  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.
