Disease progress of non‐specialised fungal pathogens in intraspecific mixed stands of cereal cultivars. I. Models

SUMMARY Two mathematical models are presented which describe progress of disease, caused by an unspecialised pathogen, in pure and mixed stands of cereal cultivars. One is a simple, discrete model utilising the parameters infection frequency (lesions/spore) and sporulation rate (spores/lesion/event) on each cultivar. The model predicts that, in most circumstances, the amount of disease in mixtures will be equal to or less than the arithmetic mean of the component pure stands. An increase in disease is only predicted in situations where the ranking of cultivars with respect to infection frequency and sporulation rate is opposed. In the other model differential equations are proposed. Solutions of these equations indicate that disease amelioration can usually be expected in such mixtures, confirming the conclusions of the discrete model and that disease levels will deviate around the geometric, rather than arithmetic, mean of the pure stands. However the advantages of this model lie in wider generality and conceptual, rather than practical, utility.