The spatial limitations of current neutral models of biodiversity

The unified neutral theory of biodiversity and biogeography is increasingly accepted as an informative null model of community composition and dynamics. It has successfully produced macro-ecological patterns such as species-area relationships and species abundance distributions. However, the models employed make many unrealistic auxiliary assumptions. For example, the popular spatially implicit version assumes a local plot exchanging migrants with a large panmictic regional source pool. This simple structure allows rigorous testing of its fit to data. In contrast, spatially explicit models assume that offspring disperse only limited distances from their parents, but one cannot as yet test the significance of their fit to data. Here we compare the spatially explicit and the spatially implicit model, fitting the most-used implicit model (with two levels, local and regional) to data simulated by the most-used spatially explicit model (where offspring are distributed about their parent on a grid according to either a radially symmetric Gaussian or a 'fat-tailed' distribution). Based on these fits, we express spatially implicit parameters in terms of spatially explicit parameters. This suggests how we may obtain estimates of spatially explicit parameters from spatially implicit ones. The relationship between these parameters, however, makes no intuitive sense. Furthermore, the spatially implicit model usually fits observed species-abundance distributions better than those calculated from the spatially explicit model's simulated data. Current spatially explicit neutral models therefore have limited descriptive power. However, our results suggest that a fatter tail of the dispersal kernel seems to improve the fit, suggesting that dispersal kernels with even fatter tails should be studied in future. We conclude that more advanced spatially explicit models and tools to analyze them need to be developed.