Abstract
By constantly selecting for novel genotypes, coevolution between hosts and parasites can favour elevated mutation rates. Models of this process typically assume random encounters. However, offspring are often more likely to encounter their mother's parasites. Because parents and offspring are genetically similar, they may be susceptible to the same parasite strains and thus, in hosts, maternal transmission should select for mechanisms that decrease intergenerational genetic similarity. In parasites, however, maternal transmission should select for genetic similarity. We develop and analyse a model of host and parasite mutation rate evolution when parasites are maternally inherited. In hosts, we find that maternal transmission has two opposing effects. First, it eliminates coevolutionary cycles that previous work shows select for higher mutation. Second, it independently selects for higher mutation rates, because offspring that differ from their mothers are more likely to avoid infection. In parasites, however, the two effects of maternal transmission act in the same direction. As for hosts, maternal transmission eliminates coevolutionary cycles, thereby reducing selection for increased mutation. Unlike for hosts, however, maternal transmission additionally selects against higher mutation by favouring parasite offspring that are the same as their mothers.