Tests for deletion

It has been suggested in the ecological literature that species may be excluded (or "deleted") from an environment because they do not differ sufficiently from other species in the environment. We develop tests of various deletion hypotheses based on the assumption of a random distribution of species sizes. The results provide information on the behavior of quantities of interest to ecologists studying this phenomenon, namely contiguous ratios, and allow us to gauge the extent of deletion required before we can be confident of detecting it. The results indicate that this random-effects approach leads to tests which have low power for ecological applications but may be more useful in fields which permit larger sample sizes.