Sampling Hubbell's neutral theory of biodiversity

In the context of neutral theories of community ecology, a novel genealogy-based framework has recently furnished an analytic extension of Ewens' sampling multivariate abundance distribution, which also applies to a random sample from a local community. Here, instead of taking a multivariate approach, we further develop the sampling theory of Hubbell's neutral spatially implicit theory and derive simple abundance distributions for a random sample both from a local community and a metacommunity. Our result is given in terms of the average number of species with a given abundance in any randomly extracted sample. Contrary to what has been widely assumed, a random sample from a metacommunity is not fully described by the Fisher log-series, but by a new distribution. This new sample distribution matches the log-series expectation at high biodiversity values (theta > 1) but clearly departs from it for species-poor metacommunities (theta < 1). Our theoretical framework should be helpful in the better assessment of diversity and testing of the neutral theory by using abundance data.