Estimation of population trajectories from count data

Monitoring of changes in animal population size is rarely possible through complete censuses; frequently, the only feasible means of monitoring changes in population size is to use counts of animals obtained by skilled observers as indices to abundance. Analysis of changes in population size can be severely biased if factors related to the acquisition of data are not adequately controlled for. In particular we identify two types of observer effects: these correspond to baseline differences in observer competence, and to changes through time in the ability of individual observers. We present a family of models for count data in which the first of these observer effects is treated as a nuisance parameter. Conditioning on totals of negative binomial counts yields a Dirichlet compound multinomial vector for each observer. Quasi-likelihood is used to estimate parameters related to population trajectory and other parameters of interest; model selection is carried out on the basis of Akaike's information criterion. An example is presented using data on Wood thrush from the North American Breeding Bird Survey.