Representing mortality risk in mechanistic models

Mortality risk is a critical and complex component of individual fitness and individual-based ecology, especially when risk-avoidance behaviors are considered. Organisms are subject to multiple kinds of risk that can vary with habitat, time, individual state, individual activity and behavior, and population status. Yet risk is often represented very simply in models and there is little literature on practical ways to model its variation. In our experience, desirable characteristics of risk models include: (a) survival probability can vary with multiple variables of individuals, habitat, and other entities; (b) relations between survival and specific variables can be added or removed or modified without re-fitting the entire model; (c) relations between variables and survival can take different forms, including continuous and nonlinear functions and discrete values; (d) relations between variables and survival are easy to understand and fit to many kinds of data or assumptions; and (e) they can be calibrated by adjusting only one parameter. We review the terminology and conventions that ecologists often use to model risk, and provide a mathematical framework for modeling risk. For complex risks, we describe and illustrate a method with “survival increase functions” that each relate survival probability to one variable. These functions can have a different form for each variable and can each be based on different information. The multiple functions are combined into a single survival probability value that is easily calibrated. We discuss methods for evaluating survival increase functions, ranging from general field observations to controlled field experiments, knowledge and data on mechanisms driving survival, and even conceptual models of those mechanisms. This approach has proven practical for representing complex effects of multiple variables on survival probability in models that represent how individual behavior and fitness depend on risk.