to reestablish. The statistics of these local extinction-recolonization events for birds in North America was recently analyzed by [@bertuzzo2011spatial], below we will consider the relations between our model and their empirical results.

Community dynamics theories are usually classified along the line between niche and neutral. A niche theory assumes that every species that have a non-sporadic presence on the island has its own niche. For example, a few bird species each having a different beak size and (correspondingly) different diet may coexist on the island if the overlap between the niches is not too large. In the other extreme, in a perfectly neutral dynamics there is no niche partitioning at all, all species are using the same resources with the same efficiency, and the dynamics is governed solely by stochasticity. In between one can find a few “continuum models” [@kadmon; @gravel; @pacala; @zillio] that were suggested in the last decade and incorporate elements of neutral dynamics with (usually weak) selective effects.

The simplest model for island dynamics is the generalized competitive Lotka-Volterra model (GCLV) with migration. This model is widely used in ecology and for other applications [@tilman1987importance; @pigolotti2007species; @fort2013statistical]. It turns out that the model has a very rich 