Modeling and Mapping Abundance of American Woodcock Across the Midwestern and Northeastern United States

ABSTRACT We used an over-dispersed Poisson regression with fixed and random effects, fitted by Markov chain Monte Carlo methods, to model population spatial patterns of relative abundance of American woodcock (Scolopax minor) across its breeding range in the United States. We predicted North American woodcock Singing Ground Survey counts with a log-linear function of explanatory variables describing habitat, year effects, and observer effects. The model also included a conditional autoregressive term representing potential correlation between adjacent route counts. Categories of explanatory habitat variables in the model included land-cover composition, climate, terrain heterogeneity, and human influence. Woodcock counts were higher in landscapes with more forest, especially aspen (Populus tremuloides) and birch (Betula spp.) forest, and in locations with a high degree of interspersion among forest, shrubs, and grasslands. Woodcock counts were lower in landscapes with a high degree of human development. The most noteworthy practical application of this spatial modeling approach was the ability to map predicted relative abundance. Based on a map of predicted relative abundance derived from the posterior parameter estimates, we identified major concentrations of woodcock abundance in east-central Minnesota, USA, the intersection of Vermont, USA, New York, USA, and Ontario, Canada, the upper peninsula of Michigan, USA, and St. Lawrence County, New York. The functional relations we elucidated for the American woodcock provide a basis for the development of management programs and the model and map may serve to focus management and monitoring on areas and habitat features important to American woodcock.     

Multinomial N-mixture models for removal sampling

Multinomial $N$-mixture models are commonly used to fit data from a removal sampling protocol. If the mixing distribution is negative binomial, the distribution of the counts does not appear to have been identified, and practitioners approximate the requisite likelihood by placing an upper bound on the embedded infinite sum. In this paper, the distribution which underpins the multinomial $N$-mixture model with a negative binomial mixing distribution is shown to belong to the broad class of multivariate negative binomial distributions. Specifically, the likelihood can be expressed in closed form as the product of conditional and marginal likelihoods and the information matrix shown to be block diagonal. As a consequence, the nature of the maximum likelihood estimates of the unknown parameters and their attendant standard errors can be examined and tests of the hypothesis of the Poisson against the negative binomial mixing distribution formulated. In addition, appropriate multinomial $N$-mixture models for data sets which include zero site totals can also be constructed. Two illustrative examples are provided.