Linking species area curves to spatially explicit community models

Background/Question/Methods

The species area curve is one of the best known and extensively studied patterns in macroecology, but it is still not clear how much it tells us about the underlying biology of an ecological community. Many theories, including recent approaches such as Maximum Entropy, are based on assumptions about the statistics of patterns of abundance, and as a result are difficult to relate to explicit ecological processes. By contrast, we start from an explicit stochastic framework for ecological community dynamics, and use methods from probability theory to derive equations from which the species area relationship can be calculated.

Results/Conclusions

Our method does not make it straightforward to calculate the complete species area relationship for a particular demographic model, but it does make it possible to relate some of the properties of the species area curve to the underlying biology. We show that the species area relationship has to follow particular mathematical forms at small and large areas. We show further how the details of this relationship are related to the spatiotemporal properties of the constituent species, which in turn are determined by the underlying demographic processes.  We illustrate our approach by applying it to a spatially explicit neutral model.  We show that our method correctly predicts the species area relationship at small and large scales, use it to quantify how fat-tailed dispersal imitates speciation at local scales, and highlight some problems with other analytical methods such as field theory.