Species occurrence and occupancy

Arguably, one of the most fundamental units of biodiversity is the presence or absence of a species in a given site (a resource or habitat patch, an island, a mapping unit, etc.). This is evidenced by the fact that simple species × sites (r × c) matrices, in which the presence/absence of different species (in rows r ) is given for a set of different sites (in columns c), lie at the heart of probably the vast majority of biodiversity studies (Simberloff & Connor 1979; Bell 2003; Arita et al. 2008; Gaston et al. 2008a). Indeed, some of the most basic patterns which emerge from presence/absence r × c matrices have long intrigued ecologists, such as species– area relationships, nestedness, and gradients in β diversity. Summing the presences along a row of an r × c matrix gives the level of occupancy of a given species, often most usefully expressed in terms of the proportion (p) of the available sites that are actually occupied (or, equivalently, the probability that the species occurs in any one site). This may vary greatly from one species to another, and the question of why some species are widely distributed and others narrowly has long been a staple of ecological discourse (e.g. Darwin 1859; Harper 1981; Rabinowitz 1981; Gaston 1994; Kunin & Gaston 1997). The actual area over which a species is distributed (i.e. the summed areas of the sites at which it occurs) has been termed its ‘area of occupancy’ (Gaston 1991; Gaston & Fuller 2009), and is important for some, particularly applied, considerations, such as evaluating the risk of extinction that species face in the short term as a consequence of anthropogenic pressures (Mace et al. 2008). The level of occupancy attained by a species is strongly influenced by the spatial resolution of the occurrence data (i.e. by the size of a ‘site’). This is simply because the level of occupancy itself fails to capture other significant features of spatial distribution, particularly the way in which at a fine resolution occupied sites are spatially dispersed. On average, of two species with the same occupancy at a fine scale, that with the more dispersed pattern of occurrences will have the greater occupancy at a coarser resolution (one simple widely used measure of this dispersion is the area contained within the geographically outermost occurrences of a species, its ‘extent of occurrence’; Gaston 1991; Gaston & Fuller 2009). Although it is only relatively recently that the analytical form of the relationship between spatial resolution and the observed level of occupancy of a species (Fig. 11.1; the occupancy–area relationship) has come to the fore, the potential significance of spatial resolution on observed patterns of occupancy has been recognized for much longer (e.g. Erickson 1945; Rapoport 1982). The occupancy of a species is only a crude caricature of the distribution of its individuals. However, the level of occupancy attained across a set of sites is inevitably a function of the number of individuals summed across those sites. Only one site can be occupied when there is a single individual (assuming that sites are defined to be at least larger than an individual), and there is almost invariably some upper limit to the number of individuals that can physically co-occur in a single site, even ignoring all of the factors that can act to disperse individuals more widely (e.g. air and water currents, life history, behaviour). Much attention has been paid to the actual form taken by occupancy–abundance relationships (Fig. 11.1), being motivated initially mostly by the wish to be able to estimate the abundance of a species from its much more readily (and