Disentangling the sources of variation in functional responses: between-individuals variability, measurements errors and inherent stochasticity of the prey-predator interaction process

The consumption rate of prey by predators, or functional responses, are known to be highly variable even within a single population. Identifying and estimating the different sources of variation of functional responses is a long-standing challenge. We develop here a statistical framework derived from a mechanistic stochastic process model that explicitly accounts for inter-individual variability, intrinsic stochasticity due to the foraging and interactions processes themselves, and measurement error. We show that it is possible to estimate all sources of variation under realistic experimental conditions. Our results also show that model fitting can compensate by overestimating residual source of variation, leading to biased parameter estimates when the mechanistic noise is misspecified. Applied to empirical data, the model reveals that standard assumptions, such as prey renewal and lack of spatial structure, fail to capture observed variability. We also show how experimental design affects parameter identifiability, highlighting the trade-off between the number of individuals and repeated observations.