The flaws of fitness functions in changing environments

When predicting species responses to changing environments, one can use mathematical functions that describe how individual fitness components depend on the environment, or a single "composite" function that directly links fitness to the environmental state. The former approach is a cornerstone of process-based modelling, but the latter remains standard for developing fundamental theory and making ecological predictions. Yet, fitness is not a single instantaneous trait, but an integrated outcome of multiple underlying processes accruing throughout an organisms life. We show that by ignoring the distinct environmental dependence of the underlying processes, predictions from composite fitness functions become inherently flawed in variable environments. We explore the magnitude of this error by leveraging empirical thermal reaction norms for four important life-history processes in an insect pest, the seed beetle Callosobruchus maculatus. We parameterize two fitness functions: one explicitly modelling the temperature-dependence of the four life-history traits independently (the "ground truth") and one composite function, which treats fitness as a single, instantaneous outcome of the environment. By combining these two functions with hourly temperature data, we projected demographic responses under different warming scenarios across 300 sites over three beetle population origins (California, USA; Yemen; Brazil). We show that the composite function over- or underestimates fitness depending on subtle climatic differences and whether fitness is assumed to accumulate additively or multiplicatively, highlighting the problems of applying composite fitness functions to variable conditions. We conclude that explicitly modeling trait-specific processes will become increasingly important for accurate eco-evolutionary forecasting under future environmental change.