Interfaculty Bioinformatics Unit, University of Bern, 3012, Switzerland.
Computational and Molecular Population Genetics Laboratory, Institute of Ecology and Evolution, University of Bern, 3012, Switzerland.
Genetics. 2018 Jul;209(3):885-895. doi: 10.1534/genetics.118.301104. Epub 2018 May 17.
We study the establishment probabilities of locally adapted mutations using a multi-type branching process framework. We find a surprisingly simple and intuitive analytical approximation for the establishment probabilities in a symmetric two-deme model under the assumption of weak (positive) selection. This is the first analytical closed-form approximation for arbitrary migration rate to appear in the literature. We find that the establishment probability lies between the weak and the strong migration limits if we condition the origin of the mutation to the deme where it is advantageous. This is not the case when we condition the mutation to first occur in a deme where it is disadvantageous. In this case we find that an intermediate migration rate maximizes the probability of establishment. We extend our results to the cases of multiple demes, two demes with asymmetric rates of gene flow, and asymmetric carrying capacities. The latter case allows us to illustrate how density regulation can affect establishment probabilities. Finally, we use our results to investigate the role of gene flow on the rate of local adaptation and identify cases in which intermediate amounts of gene flow facilitate the rate of local adaptation as compared to two populations without gene flow.
我们使用多类型分支过程框架研究局部适应突变的建立概率。在弱（正）选择的假设下，我们发现了一种非常简单和直观的分析近似，用于对称的两区域模型中的建立概率。这是首次在文献中出现的任意迁移率的分析闭式近似。如果我们将突变的起源条件到有利的区域，那么建立概率介于弱迁移极限和强迁移极限之间。如果我们将突变的起源条件到最初不利的区域，那么情况就不是这样。在这种情况下，我们发现中间迁移率会最大化建立的概率。我们将我们的结果扩展到多个区域、具有不对称基因流动率的两个区域以及不对称承载能力的情况。后一种情况使我们能够说明密度调节如何影响建立概率。最后，我们使用我们的结果来研究基因流对局部适应速度的作用，并确定中间数量的基因流相对于没有基因流的两个种群如何促进局部适应速度的情况。
