Adaptive walks on high-dimensional fitness landscapes and seascapes with distance-dependent statistics

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 involving large numbers of epistatic mutations is difficult. A key step is 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. The Gaussian character allows for tractable computational and analytic understanding. We study the properties of these landscapes and the simplest evolutionary process, random adaptive (uphill) walks. We find that conventional measures of "ruggedness" do not much affect these. Instead, the long-distance statistics of epistasis cause properties to be highly conditioned 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. We also show that greedier walks tend to get stuck sooner at local fitness maxima. We then model the effects of slowly changing environments. These fitness "seascapes" cause a statistical steady state with highly intermittent evolutionary dynamics: populations undergo bursts of rapid adaptation, interspersed with periods where adaptive mutations are rare and the population must wait for new directions to be opened-up by changes in the environment. Finally, we introduce a computational framework for studying more complex evolutionary dynamics and on broader classes of high-dimensional landscapes and seascapes.