An efficient extension of N-mixture models for multi-species abundance estimation

In this study we propose an extension of the N-mixture family of models that targets an improvement of the statistical properties of rare species abundance estimators when sample sizes are low, yet typical for tropical studies. The proposed method harnesses information from other species in an ecological community to correct each species' estimator. We provide guidance to determine the sample size required to estimate accurately the abundance of rare tropical species when attempting to estimate the abundance of single species.We evaluate the proposed methods using an assumption of 50 m radius plots and perform simulations comprising a broad range of sample sizes, true abundances and detectability values and a complex data generating process. The extension of the N-mixture model is achieved by assuming that the detection probabilities are drawn at random from a beta distribution in a multi-species fashion. This hierarchical model avoids having to specify a single detection probability parameter per species in the targeted community. Parameter estimation is done via Maximum Likelihood.We compared our multi-species approach with previously proposed multi-species N-mixture models, which we show are biased when the true densities of species in the community are less than seven individuals per 100 hectares. The beta N-mixture model proposed here outperforms the traditional Multi-species N-mixture model by allowing the estimation of organisms at lower densities and controlling the bias in the estimation.We illustrate how our methodology can be used to suggest sample sizes required to estimate the abundance of organisms, when these are either rare, common or abundant. When the interest is full communities, we show how the multi-species approaches, and in particular our beta model and estimation methodology, can be used as a practical solution to estimate organism densities from rapid inventory datasets. The statistical inferences done with our model via Maximum Likelihood can also be used to group species in a community according to their detectabilities.