A mathematical model for wing dimorphism in maleCardiocondyla ants

Abstract

Several species ofCardiocondyla ants have dimorphic males: wingless (ergatoid) and winged (alate) males, while otherCardiocondyla species includingC. nuda have only wingless males. We made an evolutionarily stable strategy model for explaning the male polymorphism and the ratios of wingless males in the genusCardiocondyla. Wingless males emerge earlier than winged males in each reproductive season. Females (F ₁) which have emerged before winged males copulate only with wingless males, and females (F ₂) which emerge after winged males copulate with both wingless and winged males. Wingless males have a lower copulation ability (b _n) than winged males (b _w). The reproductive success of females which copulate at the early stage (v ₁) is assumed to be larger than that of females which copulate at the late stage (v ₂). The model predicts that there are 3 different evolutionarily stable states: 2 monomorphic states of wingless and winged males, and a dimorphism of the 2 types of males. In the dimorphic state, the rate of wingless males increases as the survival rate of wingless males (s) increases,v ₁/v ₂ increases,F ₁/F ₂ increases andb _n/b _w increases. For dimorphism to exist,s b _n/b _w<1 must be satisfied, and this condition corresponds to the value of observed data. The value ofv ₁/v ₂ would be difficult to be obtained by actual data, but we can estimate this value with the model.