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Why don't asexual females replace sexual females in most natural populations of eukaryotes? One promising explanation is that parasites could counter the reproductive advantages of asexual reproduction by exerting frequency-dependent selection against common clones (the Red Queen hypothesis). One apparent limitation of the Red Queen theory, however, is that parasites would seem to be required by theory to be highly virulent. In the present study, I present a population-dynamic view of competition between sexual females and asexual females that interact with co-evolving parasites. The results show that asexual populations have higher carrying capacities, and more unstable population dynamics, than sexual populations. The results also suggest that the spread of a clone into a sexual population could increase the effective parasite virulence as population density increases. This combination of parasite-mediated frequency-dependent selection, and density-dependent virulence, could lead to the coexistence of sexual and asexual reproductive strategies and the long-term persistence of sex.