Bi-trophic mathematical model for pest adaptation to a resistant crop

A version of the Lotka-Volterra predator-prey model with logistic crop growth is modified to explore the rate of adaptation of a herbivore to a pest-resistant crop. This provides a phenotypic model for the evolution of resistance in a population comprising three different pest types each defined by differing parameter values for respiration rate and crop palatability. Expressions estimating the rates of increase of the fitter pest types are obtained as a function of the food qualities, and respiration and mortality rates. Potential strategies for delaying the rate of adaptation with regard to the expressions derived above, via the use of pest-susceptible refugia and natural enemies, are discussed. Although the model is formulated as one in which a single gene is the factor conferring resistance it can be interpreted and used independently of this.