Mounting evidence has indicated that engaging in extra-pair copulations (EPCs) might be maladaptive or detrimental to females. It is unclear why such non-adaptive female behavior evolves. In this study, we test two hypotheses about the evolution of female EPC behavior using population genetic models. First, we find that both male preference for allocating extra-effort to seek EPCs and female pursuit behavior without costs can be maintained and remain polymorphic in a population via frequency dependent selection. However, both behaviors cannot evolve when females with pursuit behavior suffer from a decline in male parental care. Second, we present another novel way in which female pursuit behavior can evolve; indirect selection can act on this behavior through a ratchet-like mechanism involving oscillating linkage disequilibria between the target EPC pursuit locus and two other loci determining male mate choice and a female sexual signal. Although the overall positive force of such indirect selection is relatively weak, our results suggest that it may still play a role in promoting the evolution of female EPC behavior when this behavior is non-adaptive (i.e., it is neutral) or only somewhat maladaptive (e.g., males only occasionally lower parental care when their mates pursue EPCs).