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.
Read more about this topic: Occupancy-abundance Relationship, Possible Explanations
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