Zonneveld C, Metz J A
Department of Biology, Vrije Universiteit, Amsterdam, The Netherlands.
Theor Popul Biol. 1991 Dec;40(3):308-21. doi: 10.1016/0040-5809(91)90058-n.
Current models on protandry in butterflies assume that females are mated instantaneously upon eclosion. However, for most butterfly species this assumption is not realistic. In this paper a model is formulated in which the mating rate depends on both male and female density. Given the female presence curve, protandry is an evolutionarily stable strategy (ESS) for males. The evolutionarily stable amount of protandry decreases with increasing death rate and decreasing encounter rate. Given the male presence curve, protandry also is an ESS for females. However, male and female ESS are not identical; moreover, in the present model a simultaneous ESS does not exist. Protandry critically depends on the assumption that females mate only once, whereas males are capable of multiple mating. If females too are capable of multiple mating, absence of protandry is the ESS for males as well as females. The model predicts that protandry depends on population density: protandry should be more pronounced in populations with high density than in populations with low density. Protandry also depends on sex ratio. It becomes more pronounced when the proportion of males among emerging adults increases.
当前关于蝴蝶雄性先熟的模型假定雌性羽化后会立即交配。然而，对于大多数蝴蝶物种而言，这一假设并不现实。本文构建了一个模型，其中交配率取决于雄性和雌性的密度。在给定雌性出现曲线的情况下，雄性先熟是一种进化稳定策略（ESS）。进化稳定的雄性先熟程度会随着死亡率的增加和相遇率的降低而降低。在给定雄性出现曲线的情况下，雄性先熟对雌性来说也是一种ESS。然而，雄性和雌性的ESS并不相同；此外，在当前模型中不存在同时的ESS。雄性先熟严重依赖于雌性只交配一次而雄性能够多次交配这一假设。如果雌性也能够多次交配，那么不存在雄性先熟对雄性和雌性来说都是ESS。该模型预测，雄性先熟取决于种群密度：在高密度种群中，雄性先熟应比在低密度种群中更为明显。雄性先熟还取决于性别比例。当羽化成虫中雄性的比例增加时，雄性先熟会变得更加明显。
