A unified model of species immigration, extinction and abundance on islands

Aim MacArthur and Wilson's theory of island biogeography was revolutionary, and also inspired the more recent unified neutral theory of biodiversity and biogeography. The unified neutral theory has the potential to make predictions about island biogeography that are not well studied. Here we aim to unify the two theories by using an ecological neutral model to study immigration and extinction rates on islands the cornerstone of MacArthur and Wilson's theory. Methods We conduct simulations of a spatially implicit neutral model and measure species abundances, immigration rates and extinction rates. We study the behaviour of the model at dynamic equilibrium and on approach to dynamic equilibrium both from volcanic origin (low initial diversity) and from land bridge origin (high initial diversity). We extend the model to study the effects of clustered immigration and to explicitly account for the distinction between immigration and colonization. Results Our model, in accord with the simplest version of MacArthur and Wilson's theory, predicts linear immigration and extinction rates as functions of species richness at dynamic equilibrium. In contrast, the approach to dynamic equilibrium produces rich and unexpected behaviour where immigration and extinction rates are non-monotonic functions of species richness, at odds with other theory. Once examined, however, this behaviour makes biological sense and results from the influence of the species abundance distribution over immigration and extinction rates. The turnover predicted by our first model appears high, but can be lowered to realistic levels with an alternative model of clustered immigration or by accounting for the difference between the immigration of a new species and its true colonization of the island. Main conclusions MacArthur and Wilson's theory of island biogeography and ecological neutral theory are different, but there are strong similarities in their assumptions and predictions that should not be overlooked when evaluating them. Our results highlight the importance of species abundances as indicators of immigration and extinction rates; species richness alone is insufficient. In particular, extinction rate and species abundances are unavoidably linked, as rarity usually precedes extinction.