论文标题
双向波中的家谱
Genealogies in bistable waves
论文作者
论文摘要
我们研究了作用于二倍体种群的选择模型（每个人都携带每个基因的两个副本），生活在一个空间维度中。我们认为一个特定的基因以两种形式出现（等位基因）$ a $ and $ a $，并且携带$ aa $的个人的健身性高于$ aa $个体，而$ aa $个人的健身性低于$ aa $ and $ aa $个人。有利的$ a $等位基因的比例大约根据人口扩展。我们证明，在合适的时间范围内，随着人口密度为无穷大，从波前收敛到金曼聚集的样本$ a $等位基因的家谱。这与定向选择的情况形成鲜明对比，其中相应的极限被认为是Bolthausen-Sznitman合并的情况。证明使用“示踪动力学”。
We study a model of selection acting on a diploid population (one in which each individual carries two copies of each gene) living in one spatial dimension. We suppose a particular gene appears in two forms (alleles) $A$ and $a$, and that individuals carrying $AA$ have a higher fitness than $aa$ individuals, while $Aa$ individuals have a lower fitness than both $AA$ and $aa$ individuals. The proportion of advantageous $A$ alleles expands through the population approximately according to a travelling wave. We prove that on a suitable timescale, the genealogy of a sample of $A$ alleles taken from near the wavefront converges to a Kingman coalescent as the population density goes to infinity. This contrasts with the case of directional selection in which the corresponding limit is thought to be the Bolthausen-Sznitman coalescent. The proof uses 'tracer dynamics'.
