Abundance, spatial variance and occupancy: arthropod species distribution in the Azores.

1. The positive abundance-occupancy and abundance-variance relationships are two of the most widely documented patterns in population and community ecology. 2. Recently, a general model has been proposed linking the mean abundance, the spatial variance in abundance, and the occupancy of species. A striking feature of this model is that it consists explicitly of the three variables abundance, variance and occupancy, and no extra parameters are involved. However, little is known about how well the model performs. 3. Here, we show that the abundance-variance-occupancy model fits extremely well to data on the abundance, variance and occupancy of a large number of arthropod species in natural forest patches in the Azores, at three spatial extents, and distinguishing between species of different colonization status. Indeed, virtually all variation about the bivariate abundance-occupancy and abundance-variance relationships is effectively explained by the third missing variable (variance in abundance in the case of the abundance-occupancy relationship, and occupancy in the case of the abundance-variance relationship). 4. Introduced species tend to exhibit lower densities, less spatial variance in these densities, and occupy fewer sites than native and endemic species. None the less, they all lie on the same bivariate abundance-occupancy and abundance-variance, and trivariate abundance-variance-occupancy, relationships. 5. Density, spatial variance in density, and occupancy appear to be all the things one needs to know to describe much of the spatial distribution of species.