Novel methods for improved tree breeding

The development and implementation of statistical tools to improve inference in sustainable forest tree breeding are presented here. By combining classical quantitative genetic theory and novel statistical methods, a number of parameters are optimized. The results obtained are compared to those achieved by traditional methods for visualizing improvements to genetic parameters. The methods are tested on both simulated data and on a real Scots pine pedigree. Modeling non-additive gene action using a finite loci model indicates that the development of the additive variance component does not decay initially as the underlying theory predicts. This phenomenon is shown for different sets of genetic components and models. In addition, variable numbers of loci were used so that different numbers of interactions could be captured. To draw inferences about the genetic parameters, a powerful Bayesian Markov chain Monte Carlo method was developed. The method utilizes transformation of the genetic covariance structure to improve computational speed. By combining two different Bayesian Gibbs samplers, a useful hybrid sampler was developed; this was found to enhance convergence statistics and computational speed. A method that finds the number of trees and their respective mating proportions that will maximize genetic gain was implemented and modified to handle a large number of selection candidates. When testing the selection method on a real pedigree an increase in genetic gain of up to 30 % was found compared to traditional methods in which the same restrictions were placed on relatedness. In order to provide a long-term breeding perspective, the selection method was combined with various mating schemes to examine the development of genetic parameters. A modified minimum coancestry mating scheme resulted in a level of genetic gain closest to the theoretically achievable limit while reducing the level of inbreeding in the population

Efficient Markov Chain Monte Carlo Implementation of Bayesian Analysis of Additive and Dominance Genetic Variances in Noninbred Pedigrees

Accurate and fast computation of quantitative genetic variance parameters is of great importance in both natural and breeding populations. For experimental designs with complex relationship structures it can be important to include both additive and dominance variance components in the statistical model. In this study, we introduce a Bayesian Gibbs sampling approach for estimation of additive and dominance genetic variances in the traditional infinitesimal model. The method can handle general pedigrees without inbreeding. To optimize between computational time and good mixing of the Markov chain Monte Carlo (MCMC) chains, we used a hybrid Gibbs sampler that combines a single site and a blocked Gibbs sampler. The speed of the hybrid sampler and the mixing of the single-site sampler were further improved by the use of pretransformed variables. Two traits (height and trunk diameter) from a previously published diallel progeny test of Scots pine (Pinus sylvestris L.) and two large simulated data sets with different levels of dominance variance were analyzed. We also performed Bayesian model comparison on the basis of the posterior predictive loss approach. Results showed that models with both additive and dominance components had the best fit for both height and diameter and for the simulated data with high dominance. For the simulated data with low dominance, we needed an informative prior to avoid the dominance variance component becoming overestimated. The narrow-sense heritability estimates in the Scots pine data were lower compared to the earlier results, which is not surprising because the level of dominance variance was rather high, especially for diameter. In general, the hybrid sampler was considerably faster than the blocked sampler and displayed better mixing properties than the single-site sampler

Bayesian Inference of Genetic Parameters Based on Conditional Decompositions of Multivariate Normal Distributions

It is widely recognized that the mixed linear model is an important tool for parameter estimation in the analysis of complex pedigrees, which includes both pedigree and genomic information, and where mutually dependent genetic factors are often assumed to follow multivariate normal distributions of high dimension. We have developed a Bayesian statistical method based on the decomposition of the multivariate normal prior distribution into products of conditional univariate distributions. This procedure permits computationally demanding genetic evaluations of complex pedigrees, within the user-friendly computer package WinBUGS. To demonstrate and evaluate the flexibility of the method, we analyzed two example pedigrees: a large noninbred pedigree of Scots pine (Pinus sylvestris L.) that includes additive and dominance polygenic relationships and a simulated pedigree where genomic relationships have been calculated on the basis of a dense marker map. The analysis showed that our method was fast and provided accurate estimates and that it should therefore be a helpful tool for estimating genetic parameters of complex pedigrees quickly and reliably