Travelling waves of resistance in a bi-trophic pest adaptation model.

We consider a reaction-diffusion system for spatial spread of pest resistance to host plant resistance genes which is based on the Lotka-Volterra predator-prey equations, with logistic growth of the resource level and a diffusion term added to account for spatial spread of the pest. The model is phenotype specific, in which a pest subpopulation's fitness comes down to a balance between its resource assimilation rate and its respiration rate. We derive an expression for the rate of spatial spread of the resistant pest types from an initial point source, and discuss its relevance for adaptive pest resistance management strategies.

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.