Biological pest control and crop–tree competition in agroforestry: a dynamical systems analysis

Agroforestry is a land-use system based on the simultaneous cultivation of crops and trees. The abundance and diversity of species living in agroforestry is usually higher than in monoculture. Hence, agroforestry may naturally control agricultural pests, by conserving their natural enemies. In monoculture, pest control requires the application of synthetic pesticides, which can cause harmful effects. In agroforestry, however, crops and trees compete for resources, which may reduce the crop production, as compared to monoculture. Here, a mathematical model is proposed to analyze this scenario. The model is written as a set of three nonlinear differential equations, in which the variables are the densities of crops, pests, and trees. It is analytically shown that transcritical and Hopf bifurcations can occur. Thus, by varying the parameter values, the pest can either be eradicated or endemically persist at constant level or endemically persist in oscillatory regime. For the Hopf bifurcation, the first Lyapunov exponent is computed. The analytical results are illustrated by computer simulations and discussed from an agroecological perspective.