A new parameterization for estimating co-occurrence of interacting species.

Models currently used to estimate patterns of species co-occurrence while accounting for errors in detection of species can be difficult to fit when the effects of covariates on species occurrence probabilities are included. The source of the estimation problems is the particular parameterization used to specify species co-occurrence probability. We develop a new parameterization for estimating patterns of co-occurrence of interacting species that allows the effects of covariates to be specified quite naturally without estimation problems. In our model, the occurrence of one species is assumed to depend on the occurrence of another, but the occurrence of the second species is not assumed to depend on the presence of the first species. This pattern of co-occurrence, wherein one species is dominant and the other is subordinate, can be produced by several types of ecological interactions (predator-prey, parasitism, and so on). A simulation study demonstrated that estimates of species occurrence probabilities were unbiased in samples of 50-100 locations and three surveys per location, provided species are easily detected (probability of detection > or = 0.5). Higher sample sizes (>200 locations) are needed to achieve unbiasedness when species are more difficult to detect. An analysis of data from treefrog surveys in southern Florida indicated that the occurrence of Cuban treefrogs, an invasive predator species, was highest near the point of its introduction and declined with distance from that location. Sites occupied by Cuban treefrogs were 9.0 times less likely to contain green treefrogs and 15.7 times less likely to contain squirrel treefrogs compared to sites without Cuban treefrogs. The detection probabilities of native treefrog species did not depend on the presence of Cuban treefrogs, suggesting that the native treefrog species are naive to the introduced species.