Abstract
Parameter estimation for the functional response of predator-prey systems is a critical methodological problem in population ecology. In this paper we consider a stochastic predator-prey system with non-linear Ivlev functional response and propose a method for model parameter estimation based on time series of field data. We tackle the problem of parameter estimation using a Bayesian approach relying on a Markov Chain Monte Carlo algorithm. The efficiency of the method is tested on a set of simulated data. Then, the method is applied to a predator-prey system of importance for Integrated Pest Management and biological control, the pest mite Tetranychus urticae and the predatory mite Phytoseiulus persimilis. The model is estimated on a dataset obtained from a field survey. Finally, the estimated model is used to forecast predator-prey dynamics in similar fields, with slightly different initial conditions.
Highlights
Integrated Pest Management (IPM) programs are implemented with the objective of minimizing losses due to plant pests and controlling insect vectors of important plant, animal, and human diseases, reducing the impact of control techniques on environment and human health [9]
The following model characteristics and procedures are of critical importance for a possible contribution of trophic interaction models supporting the design of IPM and biological control schemes. (a) Models should mimic the qualitative behavior of predator-prey populations systems relevant to biological control tactics and strategies, for instance, admitting either stable solutions with prey extinction or an equilibrium with limit cycle
We follow a Bayesian approach for parameter estimation and forecast in a stochastic predator-prey model with a nonlinear functional response
Summary
Integrated Pest Management (IPM) programs are implemented with the objective of minimizing losses due to plant pests and controlling insect vectors of important plant, animal, and human diseases, reducing the impact of control techniques on environment and human health [9]. Biological control techniques are available to IPM specialists and are based on manipulation of inter-specific relationships (use of predators, parasites, diseases and plant resistance to suppress pest populations) [24]. Population dynamics models can provide insight into the complexity of interacting populations systems under the effect of control operations [1] and contribute to the evaluation and improvement of IPM tactics and strategies. The following model characteristics and procedures are of critical importance for a possible contribution of trophic interaction models supporting the design of IPM and biological control schemes. (a) Models should mimic the qualitative behavior of predator-prey populations systems relevant to biological control tactics and strategies, for instance, admitting either stable solutions with prey extinction or an equilibrium with limit cycle. MCMC algorithm, latent data, Ivlev model, biological control
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