Estimating thresholds in occupancy when species detection is imperfect.

Identification of thresholds (state changes over a narrow range of values) is of basic and applied ecological interest. However, current methods of estimating thresholds in occupancy ignore variation in the observation process and may lead to erroneous conclusions about ecological relationships or to the development of inappropriate conservation targets. We present a model to estimate a threshold in occupancy while accounting for imperfect species detection. The threshold relationship is described by a break-point (threshold) and the change in slope (threshold effect). Imperfect species detection is incorporated by jointly modeling species occurrence and species detection. We used WinBUGS to evaluate the model through simulation and to fit the model to avian occurrence data for three species from 212 sites with two replicate surveys in 2007-2008. To determine if accounting for imperfect detection changed the inference about thresholds in avian occupancy in relation to habitat structure, we compared our model to results from a commonly used threshold model (segmented logistic regression). We fit this model in both frequentist and Bayesian modes of inference. Results of the simulation study showed that 95% posterior intervals contained the true value of the parameter in approximately 95% of the simulations. As expected, the simulations indicated more precise threshold and parameter estimates as sample size increased. In the empirical study, we found evidence for threshold relationships for four species by covariate combinations when ignoring species detection. However, when we included variation from the observation process, threshold relationships were not supported in three of those four cases (95% posterior intervals included 0). In general, confidence intervals for the threshold effect were larger when we accounted for species nondetection than when we ignored nondetection. This model can be extended to investigate abundance thresholds as a function of ecological and anthropogenic factors, as well as multispecies hierarchical models.