Dynamic N-mixture models with temporal variability in detection probability

In theory parameters of dynamic N-mixture models can be estimated with multiple years of data without the robust design under the assumption of constant detection probability. However, such an assumption can rarely be met in long-term studies, and the consequences of violating this assumption in the inferences of dynamic N-mixture models have not been assessed. In this study we used simulation studies to evaluate inferences of the original dynamic N-mixture model and two of its spatial extensions in the face of temporal variability in detection probability. We first evaluated the dynamic N-mixture models when detection probability that varied temporally was wrongly treated as a constant. We then evaluated if the robust design was necessary for dynamic N-mixture models to provide valid parameter estimates when detection probability was correctly assumed to vary temporally. Our results showed that, when detection probability that varied temporally was wrongly treated as a constant, biases were introduced in the parameter estimates of dynamic N-mixture models. When detection probability was correctly assumed to vary temporally, the models could provide valid parameter estimates with the robust design. The model could also provide valid parameter estimates when detection probability was a random effect, even without the robust design. Based on our results, we strongly recommended considering temporal variability in detection probability when using dynamic N-mixture models to analyze long-term data and adopting the robust design in long-term surveys. Our work here is not only useful for data analysis but also important for research design, and thus are relevant to a wide range of studies.