Male Dimorphism and Emergence Strategies: A Mathematical Model of Protandry in Fabriciana nerippe Felder, 1862

In many butterfly species, males emerge earlier than females as part of a strategy to maximize male reproductive success. Although behavioral ecological studies using mathematical models have been conducted to explain this phenomenon, certain emergence patterns remain unexplained. In the butterfly species Fabriciana nerippe, some males emerge at the same time as females, in addition to males that emerge earlier than the females. However, it is unclear what emergence patterns occur in populations with male dimorphism, as observed in this species. In this study, we showed the existence of male body size dimorphism in Fabriciana nerippe by conducting a comparative analysis of forewing lengths between males and females. In addition, we developed a comprehensive mathematical model to investigate emergence patterns in the presence of dimorphic males. By introducing a trade-off between large size and early emergence, the model considered a scenario where small early-emerging and large late-emerging males could coexist. Numerical analysis demonstrated the emergence patterns of these two male types with a switch in emergence time. Furthermore, the higher the death rate before emergence, the earlier the emergence switch. These findings suggested that the timing of the switch depends on the death rate and is influenced by environmental factors. This work contributes to ecological and theoretical studies on timing dimorphism in life-history strategies across a broader range of species. HighlightsO_LIWe confirmed the existence of male body-size dimorphism corresponding to emergence timing in Fabriciana nerippe. C_LIO_LIWe developed a comprehensive model of male emergence patterns incorporateing male dimorphism. C_LIO_LIWe assumed a trade-off between early emergence and large body size. C_LIO_LIThe timing of male emergence switching is influenced by death rate and reproductive advantage of large males. C_LI