The pattern described here, closely related species that never turn up on the same island even when islands sit close together, is a well known finding from island biogeography, first worked out in detail for birds in New Guinea and its satellite islands. Let's test each process against this pattern.
The mutual exclusion of sister species from the same island is the signature of competitive exclusion between ecologically similar rivals.
Let's summarize:
So competition between ecologically similar sister species best explains the checkerboard distribution.
