Abstract：
In this paper, we investigate the consequences of dormancy in the \'rare mutation\' and \'large population\' regime of stochastic adaptive dynamics. Starting from an individual-based micro-model, we first derive the Polymorphic Evolution Sequence of the population, based on a previous work by Baar and Bovier (2018). After passing to a second \'small mutations\' limit, we arrive at the Canonical Equation of Adaptive Dynamics, and state a corresponding criterion for evolutionary branching, extending a previous result of Champagnat and Méléard (2011). The criterion allows a quantitative and qualitative analysis of the effects of dormancy in the well-known model of Dieckmann and Doebeli (1999) for sympatric speciation. In fact, quite an intuitive picture emerges: Dormancy enlarges the parameter range for evolutionary branching, increases the carrying capacity and niche width of the post-branching sub-populations, and, depending on the model parameters, can either increase or decrease the \'speed of adaptation\' of populations. Finally, dormancy increases diversity by increasing the genetic distance between subpopulations.
摘要：
在本文中,我们研究了随机适应动力学的“罕见突变”和“大种群”机制中休眠的后果。从基于个人的微观模型开始，我们首先推导了种群的多态进化序列，基于Baar和Bovier(2018)的先前工作。在达到第二个“小突变”极限后，我们得出了自适应动力学的典型方程，并说明进化分支的相应标准，扩展了Champagnat和Méléard(2011)的先前结果。该标准可以对著名的Dieckmann和Doebeli（1999）同族物种形成模型中休眠的影响进行定量和定性分析。事实上,相当直观的画面浮现：休眠扩大了进化分支的参数范围，增加后分支子种群的承载能力和生态位宽度，and,根据模型参数，可以增加或减少人口的适应速度。最后,休眠通过增加亚群之间的遗传距离来增加多样性。
