A dispersal-limited sampling theory for species and alleles.

The importance of dispersal for biodiversity has long been recognized. However, it was never advertised as vigorously as Stephen Hubbell did in the context of his neutral community theory. After his book appeared in 2001, several scientists have sought and found analytical expressions for the effect of dispersal limitation on community composition, still in the neutral context. This has been done along two relatively independent lines of research that have a different mathematical approach and focus on different, yet related, types of results. Here, we study both types in a new framework that makes use of the sampling nature of the theory. We present sampling distributions that contain binomial or hypergeometric sampling on the one hand, and dispersal limitation on the other, and thus views dispersal limitation as ubiquitous as sampling effects. Further, we express the results of one line of research in terms of the other and vice versa, using the concept of subsamples. A consequence of our findings is that metacommunity size does not independently affect the outcome of neutral models in contrast to a previous assertion (Ecol. Lett., 7, 2004, p. 904) based on an incorrect formula (Phys. Rev. E, 68, 2003, p. 061902, eqns 11-14). Our framework provides the basis for development of a dispersal-limited non-neutral community theory and applies in population genetics as well, where alleles and mutation play the roles of species and speciation respectively.