Population dynamics models can be used to evaluate the effectiveness of predator control. On a restricted area, one key process is the rate at which removed individuals are replaced by immigration. Since this rate is difficult and costly to estimate by field study, we develop an analytical method to approximate immigration rate that makes use of data obtained through the removal process itself. In Britain, red fox Vulpes vulpes control is undertaken by gamekeepers on privately‐owned shooting estates. The fox cull on each estate derives from both local reproduction and immigration. The proportional contribution of immigration to the cull can be expected to be greater on smaller estates. We describe a mechanism by which the average annual cull per unit estate area on a very small estate approximates the annual rate of immigration. We used fox culling records from 534 estates across seven different landscape types and a Bayesian hierarchical model to relate the density of foxes culled to estate area, with immigration rate assumed to be equal to the model intercept. The posterior predictive distribution of annual immigration rate was lognormal with a median of 2.41 fox km‐2 year‐1 and a CV of 0.84. Posterior median estimates of immigration rate varied between landscapes, ranging from 0.86 to 4.13 fox km‐2 year1. Immigration rate was higher in arable and pastural landscapes compared to upland landscapes. Variation in immigration rate broadly matched differences in fox density characteristic of the regional landscape type. This study presents a widely applicable method for quantifying immigration rate in populations that are subject to depletion, e.g. through culling. The use of the fox immigration rate estimate as an informative prior distribution in population dynamics models could help in evaluating effects of control on local fox populations and lead to improved control strategies.

American mink (Neovison vison) are an ecologically damaging invasive species in Europe and Iceland where attempts to control them typically rely on trapping. The focus and efficiency of trapping can be improved by using track-recording mink rafts to identify where mink are present before traps are deployed. This paper describes development of operating strategy for the use of mink rafts with traps, to optimise capture efficiency against costs. We worked sequentially on two unconnected chalk streams in central southern England. On 17 km of the River Itchen, we operated a very high density of rafts (5.9 per km) through spring and summer to generate multiple detections of each mink present. All rafts recording mink tracks were armed with traps, and captured mink were euthanased. After removal of mink until no further detections were made, we calculated that each mink was detected 5.3 times at 5.1 raft sites, and on this basis, rationalised raft density to a standard one per kilometer of river. We set a trap deployment time (10 days) that encompassed the longest observed lapse from detection to capture (7 days), and extended the check interval for rafts in monitoring mode from 1 week to 2 weeks to further reduce costs. These operating rules were then deployed for 12 months on the 44-km River Wylye beginning in autumn. Rafts indicated that the river was cleared of mink through the capture of seven individuals, each of which was detected 3.6 times at 2.7 raft sites, on average, and was trapped within 6 days of detection giving a response time of less than 20 days. Although these operating rules may need refinement for other environments, we believe this is a sound basis for effective mink control.

Lethal control is widely employed to suppress the numbers of target wildlife species within restricted management areas. The success of such measures is expected to vary with local circumstances affecting rates of removal and replacement. There is a need both to evaluate success in individual cases and to understand variability and its causes. In Britain, red fox (Vulpes vulpes) populations are culled within the confines of shooting estates to benefit game and wildlife prey species. We developed a Bayesian state-space model for within-year fox population dynamics within such restricted areas and fitted it to data on culling effort and success obtained from gamekeepers on 22 shooting estates of 2 to 36 km2. We used informative priors for key population processes—immigration, cub recruitment and non-culling mortality–that could not be quantified in the field. Using simulated datasets we showed that the model reliably estimated fox density and demographic parameters, and we showed that conclusions drawn from real data were robust to alternative model assumptions. All estates achieved suppression of the fox population, with pre-breeding fox density on average 47% (range 20%–90%) of estimated carrying capacity. As expected, the number of foxes killed was a poor indicator of effectiveness. Estimated rates of immigration were variable among estates, but in most cases indicated rapid replacement of culled foxes so that intensive culling efforts were required to maintain low fox densities. Due to this short-term impact, control effort focussed on the spring and summer period may be essential to achieve management goals for prey species. During the critical March-July breeding period, mean fox densities on all estates were suppressed below carrying capacity, and some maintained consistently low fox densities throughout this period. A similar model will be useful in other situations to quantify the effectiveness of lethal control on restricted areas.

American mink (Neovison vison) are an ecologically damaging invasive species where they have been introduced in Europe. Effectiveness of mink population control by trapping has been difficult to assess, without knowing how efficiently mink are caught by traps or detected by other methods. Use of track‐recording rafts to detect mink and guide trapping effort has proved efficient and leads to a supposition that no detection indicates absence of mink. To draw this conclusion with any confidence requires a measure of detectability. We applied occupancy models to data from an earlier study to estimate detectability of individual American mink on track‐recording rafts. Estimated detectability of individual mink, per raft, and 2‐week check period varied between 0.4 in late summer and 0.6 in late autumn. By inference, risk of failing to detect a mink that was present would be <5% given 4–6 independent opportunities to detect it. These opportunities could be created either by using a raft spacing that ensured multiple detections of each mink or by monitoring rafts through a succession of check intervals. Within certain simple constraints, raft location did not contribute substantially to detection probability. These findings will allow field operators, strategists, and funders to assess with confidence the success of efforts to control mink density. We expect the estimation of individual detectability to be similarly valuable in population control or eradication of other species.

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.