Establishing Bayesian priors for natural mortality rate in carnivore populations

Abstract

In managed carnivore populations, natural mortality rate (d) is difficult to estimate directly, and context‐specific data are typically weakly informative about it. Nevertheless, natural mortality is potentially an important component of total mortality, particularly if additive to harvest or culling mortality. The natural mortality rate exhibits allometric or life‐history relationships that are invariant across diverse taxonomic groups, and it is valuable to derive estimates on this basis to serve as priors in later Bayesian models, steering parameter uncertainty towards biologically plausible values, and leading to more reliable model predictions and improved management recommendations. We used Bayesian hierarchical modeling and data from the literature to establish informative priors for instantaneous d as predictions scaled from body mass or maximum age. Posterior mean estimates of the scaling parameters of these models were −0.27 (body mass) and −1.07 (maximum age), respectively, conforming to expected values of −0.25 and −1.00. Direct estimates of d from published studies of coyotes (Canis latrans) in southern Texas, fisher (Pekania pennanti) in Sierra Nevada, and slender mongoose (Galerella sanguinea) in the Kalahari Desert were within the credible intervals of predictions for d using both models. We also compared survivorship curves based on model predictions with observed survivorship of red fox (Vulpes vulpes) from a variety of studies in Britain, among which intensity of culling varied markedly. Across all species, there was better support for the d prediction from maximum age, than from body mass. We thus recommend use of maximum age data to establish informative priors for d where possible. Posterior median predictions of d from maximum age were within 0.01–0.14/year of the direct estimates, whereas the differences between direct estimates and predictions from body mass were 0.04–0.27/year. Sensitivity analysis showed trivial effects of between‐sex differences in body mass, and age‐specific mortality, on predictions of d. Differences between body mass and maximum age model predictions were attributed to the relative importance of intrinsic and extrinsic mortality factors in the 2 approaches (i.e., maximum age predictions allowed for extrinsic factors to affect predicted mortality). © 2018 The Wildlife Society.

Population dynamics of foxes during restricted-area culling in Britain: Advancing understanding through state-space modelling of culling records

“…This gave a lognormally-distributed prediction for v across all landscape types with a median of 2.41 fox km -2 yr -1 and a coefficient of variation (CV) of 0.84. The prior for instantaneous non-culling mortality rate was obtained from a meta-analytic model that predicts annual M across varied taxonomic groups from maximum age data, which for fox populations in Britain was assumed to be nine years, giving a lognormal distribution with median of 0.34 yr -1 and a CV of 0.58 [46]. This is equivalent to a finite annual mortality rate (or the proportion of the population that suffers non-culling mortality in a given year, obtained as 1– e – M ) of 0.29.…”

“…We also examined sensitivity to a lower upper bound for N 0 of 6.95 fox km -2 . The informative lognormal prior chosen for M was based upon a model prediction of M from maximum age, as this allows for both extrinsic and intrinsic mortality factors to affect predicted mortality [46]. An alternative meta-analytic model can predict M from body mass, but this model only allows for intrinsic mortality factors to affect predicted mortality.…”

“…An alternative meta-analytic model can predict M from body mass, but this model only allows for intrinsic mortality factors to affect predicted mortality. We examined sensitivity of the results to our choice of prior for M using a lognormal prior based upon the body mass prediction of M , where the prior median was ln(0.27/26) with a CV of 0.60 [46]. The informative prior for r developed in S3 Appendix had a lower CV (0.34) than the >0.5 value recommended for the CV of informative priors in population dynamics models [64], so we examined sensitivity of the results to this prior by using a vague uniform prior for r with a lower bound at zero and an upper bound at 6.0 cub fox -1 yr -1 .…”

Quantifying the rate of replacement by immigration during restricted‐area control of red fox in different landscapes

“…On this time-step the mean value for R, the averaged weekly per capita birth rate, is 0.054 cub fox -1 week -1 (Porteus 2015). Over the same time-step, the mean value for M, the weekly instantaneous non-culling mortality rate, is 0.007 week -1 (Porteus et al 2018). Given N ij on a small estate is very small, the terms in Eq.…”

Efficient use of harvest data: a size‐class‐structured integrated population model for exploited populations

“…Furthermore, the Bayesian implementation of IPMs allows including biological knowledge from alternative sources via informative priors to compensate for the lack of mark–recapture data. Natural mortality, in particular, often requires assumptions and/or informative priors, and these can be obtained from published studies on similar (non‐exploited) populations, expert knowledge (Servanty et al 2010), or using promising new approaches involving phylogenetic meta‐analyses (Abadi et al 2014, Porteus et al 2018).…”