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 different sources of variation. We apply it to disentangle and estimate in particular 1) residual variance due to measurement errors and model mis-specification, 2) between-predators variability, and 3) the interaction stochasticity, i.e. the intrinsic and mechanistic variability due to interactions processes between prey and predators. We show that it is possible to estimate these 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 interaction stochasticity 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.