Bayesian shared frailty models for regional inference about wildlife survival

Abstract

The estimation of survival is an essential but difficult task important for developing rigorous conservation programs. Radio telemetry studies of wildlife survival are often characterized by small sample sizes and high rates of censoring. In cases where multiple radio telemetry studies of a species exist, shared frailty models of survival offer the ability to combine data from multiple studies and improve the precision of survival estimates. We used Bayesian analysis of shared frailty models to examine survival of adult females of the giant gartersnake (Thamnophis gigas) in the Sacramento Valley, California, USA, and to examine the effects of individual and habitat characteristics on daily risk of mortality. Posterior mean annual survival probability of adult females was 0.61 [95% credible interval (CI) = 0.41-0.79]. The daily risk of mortality for adult female giant gartersnakes while in terrestrial habitats was 0.38 (0.09-0.89) times as great as when they inhabited aquatic habitats. Although 95% CIs for hazard ratios of other covariates included one, sites varied substantially in the effect of linear habitats, which appear to have context-dependent effects on survival. Assessing survival with shared frailty models allows the prediction of survival probabilities at novel sites and identifies regional and context-specific mortality risks that can be targeted for conservation action.

The High Cost of Motherhood: End-Lactation Syndrome in Southern Sea Otters (Enhydra Lutris Nereis) on the Central California Coast, Usa

“…Our model incorporated both fixed effects of age, sex, reproductive status and mean body condition, as well as random site effects, also referred to as shared frailties (Banerjee et al 2003, Halstead et al 2012. Because independent hazards are multiplicative in nature (as with many time-dependent biological processes), it is more convenient to formulate hazard models in terms of log(hazards), which are additive and thus lend themselves to the fitting of linear models using maximum likelihood or Bayesian methods.…”

“…In essence, we can think of the instantaneous "hazards" at any point in time, h(t), as an approximation of the conditional mortality probability over a short interval. Modeling instantaneous hazards as opposed to modeling survival directly has a number of biological and mathematical advantages, including the fact that instantaneous hazards are independent of time scale, and lead to simple multiplicative models (so called "proportional hazards models") where the relative levels of mortality risk associated with particular covariates can be estimated as hazard ratios (Heisey and Patterson 2006, Heisey et al 2007, Halstead et al 2012. We employed a non-parametric Kaplan-Meier approach (Sinha and Dey 1997) to estimate instantaneous proportional hazards from staggered-entry monitoring data, and then used these to estimate the contribution of various fixed and random effects to survival rates.…”

Sunning themselves in heaps, knots, and snarls: The extraordinary abundance and demography of island watersnakes

“…Historically, game species and species of economic importance have been the targets of such monitoring, but increasingly, efforts have broadened to include species of conservation concern. At the same time, analytical methods for generating demographic parameter estimates have improved and increased in sophistication (Halstead, Wylie, Coates, Valcarcel, & Casazza, 2012; White & Burnham, 1999). Consequently, demographic parameter estimates are becoming available for a widening range of taxa (Mesquita et al., 2015; Salguero‐Gómez et al., 2015, 2016), offering the possibility of improved interpretation and generalization, including evaluations of r ‐ K , slow‐fast, and pace‐of‐life syndromes (Bielby et al., 2007; Dunham, Miles, & Reznick, 1988; Gaillard et al., 1989, 2005; Gangloff et al., 2017; Hille & Cooper, 2015; Réale et al., 2010; Ricklefs & Wikelski, 2002; Wiersma, Muñoz‐Garcia, Walker, & Williams, 2007) and niche classification (Pianka, Vitt, Pelegrin, Fitzgerald, & Winemiller, 2017; Winemiller, Fitzgerald, Bower, & Pianka, 2015).…”

Influence of Wildland Fire Along a Successional Gradient in Sagebrush Steppe and Western Juniper Woodlands

“…We carried out a post hoc survival analysis and fit sage-grouse associations with cover classes as time-varying covariates following similar procedures as Halstead et al (2012). This analysis provided direct estimates of relationships between pinyon-juniper and survival that are often more useable for managerial decisions.…”

“…In other words, this random effects structure allowed individual slope estimation for each bird to then relate to survival. In a simultaneous second stage, a frailty model (Halstead et al, 2012) was used to fit individual-level avoidance of each pinyonjuniper cover class (PJAI) on individual survival probability. Hence, avoidance was formally linked to survival by randomly sampling the posterior distribution of slope coefficients (β PJ,i ) for individual sagegrouse.…”