具有突变和选择的径向Domany-Kinzel模型
Radial Domany-Kinzel Models with Mutation and Selection
摘要：
我们研究了空间结构，遗传漂变，突变和选择压力的进化动力学在一个简化的模型无性生物殖民一个新的领土。在一个适当的粗粒化，进化动力学有关的定向渗流过程中出现的选民模型，Domany-Kinzel（DK）模型，接触过程等，我们探讨线性（平坦的前面）的扩张和不太熟悉的径向（弯曲的前面）范围扩张之间的差异。对于径向膨胀，我们开发了一个广义的，非晶格DK模型，以尽量减少其他持久的晶格文物。通过模拟和分析技术，我们研究了有利突变体的生存概率，中性菌株结构域之间的空间相关性，以及有害突变群体的动态。边界上的“暴胀”导致了径向扩张和线性扩张之间的显著差异。对于初始半径为$R_0$、以速度$v$扩张的菌落，由局部遗传漂变引起的显著遗传分层仅在有限时间$t^* = R_0/v$内发生，在此之后，由于扩张前沿的膨胀周长，菌落的部分变得因果地断开。因此，相对于遗传漂变，选择优势的影响被放大，增加了有利突变体的存活概率。通货膨胀也修改了潜在的定向渗流过渡，引入新的标度函数和修改类似的有限尺寸效应。最后，我们考虑径向范围扩张与紧缩周长，可能会出现从殖民开始沿海岸的岛屿。
英文摘要：
We study the effect of spatial structure, genetic drift, mutation, and selective pressure on the evolutionary dynamics in a simplified model of asexual organisms colonizing a new territory. Under an appropriate coarse-graining, the evolutionary dynamics is related to the directed percolation processes that arise in voter models, the Domany-Kinzel (DK) model, contact process, etc. We explore the differences between linear (flat front) expansions and the much less familiar radial (curved front) range expansions. For the radial expansion, we develop a generalized, off-lattice DK model that minimizes otherwise persistent lattice artifacts. With both simulations and analytical techniques, we study the survival probability of advantageous mutants, the spatial correlations between domains of neutral strains, and the dynamics of populations with deleterious mutations. "Inflation" at the frontier leads to striking differences between radial and linear expansions. For a colony with initial radius $R_0$ expanding at velocity $v$, significant genetic demixing, caused by local genetic drift, only occurs up to a finite time $t^* = R_0/v$, after which portions of the colony become causally disconnected due to the inflating perimeter of the expanding front. As a result, the effect of a selective advantage is amplified relative to genetic drift, increasing the survival probability of advantageous mutants. Inflation also modifies the underlying directed percolation transition, introducing novel scaling functions and modifications similar to a finite size effect. Finally, we consider radial range expansions with deflating perimeters, as might arise from colonization initiated along the shores of an island.
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