Estimating abundance while accounting for rarity, correlated behavior, and other sources of variation in counts.

The class of N-mixture models allows abundance to be estimated from repeated, point count surveys while adjusting for imperfect detection of individuals. We developed an extension of N-mixture models to account for two commonly observed phenomena in point count surveys: rarity and lack of independence induced by unmeasurable sources of variation in the detectability of individuals. Rarity increases the number of locations with zero detections in excess of those expected under simple models of abundance (e.g., Poisson or negative binomial). Correlated behavior of individuals and other phenomena, though difficult to measure, increases the variation in detection probabilities among surveys. Our extension of N-mixture models includes a hurdle model of abundance and a beta-binomial model of detectability that accounts for additional (extra-binomial) sources of variation in detections among surveys. As an illustration, we fit this model to repeated point counts of the West Indian manatee, which was observed in a pilot study using aerial surveys. Our extension of N-mixture models provides increased flexibility. The effects of different sets of covariates may be estimated for the probability of occurrence of a species, for its mean abundance at occupied locations, and for its detectability.