Estimating thresholds in occupancy when species detection is imperfect

Background/Question/Methods

Identification of ecological 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 detection process and may lead to erroneous conclusions about ecological relationships or to the development of inappropriate conservation targets. Here, 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 fit our proposed model in a Bayesian framework, avoiding potential problems with maximum likelihood inference such as non-differentiability of the likelihood surface. WinBUGS was used to evaluate the model through simulation and to fit the model to avian occurrence data for 6 species at 250 sites with two replicate surveys in 2007-2008. To determine if accounting for imperfect detection could change 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), as well as logistic regression. We fitted these models in frequentist and Bayesian modes of inference. 

Results/Conclusions

Results of the simulation showed that 95% posterior intervals for estimates from our proposed model contained the true value of the parameter in approximately 95% of the simulations. As expected, the simulations indicated more precise threshold estimates as sample size increased. In the empirical study we found evidence for threshold relationships for three species*covariate combinations when ignoring non-detection. However, when we included variation from the observation process, threshold relationships were not supported in two cases (i.e., 95% posterior intervals included 0). In general, ignoring uncertainty due to imperfect detection promotes a false sense of confidence about the existence of a threshold response. Our results emphasize the importance of imperfect detection when estimating threshold responses. This model can be extended to investigate abundance thresholds as a function of ecological and anthropogenic factors, while incorporating spatial and temporal variation in detection, as well as multi-species hierarchical models.