有向网络中固定概率的早期估计
Early appraisal of the fixation probability in directed networks
摘要：
在演化动力学中，一个突变在单个个体中发生并扩散到整个种群的概率被称为固定概率。一般来说，在给定突变体的适应度和控制突变传播的拓扑约束的情况下，不可能通过分析找到固定概率，因此人们求助于模拟。根据所使用的拓扑结构，在每个模拟事件中可能需要大量的进化步骤，特别是在那些以仅包含突变体的群体结束的模拟事件中。我们介绍了两种技术，以加快固定概率的测定。第一种方法跳过所有突变体数量不变的进化步骤，从而大大减少了每个模拟事件的步骤数量。这种技术在计算上对于一些所谓的分层网络是有利的。第二种技术不限于分层网络，它包括中止任何突变体数量增长超过某个阈值的模拟事件，并将该事件视为导致突变的总传播。对于大的人口，无论网络的拓扑结构，我们证明，无论是分析和模拟的手段，使用约100个突变体的阈值，导致固定概率的估计，偏离没有显着的方式从得到的全面的模拟。我们已经观察到两个数量级的10000个节点的分层网络的加速。
英文摘要：
In evolutionary dynamics, the probability that a mutation spreads through the whole population, having arisen in a single individual, is known as the fixation probability. In general, it is not possible to find the fixation probability analytically given the mutant's fitness and the topological constraints that govern the spread of the mutation, so one resorts to simulations instead. Depending on the topology in use, a great number of evolutionary steps may be needed in each of the simulation events, particularly in those that end with the population containing mutants only. We introduce two techniques to accelerate the determination of the fixation probability. The first one skips all evolutionary steps in which the number of mutants does not change and thereby reduces the number of steps per simulation event considerably. This technique is computationally advantageous for some of the so-called layered networks. The second technique, which is not restricted to layered networks, consists of aborting any simulation event in which the number of mutants has grown beyond a certain threshold value, and counting that event as having led to a total spread of the mutation. For large populations, and regardless of the network's topology, we demonstrate, both analytically and by means of simulations, that using a threshold of about 100 mutants leads to an estimate of the fixation probability that deviates in no significant way from that obtained from the full-fledged simulations. We have observed speedups of two orders of magnitude for layered networks with 10000 nodes.
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