Optimal cultivar mixtures in focal plant diseases

This paper deals with a study on the effects of mixtures of partially resistant cultivars in focus forming plant diseases. The focus expansion velocity in a mixture of two partially resistant cultivars depends on four parameters, the focus expansion velocity in a crop of cultivar 1 only and in a crop of cultivar 2 only, the net-reproduction in a crop of cultivar 1 and of cultivar 2, respectively. An explicit equation is developed for the damage of a cultivar mixture where the crop is infected by two physiological races of the pathogen. It is shown that cultivar mixtures exist where damage is smaller than in crops of either of the two cultivars only. A simple explicit formula is given on the basis of which it can be decided whether an optimal mixture exists for a given pathosystem.