Rodolfo Juan Carlos Cantet

Direct and Competition Additive Effects in Tree Breeding: Bayesian Estimation From an Individual Tree Mixed Model

Abstract An individual tree model with additive direct and competition effects is introduced to account for competitive effects in forest genetics evaluation. The mixed linear model includes fixed effects as well as direct and competition breeding values plus permanent environmental effects. Competition effects, either additive or environmental, are identified in the phenotype of a competitor tree by means of ‘intensity of competition’ elements (IC), which are non-zero elements of the incidence matrix of the additive competition effects. The ICs are inverse function of the distance and the number of competing individuals, either row-column wise or diagonally. The ICs allow standardization of the variance of competition effects in the phenotypic variance of any individual tree, so that the model accounts for unequal number of neighbors. Expressions are obtained for the bias in estimating additive variance using the covariance between half-sibs, when ignoring competition effects for row-plot designs and for single-tree plot designs. A data set of loblolly pines on growth at breast height is used to estimate the additive variances of direct and competition effects, the covariance between both effects, and the variance of permanent environmental effects using a Bayesian method via Gibbs sampling and Restricted Maximum Likelihood procedures (REML) via the Expectation- Maximization (EM) algorithm. No problem of convergence was detected with the model and ICs used when compared to what has been reported in the animal breeding literature for such models. Posterior means (standard error) of the estimated parameters were σ̂2Ad = 12.553 (1.447), σ̂2Ac = 1.259 (0.259), σ̂AdAc = -3.126 (0.492), σ̂2 p = 1.186 (0.289), and σ̂2e = 5.819 (1.07). Leaving permanent environmental competition effects out of the model may bias the predictions of direct breeding values. Results suggest that selection for increasing direct growth while keeping a low level of competition is feasible.

Bayesian estimation of a surface to account for a spatial trend using penalized splines in an individual-tree mixed model

Unaccounted for spatial variability leads to bias in estimating genetic parameters and predicting breeding values from forest genetic trials. Previous attempts to account for large-scale continuous...

Full conjugate analysis of normal multiple traits with missing records using a generalized inverted Wishart distribution

A Markov chain Monte Carlo (MCMC) algorithm to sample an exchangeable covariance matrix, such as the one of the error terms (R0) in a multiple trait animal model with missing records under normal-inverted Wishart priors is presented. The algorithm (FCG) is based on a conjugate form of the inverted Wishart density that avoids sampling the missing error terms. Normal prior densities are assumed for the fixed effects and breeding values, whereas the covariance matrices are assumed to follow inverted Wishart distributions. The inverted Wishart prior for the environmental covariance matrix is a product density of all patterns of missing data. The resulting MCMC scheme eliminates the correlation between the sampled missing residuals and the sampled R0, which in turn has the effect of decreasing the total amount of samples needed to reach convergence. The use of the FCG algorithm in a multiple trait data set with an extreme pattern of missing records produced a dramatic reduction in the size of the autocorrelations among samples for all lags from 1 to 50, and this increased the effective sample size from 2.5 to 7 times and reduced the number of samples needed to attain convergence, when compared with the data augmentation algorithm.

Statistical methods in animal breeding and Bach’s harpsichord concertos

Fil: Cantet, Rodolfo Juan Carlos. Consejo Nacional de Investigaciones Cientificas y Tecnicas; Argentina. Universidad de Buenos Aires; Argentina