Modeling species distributions by breaking the assumption of self-similarity

Extrapolating population size from the occupancy-abundance relationship and the scaling pattern of occupancy

The estimation of species abundances at regional scales requires a cost-efficient method that can be applied to existing broadscale data. We compared the performance of eight models for estimating species abundance and community structure from presence-absence maps of the southern African avifauna. Six models were based on the intraspecific occupancy-abundance relationship (OAR); the other two on the scaling pattern of species occupancy (SPO), which quantifies the decline in species range size when measured across progressively finer scales. The performance of these models was examined using five tests: the first three compared the predicted community structure against well-documented macroecological patterns; the final two compared published abundance estimates for rare species and the total regional abundance estimate against predicted abundances. Approximately two billion birds were estimated as occurring in South Africa, Lesotho, and Swaziland. SPO models outperformed the OAR models, due to OAR models assuming environmental homogeneity and yielding scale-dependent estimates. Therefore, OAR models should only be applied across small, homogenous areas. By contrast, SPO models are suitable for data at larger spatial scales because they are based on the scale dependence of species range size and incorporate environmental heterogeneity (assuming fractal habitat structure or performing a Bayesian estimate of occupancy). Therefore, SPO models are recommended for assemblage-scale regional abundance estimation based on spatially explicit presence-absence data.