Formulation of a mathematical model for insect pest ecosystems—The cereal leaf beetle problem

Abstract

A general population model is developed as a partial differential equation to describe the maturity distribution of the population density as a function of time. The model is applied to the cereal leaf beetle Oulema melanopus (L.) (Coleoptera: Chrysomelidae) and its principal parasite Tetrastichus julis (Walker) (Hymenoptera: Eulophidae). Ordinary differential equations are developed to describe the growth of cereal grains such as oats for which the cereal leaf beetle is a major economic pest. The temperature dependency of the physiological processes is treated by introducing physiological time scales for the pest, parasite, and plant. Simplification of the pest and parasite models is accomplished through the use of mortalities at the transitions between life stages of the insects. The non-linearities due to density-dependent mortalities by both competition and parasitism are incorporated in the boundary conditions of the models. The selective attack probability of parasite adults on pest larvae characterizes the pest-parasite coupling in the boundary conditions. The pest population is coupled to the crop dynamics by the reduced leaf surface area which results from larval feeding. An analytical solution is presented for the pest dynamics. Procedures are given for evaluating the parameters in the coupled pest-parasite-plant model using field measurements. Results of a complete computer simulation of the coupled model and comparisons with experimental data are presented.