Stability Analysis of a Three-Trophic Rice Ecosystem with Holling Type II and Crowley--Martin Responses

Abstract

This study examines three-trophic-level ecological dynamics in rice field ecosystems involving rice as the producer, brown planthoppers Nilaparvata lugens as herbivores, and Pardosa sp. as top predators. Population interactions were modeled using logistic growth for rice and two response functions: the Holling type II response for planthopper predation on rice, and the Crowley--Martin response for Pardosa sp. predation on planthoppers to capture predator interference. The resulting model was formulated as a system of nonlinear differential equations. Analytically, four equilibrium points were obtained: total population extinction, extinction of planthoppers and Pardosa sp., extinction of Pardosa sp., and coexistence of all three species. Local stability analysis at each equilibrium point was conducted using the Jacobian matrix and the Routh--Hurwitz criterion. Numerical simulations were performed for several parameter combinations by varying planthopper growth efficiency and Pardosa sp. predation intensity. Parameter values are obtained from relevant literature where available, and the remaining parameters are considered reasonable biological assumptions for exploring the dynamics of the system qualitatively. The simulation results were consistent with the theoretical analysis and showed that small changes in biological parameters could shift the system from stable coexistence to near extinction of the planthopper population. Ecologically, the model demonstrates that rice field ecosystem balance is strongly influenced by the interaction between planthopper reproductive capacity and the predatory strength of Pardosa sp., providing theoretical insights that may support the development of sustainable planthopper pest management strategies.