Program for Evolutionary Dynamics, Harvard University, One Brattle Square, Suite 6, Cambridge, MA 02138, USA.
Program for Evolutionary Dynamics, Harvard University, One Brattle Square, Suite 6, Cambridge, MA 02138, USA
J R Soc Interface. 2017 Oct;14(135). doi: 10.1098/rsif.2017.0509.
In evolutionary processes, population structure has a substantial effect on natural selection. Here, we analyse how motion of individuals affects constant selection in structured populations. Motion is relevant because it leads to changes in the distribution of types as mutations march towards fixation or extinction. We describe motion as the swapping of individuals on graphs, and more generally as the shuffling of individuals between reproductive updates. Beginning with a one-dimensional graph, the cycle, we prove that motion suppresses natural selection for death-birth (DB) updating or for any process that combines birth-death (BD) and DB updating. If the rule is purely BD updating, no change in fixation probability appears in the presence of motion. We further investigate how motion affects evolution on the square lattice and weighted graphs. In the case of weighted graphs, we find that motion can be either an amplifier or a suppressor of natural selection. In some cases, whether it is one or the other can be a function of the relative reproductive rate, indicating that motion is a subtle and complex attribute of evolving populations. As a first step towards understanding less restricted types of motion in evolutionary graph theory, we consider a similar rule on dynamic graphs induced by a spatial flow and find qualitatively similar results, indicating that continuous motion also suppresses natural selection.
在进化过程中，种群结构对自然选择有很大的影响。在这里，我们分析个体运动如何影响结构种群中的持续选择。运动是相关的，因为它导致类型分布的变化，因为突变朝着固定或灭绝前进。我们将运动描述为个体在图上的交换，更一般地说，是个体在生殖更新之间的混合。从一维图，即循环开始，我们证明运动抑制了死亡-出生（DB）更新或任何结合了出生-死亡（BD）和 DB 更新的过程的自然选择。如果规则仅仅是 BD 更新，那么在存在运动的情况下，固定概率不会发生变化。我们进一步研究了运动如何影响正方形晶格和加权图上的进化。在加权图的情况下，我们发现运动可以是自然选择的放大器或抑制器。在某些情况下，它是放大器还是抑制器可以是相对生殖率的函数，这表明运动是进化群体中微妙而复杂的属性。作为理解进化图论中更受限类型运动的第一步，我们考虑了由空间流引起的动态图上的类似规则，并得到了定性上相似的结果，表明连续运动也抑制了自然选择。
