Abstract
Aim MacArthur and W ilson's original formulation of the theory of island biogeography ( TIB ) included the corollary hypothesis that species richness might affect immigration and extinction rates. Building on this, other researchers have suggested additional top‐down and bottom‐up effects. We compare these hypotheses to identify the strongest candidates for inclusion in a ‘trophic TIB ’. Location Six mangrove islands in the F lorida K eys, USA Methods We studied a classic island biogeography time series featuring lists of species observed on six mangrove islands during roughly 16 censuses each across 700 days. We first used this time series to determine the number of opportunities for species to immigrate to an island for the first time ( n = 18,420), to go locally extinct ( n = 1943) or to re‐immigrate to an island after having previously gone extinct ( n = 1813). We then leveraged information on the predators and prey of those species to estimate the potential for top‐down and bottom‐up interactions during each census period. Finally, we constructed statistical models to test for species richness, top‐down, and bottom‐up effects on per‐species immigration and extinction probabilities and validated them by comparing each model with a similar model based on the classic TIB . Results We found that models including bottom‐up effects gave the greatest improvement over the classic TIB models. Extinction probability in particular decreased sharply for species with both basal resources and animal prey available. Species richness and top‐down effects had far weaker impacts on per‐species probabilities of immigration and extinction. Main conclusions Our findings suggest that incorporating information on the trophic structure of island communities – particularly the species‐specific availability of resources – can substantially alter predictions of extinction probabilities. Immigration probability, on the contrary, appeared largely stochastic. Incorporating trophic information into predictions of extinction rates therefore represents the most promising and best‐supported way to extend the TIB .