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.