The effect of natural selection on genealogies

自然选择以各种方式塑造种群内的系谱。在我们的建议中，我们建议，一个一般的定性研究的某些方面的家谱下选择，和定量处理的具体相关模型。更确切地说，我们研究模型与无界选择（所以有任意有益和/或有害的健身类）使用Girsanov变换和近似对偶，并选择在波动的环境（其中等位基因可以是有益的或有害的，这取决于环境）使用的一般结果随机平均在快速的环境变化的限制。对于这两个模型，我们使用以前开发的技术，治疗家谱树作为度量测度空间，导致树值随机马尔可夫过程。定性的工作是处理比较的系谱距离下的中立性和选择。我们推测，许多ssituations，包括选择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.