We studied the evolution of juvenile hormone (JH) regulation in wing-polymorphic insects. We considered an asexual species that undergo larval and adult stages living in many patches. The rate of larval growth depends on within-patch resources which can be depleted by larvae. Dispersal-type adults migrate out of the natal patch just before reproductive stage; reproductive-type adults have a greater fertility than those of dispersal-type adults but no dispersal ability. The wing type was determined by the juvenile hormone (JH) level in a critical period if the larval stage. The carrying capacity of resources fluctuates between high and low values. The JH level follows a normal distribution. Evolution modifies the mean and the variance of JH level. The mean of JH level is determined by the basal JH level and density dependent degradation. The variance of JH level is constant.
First, we calculated when the mean and the variance of the JH level were evolved separately. In the evolution of mean of JH level, both of the basal JH level and density response affected the dispersal type production. In the evolution of variance of JH level, the variance evolved smaller when the environmental fluctuation was large. In both cases, the production of dispersal type was small if the density was low, and it increased rapidly if the density was large. The production of dispersal type was larger when the environmental fluctuation was larger. The growth rate and mortality of insects, and recovery of resources also affected the dispersal type production. Second, we calculated when the mean and the variance of the JH level were evolved simultaneously. When the environmental fluctuation was large, the variance was converged into minimum value. When the environmental fluctuation was small, all of these values affected the wing determination.