Models of fungicide resistance dynamics

We describe two classes of models used for fungicide and antibiotic resistance dynamics. One class assumes that the density of the pathogen (or severity of the disease caused by the pathogen) has no feedback effects on the rate at which new infections arise. The second class does not make this assumption. A quantitative relationship between these two classes is derived. We then discuss the two sets of assumptions made in the literature about initial conditions: either both the fungicide-sensitive strain and the -resistant strain are initially at low density, or the sensitive strain is resident at nonlow density and the resistant strain is initially at low density. We show that models of fungicide resistance dynamics with and without density-dependent feedback give contrasting predictions on the effects of pathogen life-cycle parameters and the effects of the fungicide (dose, frequency, use of mixtures, spatial usage restrictions) on the evolution, invasion, and spread of fungicide resistance. We further show that the evaluation of a resistance management strategy requires a very precise definition of what constitutes a good strategy.