  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.
