On the robustness of N-mixture models

N-mixture models provide an appealing alternative to mark-recapture models, in that they allow for estimation of detection probability and population size from count data, without requiring that individual animals be identified. There is, however, a cost to using the N-mixture models: inference is very sensitive to the model's assumptions. We consider the effects of three violations of assumptions that might reasonably be expected in practice: double counting, unmodeled variation in population size over time, and unmodeled variation in detection probability over time. These three examples show that small violations of assumptions can lead to large biases in estimation. The violations of assumptions we consider are not only small qualitatively, but are also small in the sense that they are unlikely to be detected using goodness-of-fit tests. In cases where reliable estimates of population size are needed, we encourage investigators to allocate resources to acquiring additional data, such as recaptures of marked individuals, for estimation of detection probabilities.