Materials and Methods
Open pollinated seeds were collected from 81 mother trees in south
eastern Australia, representing all of the known native populations of
E. bosistoana at this time. The seeds were later germinated and
planted into an alpha lattice experimental layout with plots of 8 half
sibling families arranged in replicates. Due to poor germination of some
families, only the first two (of eight) replicates were complete. The
trials were planted into a uniform, irrigated nursery site in Woodville,
New Zealand (40°19’28.9”S 175°52’43.3”E). Soon after planting a wind
storm caused some ‘socketing’ (trees swirl in the wind and create a bowl
in the soil around the stem resulting in lowered support from the soil).
A number of individuals were tethered to bamboo stakes in order to
correct their growing posture. Analysis showed that while there was a
geographical effect on where staking was likely to occur, there was no
discernable genetic predisposition to the need for staking. The trees
were pruned to approximately 500 mm from ground level during growth to
ensure a clean stem section for wood property testing. As part of a
pilot study to investigate the usability of wound wood as a proxy for
early section of good heart wood \cite{Harju2009}, some trees were drilled (to create a wound-wood reaction)
above the clear wood testing zone, approximately one month prior to
harvest. In the month preceding harvest the height of each tree was
measured using a height pole. Harvesting was undertaken in two cuts
(1425 individuals in the first cut and 1261 individuals in the second
cut two weeks later), the stems were labeled, toped (at the top of the
clear wood zone) and felled at ground level. The samples were stored in
insulated bins with excess water and processed within two weeks of
harvest. No deterioration of the samples was detectable visibly or
statistically. At harvest, stems were rejected if they did not met the
visually estimated criteria (400 mm clear stem, minimum over bark
diameter of 25mm) required for the assessment of strain. Due to resource
limitations, two sampling procedures were used, collecting every
individual which meets the above criteria (the first five replicates,
2138 individuals), and selecting the largest three (visually assessed
diameter) individuals with good stem form in each plot of eight trees
(the last three replicates, 548 individuals).
The samples were manually debarked and under bark diameter was measured
using calipers. The longest slit length appropriate for the sample
(longest length of clear wood without bends or knots, staying at least
100 mm from the small end of the sample) was marked for conducting the
rapid-splitting test. The rapid-splitting test
acoustic velocity (resonance).
Strain (ϵ) was calculated using Equation \ref{eq:splitting_test_strain} from \citet{Davies2017} where; o is the opening at the big end after splitting,
d is the big end under bark diameter, and L is the length
of the split. Dry density (ρ) was calculated using Equation \ref{eq:wv_density} where
m is dry mass, V is dry volume and subscripts represent
the sample side, volumetric shrinkage (vs ) was calculated using
Equation \ref{eq:wv_vs} where gV is green volume, acoustic velocity
(av ) from Equation \ref{eq:wv_av} and stiffness (k ) from Equation \ref{eq:wv_stiffness}.
A multivariate linear mixed animal model (Equation \ref{eq:wv_model_1}) was implemented in
the MCMCglmm package \cite{Hadfield2015} or the statistical system R ----(Team 2013)---
and used to estimate the genetic parameters of the population. The
response variables were; growth-strain, under-bark diameter, dry
density, stiffness, volumetric shrinkage, height and acoustic velocity.
The model ‘fixed’ effects were; replicates, staking and edge effects,
with plot and additive genetic effects included as ‘random’ effects. The
response vectors yi for all individuals for the
i th trait, m fixed effects, p
plot effects, a the individual and e error. The incidence
matrices, \(X,Z1,Z2\) link the \(i^{th}\)
trait to the fixed, random plot and random additive genetic effects
respectively. It is assumed that the traits were correlated with
heterogeneous variances, and hence the variance-covariance
\((G)\) and residual variance-covariance \((R)\)
matrix structures are not diagonal, using unstructured matrices to model
the genetic correlations between traits and residuals. Further, it is
assumed that Equation \ref{eq:wv_model_2} holds, where \(P\) is the plot
variance covariance matrix and \(A\) is the numerator
relationship matrix.
Priors for the fixed effects were the default MCMCglmm priors, the
expected value of all fixed effects was 0, and the degree of belief
matrix was set as I multiplied by \(1^{10}\) where
\(I\) is the identity matrix of the appropriate dimension \cite{Hadfield2014}. The priors for both the
plot and additive genetic effects were vaguely informative, using an
inverse Whishart distribution with the degree of belief parameter set to
1 and the expected variance covariance matrix obtained by multiplying
the phenotypic variance-covariance matrix by 0.25. The residuals prior
was set in the same way; however, using a multiplier of 0.5. In a
separate instance an uninformative prior \cite{Hadfield2014} was used on the model to
ensure that using the phenotypic variance-covariance matrix to inform
the priors was not drastically influencing the outcome. The
uninformative prior provided similar results, however took substantially
longer to run and did not mix so well. A burnin of 20000 iterations was
used with a total of 100000 iterations, all models showed good
convergence diagnostics.