Scaling pattern of occupancy

In spatial ecology and macroecology, scaling pattern of occupancy (SPO), also known as the area-of-occupancy (AOO) is the way in which species distribution changes across spatial scales. In physical geography and image analysis, it is similar to the modifiable areal unit problem. Simon A. Levin (1992) states that the problem of relating phenomena across scales is the central problem in biology and in all of science. Understanding the SPO is thus one central theme in ecology.

This pattern is often plotted as log-transformed grain (cell size) versus log-transformed occupancy. Kunin (1998) presented a log-log linear SPO and suggested a fractal nature for species distributions. It has since been shown to follow a logistic shape, reflecting a percolation process. Furthermore, the SPO is closely related to the intraspecific occupancy-abundance relationship. For instance, if individuals are randomly distributed in space, the number of individuals in an α-size cell follows a Poisson distribution, with the occupancy being P_α = 1 − exp(−μα), where μ is the density. Clearly, P_α in this Poisson model for randomly distributed individuals is also the SPO. Other probability distributions, such as the negative binomial distribution, can also be applied for describing the SPO and the occupancy-abundance relationship for non-randomly distributed individuals.

Other occupancy-abundance models that can be used to describe the SPO includes Nachman's exponential model, Hanski and Gyllenberg's metapopulation model, He and Gaston's improved negative binomial model by applying Taylor's power law between the mean and variance of species distribution, and Hui and McGeoch's droopy-tail percolation model. One important application of the SPO in ecology is to estimate species abundance based on presence-absence data, or occupancy alone. This is appealing because obtaining presence-absence data is often cost-efficient. Using a dipswitch test consisting of 5 subtests and 15 criteria, Hui et al. confirmed that using the SPO is a robust and reliable for assemblage-scale regional abundance estimation. The other application of SPOs includes trends identification in populations, which is extremely valuable for biodiversity conservation.

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