Richard J. Kerr

Genetic control of interactions among individuals: contrasting outcomes of indirect genetic effects arising from neighbour disease infection and competition in a forest tree

Indirect genetic effects (IGEs) are heritable effects of individuals on trait values of their conspecifics. IGEs may substantially affect response to selection, but empirical studies on IGEs are sparse and their magnitude and correlation with direct genetic effects are largely unknown in plants. Here we used linear mixed models to estimate genetic (co)variances attributable to direct and indirect effects for growth and foliar disease damage in a large pedigreed population of Eucalyptus globulus. We found significant IGEs for growth and disease damage, which increased with age for growth. The correlation between direct and indirect genetic effects was highly negative for growth, but highly positive for disease damage, consistent with neighbour competition and infection, respectively. IGEs increased heritable variation by 71% for disease damage, but reduced heritable variation by 85% for growth, leaving nonsignificant heritable variation for later age growth. Thus, IGEs are likely to prevent response to selection in growth, despite a considerable ordinary heritability. IGEs change our perspective on the genetic architecture and potential response to selection. Depending on the correlation between direct and indirect genetic effects, IGEs may enhance or diminish the response to natural or artificial selection compared with that predicted from ordinary heritability.

Accounting for competition in genetic analysis, with particular emphasis on forest genetic trials

Available experimental evidence suggests that there are genetic differences in the abilities of trees to compete for resources, in addition to non-genetic differences due to micro-site variation. The use of indirect genetic effects within the framework of linear mixed model methodology has been proposed for estimating genetic parameters and responses to selection in the presence of genetic competition. In this context, an individual’s total breeding value reflects the effects of its direct breeding value on its own phenotype and its competitive breeding value on the phenotype of its neighbours. The present study used simulated data to investigate the relevance of accounting for competitive effects at the genetic and non-genetic levels in terms of the estimation of (co)variance components and selection response. Different experimental designs that resulted in different genetic relatedness levels within a neighbourhood and survival were other key issues examined. Variances estimated for additive genetic and residual effects tended to be biased under models that ignored genetic competition. Models that fitted competition at the genetic level only also resulted in biased (co)variance estimates for direct additive, competitive additive and residual effects. The ability to detect the correct model was reduced when relatedness within a neighbourhood was very low and survival decreased. Selection responses changed considerably between selecting on breeding value estimates from a model ignoring genetic competition and total breeding estimates using the correct model. Our results suggest that considering a genetic basis to competitive ability will be important to optimise selection programmes for genetic improvement of tree species.

Use of the numerator relationship matrix in genetic analysis of autopolyploid species

Mixed models incorporating the inverse of a numerator relationship matrix (NRM) are widely used to estimate genetic parameters and to predict breeding values in animal breeding. A simple and quick method to directly calculate the inverse of the NRM has been historically developed for diploid animal species. Mixed models are less used in plant breeding partly because the existing method for diploids is not applicable to autopolyploid species. This is because of the phenomenon of double reduction and the possibility that gametes carry alleles which are identical by descent. This paper generalises the NRM and its inverse for autopolyploid species, so it can be easily incorporated into their genetic analysis. The technique proposed is to first calculate the kinship coefficient matrix and its inverse as a precursor to calculating the NRM and its inverse. This allows the NRM to be calculated for populations containing individuals of mixed ploidy levels. This generalization can also accommodate uncertain parentage by generating the “average” relationship matrix. The possibility that non-inbred parents can produce inbred progeny (double reduction) is also discussed. Rules are outlined that are applicable for any level of ploidy. Examples of use of the matrix are provided using simulated pedigrees.

Association mapping for wood quality and growth traits in Eucalyptus globulus ssp. globulus Labill identifies nine stable marker-trait associations for seven traits

The moderate to high levels of nucleotide diversity and low linkage disequilibrium found in many forest tree species make them ideal candidates for association mapping. Here, we report candidate gene-based association mapping results for complex wood quality and growth traits in Eucalyptus globulus Labill. ssp. globulus, the most widely grown eucalypt in temperate regions of the world. Ninety-eight single nucleotide polymorphisms (SNPs) from 20 wood quality candidate genes were assayed in a discovery population consisting of 385 trees sourced from a provenance-progeny trial. Twenty-five selected SNPs with significant associations (P < 0.05) in the discovery population were assayed for validation in 296 trees sourced from an independent second-generation breeding trial. To account for background genetic structure, mixed models were used in the association analyses. Two associations identified in the discovery population were independently supported in the validation testing. However, combining the discovery and validation results in a combined analysis, we discovered nine stable marker-trait associations for seven traits. These associations link underlying complex wood and growth phenotypes to earlier putative selection signatures opening new avenues to accelerate the dissection of these traits.

Genetic-based interactions among tree neighbors: identification of the most influential neighbors, and estimation of correlations among direct and indirect genetic effects for leaf disease and growth in Eucalyptus globulus

An individual’s genes may influence the phenotype of neighboring conspecifics. Such indirect genetic effects (IGEs) are important as they can affect the apparent total heritable variance in a population, and thus the response to selection. We studied these effects in a large, pedigreed population of Eucalyptus globulus using variance component analyses of Mycosphearella leaf disease, diameter growth at age 2 years, and post-infection diameter growth at ages 4 and 8 years. In a novel approach, we initially modeled IGEs using a factor analytic (FA) structure to identify the most influential neighbor positions, with the FA loadings being position-specific regressions on the IGEs. This involved sequentially comparing FA models for the variance–covariance matrices of the direct and indirect effects of each neighbor. We then modeled IGEs as a distance-based, combined effect of the most influential neighbors. This often increased the magnitude and significance of indirect genetic variance estimates relative to using all neighbors. The extension of a univariate IGEs model to bivariate analyses also provided insights into the genetic architecture of this population, revealing that: (1) IGEs arising from increased probability of neighbor infection were not associated with reduced growth of neighbors, despite adverse fitness effects being evident at the direct genetic level; and (2) the strong, genetic-based competitive interactions for growth, established early in stand development, were highly positively correlated over time. Our results highlight the complexities of genetic-based interactions at the multi-trait level due to (co)variances associated with IGEs, and the marked discrepancy occurring between direct and total heritable variances.

Managing the rate of increase in average co-ancestry in a rolling front tree breeding strategy

In breeding forest trees, as for livestock, the goal is to capture as much genetic gain as possible for the breeding objective, while limiting long- and short-term inbreeding. The Southern Tree Breeding Association (STBA) is responsible for breeding Australias two main commercial forest tree species and has adopted algorithms and methods commonly used in animal breeding to achieve this balance. Discrete generation breeding is the norm for most tree breeding programmes. However, the STBA uses an overlapping generation strategy, with a new stream of breeding initiated each year. A feature of the species bred by the STBA (Pinus radiata and Eucalyptus globulus) is the long interval (up to 7 years) between when an individual is mated and when its progeny is first assessed in field trials and performance data included in the national performance database. Mate selection methods must therefore recognize the large pool of unmeasured progeny generated over recent years of crossing. In addition, the substantial delay between when an individual is selected in a field trial and when it is clonally copied into a mating facility (breeding arboretum) means that selection and mating must occur as a two-step process. In this article, we describe modifications to preselection and mate selection algorithms that allow unmeasured progeny (juveniles) to be recognized. We also demonstrate that the addition of hypothetical new progeny to the juvenile pool is important for computing the increase in average co-ancestry in the population. Methods outlined in this article may have relevance to animal breeding programmes where between mating and progeny measurement, new rounds of mating are initiated.