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 regionWebb T.J., Noble D. & Freckleton R.P. (2007). Abundance-occupancy dynamics in a human dominated environment: linking interspecific and intraspecific trends in British farmland and woodland birds. Journal of Animal Ecology, 76, 123–134.

Measures of species' geographic range

In the discussion of relationships with range size, it is important to define which range is under investigation. GastonGaston, K.J. 2003. The Structure and Dynamics of Geographic Ranges. Oxford University Press. Oxford, UK. 266 pp. (following UdvardyUdvardy, M.D.F. 1969. Dynamic Zoogeography: with special reference to land animals. Van Nostrand Reinhold, New York.) 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.Quinn, R.M., K.J. Gaston, and H.R. Arnold. 1996. Relative measures of geographic range size: empirical comparisons. Oecologia 107: 179–188. found that the occupancy at the finest resolution (10 x 10 km squares) best explained abundance patterns. In a similar manner, Zuckerberg et al.Zuckerberg, B., W.F. Porter, and K. Corwin. 2009. The consistency and stability of abundance-occupancy relationships in large-scale population dynamics. Journal of Animal Ecology 78: 172–181. 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 FullerGaston, K.J. and R.A. Fuller. 2009. The sizes of species geographic ranges. Journal of Applied Ecology 46: 1–9. 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.Hui, C., Veldtman, R. & McGeoch, M.A. 2010. Measures, perceptions and scaling patterns of aggregated species distributions. Ecography 33: 95–102. 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,Hui, C. & McGeoch, M.A. (2007) Capturing the "droopy-tail" in the occupancy-abundance relationship. Ecoscience, 14, 103–108.

Temporal occupancy-abundance relationship The temporal version of the occupancy-abundance relationship has been studied less extensively than the spatial version above, a similar pattern emerges. In a long-term time series of fish abundance in the Bristol Channel, it was observed that species that were present very occasionally were also in low abundance (comprising most species; a well-known general pattern observed in species abundance distributions), whereas species that were frequently present were also the most abundant. This is also a temporal analogue of Hanski's core-satellite hypothesis -- that species may be split into occasionally present and frequently present species.

Possible explanations A suite of possible explanations have been proposed to describe why positive intra- and interspecific O–A relationships are observed. Following Gaston et al. 1997Gaston, K.J., T.M. Blackburn, and J.H. Lawton. 1997. Interspecific abundance–range size relationships: an appraisal of mechanisms. Journal of Animal Ecology 66: 579–601. Gaston and Blackburn 2000<Gaston, K.J., and T.M. Blackburn. 2000. Pattern and Process in Macroecology. Blackwell Science Ltd. United Kingdom. 377 pp. Gaston et al. 2000, and Gaston 2003 these reasons include:

Statistical explanations One way to deal with observed O–A relationships is, in essence, to deny their existence. An argument against the existence of O–A relationships is that they are merely sampling artefacts. Given that rare species are less likely to be sampled, at a given sampling effort, one can expect to detect rare species occupying fewer sites than common ones, even if the underlying occupancy distribution is the same. However, this explanation makes only one prediction, that is, that with sufficient sampling, no relationship will be found to exist. This prediction is readily falsified, given that exceptionally well studied taxa such as breeding birds (e.g. Zuckerberg et al. 2009, Gaston) show well documented O-A relationships.

A second statistical explanation involves the use of statistical distributions such as the Poisson or negative-binomial. This explanation suggests that due to the underlying distribution of aggregation and density, and observed O–A relationship would be expected. However, Gaston et al. question whether this is a suitably mechanistic explanation. Indeed, Gaston et al. suggest that "to argue that spatial aggregation explains abundance-occupancy relationships is simply to supplant one poorly understood pattern with another".

The phylogenetic non-independence hypothesis is a third statistical explanation, specific to observed interspecific O–A relationships. This hypothesis suggests that, as closely related species are not truly independent their inclusion into analyses artificially inflates the degrees of freedom available for testing the relationship. However Gaston et al. cite several studies documenting significant O–A relationships in spite of controlling for phylogenetic non-independence.

Range position Most evaluations of O–A relationships do not evaluate species over their entire (global) range, but document abundance and occupancy patterns within a specific region. It is believed that species decline in abundance and become more patchily distributed towards the margin of their range. If this is true, then it can be expected that as a species expands or contracts its range within the region of interest, it will more or less closely resemble populations at the core of its range, leading to a positive intraspecific O–A relationship. In the same manner, an assemblage of species within the study region can be expected to contain some species near the core and some near the periphery of their ranges, leading to a positive interspecific O–A relationship. Although this explanation may contribute to the understanding of O–A relationships where partial ranges are considered, it cannot explain relationships documented for entire geographic ranges.

Resource use explanations