Modeling survival: application of the Andersen-Gill model to Yellowstone grizzly bears

 Wildlife ecologists often use the Kaplan-Meier procedure or Cox proportional hazards model to estimate survival rates, distributions, and magnitude of risk factors. The Andersen-Gill formulation (A-G) of the Cox proportional hazards model has seen limited application to mark-resight data but has a number of advantages, including the ability to accommodate left-censored data, time-varying covariates, multiple events, and discontinuous intervals of risks. We introduce the A-G model including structure of data, interpretation of results, and assessment of assumptions. We then apply the model to 22 years of radiotelemetry data for grizzly bears (Ursus arctos) of the Greater Yellowstone Grizzly Bear Recovery Zone in Montana, Idaho, and Wyoming, USA. We used Akaike's Information Criterion (AIC_c) and multi-model inference to assess a number of potentially useful predictive models relative to explanatory covariates for demography, human disturbance, and habitat. Using the most parsimonious models, we generated risk ratios, hypothetical survival curves, and a map of the spatial distribution of high-risk areas across the recovery zone. Our results were in agreement with past studies of mortality factors for Yellowstone grizzly bears. Holding other covariates constant, mortality was highest for bears that were subjected to repeated management actions and inhabited areas with high road densities outside Yellowstone National Park. Hazard models developed with covariates descriptive of foraging habitats were not the most parsimonious, but they suggested that high-elevation areas offered lower risks of mortality when compared to agricultural areas.