Models of incomplete selection for virulence of potato cyst nematodes caused by sex determination that depends on host resistance

Sex determination of potato cyst nematodes (Globodera rostochiensis andG. pallida) is strongly affected by host resistance. Larvae may develop more frequently into males in case of poorly compatible host parasite combinations than in case of fully compatible combinations. As a consequence, the number of males on a resistant host may be higher in case of a virulence than in case of virulence. To development into females, in contrast, virulence is more advantageous. According to logical reasoning, these conflicting interests of the two sexes may give rise to an equilibrium frequency of virulent nematodes, and therewith to incomplete selection for virulence when a resistant host is grown during a long period. This incomplete selection would manifests itself as durable partial resistance of the host.This new idea was studied theoretically for a host that is completely resistant to avirulent females on the basis of a gene-for-gene relationship. One calculation route to the equilibrium frequency of virulent nematodes was a numerical approach, by means of computer simulation, and the other route was an analytical approach, i.e. algebraic derivation.In case of excess of virulence allele a, the resistant host may even select for avirulence, according to the models. The equilibrium frequency of virulent nematodes equals 0.5/(1-α), where α represents the proportion of eggs that develop into males in case of virulence (aa) divided by that proportion in case of avirulence (Aa). If α≥0.5, then selection for virulence becomes complete. Consequences for purification of potato cyst nematodes to complete virulence are discussed.