HTWK Leipzig University of Applied Sciences, Leipzig, Germany.
J Math Biol. 2021 May 16;82(7):61. doi: 10.1007/s00285-021-01609-y.
A central question of evolutionary dynamics on graphs is whether or not a mutation introduced in a population of residents survives and eventually even spreads to the whole population, or becomes extinct. The outcome naturally depends on the fitness of the mutant and the rules by which mutants and residents may propagate on the network, but arguably the most determining factor is the network structure. Some structured networks are transient amplifiers. They increase for a certain fitness range the fixation probability of beneficial mutations as compared to a well-mixed population. We study a perturbation method for identifying transient amplifiers for death-birth updating. The method involves calculating the coalescence times of random walks on graphs and finding the vertex with the largest remeeting time. If the graph is perturbed by removing an edge from this vertex, there is a certain likelihood that the resulting perturbed graph is a transient amplifier. We test all pairwise nonisomorphic regular graphs up to a certain order and thus cover the whole structural range expressible by these graphs. For cubic and quartic regular graphs we find a sufficiently large number of transient amplifiers. For these networks we carry out a spectral analysis and show that the graphs from which transient amplifiers can be constructed share certain structural properties. Identifying spectral and structural properties may promote finding and designing such networks.
图上进化动力学的一个核心问题是，在居民群体中引入的突变是否会存活下来，最终甚至传播到整个群体，或者灭绝。结果自然取决于突变体的适应性以及突变体和居民在网络上传播的规则，但可以说最决定性的因素是网络结构。一些结构网络是瞬时放大器。与混合良好的种群相比，它们在一定的适应度范围内增加了有益突变的固定概率。我们研究了一种用于识别死亡-出生更新的瞬时放大器的摄动方法。该方法涉及计算图上随机游走的合并时间，并找到具有最大重聚时间的顶点。如果从该顶点删除图中的一条边，则该图很可能是一个瞬时放大器。我们测试了所有成对的非同构正则图，直到一定的阶数，从而覆盖了这些图所表示的整个结构范围。对于三次和四次正则图，我们找到了足够多的瞬时放大器。对于这些网络，我们进行了谱分析，并表明可以构造瞬时放大器的图具有某些结构特性。识别谱和结构特性可以促进寻找和设计此类网络。
