Bayesian inference for stochastic individual-based models of ecological systems: a pest control simulation study

Abstract

Mathematical models are of fundamental importance in the understanding of complex population dynamics. For instance, they can be used to predict the population evolution starting from different initial conditions or to test how a system responds to external perturbations. For this analysis to be meaningful in real applications, however, it is of paramount importance to choose an appropriate model structure and to infer the model parameters from measured data. While many parameter inference methods are available for models based on deterministic ordinary differential equations, the same does not hold for more detailed individual-based models. Here we consider, in particular, stochastic models in which the time evolution of the species abundances is described by a continuous-time Markov chain. These models are governed by a master equation that is typically difficult to solve. Consequently, traditional inference methods that rely on iterative evaluation of parameter likelihoods are computationally intractable. The aim of this paper is to present recent advances in parameter inference for continuous-time Markov chain models, based on a moment closure approximation of the parameter likelihood, and to investigate how these results can help in understanding, and ultimately controlling, complex systems in ecology. Specifically, we illustrate through an agricultural pest case study how parameters of a stochastic individual-based model can be identified from measured data and how the resulting model can be used to solve an optimal control problem in a stochastic setting. In particular, we show how the matter of determining the optimal combination of two different pest control methods can be formulated as a chance constrained optimization problem where the control action is modeled as a state reset, leading to a hybrid system formulation.