Randomizations of range size may preserve extent of occurrence or area of occurrence. When area of occurrence is preserved, this may occur in one of two ways. Ideally, it is quantified by means of extensive presence–absence data, by summing up the number of sampling units (e.g., grid squares) in which a species is present (Gaston and Blackburn 2000). Often, however, these data are unavailable, and area of occurrence is approximated as the area enclosed by a species' range boundary (e.g., Jetz and Rahbek 2001). For contiguous habitat, two of these measures are concordant—extent of occurrence and area enclosed by a species' range boundary. For non-contiguous habitat, however, they are not. For instance, the range of a species found in the area-rich Indo-Australian Archipelago may have a relatively small extent of occurrence but a large area of occurrence, relative to a species that spans the Pacific Ocean, where habitat area is sparse. In this paper, we preserve range extents, rather than areas encompassed, for three reasons. Firstly, available data on the distribution of coral reef area are incomplete; for a substantial portion of the world's tropical coastlines, identifying the presence or absence of reef habitat is compromised by lack of observations (Spalding et al. 2001). Secondly, coral reef area is not a complete measure of available habitat for corals and reef fishes, since both may be found in non-reef habitat (indeed, many extend beyond the latitudinal limits of reef growth). Thirdly, extensive data on presence–absence, necessary for the preferred approach to measuring area of occurrence (Gaston and Blackburn 2000), is unavailable.
However, measuring extent of occurrence for highly non-contiguous habitat is not without its own problems. Range boundaries are drawn based on patches of habitat that represent the locations of a species' most distal populations. However, most of the range boundary consists of interpolation between these locations, and thus the area it encloses may be sensitive to the way in which the envelope is drawn. Therefore we measure latitudinal range extent in one dimension, as the latitudinal distance between the most distal populations along a latitudinal axis (an axis extending from the North Pole to the South Pole). Similarly, we measure longitudinal range extent as the longitudinal distance between the most distal habitats along a longitudinal axis (an axis extending parallel to latitudinal bands from Africa to South America). This insures that our measure of range extent is based on actual observational data—the latitudinal or longitudinal distance between the most distal habitats containing populations. We viewed this as preferable to relying on the shapes of range boundaries. However, it does have drawbacks. In particular, it forces analyses of species richness to be conducted separately along perpendicular axes (in this case, latitudinal and longitudinal axes), rather than explicitly in two dimensions. Because of this one-dimensional approach, we measure species richness at a particular degree of latitude or longitude as the sum of all species whose range extents encompass that latitudinal or longitudinal band ("band sums"; Jetz and Rahbek 2001).
It is difficult to state, a priori, which of these randomization alternatives (extent-preserving or habitat area-preserving) best approximates the biological expectation that mid-domain models are meant to represent: the expected pattern of species richness within a bounded domain in the absence of gradients in environmental conditions that influence species richness. Some processes presuppose the presence of the habitat type necessary for the species group being analyzed (e.g., rate of encounter of species-specific suitable environmental conditions). Thus, a null model might reasonably treat such processes as operating per unit of appropriate habitat type (e.g., shallow-water habitat). Other processes, however, such as the rate of encounter of barriers to dispersal and range expansion, are probably more dependent on actual distances (in this case, extent of ocean), particularly for systems in which the bulk of a species' extent of occurrence consists of expanses of inhospitable habitat in between suitable habitat patches. From this perspective, randomization analyses represent only the first stage of more comprehensive theories of species distributions, in which rates of encounter of suitable environmental conditions and barriers to dispersal are explicitly represented in units most appropriate to the relevant expectation, whether this is a null expectation of no gradients across the domain, or an alternative expectation representing effects of habitat area, energy availability, seasonality, etc. At present, such a theory does not exist, at least in a form that allows explicit comparison of observed and expected species richness patterns. In the meantime, careful interpretation of randomization analyses appears to be the best available means of characterizing the patterns that putative causes of species richness patterns must explain.
Literature Cited
Gaston, K. J., and T. M. Blackburn. 2000. Pattern and process in macroecology. Blackwell Science, Oxford, UK.
Jetz, W., and C. Rahbek. 2001. Geometric constraints explain much of the species richness pattern in African birds. Proceedings of the National Academy of Sciences, USA 98:5661–5666.
Spalding, M. D., C. Ravilious, and E. P. Green. 2001. World atlas of coral reefs. University of California Press, Berkeley, California, USA.