Out-of-equlibrium inference of stochastic model parameters through population data from generic consumer-resource dynamics

Consumer-resource dynamics is central in determining biomass transport across ecosystems. The assumptions of mass action, chemostatic conditions and stationarity in stochastic feeding dynamics lead to Holling type II functional responses, whose use is widespread in macroscopic models of population dynamics. However, to be useful for parameter inference, stochastic population models need to be identifiable, this meaning that model parameters can be uniquely inferred from a large number of model observations. In this contribution we study parameter identifiability in a multi-resource consumer-resource model, for which we can obtain the steady-state and out-of-equilibrium probability distributions of predator's abundances by analytically solving the master equation. Based on these analytical results, we can conduct in silico experiments by tracking the abundance of consumers that are either searching for or handling prey, data then used for maximum likelihood parameter estimation. We show that, when model observations are recorded out of equilibrium, feeding parameters are truly identifiable, whereas if sampling is done at stationarity, only ratios of rates can be inferred from data. We discuss the implications of our results when inferring parameters of general dynamical models.