Islands, equilibria, and speciation.

Ricklefs and Bermingham (1) demonstrated that divergence times of Lesser Antillean avifauna from sister taxa do not follow the exponential distribution predicted with constant colonization and extinction rates (2). Their explanation for this observation was a lack of equilibrium due to historical changes in colonization or extinction rates. However, they mistakenly estimated species numbers from the distribution of divergence time, and they neglected the possibility that migration and speciation could have generated the observed pattern. Ricklefs and Bermingham have confounded the measured cumulative distributions with the time course of colonization of empty islands. Only the latter has an asymptote at the equilibrium number of species. The asymptote of the fitted exponential curve, at 30.8, differs from the total number of bird lineages on the Lesser Antilles not because the model is inadequate, but because it estimates only the number of data points, at 37. This “test” would have rejected the exponential prediction even if the data had fit an exponential distribution perfectly. The fitted constants, even in more complex models, cannot estimate absolute colonization rates, but only relative rates (e.g., the ratio of rates in a two-phase model). The deviation from an exponential distribution is, however, supported by other tests. To explain that deviation, Ricklefs and Bermingham proposed temporal changes in extinction or colonization rates. They did not consider that island populations may receive migrants from a source population after colonization and that this process may cease when a reproductive barrier arises (speciation) (3). We used maximum likelihood to fit their data to five models: (i) the exponential distribution; (ii) variable extinction rate (two phase); (iii) a mass extinction event; (iv) migration with speciation occurring deterministically at a fixed genetic distance; and (v) migration with speciation times following an exponential distribution. The exponential distribution can be rejected in favor of any of the other models, and the speciation and variable-rate models are all statistically indistinguishable (log likelihoods differ by much less than two). The migration-and-speciation models consistently estimate migration rates of about 140 per unit of genetic distance (about two to three fixations of migrant alleles per million years) and genetic distances for speciation in the range of 0.03 to 0.13 (support intervals include significantly lower values). This viable alternative model for the deviation from an exponential distribution deserves further consideration.