Goodness of fit checks for binomial N-mixture models

O_LIBinomial N-mixture models are commonly applied to analyze population survey data. By estimating detection probabilities, N-mixture models aim at extracting information about abundances in terms of actual and not just relative numbers. This separation of detection probability and abundance relies on parametric assumptions about the distribution of individuals among sites and of detections of individuals among repeat visits to sites. Current methods for checking assumptions are limited, and their computational complexity have hindered evaluations of their performances.\nC_LIO_LIWe develop computationally efficient graphical goodness of fit checks and measures of overdispersion for binomial N-mixture models. These checks are illustrated in a case study, and evaluated in simulations under two scenarios. The two scenarios assume overdispersion in the abundance distribution via a negative binomial distribution or in the detection probability via a beta-binomial distribution. We evaluate the ability of the checks to detect lack of fit, and how lack of fit affects estimates of abundances.\nC_LIO_LIThe simulations show that if the parametric assumptions are incorrect there can be severe biases in estimated abundances: negatively if there is overdispersion in abundance relative to the fitted model and positively if there is overdispersion in detection. Our goodness of fit checks performed well in detecting lack of fit when the abundance distribution is overdispersed, but struggled to detect lack of fit when detections were overdispersed. We show that the inability to detect lack of fit due to overdispersed detection is caused by a fundamental similarity between N-mixture models with beta-binomial detections and N-mixture models with negative binomial abundances.\nC_LIO_LIThe strong biases in estimated abundances that can occur in the binomial N-mixture model when the distribution of individuals among sites, or the detection model, is mis-specified implies that checking goodness of fit is essential for sound inference in ecological studies that use these methods. To check the assumptions we provide computationally efficient goodness of fit checks that are available in an R-package nmixgof. However, even when a binomial N-mixture model appears to fit the data well, estimates are not robust in the presence of overdispersion unless additional information about detection is collected.\nC_LI