Assimilating ecological theory with empiricism: Using constrained generalized additive models to enhance survival analyses

Integrating ecological theory with empirical methods is ubiquitous in ecology 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, but incorporating life history strategies to inform survival estimation can be challenging because mortality processes occur at multiple scales.We develop an approach to survival analysis, incorporating model constraints based on a species' life history strategy using functional analytical tools. Specifically, we structurally separate intrinsic patterns of mortality that arise from age-specific processes (e.g. increasing survival during early life stages due to growth or maturation, versus senescence) from extrinsic mortality patterns that arise over different periods of time (e.g. seasonal temporal shifts). We use shape constrained generalized additive models (CGAMs) to obtain age-specific hazard functions that incorporate theoretical information based on classical survivorship curves into the age component of the model and capture extrinsic factors in the time component.We compare the performance of our modelling approach to standard survival modelling tools that do not explicitly incorporate species life history strategy in the model structure, using metrics of predictive power, accuracy, efficiency and computation time. We applied these models to two case studies that reflect different functional shapes for the underlying survivorship curves, examining age-period survival for white-tailed deer Odocoileus virginianus in Wisconsin, USA and Columbian sharp-tailed grouse Tympanuchus phasianellus columbianus in Colorado, USA.We found that models that included shape constraints for the age effects in the hazard curves using CGAMs outperformed models that did not include explicit functional constraints. We demonstrate a data-driven 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, enhances survival analyses.