Faster Asymptotic Solutions for N-Mixtures on Large Populations

We derive an asymptotic likelihood function for open-population N-mixture models and show that it has favorable computational complexity and accuracy when compared to the traditional likelihood function for large population sizes. We validate our asymptotic model with simulation studies and apply our model to estimate the population size of Ancient Murrelet chicks, comparing against results obtained using the traditional N-mixture likelihood and an alternative asymptotic model based on the multivariate normal distribution. For the Ancient Murrelet case study, our asymptotic model computes twice as fast as the traditional models, eleven times faster when parallel processing is used, and provides higher-precision estimates than the asymptotic multivariate normal model. We provide an open-source implementation of our methods in the quickNmix R package.Supplementary material to this paper is provided online.