Independent species in independent niches behave neutrally

The mathematical structure of the two models is summarized in Table 1. The metacommunity composition inside a niche is given by Hubbell’s metacommunity distribution. The model of CP10 imposes the zero-sum constraint, whereas our model does not. Hence, the two models differ only in the sizes of the metacommunity niches. The absolute niche sizes (i.e. the number of individuals in a niche) are infinite in both models; the relative niche sizes (i.e. the fraction of individuals in a niche) are fixed in the model of CP10, and are randomly distributed in our model. This distribution tends to the fixed niche sizes of CP10’s model for high diversity, so that the two models coincide for highly diverse metacommunities. The local community is a sample from the metacommunity, that can be taken with or without dispersal limitation. For both models, the local community SAD inside a niche is given by the Ewens (without dispersal limitation; Ewens 1972) or the Etienne (with dispersal limitation; Etienne 2005) distribution. The models only differ in the niche sizes: fixed in the model of CP10, and randomly distributed in our model. Again, the latter distribution tends to the fixed niche sizes of CP10’s model when the diversity in the local community is high, so that the two models coincide for highly diverse communities.