Growth and Survival of Eucalyptus grandis - a study based on modelling lifetime distributions

Abstract

The objective of this study is to analyse the density-dependent dynamics of growth and mortality in an unthinned Eucalyptus grandis spacing experiment on a homogenous site in Zululand/South Africa. Specifically we propose models that describe how the (log) basal area develops in unthinned stands. Our data clearly indicate that mortality varies enormously with planting density. We therefore develop and investigate models that explicitly take mortality into account. To do so we first model the conditional distribution of log basal area as a function of age and the number of trees that are concurrently alive. The last of these covariates is generally unknown in advance, which would seem to render it inapplicable for the purpose of modeling the distribution of future basal area. We show how it is nevertheless possible to estimate the distribution of the number of surviving trees from the available data, and thereby to ‘integrate out’ the effect of this random variable in order to estimate the (unconditional) distribution of the log basal area for each planting density. This is achieved by fitting Weibull distributions to the lifetimes of the trees in the four available plots. A number of different models for the log basal area are compared. Our estimates indicate that the distribution of the future basal area in an unthinned Eucalyptus grandis forest is not independent of the planting density, within the range of the experimental densities investigated in this study. Our results provide clear evidence that planting density has strong and long-lasting effects on basal area. Furthermore the estimates indicate that these effects persist for at least 40 years and that, even after length of time, the rate of convergence to a common condition is very slow.