Potentiality and limitations of N‐mixture and Royle‐Nichols models to estimate animal abundance based on noninstantaneous point surveys

Reliable and accurate information on animal abundance is fundamental for the conservation and management of wildlife. Recently, a number of innovative devices (such as camera traps) have been widely used in field surveys and have largely improved survey efficiency. However, these devices often constitute noninstantaneous point surveys, resulting in the multiple counts of the same animal individuals within a single sampling occasion (i.e., false‐positive errors). Many commonly‐used statistical models do not explicitly account for the false‐positive error, with its effects on estimates being poorly understood. Here, I tested the performance of the commonly‐used Poisson‐binomial N‐mixture and the Royle‐Nichols model in the presence of both false‐positive and negative errors (i.e., individuals in a population might not be detected). I also implemented the Poisson‐Poisson mixture model in the Bayesian framework to evaluate its reliability. The results of the simulation using random walks based on Ornstein‐Uhlenbeck processes showed that the Poisson‐binomial model was not robust to false‐positive errors. In comparison, the Royle‐Nichols and Poisson‐Poisson models provided reasonable estimates of the number of animals whose home range included the survey point. However, the number of animals whose home range included the survey point is inherently influenced by the size of animal home ranges, and thus cannot be used as a surrogate of animal density. Although the N‐mixture and Royle‐Nichols models are widely used, their utility might be restricted by this limitation. In conclusion, studies should clearly define the objective of surveys and carefully consider whether the models used are valid. I tested the performance of the commonly used Poisson‐binomial N‐mixture (PB) and the Royle‐Nichols (RN) model in the presence of both false‐positive and negative errors. I also implemented the Poisson‐Poisson (PP) mixture model in the Bayesian framework. The results of the simulation using random walks showed that the PB model was not robust to false‐positive errors, while the RN and PP models provided reasonable estimates of the number of animals whose home range included the survey point.