Effect of prey-taxis on biological control of the two-spotted spider mite — A numerical approach

This study concerns the interactions of the two-spotted spider mite Tetranychus urticae and its predator Phytoseiulus persimilis. The logistic Lotka–Volterra predator–prey-taxis equations with diffusion and advection are solved numerically using two different response functions with one data set. The aim of this paper is to re-estimate parameters by using prey-taxis in the predator–prey system and to achieve successful biological control using prey-taxis. We show that both response functions and initial conditions have major contributions in biological control of the prey population. We also show that it is possible to achieve successful biological control in space over a longer time-scale with prey population density below the economic threshold provided the predator population density is at least twice that of the prey during most of the time.