Modelling the rate of successful search of red foxes during population control

Abstract

Context Relative abundance indices of wildlife can be scaled to give estimates of absolute abundance. Choice of scaling parameter depends on the data available and assumptions made about the relationship between the index and absolute abundance. Predation-mechanics theory suggests that a parameterisation involving the rate of successful search, s, will be useful where the area searched is unknown. An example arises during fox culling on shooting estates in Britain, where detection and cull data from gamekeepers using a spotlight and rifle are available, and can potentially be used to understand the population dynamics of the local population. Aims We aimed to develop an informative prior for s for use within a Bayesian framework to fit a fox population-dynamics model to detection data. Methods We developed a mechanistic model with a rate of successful search parameter for the gamekeeper–fox system. We established a mechanistic prior for s, using Monte Carlo simulation to combine relevant information on its component factors (detection probability, observer field of view and speed of travel). We obtained empirical estimates of s from a distance-sampling study of fox populations using similar survey methods, and used these as data in a Bayesian model to develop a mechanistic–empirical prior. We then applied this informative prior within a state–space model to estimate fox density from fox-detection rate on four estates. Key results The mechanistic–empirical prior for the rate of successful search was lognormally distributed with a median of 2.01 km2 h–1 (CV = 0.56). Underlying assumptions of the parameterisation were met. Local fox-density estimates obtained using informative priors closely reflected regional density. Conclusions A mechanistic understanding of the search process leading to fox detections by gamekeepers, and the use of Bayesian models, allowed the use of diverse sources of information to develop an informative prior for s that was useful in estimating fox density from detection data. Implications Careful use of prior knowledge within a Bayesian modelling framework can reduce uncertainty in population estimates derived from index data, and lead to improved management decisions. The mechanistic approach we have used will have parallel applications in many other contexts.