Evolutionary games on isothermal graphs
Evolutionary games on isothermal graphs
复制标题
DOI：
10.1038/s41467-019-13006-7
复制
发表时间：
2019-11-08
影响因子：
16.6
通讯作者：
Nowak, Martin A.
中科院分区：
文献类型：
--
作者：
Allen, Benjamin;Lippner, Gabor;Nowak, Martin A.
种群结构影响着自然选择的结果。这些影响可以用进化博弈的图形来建模。最近，根据随机游走的聚结次数，导出了在任意加权图上弱选择下性状被偏爱的条件。这里我们考虑等温图，每个节点的总边权相同。在等温图上成功的条件采用一种简单的形式，其中图结构的影响被捕获在“有效度”中-每个个体的有效邻居数的度量。对于两个更新规则（死亡-出生和出生-死亡），当收益成本比超过有效度时，在大等温图上有利于合作行为。对于另外两个更新规则（出生-死亡和死亡-出生），合作从来不受欢迎。我们将图的有效度与其谱隙联系起来，从而将演化动力学与展开图理论联系起来。令人惊讶的是，我们发现无限平均度的图形仍然为合作提供了强有力的支持。
Population structure affects the outcome of natural selection. These effects can be modeled using evolutionary games on graphs. Recently, conditions were derived for a trait to be favored under weak selection, on any weighted graph, in terms of coalescence times of random walks. Here we consider isothermal graphs, which have the same total edge weight at each node. The conditions for success on isothermal graphs take a simple form, in which the effects of graph structure are captured in the 'effective degree'-a measure of the effective number of neighbors per individual. For two update rules (death-Birth and birth-Death), cooperative behavior is favored on a large isothermal graph if the benefit-to-cost ratio exceeds the effective degree. For two other update rules (Birth-death and Death-birth), cooperation is never favored. We relate the effective degree of a graph to its spectral gap, thereby linking evolutionary dynamics to the theory of expander graphs. Surprisingly, we find graphs of infinite average degree that nonetheless provide strong support for cooperation.