School of Mathematics and Statistics, University of Sydney, Sydney, NSW, 2006, Australia.
Department of Anthropology, University of Utah, Salt Lake City, UT, 84112, USA.
Bull Math Biol. 2017 Sep;79(9):2132-2148. doi: 10.1007/s11538-017-0323-0. Epub 2017 Jul 13.
We present a mathematical simplification for the evolutionary dynamics of a heritable trait within a two-sex population. This trait is assumed to control the timing of sex-specific life-history events, such as the age of sexual maturity and end of female fertility, and each sex has a distinct fitness trade-off associated with the trait. We provide a formula for the fitness landscape of the population and show a natural extension of the result to an arbitrary number of heritable traits. Our method can be viewed as a dynamical systems generalisation of the Price equation to include two sexes, age structure and multiple traits. We use this formula to examine the effect of grandmothering, whereby post-fertile females subsidise their daughter's fertility by provisioning grandchildren. Grandmothering can drive a shift towards increasingly male-biased mating sex ratios due to a post-fertile life stage in females, while male fertility continues to older ages. Our fitness landscapes show a net increase in fitness for both males and females at longer lifespans, and as a result, we find that grandmothering alone provides an evolutionary trajectory to higher longevities.
我们提出了一种简化的数学模型，用于研究具有两性的种群中可遗传特征的进化动态。该特征被假定为控制与性别相关的生命史事件（如性成熟年龄和女性生育力结束的年龄）的时间，并且每个性别都与该特征相关联有一个独特的适应度权衡。我们提供了种群适应度景观的公式，并展示了将该结果自然扩展到任意数量可遗传特征的方法。我们的方法可以看作是 Price 方程的动力系统推广，包括两性、年龄结构和多个特征。我们使用这个公式来研究祖母效应的影响，即有生育能力的女性通过为孙辈提供资源来补贴女儿的生育能力。由于女性有一个有生育能力的生命阶段，祖母效应可能导致交配性别比越来越偏向男性，而男性的生育能力则持续到更老的年龄。我们的适应度景观显示，在更长的寿命下，男性和女性的适应度都有净增加，因此，我们发现仅仅是祖母效应就提供了一条通往更高寿命的进化轨迹。
