Likelihood-based modelling and analysis of possum trapping data

Possums are a major environmental threat in New Zealand. There is no simple way to estimate possum numbers directly, and most estimates are based on an index of the proportion of leg-hold traps that catch possums. In this article, possum trapping data are used in conjunction with a plausible stochastic model and maximum likelihood estimation to construct a direct estimate of the number of possums in the vicinity of the trap lines. The model assumes that possums are caught in the traps in a Poisson process at a rate that is proportional to the product of the declining density of possums and the number of free traps, with the constant of proportionality log-linearly dependent on the accumulating number of trapped possums and the number of possums caught on previous nights. Numerical solutions of the differential equations for the probabilities associated with this stochastic process were used to construct a full likelihood of the data and hence maximum likelihood estimation of all parameters specifying the model. Based on the likelihood ratio statistic, strong serial dependence of successive nightly numbers of trapped possums was found, together with a weaker attractive effect whereby trapped possums tended to attract other possums into neighboring traps. Additionally, a maximum likelihood estimate of the local number of possums present in the vicinity of the trap lines was determined, with confidence intervals constructed from the profile log likelihood.