Maintenance of butterfly populations with all-female broods under recurrent extinction and recolonization

A theory is considered which can explain the apparent persistence of butterfly populations containing a special type of females producing all-female broods. Under normal circumstances it would be expected that these populations should become extinct, but this does not happen in nature. The theory is based on the possibility of a balance between populations dying out and habitats being recolonized. It is shown that a stable equilibrium can exist in a simple model leading to a set of differential equations and also in a more realistic simulation model. The first approach may have a bearing on certain prey-predator systems as well.