Growth-curve differentiation among Japanese larch provenances

Abstract

Height–age regression models were fitted to observed heights at ages 7, 11, 15, 22, and 29 years in 20 Japanese larch (Larixleptolepis (Sieb. & Zucc.) Gord.) provenances. A generalized least squares approach with maximum-likelihood estimation of the autocorrelation function and the variance function (heteroscedasticity) is proposed as a framework for growth-curve analysis. Ignoring autocorrelation and variance heteroscedasticity led to serious bias of error estimates that may invalidate statistical comparisons. Normality of log-transformed heights and homogeneity of covariance matrices were confirmed statistically. Cluster analyses followed up by likelihood-ratio tests identified three significantly different growth patterns. Ten provenances belonged to a fast-growing group, nine to a slow-growing group, and one was deemed aberrant (very slow growing). Discriminant analyses on geographic variables and clusters achieved a 95% posterior rate of correct classification. The growth-curve approach was extended to the analyses of age to age correlations and compared with observed correlations. It is concluded that a multivariate approach to growth-curve analysis is preferable to the univariate approach owing to correlations among estimated regression coefficients.