Reef size and isolation determine the temporal stability of coral reef fish populations.

Temporal variance in species abundance, a potential driver of extinction, is linked to mean abundance through Taylor's power law, the empirical observation of a linear log-log relationship with a slope between 1 and 2 for most species. Here we test the idea that the slope of Taylor's power law can vary both among species and spatially as a function of habitat area and isolation. We used the world's most extensive database of coral reef fish communities comprising a 15-year series of fish abundances on 43 reefs of Australia's Great Barrier Reef. Greater temporal variances were observed at small and isolated reefs, and lower variances at large and connected ones. The combination of reef area and isolation was associated with an even greater effect on temporal variances, indicating strong empirical support for the idea that populations on small and isolated reefs will succumb more frequently to local extinction via higher temporal variability, resulting in lower resilience at the community level. Based on these relationships, we constructed a regional predictive map of the dynamic fragility of coral reef fish assemblages on the Great Barrier Reef.