Evolution of altruistic defense traits in structured populations

在项目的第一阶段，我们调查了在何种条件下，一种可遗传的防御寄生虫的行为特征可以在一个结构化的群体中传播，即使它是昂贵的，因为具有防御基因的个体往往会有更少的后代。在这个建议的延续项目中，我们研究了在多个领域中，直到罕见突变产生的防御等位基因的第一次固定的时间限制。我们将证明，第一次固定的时间是逆突变率的对数。因此，即使是很小的突变率，防御特征也可能出现在进化相关的时间尺度上。在数学上，我们的主要贡献是证明和推广Dawson和Greven（2011）的结果，而不使用大类过程的对偶过程。此外，我们将模拟我们的模型在一个二维晶格与最近邻迁移。这将表明我们的结果多demes限制也适用于生物学上更相关的人口结构。

In the first project phase we investigated under which conditions an inheritable behavioral trait of defense against parasites can spread in a structured population even if it is costly in the sense that individuals having a defense gene tend to have less offspring. In this proposed continuation project we study in a many-demes limit the time until the first fixation of a defense allele arising from rare mutations. We are going to show that this time to first fixation is logarithmic in the inverse mutation rate. So even for small mutation rates defense traits can appear on an evolutionary relevant time scale. Mathematically our central contribution is to prove and generalize the results of Dawson and Greven (2011) without using dual processes for a large class of processes. Moreover we are going to simulate our model on a two-dimensional lattice with nearest-neighbour migration. This will show whether our results for the many-demes limit also apply to biologically more relevant population structures.