Negative binomial models for abundance estimation of multiple closed populations

Counts of uniquely identified individuals in a population offer opportuniti es to estimate abundance. However, for various reasons such counts may be b urdened by heterogeneity in the probability of being detected. Theoretical arguments and empirical evidence demonstrate than the negative binomial dis tribution (NBD) is a useful characterization for counts from biological pop ulations with heterogeneity. We propose a method that focuses on estimating multiple populations by simultaneously using a suite of models derived fro m the NBD. We used this approach to estimate the number of female grizzly b ears (Ursus arctos) with cubs-of-the-year in the Yellowstone ecosystem, for each year, 1986-1998. Akaike's Information Criteria (AIC) indicated that a negative binomial model with a constant level of heterogeneity across all years was best for characterizing the sighting frequencies of female grizzl y bears. A lack-of-fit test indicated the model adequately described the co llected data. Bootstrap techniques were used to estimate standard errors an d 95% confidence intervals. We provide a Monte Carlo technique, which confi rms that the Yellowstone ecosystem grizzly bear population increased during the period 1986-1998.