Alcalde Cuesta Fernando, González Sequeiros Pablo, Lozano Rojo Álvaro
Departamento de Matemáticas, Universidade de Santiago de Compostela, E-15782 Santiago de Compostela, Spain.
GeoDynApp - ECSING Group, Spain.
PLoS One. 2017 Jul 10;12(7):e0180549. doi: 10.1371/journal.pone.0180549. eCollection 2017.
Inspired by recent works on evolutionary graph theory, an area of growing interest in mathematical and computational biology, we present examples of undirected structures acting as suppressors of selection for any fitness value r > 1. This means that the average fixation probability of an advantageous mutant or invader individual placed at some node is strictly less than that of this individual placed in a well-mixed population. This leads the way to study more robust structures less prone to invasion, contrary to what happens with the amplifiers of selection where the fixation probability is increased on average for advantageous invader individuals. A few families of amplifiers are known, although some effort was required to prove it. Here, we use computer aided techniques to find an exact analytical expression of the fixation probability for some graphs of small order (equal to 6, 8 and 10) proving that selection is effectively reduced for r > 1. Some numerical experiments using Monte Carlo methods are also performed for larger graphs and some variants.
受进化图论近期研究成果的启发（进化图论是数学和计算生物学中一个日益受到关注的领域），我们给出了无向结构的示例，这些结构对于任何适应度值(r>1)都充当选择抑制器。这意味着放置在某个节点上的有利突变体或入侵个体的平均固定概率严格小于放置在充分混合种群中的该个体的平均固定概率。这为研究更不易被入侵的更稳健结构开辟了道路，这与选择放大器的情况相反，在选择放大器中，有利入侵个体的固定概率平均会增加。虽然需要一些努力来证明，但已知有几类放大器。在这里，我们使用计算机辅助技术来找到一些小阶数（等于6、8和10）的图的固定概率的精确解析表达式，证明对于(r>1)，选择实际上会降低。还针对更大的图和一些变体进行了一些使用蒙特卡罗方法的数值实验。
