Analysis of longitudinal data from progeny tests: Some multivariate approaches

Longitudinal data arise when trees are repeatedly assessed over time, The d egree of genetic control of tree performance typically changes over time, c reating relationships between breeding values at different ages. Longitudin al data allow modeling the changes of heritability and genetic correlation with age. This article presents a tree model (i.e., a model that explicitly includes a term for additive genetic effects of individual trees) for the analysis of longitudinal data from a multivariate perspective. The additive genetic covariance matrix for several ages can be expressed in terms of a correlation matrix pre- and post-multiplied by a diagonal matrix of standar d deviations, Several models to represent this correlation matrix (unstruct ured, banded correlations, autoregressive, full-fit and reduced-fit random regression, repeatability, and uncorrelated) are presented, and the relatio nships among them explained, Kirkpatrick's alternative approach for the ana lysis of longitudinal data using covariance functions is described, and its similarities with the other models discussed in this article are detailed, The use of Akaike's information criterion for model selection considering likelihood and number of parameters is detailed, All models are illustrated through the analysis of weighed basic wood density tin kg/m(3)) at four ag es (5, 10, 15, and 20 yr) from radiata pine increment cores.