In ecology, the occupancy–abundance (O–A) relationship is the relationship between the abundance of species and the size of their ranges within a region. This relationship is perhaps one of the most well-documented relationships in macroecology, and applies both intra- and interspecifically (within and among species). In most cases, the O–A relationship is a positive relationship. Although an O–A relationship would be expected, given that a species colonizing a region must pass through the origin (zero abundance, zero occupancy) and could reach some theoretical maximum abundance and distribution (that is, occupancy and abundance can be expected to co-vary), the relationship described here is somewhat more substantial, in that observed changes in range are associated with greater-than-proportional changes in abundance. Although this relationship appears to be pervasive (e.g. Gaston 1996 and references therein), and has important implications for the conservation of endangered species, the mechanism(s) underlying it remain poorly understood.
Important terms Range – means the total area occupied by the species of interest in the region under study (see below 'Measures of species geographic range') Abundance – means the average density of the species of interest across all occupied patches (i.e. average abundance does not include the area of unoccupied patches) Intraspecific occupancy–abundance relationship – means the relationship between abundance and range size within a single species generated using time series data Interspecific occupancy–abundance relationship – means the relationship between relative abundance and range size of an assemblage of closely related species at a specific point in time (or averaged across a short time period). The interspecific O-A relationship may arise from the combination of the intraspecific O–A relationships within the region
Measures of species' geographic range
In the discussion of relationships with range size, it is important to define which range is under investigation. Gaston (following Udvardy) describes the potential range of a species as the theoretical maximum range that a species could occupy should all barriers to dispersal be removed, while the realized range is the portion of the potential range that the species currently occupies. The realized range can be further subdivided, for example, into the breeding and non-reproductive ranges. Explicit consideration of a particular portion of the realized range in analysis of range size can significantly influence the results. For example, many seabirds forage over vast areas of ocean, but breed only on small islands, thus the breeding range is significantly smaller than the non-reproductive range. However, in many terrestrial bird species, the pattern is reversed, with the winter (non-reproductive) range somewhat smaller than the breeding range. The definition of range is further confounded by how the total realized range size is measured. There are two types of measurements commonly in use, the extent of occurrence (EOO) (For definition: see ALA and Fig.1) and the area of occupancy (AOO) (see also the Scaling pattern of occupancy, and for a definition, see Fig. 2 and ALA). The EOO can best be thought of as the minimum convex polygon encompassing all known normal occurrences of a particular species and is the measure of range most commonly found in field guides. The AOO is the subset of the EOO where the species actually occurs. In essence, the AOO acknowledges that there are holes in the distribution of a species within its EOO, and attempts to correct for these vacancies. A common way to describe the AOO of a species is to divide the study region into a matrix of cells and record if the species is present in or absent from each cell. For example, in describing O–A relationships for common British birds, Quinn et al. found that the occupancy at the finest resolution (10 x 10 km squares) best explained abundance patterns. In a similar manner, Zuckerberg et al. used Breeding Bird Atlas data measured on cells 5 × 5 km to describe breeding bird occupancy in New York State. IUCN typically uses a cell size of 2 × 2 km in calculating AOO. In much of macroecology, the use of EOO as a measure of range size may be appropriate; however, AOO is a more appropriate measure when evaluating O–A relationships. In macroecological investigations that are primarily biogeographical in nature, the variables of interest can be expected to vary most from one extent of occurrence to the opposite, and less so through discontinuities contained within the total EOO. However, when investigating O-A relationships, the area occupied by a species is the variable of interest, and the inclusion of discontinuities within the EOO could significantly influence results. In the extreme case where occupied habitats are distributed at random throughout the EOO, a relationship between abundance and range size (EOO) would not be expected. Because O–A relationships have strong conservation implications, Gaston and Fuller have argued that clear distinctions need to be made as to the purpose of the EOO and AOO as measures of range size, and that in association with O-A relationships the AOO is the more useful measure of species abundance. No matter which concept we use in studies, it is essential to realize that occupancy is only a reflection of species distribution under a certain spatial scale. Occupancy, as well as other measures of species distributions (e.g. over-dispersion and spatial autocorrelation), is scale-dependent. As such, studies on the comparison of O–A relationships should be aware of the issue of scale sensitivity (compare text of Fig 1 & Fig.2). Furthermore, measuring species range, whether it is measured by the convex hull or occupancy (occurrence), is part of the percolation process and can be explained by the percolation theory,
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