Heritability of growth strain in Eucalyptus bosistoana: a Bayesian approach with left-censored data

Nicholas T. Davies, Luis A. Apiolaza, Monika Sharma


Narrow-sense heritabilities of the wood properties of two-year-old Eucalyptus bosistoana were estimated from 623 stems. Heritability estimates for growth-strain (0.63), density (0.54), diameter (0.76), volumetric shrinkage (0.29), acoustic velocity (0.97) and stiffness (0.82) are presented. A modified version of the splitting test for detecting growth-strain is described. The modified rapid testing procedure results in left-censored growth-strain data, a Bayesian approach is implemented to reduce errors associated with censored data sets. Correlations between wood properties are presented and discussed, as well as trade-offs when shifting trait means by selective breeding.


The main use of plantation 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 (Yamamoto, 2007).

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 (Yamamoto, 2007). An alternative approach to the problem is to rely on the genetic control of growth-strain—shown in this article to be highly heritable—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 (Murphy et al., 2005) and 216 (Naranjo et al., 2012) trees.

The University of Canterbury has developed and implemented a rapid growth-strain testing procedure, based on the work by Chauhan et al. (2010) and Entwistle et al. (2014). 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 (e.g. 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 (Cappa et al., 2006). There are several examples of Bayesian applications in forest genetics; for example: (Soria et al., 1998) (univariate analysis of growth traits), (Cappa et al., 2006) (multivariate analysis of growth traits) and (Apiolaza et al., 2011) (multivariate analysis of early wood properties).

We ran a pilot study consisting of two Eucalyptus bosistoana 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 Methods

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, an