Department of Mathematics, Harvard University, Cambridge, MA, 02138, USA.
Department of Computer Science, Aarhus University, Aabogade 34, 8200, Aarhus, Denmark.
Nat Commun. 2021 Jun 29;12(1):4009. doi: 10.1038/s41467-021-24271-w.
Selection and random drift determine the probability that novel mutations fixate in a population. Population structure is known to affect the dynamics of the evolutionary process. Amplifiers of selection are population structures that increase the fixation probability of beneficial mutants compared to well-mixed populations. Over the past 15 years, extensive research has produced remarkable structures called strong amplifiers which guarantee that every beneficial mutation fixates with high probability. But strong amplification has come at the cost of considerably delaying the fixation event, which can slow down the overall rate of evolution. However, the precise relationship between fixation probability and time has remained elusive. Here we characterize the slowdown effect of strong amplification. First, we prove that all strong amplifiers must delay the fixation event at least to some extent. Second, we construct strong amplifiers that delay the fixation event only marginally as compared to the well-mixed populations. Our results thus establish a tight relationship between fixation probability and time: Strong amplification always comes at a cost of a slowdown, but more than a marginal slowdown is not needed.
选择和随机漂变决定了新突变在种群中固定的概率。已知种群结构会影响进化过程的动态。选择的放大器是指与混合良好的种群相比，增加有益突变体固定概率的种群结构。在过去的 15 年中，广泛的研究产生了显著的结构，称为强放大器，保证每个有益突变都以高概率固定。但是，强放大是以极大地延迟固定事件为代价的，这可能会降低整体进化速度。然而，固定概率和时间之间的确切关系仍然难以捉摸。在这里，我们描述了强放大的减速效应。首先，我们证明所有强放大器都必须在某种程度上延迟固定事件。其次，我们构建了与混合良好的种群相比，仅略微延迟固定事件的强放大器。因此，我们的结果在固定概率和时间之间建立了紧密的关系：强放大总是以减速为代价，但不需要超过边际减速。
