J., AND Y.S. PARK. 1992. Estimating genetic gains from
alternative breeding strategies for clonal forestry. Can. J. For.
Res. 22:14–23.
MULLIN, T.J., E.K. MORGENSTERN, Y.S. PARK, AND D.P. FOWLER. 1992.
Genetic parameters from a clonally replicated test of black spruce
(Picea mariana). Can. J. For. Res. 22:24–36.
MULLIN, T.J., AND Y.S. PARK. 1994. Genetic parameters and age-age
correlations in a clonally replicated test of black spruce after 10
years. Can. J. For. Res. 24:2330–2341.
PATERSON, A.H., E.S. LANDER, J.D. HEVWITT, S. PETERSON, S.E.
LINCOLN, AND S.D. TANKSLEY. 1988. Resolution of quantitative
traits in Mendelian factors using a complete linkage map of
restricted fragment length polymorphism. Nature 335:721–726.
PATERSON, A.H., J.W. DEVERNA, B.S. LANINI, AND S.D. TANKSLEY.
1990. Fine mapping of quantitative trait loci using selected
overlapping recombinant chromosomes in an interspecies cross
of tomato. Genetics 124:735–742.
P ATERSON , A.H., S. D AMON , J.D. H EWITT , D. Z AMIR , H.D.
RABINOWITCH, S.E. L INCOLN, S. LANDER , AND S.D. T ANKSLEY.
1991. Mendelian factors underlying quantitative traits in
tomato: comparison across species, generations and environments. Genetics 127:181–197.
PAUL, A.D., G.S. FOSTER, AND D.T. LESTER. 1993. Field performance,
C effects, and their relationship to initial rooting ability for
western hemlock clones. Can. J. For. Res. 23:1947–1952.
LIBBY, W.J. 1964. Clonal selection and an alternative seed orchard
scheme. Silvae Genet. 13:32–40.
PAUL, A.D., G.S. FOSTER, T. CALDWELL, AND J. MCRAE. 1997. Trends
in genetic and environmental parameters for height, diameter,
and volume in a multilocation clonal study with loblolly pine.
For. Sci. 43:87–98.
LIBBY, W.J., AND E. JUND. 1962. Variance associated with cloning.
Heredity 17:533–540.
SAS INSTITUTE INC. 1989. SAS/STAT User’s Guide, Version 6,
Fourth Edition, Volume 2,SAS Institute Inc., Cary, NC. 846 p.
Forest Science 49(1) 2003
87
SNYDER, E.B., AND G. NAMKOONG. 1978. Inheritance in a diallel
crossing experiment with longleaf pine. USDA For. Serv. South.
For. Exp. Sta. Res. Pap. SO-140.
STEEL, R.G.D., J.H. TORRIE, AND D.A. DICKEY. 1997. Principles and
procedures of statistics. A biometrical approach. Ed. 3. McGrawHill, New York. 666 p.
STONECYPHER, R.W., AND R.B. MCCULLOUGH. 1986. Estimates of
additive and non-additive genetic variances from a clonal diallel
of Douglas-fir Pseudotsuga menziesii (Mirb.) Franco. P. 211–
227 in IUFRO Conf. A joint meeting of working parties on
breeding theory, progeny testing, seed orchards. Conf. proc.,
North Carolina State University, Raleigh, NC.
STUART, A., AND J.K. ORD. 1991. Kendall’s advanced theory of
statistics. Classical inference and relationship. Ed. 5. Vol. 2.
Oxford University Press, New York. 1323 p.
88
Forest Science 49(1) 2003
WELLER, S.G. 1976. The genetic control of tristyly in Oxalis section
Ionoxalis. Heredity 37:387–393.
WILCOX, P.L., H.V. AMERSON, E.G. KUHLMAN, B. LIU, D.M. O’MALLEY,
AND R.R. SEDEROFF. 1996. Detection of major gene for resistance
to fusiform rust disease in loblolly pine by genomic mapping.
PNAS, Biolog. Ser. 93: 3859–3864.
WRIGHT, S. 1980. Genic and organismic selection. Evolution
34:825–843.
WU, R.L. 1996. Detecting epistatic genetic variance with clonally
replicated design: Models for low vs high order nonallelic interaction. Theor. Appl. Genet. 93:102–109.