Occupancy-abundance relationship

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The intraspecific occupancy-abundance relationship describes the relationship between the abundance and occupancy (range size) of a species over time or across regions. It is in widespread use as a species descriptor in conservation and species management as it can potentially provide an estimate of the abundance of species based only on its presence-absence map. Hithero, there are around seven different models describe the occupancy-abundance relationship. Nachman (1981)[1] presented a wonderful formula from empiricial studies. Hanski and Gyllenberg (1997)[2] generated this relationship based on the metapopulation dynamics. Wright (1991)[3] suggested that the probability distribution, such as the Poisson distribution can capture the characteristics of this distribution. He and Gaston (2000a[4], b[5]; 2003[6]) suggested to use the negative binomial distribution to describe this relationship, and they further use Taylor's power law, i.e. the variance-mean abundance in samples, to adjust their relationship.

Holt et al. (2002)[7] and He et al. 2002[8] reviewed those methods and suggested that the negative binomial distribuiton will give the best description. Hui and McGeoch (2007)[9] indicated the above method could essentially underestimate the real estimation due to a percolation effect, named the "droopy tail" in the occupancy-abundance relationship. They further presented a logistic-like equation (tested by several datasets) and suggested the usage of this equation in further application. The intraspecific occupancy-abundance relationship is also linked with the scaling pattern of occupancy.

[edit] Formula

(He and Gaston 2000)
p=1 - {\left(1 + \frac{\mu }{k} \right) }^{-k}
where p is the occupancy, k is a parameter of overdispersal, and μ is the mean abundance in samples.

(Hui and McGeoch 2007)
{p_a}=1 - {\left( \frac{\left( A + a\,N\,r \right) \,a' }{A\, \left( -a + a' \right) } \right) }^ {-\left( \frac{N\,a'} {A + N\,r\,a'} \right) }
where pa is the occupancy observed under the grain (or sample size) a; N is total abundance; A is extent; a' is the minimal grain for which the occupancy equals one; r is a parameter that describes the intrinsic rate of change of occupancy with grain. A more complicted version of this formula can be found in Hui and McGeoch (2007).

Comparison of those formula can be found in Holt et al. (2002), He et al. (2002) and Hui and McGeoch (2007).

[edit] References

  1. ^ 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
  2. ^ Hanski, I., Gyllenberg, M. 1997. Uniting two general patterns in the distribution of species. Science, 275: 397-400.
  3. ^ Wright, DH. 1991. Correlations between incidence and abundance are expected by chance. Journal of Biogeography, 18: 463-466
  4. ^ He, F., Gaston, KJ. 2000a. Estimating species abundance from occurrence. American Naturalist, 156: 553-559
  5. ^ He, F., Gaston, KJ. 2000b. Occupancy-abundance relationships and sampling scales. Ecography, 23: 503-511
  6. ^ He, F., Gaston, KJ. 2003. Occupancy, spatial variance, and the abundance of species. American Naturalist, 162: 366-375
  7. ^ Holt, AR, Gaston, KJ., He, F. 2002. Occupancy-abundance relationships and spatial distribution: a review. Basic and Applied Ecology, 3: 1-13
  8. ^ He, F., Gaston, KJ., Wu, J. 2002. On species occupancy-abundance models. Ecoscience, 9: 119-126.
  9. ^ Hui, C., McGeoch, MA. 2007. Capturing the "droopy-tail" in the occupancy-abundance relationship. Ecoscience, 14: 103-108.