Persistence of abnormal females that produce only female progeny with occasional recovery to normal females in Lepidoptera

In Lepidoptera, females that produce only female progeny have been found in wild populations of at least 12 species. In some species, recoveries, where abnormal females return to normal females, have been observed. A mathematical model of the population dynamics with recovery was developed to identify the conditions for realizing the persistence of abnormal females. Analysis indicated normal and abnormal females coexist and reach an equilibrium state at certain recovery rate values. The equilibrium values of normal and abnormal females were determined. When a population was in equilibrium it was shown that the ratio of normal to abnormal females and the sex ratio after reproduction are always functions of the recovery rate and the proportion of female offspring from an abnormal female to that from a normal female. Using the simulation it was found that, even when a population fluctuates under variable environmental conditions, the two ratios mentioned above reach equilibrium. Equilibrium relationships were applied to published data, and it was concluded that recovery from abnormal to normal females explains the persistence of abnormal females in some species of Lepidoptera. The model developed in this paper can also be used for analysing the persistence of abnormal females of other insect species.