Variance modelling of longitudinal height data from aPinus radiataprogeny test

Abstract

Variance components were estimated using alternative structures for the additive genetic covariance matrix (G0), for height (m) of trees measured at 10 unequally spaced ages in an open-pollinated progeny test. These structures reflected unstructured, autoregressive, banded correlation and random regressions models. The residual matrix (R0) was unstructured, and the block and plot strata matrices were autoregressive. The best model for G0considering the likelihood value and number of parameters was the autoregressive correlation form with age-specific variances and time on a natural logarithm basis. The genetic correlation between successive measures ranged from 0.93 at age 1 to 0.99 at age 14 years. Heritability increased with age from 0.09 (age 1) to 0.24 (age 7) and then declined to 0.13 at age 15. Heritabilities from the unstructured model were similar, while heritabilities assuming banded correlations were lower after age 7. The covariance structure implicit in the random regressions model was considered unsatisfactory. Using structures in G0facilitated model fitting and convergence of the likelihood maximisation algorithm. Fitting a structured matrix that reflects the relationships present in repeated measures may overcome problems of nonpositive definiteness of unstructured matrices from longitudinal data, especially when genetic variation is small.