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，在居民种群中引入的突变是存活下来并最终扩散到整个种群，还是灭绝。结果自然取决于突变体的适应度以及突变体和居民在网络上传播的规则，但可以说最具决定性的因素是网络结构。一些结构化网络是瞬态放大器。与混合良好的群体相比，它们在一定的适应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用于死亡-出生更新的瞬态放大器的扰动方法。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结时间的顶点。如果通过从该顶点移除边来扰动图，则产生的扰动图很可能是瞬态放大器。我们测试所有成对非同构正则图达到某个顺序，从而覆盖这些图可表达的整个结构范围。对于三次和四次正则图，我们发现了足够多的瞬态放大器。对于这些网络，我们进行了频谱分析，并表明可以构建瞬态放大器的图具有某些结构特性。识别光谱和结构特性可以促进发现和设计这样的网络。我们测试所有成对非同构正则图达到某个顺序，从而覆盖这些图可表达的整个结构范围。对于三次和四次正则图，我们发现了足够多的瞬态放大器。对于这些网络，我们进行了频谱分析，并表明可以构建瞬态放大器的图具有某些结构特性。识别光谱和结构特性可以促进发现和设计这样的网络。我们测试所有成对非同构正则图达到某个顺序，从而覆盖这些图可表达的整个结构范围。对于三次和四次正则图，我们发现了足够多的瞬态放大器。对于这些网络，我们进行了频谱分析，并表明可以构建瞬态放大器的图具有某些结构特性。识别光谱和结构特性可以促进发现和设计这样的网络。