Models and statistics for species diversity

Abstract

INTEREST in the pattern of species abundances in a population takes two forms. On the one hand a study of the full distribution of the relative abundances of species may be sought to give insight into the internal mechanisms of the community; in other cases one or more summary statistics which suitably characterise the population may be required to investigate effects of evolutionary or environmental change. The first approach has led to much argument over the appropriate mathematical form for the distribution of abundances, often in the belief that the acceptance of a particular mathematical model will tell us something about the causal biological mechanism. In our opinion, however, the primary purpose of fitting a mathematical model is to smooth the data and enable efficient estimation of population statistics from the parameters of the model; for this we would choose the simplest model which adequately describes the data. Further, there are clear advantages in fitting a single model to describe a series of sets of data—even if this model does not give the best fit to each one—rather than fitting several different models, as has often been suggested, particularly in the literature on succession.