A general and dynamic species abundance model, embracing the lognormal and the gamma models

One aspect of community ecology that has been given particular attention is the pattern of species abundances in a community. The species may have a wide range of abundances; some are very common and others rare. When species abundance models are fitted to observations, the lognormal model and one of the gamma models (e.g., the log-series model) are usually applied. The model that gives the best fit according to some goodness-of-fit test is then chosen. By applying a diffusion approximation for each species' dynamics with density regulation of the theta-logistic type, we here present a general species abundance model that embraces the two most widely applied species abundance models, the lognormal and the gamma. Our general model will, therefore, provide a better fit than the two special cases, except when it corresponds to one of them. In contrast to the classical models, ours is also dynamic, making it possible to evaluate the fluctuations in species abundance over time through both biotic and abiotic factors. The model is fitted to several species abundance data sets and our results compared to previous attempts to fit a model, usually either the lognormal or the log-series.