论文标题
进化空间模型中的突变时间
Mutation timing in a spatial model of evolution
论文作者
论文摘要
由癌症形成模型的动机，在这种模型中，细胞需要获得$ k $突变才能变成癌性，我们考虑了一种空间种群模型，其中人口以$ d $ d $维的侧面长度$ l $表示。最初，没有任何站点有突变，但是具有$ i-1 $突变的站点以$ $ $μ_i$单位区域的价格获得了一个$ i $ th的突变。突变以$α$的速度扩散到相邻站点，因此突变后的$ t $时间单元，获得该突变的个体的区域将是半径$αt$的球。我们计算出参数值的某些范围，某些人获得$ k $突变所需的时间的渐近分布。我们的结果是基于杜雷特，foo和leder的先前工作，当$ k = 2 $，当$μ_i=μ$ $ $ $时，我们的结果基本上是完整的。
Motivated by models of cancer formation in which cells need to acquire $k$ mutations to become cancerous, we consider a spatial population model in which the population is represented by the $d$-dimensional torus of side length $L$. Initially, no sites have mutations, but sites with $i-1$ mutations acquire an $i$th mutation at rate $μ_i$ per unit area. Mutations spread to neighboring sites at rate $α$, so that $t$ time units after a mutation, the region of individuals that have acquired the mutation will be a ball of radius $αt$. We calculate, for some ranges of the parameter values, the asymptotic distribution of the time required for some individual to acquire $k$ mutations. Our results, which build on previous work of Durrett, Foo, and Leder, are essentially complete when $k = 2$ and when $μ_i = μ$ for all $i$.
