Capturing the “droopy-tail” in the occupancy—abundance relationship

Abstract

The intraspecific occupancy—abundance relationship is a widely used descriptor of species distributions, with potential value to conservation and pest management for predicting species abundance from occurrence data. Six traditional and commonly used models for the description of this relationship include the Poisson, exponential, metapopulation, fractal, negative binomial, and improved negative binomial models. However, these models deviate systematically from empirical data. We present a model (the “droopy-tail” model or DTM) that improves estimates of occupancy at coarse scales by taking the percolation effect of scale on the occupancy—abundance relationship into account. The DTM is a fundamental departure from previous models because the slope of the scaling curve limits to negative infinity (rather than to zero) at coarse scales in addition to providing a good fit to empirical data at all spatial scales.