Estimating the effects of detection heterogeneity and overdispersion on trends estimated from avian point counts

Point counts are a common method for sampling avian distribution and abundance. Although methods for estimating detection probabilities are available, many analyses use raw counts and do not correct for detectability. We use a removal model of detection within an TV-mixture approach to estimate abundance trends corrected for imperfect detection. We compare the corrected trend estimates to those estimated from raw counts for 16 species using 15 years of monitoring data on three national forests in the western Great Lakes, USA. We also tested the effects of overdispersion by modeling both counts and removal mixtures under three statistical distributions: Poisson, zero-inflated Poisson, and negative binomial. For most species, the removal model produced estimates of detection probability that conformed to expectations. For many species, but not all, estimates of trends were similar regardless of statistical distribution or method of analysis. Within a given combination of likelihood (counts vs. mixtures) and statistical distribution, trends usually differed by both stand type and national forest, with species showing declines in some stand types and increases in others. For three species, Brown Creeper, Yellow-rumped Warbler, and Black-throated Green Warbler, temporal patterns in detectability resulted in substantial differences in estimated trends under the removal mixtures compared to the analysis of raw counts. Overall, we found that the zero-inflated Poisson was the best distribution for our data, although the Poisson or negative binomial performed better for a few species. The similarity in estimated trends that we observed among counts and removal mixtures was probably a result of both experimental design and sampling effort. First, the study was originally designed to avoid confounding observer effects with habitats or time. Second, our time series is relatively long and our sample sizes within years are large.