Introduction
\cite{Davies_2017}
The main use of plantation-grown Eucalyptus species is the
production of biomass for the pulp and paper, and bioenergy industries.
These trees are fast-growing and can potentially produce high-quality
timber for appearance, structural and engineered wood products.
Unfortunately, this potential is hindered by the frequent presence of
large growth-strains, which are associated with log splitting, warp,
collapse and brittleheart, imposing substantial costs on
processing.
A few technological mitigation strategies have been developed to reduce
the incidence of wood defects caused by growth-strain, but they are
costly and only partially effective. An alternative
approach to the problem is to rely on the genetic control of
growth-strain to select
and grow individuals with low growth-strain. However, measuring growth
strains in large numbers of trees (as needed for a successful breeding
programme) has been difficult, time consuming and expensive until now.
As an example, the largest reported studies to date assessed only 164
\cite{Murphy2005} and 216 \cite{Naranjo2012} trees.
The University of Canterbury has developed and implemented a rapid
growth-strain testing procedure, based on the work by \citet{Chauhan2010} and \citet{Entwistle2014}. In order to minimise the
time taken to measure growth-strain on each tree, the rapid testing
procedure does not account for negative values, where the wood in the
centre of the stem is under tension rather than compression, assigning
instead a zero that results in left-censored datasets.
Left-censored data are common in research areas where detection limits
are high compared to the measured values, such as testing for the
presents of drugs in an animal. There are many approaches to deal with
censoring \cite{Senn_2012} and in this article we use a Bayesian
framework to impute the missing data from known data, reducing the error
induced by zero inflation. A Bayesian approach makes it easier to
include model complexity (e.g. censoring) while accounting for the
hierarchical nature of the data. In addition, one can easily obtain
complex distributions of functions of covariance components, like
heritabilities, as a byproduct of the estimation process \cite{Cappa_2006}. There are several examples of Bayesian applications in
forest genetics; for example: \cite{Soria_1998} (univariate analysis
of growth traits), \cite{Cappa2006} (multivariate analysis of
growth traits) and \cite{Apiolaza2011} (multivariate analysis of
early wood properties).
We ran a pilot study consisting of two Eucalyptus bosistoana
F.Muell. progeny tests from both seed and coppice grown stems, which
included 623 individual stems from 40 half sibling families. Our
estimates of narrow-sense heritability were obtained from left-censored
growth-strain data and other wood properties, utilising a Bayesian
approach. These results were used to design a much larger evaluation of
the E. bosistoana breeding population currently underway.
Materials and method
An E. bosistoana open-pollinated progeny trial was established at
an irrigated nursery site in Harewood, Christchurch, New Zealand. The
trial represented 40 families from two provenances, for a total of 423
seedlings planted into 100 L bags, which were coppiced after the first
harvest, giving a total of 623 tested samples. Two separate plantings
(or trial sections) occurred in 2010 and 2012. The 2010 families
originated from South East Australia, were harvested and coppiced in
2012, and harvested again in December 2014. The 2012 families originated
from higher elevation in New South Wales and were harvested in 2013
(these data were not included in the analysis, due to the magnitude of
errors induced by small, malformed stems) and again in October 2015 (at
age two). All seedlings were established following a completely
randomised design.
When harvested, each sample was processed for growth strain, volumetric
shrinkage (displacement method, before and after drying), stem diameter
(measured under bark using digital calipers), basic density (mass and
displacement method) and dry acoustic velocity (resonance).
Growth-strain was measured using a modified version of the \citet{Chauhan2010} and \citet{Entwistle2014} log-splitting methods. The
newly developed “rapid splitting test” substantially reduces
measurement time, enabling larger numbers of samples to be processed.
The modified method involves stripping the bark and measuring the
under-bark large-end diameter of a clear section of the stem, giving an
over estimate of the average diameter used by \citet{Chauhan2010}. The sample is then cut lengthwise, with the slit length
determined by the length of clear wood and diameter of the sample.
Diameter and slit length are measured, recorded and the stem cut. The
small-end of the sample is left intact with the large-end free to
distort, which removes the need to clamp the two halves together.
Finally, the opening is measured and recorded. The calculation of strain
is unchanged (with the exception that average radius is now large-end
radius) from \citet{Chauhan2010} and calculated using Equation
\ref{eq:strain_LC}. It is important to note that the over estimate of radius slightly
reduces the strain value, but does so linearly over all samples.