Pavlogiannis Andreas, Tkadlec Josef, Chatterjee Krishnendu, Nowak Martin A
IST Austria, Klosterneuburg, A-3400, Austria.
Program for Evolutionary Dynamics, Department of Organismic and Evolutionary Biology, Department of Mathematics, Harvard University, Cambridge, MA, 02138, USA.
Sci Rep. 2017 Mar 6;7(1):82. doi: 10.1038/s41598-017-00107-w.
The fixation probability is the probability that a new mutant introduced in a homogeneous population eventually takes over the entire population. The fixation probability is a fundamental quantity of natural selection, and known to depend on the population structure. Amplifiers of natural selection are population structures which increase the fixation probability of advantageous mutants, as compared to the baseline case of well-mixed populations. In this work we focus on symmetric population structures represented as undirected graphs. In the regime of undirected graphs, the strongest amplifier known has been the Star graph, and the existence of undirected graphs with stronger amplification properties has remained open for over a decade. In this work we present the Comet and Comet-swarm families of undirected graphs. We show that for a range of fitness values of the mutants, the Comet and Comet-swarm graphs have fixation probability strictly larger than the fixation probability of the Star graph, for fixed population size and at the limit of large populations, respectively.
固定概率是指在同质群体中引入的新突变体最终占据整个群体的概率。固定概率是自然选择的一个基本量，并且已知它取决于群体结构。与完全混合群体的基线情况相比，自然选择放大器是能够增加有利突变体固定概率的群体结构。在这项工作中，我们关注以无向图表示的对称群体结构。在无向图的情况下，已知最强的放大器是星图，并且具有更强放大特性的无向图的存在十多年来一直悬而未决。在这项工作中，我们提出了无向图的彗星和彗星群族。我们表明，对于突变体的一系列适应度值，分别在固定群体大小和大群体极限情况下，彗星图和彗星群图的固定概率严格大于星图的固定概率。
