Modeling and parameters estimation of a Spatial Predator-Prey distribution

Abstract

Predator prey interactions are important in ecology and most of time in the analysis, the two antagonists are assumed to be in a closed system. The aim of this study is to model the unclosed predator-prey system. The model is built and simulated data are computed by adding noise on deterministic solution. Therefore, model parameters are estimated using least square method. We compute the two critical points and the stability analysis is carried out and results show that the population is stable at one critical point and unstable at (0,0). The model fits the synthetic data with coefficient of determination R² = 0.9693 equivalent to 96.93%. Using the residual analysis to test the validity of the model, it is shown that there is no pattern between residuals. To strengthen the validity of the model, the Markov Chain Monte Carlo algorithms are used as an alternative method in parameters estimation. Diagnostics prove the chains’ convergence which is the sign of an accurate model. As conclusion, the model is accurate and it can be applied to real data.

Keywords: predator-prey, spatial distribution, parameters, Metropolis-Hastings algorithm, model diagnostic, stability analysis