The effect of natural selection on genealogies

自然选择以不同的方式塑造了一个种群内的家谱。在我们的建议中，我们建议对正在选择的家谱的某些方面进行一般的定性研究，并对特定的相关模型进行定量处理。更准确地说，我们使用Girsanov变换和近似对偶来研究无界选择(因此存在任意有益和/或有害的适应度类别)的模型，并使用快速环境变化限制下的随机平均的一般结果来研究波动环境中的选择(其中等位基因可以是有益的也可以是有害的，取决于环境)。对于这两个模型，我们使用了先前开发的技术，将系谱树视为度量度量空间，从而导致树值随机马尔可夫过程。定性的工作是比较中立和选择下的谱系距离。我们推测，包括选择在内的许多情况会导致较短的系谱距离。

Natural selection shapes genealogies within a population in various ways. In our proposal, we suggest both, a general qualitative study of some aspects of genealogies under selection, and a quantitative treatment of specific relevant models. More precisely, we study models with unbounded selection (so there are arbitraryly beneficial and/or deleterious fitness classes) using Girsanov transforms and approximate dualities, and selection in fluctuating environment (where an allele can be beneficial or deleterious, depending on the environment) using a general result on stochastic averaging in the limit of fast environmental changes. For both models, we use the previously developed technique of treating genealogical trees as metric measure spaces, leading to tree-valued stochastic Markov processes. The qualitative work is dealing with a comparison of genealogical distances under neutrality and under selection. We conjecture that many ssituations including selection lead to shorter genealogical distances.