Fig 1.
Locations of the 22 modelled estates showing the landscape type each estate was within.
Landscape types were determined by groupings of land class strata which summarise variation in ecological, physio-geographical, and human geographical attributes (see [30] for details).
Table 1.
Symbols and description of data variables and model parameters.
Table 2.
Prior probability distributions for estimated model parameters.
Fig 2.
Marginal posterior probability distributions for the estimated parameters from the 22 estates: N0 (initial density), K (carrying capacity), v (immigration rate), r (per capita birth rate), M (non-culling mortality rate), and d (rate of successful search).
Each estate is represented by the same line type and colour combination in all panels. The prior probability distribution for each parameter is shown by the bold black line. Differences between posteriors and priors indicate updating of parameter estimates through fitting the model to the data.
Table 3.
Marginal posterior median (and CV) for estimated parameters on each estate.
Fig 3.
Panel a) shows posterior fit of the model to detection rate (Yt/Et). Panel b) shows posterior estimates of bi-weekly fox density (Nt) in relation to the cull removed by different methods. Panel c) shows estimated Nt as a proportion of carrying capacity (blue line denotes median population at posterior median K). Panel d) shows priors (or post-model-pre-data distribution) and marginal posteriors of N0 (initial density), K (carrying capacity), v (immigration rate), r (per capita birth rate), M (instantaneous non-culling mortality rate), d (rate of successful search), and fox density in the final time-step. Histograms in panel d) show posterior medians from all estates. In panels a-c) the bird nesting period (March-July) is shaded grey as a reference.
Fig 4.
The knock-down effect of culling determined by the estimated fox density at significant times of year, relative to estimated carrying capacity.
The across-year mean of posterior median fox density () on each estate during the pre-breeding period (February) and the gamebird nesting period (March-July) is compared to the posterior median of carrying capacity (K) specific to each estate.
Fig 5.
Comparison of the cumulative culling mortality and estimated cumulative non-culling mortality implied by the posterior median of M on each estate over the range of the contributed data.
Posterior median fox density and carrying capacity of each estate are shown. The scale of mortality (shown in dead foxes km-2) differed so estates are ordered by row from top-left to bottom-right by decreasing total mortality. On most estates the cull dwarfed estimated non-culling mortality and exceeded estimated initial density within 6–12 months.
Fig 6.
Sensitivity of marginal posterior distributions for parameters (columns) from six estates (rows) to different structural assumptions and prior distribution specifications.
The reference case distributions shown are from the informative prior model. These are compared to the distributions obtained under assumptions about the seasonality of immigration and timing of cub recruitment, and specification of prior distributions for M, r, K and N0. The y-axes are not labelled for clarity.
Fig 7.
Sensitivity of posterior median fox density on six estates to different structural assumptions and prior distribution specifications.
Panel (a) shows sensitivity to structural assumptions about the seasonality of immigration and timing of cub recruitment. Panel (b) shows sensitivity to specification of prior distributions for M, r, K and N0. Line colours for each assumption are shown above each set of charts. Reference case (black line) is from the informative prior model. The dashed lines show the posterior median carrying capacity for the reference case.