<i>N</i>‐Mixture Models for Estimating Population Size from Spatially Replicated Counts

TLDR

Spatial replication is common in animal count surveys, yet sparse data make estimating population size while accounting for detection probability difficult. The article introduces N‑mixture models to estimate population size from such sparse, replicated count data. N‑mixture models treat site‑specific population sizes as random variables drawn from a mixing distribution (e.g., Poisson) and estimate prior parameters via the marginal likelihood, integrating over N. Simulations show the N‑mixture estimator has lower bias and better confidence‑interval coverage than the Carroll–Lombard estimator, and application to six bird species illustrates sensitivity to the prior on detection probability and resulting differences in abundance estimates.

Abstract

Spatial replication is a common theme in count surveys of animals. Such surveys often generate sparse count data from which it is difficult to estimate population size while formally accounting for detection probability. In this article, I describe a class of models (N-mixture models) which allow for estimation of population size from such data. The key idea is to view site-specific population sizes, N, as independent random variables distributed according to some mixing distribution (e.g., Poisson). Prior parameters are estimated from the marginal likelihood of the data, having integrated over the prior distribution for N. Carroll and Lombard (1985, Journal of American Statistical Association 80, 423-426) proposed a class of estimators based on mixing over a prior distribution for detection probability. Their estimator can be applied in limited settings, but is sensitive to prior parameter values that are fixed a priori. Spatial replication provides additional information regarding the parameters of the prior distribution on N that is exploited by the N-mixture models and which leads to reasonable estimates of abundance from sparse data. A simulation study demonstrates superior operating characteristics (bias, confidence interval coverage) of the N-mixture estimator compared to the Caroll and Lombard estimator. Both estimators are applied to point count data on six species of birds illustrating the sensitivity to choice of prior on p and substantially different estimates of abundance as a consequence.