Applications of transition matrix models in forest dynamics: Araucaria in Papua New Guinea and Nothofagus in New Zealand

This paper describes the application of the Leslie matrix model to single species populations, and a similar transition matrix model to communities of more than one species. Examples are drawn from populations of Araucaria spp. in tropical rainforest in Papua New Guinea, and from Nothofagus fusca stands in temperate montane forest in New Zealand. Both species generally had λ values close to 1.0 (r, the intrinsic rate of natural increase ≃ 0) and in both cases predicted trends were consistent with other ecological information from the stands or elsewhere. Various possible sources of error and empirical tests of the sensitivity of the single species model and the accuracy of its predictions are described. It is concluded that, despite certain limitations, with careful interpretation these models constitute an important tool for the investigation of forest dynamics. The basic model may be modified in various ways, for example, to include vegetative reproduction, or put to use in practical problems such as defining a harvesting strategy for a forest tree species. In studies of succession involving long‐lived species these models are particularly valuable, not only for predicting the magnitude and direction of future changes, but also because they suggest a time scale for the trends, and this can then be evaluated in the light of other knowledge about the communities in question. Moreover, the variability of λ values obtained for differen species relates to their life cycle strategies, so that by the use of Leslie matrices it may be possible objectively to rank the species of a community along the continuum of r to k strategies.