Tobias Degen, Thomas Hovestadt, Oliver Mitesser, Franz Hölker

• Existing models explaining the evolution of sexual dimorphism in the timing of emergence (SDT) in Lepidoptera assume equal mortality rates for males and females. The limiting assumption of equal mortality rates has the consequence that these models are only able to explain the evolution of emergence of males before females, i.e. protandry-the more common temporal sequence of emergence in Lepidoptera. The models fail, however, in providing adaptive explanations for the evolution of protogyny, where females emerge before males, but protogyny isExisting models explaining the evolution of sexual dimorphism in the timing of emergence (SDT) in Lepidoptera assume equal mortality rates for males and females. The limiting assumption of equal mortality rates has the consequence that these models are only able to explain the evolution of emergence of males before females, i.e. protandry-the more common temporal sequence of emergence in Lepidoptera. The models fail, however, in providing adaptive explanations for the evolution of protogyny, where females emerge before males, but protogyny is not rare in insects. The assumption of equal mortality rates seems too restrictive for many insects, such as butterflies. To investigate the influence of unequal mortality rates on the evolution of SDT, we present a generalised version of a previously published model where we relax this assumption. We find that longer life-expectancy of females compared to males can indeed favour the evolution of protogyny as a fitness enhancing strategy. Moreover, the encounter rate between females and males and the sex-ratio are two important factors that also influence the evolution of optimal SDT. If considered independently for females and males the predicted strategies can be shown to be evolutionarily stable (ESS). Under the assumption of equal mortality rates the difference between the females' and males' ESS remains typically very small. However, female and male ESS may be quite dissimilar if mortality rates are different. This creates the potential for an 'evolutionary conflict' between females and males. Bagworm moths (Lepidoptera: Psychidae) provide an exemplary case where life-history attributes are such that protogyny should indeed be the optimal emergence strategy from the males' and females' perspectives: (i) Female longevity is considerably larger than that of males, (ii) encounter rates between females and males are presumably low, and (iii) females mate only once. Protogyny is indeed the general mating strategy found in the bagworm family.…