Exploring rarity using a general model for distribution and abundance.

Abstract

We describe a simple model for changes in the distribution and abundance of a metapopulation and use it to explore the conditions leading to different types of rarity. The model suggests that localized populations (those with low patch occupancy but high local abundance) arise from low dispersal, low heterogeneity in extant population size, and frequent local extinctions relative to the potential for recolonization. Scarce populations (with low distribution and abundance) arise when relative local extinction rate is low to moderate and heterogeneity is high or successful dispersal is relatively low. Sparse populations (widespread, but with low local abundance) arise when relative local extinction rate is very low and either spatial heterogeneity or mortality through unsuccessful dispersal is high. In sparse or common species, there may be unstable as well as stable equilibria, implying a threshold distribution and abundance for persistence. The model supports a general correlation between distribution and abundance and suggests that persistence may be threatened by dispersal rates being either too high or too low. The model provides a new perspective on rarity and suggests a simple theoretical foundation for understanding the population-dynamic mechanisms that determine distribution and abundance.