COS 74-6 - Assimilating ecological theory with empiricism: Using constrained generalized additive models to enhance survival analyses.

Background/Question/Methods

Integration of ecological theory with empirical methods is ubiquitous using hierarchical Bayesian models. However, there has been little development focused on integration of ecological theory into models for survival analysis. Survival is a fundamental process, linking individual fitness with population dynamics, and incorporating classical survivorship curves can be challenging because mortality processes occur on multiple time scales. We develop an approach to survival analysis for ecology, incorporating ecological theory with empirical estimation using functional analytical tools. We distinctly model how survival changes for different ages, and for different periods of time, to separate patterns of mortality that arise from intrinsic and extrinsic processes. We use shape constrained generalized additive models to obtain age-specific hazard functions thereby incorporating theoretical information based on classical survivorship curves into the age component of the model and capture extrinsic factors in the time component. We then compare the performance of our modeling approach to standard survival modeling tools that do not explicitly incorporate ecological theory in their structure, using metrics of predictive power, accuracy, efficiency, and computation time.

Results/Conclusions

We applied these models to two case studies that reflect multiple life history strategies, examining age-period survival for white-tailed deer in Wisconsin, USA and Columbian sharp-tailed grouse in Colorado, USA. We demonstrate a flexible and easily extendable approach to survival analysis by showing its utility to obtain hazard rates and survival probabilities, accounting for heterogeneity across ages and over time, for two very different species. We show how integration of ecological theory using constrained generalized additive models, with empirical statistical methods improves survival analyses.