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Scaling pattern of occupancy
In spatial ecology and macroecology, scaling pattern of occupancy (SPO), also known as the area-of-occupancy 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)〔Levin, SA. 1992. The problem of pattern and scale in ecology. Ecology, 73, 1943–1967.()〕 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.
== Pattern description ==
This pattern is often plotted as log-transformed grain (cell size) versus log-transformed occupancy. Kunin (1998)〔Kunin, WE. 1998. Extrapolating species abundance across spatial scales. Science, 281: 1513–1515.()〕 presented a log-log linear SPO and suggesting a fractal nature of species distribution. In reality, it has 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.〔Wright, D.H. 1991. Correlations between incidence and abundance are expected by chance. Journal of Biogeography, 18: 463–466.()〕 Clearly, Pα 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.〔He, F., Gaston, K.J. 2000. Estimating species abundance from occurrence. American Naturalist, 156: 553–559.()〕
Other occupancy-abundance models that can be used to describe the SPO includes Nachman's exponential model,〔Nachman, G. 1981. A mathematical model of the functional relationship between density and spatial distribution of a population. Journal of Animal Ecology, 50: 453–460.()〕 Hanski and Gyllenberg's metapopulation model,〔Hanski, I., Gyllenberg, M. 1997. Uniting two general patterns in the distribution of species. Science, 284: 334–336.()〕 He and Gaston's〔He, F., Gaston, K.J. 2003. Occupancy, spatial variance, and the abundance of species. American Naturalist, 162: 366–375.()〕 improved negative binomial model by applying Taylor's power law between the mean and variance of species distribution,〔Taylor, L.R. 1961. Aggregation, variance and the mean. Nature, 189: 732–735.()〕 and Hui and McGeoch's droopy-tail percolation model.〔Hui, C., McGeoch, MA. 2007. Capturing the "droopy tail" in the occupancy-abundance relationship. Ecoscience, 14: 103–108.()〕 One important application of the SPO in ecology is to estimate species abundance based on presence-absence data, or occupancy alone.〔Hartley, S., Kunin, WE. 2003. Scale dependence of rarity, extinction risk, and conservation priority. Conservation Biology, 17: 1559–1570.〕 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.〔Hui, C., McGeoch, M.A., Reyers, B., le Roux, P.C., Greve, M., Chown, S.L. 2009. Extrapolating population size from the occupancy-abundance relationship and the scaling pattern of occupancy. Ecological Applications, 19: 2038–2048.()〕 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.〔Wilson, RJ., Thomas, CD., Fox, R., Roy, RD., Kunin, WE. 2004. Spatial patterns in species distributions reveals biodiversity change. Nature, 432: 393–396.()〕
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