Variance modelling of longitudinal height data from a Pinus radiata progeny test

Variance components were estimated using alternative structures for the add itive genetic covariance matrix (G(0)), for height (m) of trees measured at 10 unequally spaced ages in an open-pollinated progeny test. These structu res reflected unstructured, autoregressive, banded correlation and random r egressions models. The residual matrix (R-0) was unstructured, and the bloc k and plot strata matrices were autoregressive. The best model for G(0) con sidering the likelihood value and number of parameters was the autoregressi ve correlation form with age-specific variances and time on a natural logar ithm 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 fro m 0.09 (age 1) to 0.24 (age 7) and then declined to 0.13 at age 15. Heritab ilities from the unstructured model were similar, while heritabilities assu ming banded correlations were lower after age 7. The covariance structure i mplicit in the random regressions model was considered unsatisfactory. Usin g structures in G(0) facilitated model fitting and convergence of the likel ihood maximisation algorithm. Fitting a structured matrix that reflects the relationships present in repeated measures may overcome problems of nonpos itive definiteness of unstructured matrices from longitudinal data, especia lly when genetic variation is small.