Evolution of altruistic defense traits in structured populations

在第一个项目阶段，我们研究了在哪些条件下，可遗传的抵御寄生虫的行为特征可以在结构化的种群中传播，即使从拥有防御基因的个体往往后代较少的意义上来说，这是代价高昂的。在这个拟议的延续项目中，我们研究了从罕见突变产生的防御等位基因首次固定之前的多个Demes限制时间。我们将证明，第一次固定的时间在反向突变率中是对数的。因此，即使突变率很小，防御特征也可以在进化相关的时间尺度上出现。从数学上讲，我们的主要贡献是证明和推广了Dawson和Greven(2011)的结果，而不使用大类过程的对偶过程。此外，我们将在最近邻迁移的二维晶格上模拟我们的模型。这将表明我们的多密度极限的结果是否也适用于生物学上更相关的种群结构。

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.