Fitting stochastic predator-prey models using both population density and kill rate data

Most mechanistic predator-prey modelling has involved either parameterization from process rate data or inverse modelling. Here, we take a median road: we aim at identifying the potential benefits of combining datasets, when both population growth and predation processes are viewed as stochastic. We fit a discrete-time, stochastic predator-prey model of the Leslie type to simulated time series of densities and kill rate data. Our model has both environmental stochasticity in the growth rates and interaction stochasticity, i.e., a stochastic functional response. We examine what the kill rate data brings to the quality of the estimates, and whether estimation is possible (for various time series lengths) solely with time series of counts or biomass data. Both Bayesian and frequentist estimation are performed. The Fisher Information Matrix suggests that models with and without kill rate data are all identifiable, although correlations remain between parameters that belong to the same functional form. However, our results show that if the attractor is a fixed point in the absence of stochasticity, identifying parameters in practice requires in fact kill rate data as a complement to the time series of population densities, due to the relatively flat likelihood in this case. Only noisy limit cycle attractors can be identified directly from ecological count data (as in inverse modelling), although even in this case, adding kill rate data - including in small amounts - can make the estimates much more precise. Our framework highlights how to combine data types in dynamical models for multiple species, and may be extended to other biotic interactions for which data on both interaction rates and population counts are available.