Two-species occupancy models: a new parameterization applied to co-occurrence of secretive rails

Two-species occupancy models that account for false absences provide a robust method for testing for evidence of competitive exclusion, but previous model parameterizations were inadequate for incorporating covariates. We present a new parameterization that is stable when covariates are included: the conditional two-species occupancy model, which can be used to examine alternative hypotheses for species' distribution patterns. This new model estimates the probability of occupancy for a subordinate species conditional upon the presence of a dominant species. It can also be used to test if the detection of either species differs when one or both species are present, and if detection of the subordinate species depends on the detection of the dominant species when both are present. We apply the model to test if the presence of the larger Virginia Rail (Rallus limicola) affects probabilities of detection or occupancy of the smaller California Black Rail (Laterallus jamaicensis coturniculus) in small freshwater marshes that range in size from 0.013 to 13.99 ha. We hypothesized that Black Rail occupancy should be lower in small marshes when Virginia Rails are present than when they are absent, because resources are presumably more limited and interference competition should increase. We found that Black Rail detection probability was unaffected by the detection of Virginia Rails, while, surprisingly, Black and Virginia Rail occupancy were positively associated even in small marshes. The average probability of Black Rail occupancy was higher when Virginia Rails were present (0.74 +/- 0.053, mean +/- SE) than when they were absent (0.36 +/- 0.069), and for both species occupancy increased with marsh size. Our results contrast with recent findings from patchy forest systems, where small birds were presumed to be excluded from small habitat patches by larger competitors.