© 2018 Casanovas et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. The success of biological control may depend on the control agent co-evolving with its target pest species, precluding the emergence of resistance that often undermines chemical control. However, recent evidence of a decline in attack rates of a sexual pest weevil by its asexual parasitoid suggests that evolutionary arms races may not prevent the emergence of resistance if the host and parasitoid do not have reproductive strategies that generate equal amounts of genetic variation. To understand how these asymmetries in reproductive strategies may drive the emergence of resistance, we combined life history data from two pest weevils and their parasitoids (one sexual and one asexual) in the New Zealand pastoral ecosystem, with a population dynamic model that allows the coevolution of hosts and parasitoids. We found that the ratio of the genetic variance of hosts to parasitoids was a key determinant of the emergence of resistance. Host resistance eventually occurred unless the parasitoids had considerably greater additive genetic variance than their host. The higher reproductive rate of asexual parasitoids did little to offset the cost of reduced additive genetic variance. The model predictions were congruent with long-term parasitism rates observed in the field for both of the pests considered (one with a sexual and one with an asexual parasitoid). We then explored the consequences of introducing two parasitoids with different reproductive strategies that attack the same sexual host. The model showed that the sexually reproducing parasitoid always out-competed the asexually reproducing one. Our study shows that any asymmetry in reproductive strategies is extremely important for predicting the long-term success of biological control agents. Fortunately, introduction of sexually reproducing individuals after an initial introduction of asexual strains may overcome the problems of host resistance. We conclude that evolution must be considered when evaluating the long-term outcomes of importation biological control.