The dynamics of evolution is intimately shaped by epistasis - interactions between genetic elements which cause the fitness-effect of combinations of mutations to be non-additive. Analyzing evolutionary dynamics that involves large numbers of epistatic mutations is intrinsically difficult. A crucial feature is that the fitness landscape in the vicinity of the current genome depends on the evolutionary history. A key step is thus developing models that enable study of the effects of past evolution on future evolution. In this work, we introduce a broad class of high-dimensional random fitness landscapes for which the correlations between fitnesses of genomes are a general function of genetic distance. Their Gaussian character allows for tractable computational as well as analytic understanding. We study the properties of these landscapes focusing on the simplest evolutionary process: random adaptive (uphill) walks. Conventional measures of "ruggedness" are shown to not much affect such adaptive walks. Instead, the long-distance statistics of epistasis cause all properties to be highly conditional on past evolution, determining the statistics of the local landscape (the distribution of fitness-effects of available mutations and combinations of these), as well as the global geometry of evolutionary trajectories. In order to further explore the effects of conditioning on past evolution, we model the effects of slowly changing environments. At long times, such fitness "seascapes" cause a statistical steady state with highly intermittent evolutionary dynamics: populations undergo bursts of rapid adaptation, interspersed with periods in which adaptive mutations are rare and the population waits for more new directions to be opened up by changes in the environment. Finally, we discuss prospects for studying more complex evolutionary dynamics and on broader classes of high-dimensional landscapes and seascapes.

中文翻译：

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自适应走在具有距离相关统计信息的高维健身景观和海景上。

进化的动力是由上位性决定的，上位性是遗传因素之间的相互作用，这些相互作用导致突变组合的适应性效应是非加性的。分析涉及大量上位突变的进化动力学本质上是困难的。一个关键特征是当前基因组附近的适应状况取决于进化史。因此，关键的一步是开发模型，以研究过去的演变对未来的演变的影响。在这项工作中，我们介绍了一大类高维随机适应度景观，其基因组适应度之间的相关性是遗传距离的一般函数。它们的高斯性质允许对计算和分析的理解很容易。我们重点研究最简单的进化过程：随机自适应（上坡）步行，研究这些景观的特性。常规的“坚固性”措施显示出对这种适应性步行没有太大影响。取而代之的是，上位性的远距离统计导致所有属性在很大程度上取决于过去的演化，从而确定了局部景观的统计信息（可用突变的适应性效应及其组合的分布），以及进化轨迹。为了进一步探讨条件对过去进化的影响，我们对缓慢变化的环境的影响进行了建模。长期以来，这种适合度的“海景”会导致统计状态处于稳定状态，并具有高度间歇性的演化动态：种群经历了快速适应的爆发，散布着很少有适应性突变的时期，而种群等待着环境变化带来更多新的方向。最后，我们讨论了研究更复杂的进化动力学以及在更大范围的高维景观和海洋景观方面的前景。