Bayesian Multi-Species N-Mixture Models for Unmarked Animal Communities

Abstract

We propose an extension of the N-mixture model which allows for the estimation of both abundances of multiple species simultaneously and their inter-species correlations. We also propose further extensions to this multi-species N-mixture model, one of which permits us to examine data which has an excess of zero counts, and another which allows us to relax the assumption of closure inherent in N-mixture models through the incorporation of an AR term in the abundance. The inclusion of a multivariate normal distribution as prior on the random effect in the abundance facilitates the estimation of a matrix of interspecies correlations. Each model is also fitted to avian point data collected as part of the NABBS 2010-2019. Results of simulation studies reveal that these models produce accurate estimates of abundance, inter-species correlations and detection probabilities at both small and large sample sizes, in scenarios with small, large and no zero inflation. Results of model-fitting to the North American Breeding Bird Survey data reveal an increase in Bald Eagle population size in southeastern Alaska in the decade examined.Our novel multi-species N-mixture model accounts for full communities, allowing us to examine abundances of every species present in a study area and, as these species do not exist in a vacuum, allowing us to estimate correlations between species' abundances.While previous multi-species abundance models have allowed for the estimation of abundance and detection probability, ours is the first to address the estimation of both positive and negative inter-species correlations, which allows us to begin to make inferences as to the effect that these species' abundances have on one another. Our modelling approach provides a method of quantifying the strength of association between species' population sizes, and is of practical use to population and conservation ecologists.