Abstract
Many pathogens transmit horizontally through usual routes and vertically from parent to offspring. Co-evolution is predicted, under certain circumstances, to produce a positive relationship between host-pathogen antagonism and the rate of vertical transmission. We cannot disentangle the roles of host demographics and the costs of host immune function in establishing this pattern. On one hand, models that assume no density-dependent growth of host populations and limit the cost of immune function to infected hosts only predict that the positive relationship is possible. On the other hand, models that assume density-dependent growth of host populations and impose the cost of immune function on all hosts, regardless of infection status, suggest that the positive relationship is not possible. Here, we seek to resolve the confusion. We model the co-evolution of a host and its pathogen when the latter can transmit both vertically and horizontally. We assume host population growth is self-limiting, and we impose the cost of immune function only on infected hosts. We find that a positive relationship between host-pathogen antagonism and vertical transmission is possible under our assumptions. Our finding points to the critical role played by assumptions about when hosts pay the cost of immune function. We also find that the combination of density-dependent host population growth and the cost-free lifestyle of uninfected hosts raises the possibility of selection-driven pathogen extinction. We discuss our findings in relation to previous theory and empirical findings.