The dynamics of adaptation on correlated fitness landscapes

Abstract

Evolutionary theory predicts that a population in a new environment will accumulate adaptive substitutions, but precisely how they accumulate is poorly understood. The dynamics of adaptation depend on the underlying fitness landscape. Virtually nothing is known about fitness landscapes in nature, and few methods allow us to infer the landscape from empirical data. With a view toward this inference problem, we have developed a theory that, in the weak-mutation limit, predicts how a population's mean fitness and the number of accumulated substitutions are expected to increase over time, depending on the underlying fitness landscape. We find that fitness and substitution trajectories depend not on the full distribution of fitness effects of available mutations but rather on the expected fixation probability and the expected fitness increment of mutations. We introduce a scheme that classifies landscapes in terms of the qualitative evolutionary dynamics they produce. We show that linear substitution trajectories, long considered the hallmark of neutral evolution, can arise even when mutations are strongly selected. Our results provide a basis for understanding the dynamics of adaptation and for inferring properties of an organism's fitness landscape from temporal data. Applying these methods to data from a long-term experiment, we infer the sign and strength of epistasis among beneficial mutations in the Escherichia coli genome.epistasis | fitness trajectory | substitution trajectory | weak mutation | evolution E volutionary theory predicts that mean fitness will increase over time when a population encounters a new environment. This behavior is observed in natural and laboratory populations. Yet evolutionary theory offers few quantitative predictions for the dynamics of adaptation (1). The primary difficulty is that adaptation depends on the shape of the underlying fitness landscape. Unfortunately, mapping out an organism's fitness landscape is virtually impossible because of its vast dimensionality and the coarse resolution of fitness measurements. Moreover, because of the scarcity of such measurements, most theoretical work has been pursued in isolation from data.Much of the theory of adaptation is concerned with understanding the dynamics on uncorrelated, or "rugged", fitness landscapes. This approach, pioneered by Kingman (2) and Kauffman and Levin (3), has generated many important results (e.g. refs. (4-7)). But many of these results do not extend to landscapes that are correlated. One striking example is the expected length of an adaptive walk: It is extremely short on rugged landscapes (3, 8), but it can be very long on correlated landscapes (9). Although data are scarce, a long-term evolution experiment in Escherichia coli has found that adaptation continues to proceed even after 20,000 generations in a constant environment (10). This observation suggests that fitness landscapes in nature are correlated.A second body of work examines relatively realistic, complex genotype-to-fitness maps-e.g. an RNA folding...

Backbones of evolutionary history test biodiversity theory for microbes

“…One of the most successful characterizations of a fitness landscape is to assume a distribution of mutational effects. In this theoretical approach, mutations cause organisms to climb up or down a ladder of fitnesses (49)(50)(51), and the resulting models can result in many cooccurring types (52). It has recently been shown that this "clonal interference" regime generates bursts of branching on coarsegrained scales (53), with fitter lineages expanding quickly toward fixation before being overtaken by yet fitter lineages.…”

Genetic background affects epistatic interactions between two beneficial mutations

“…This trend can explain the general tendency for the rate of adaptation to decline in populations that are selected in constant environments [16]. However, that work considered genetic backgrounds that differed by only a few mutations and it is not clear if the same pattern will be seen between mutations in divergent backgrounds.…”

“…For example, several studies have examined specific examples of epistasis causing evolutionary contingency [12,13]. Other studies have demonstrated a trend for beneficial mutations to interact antagonistically, causing the rate of adaptation to slow as beneficial mutations accumulate [8,9,15], a relationship predicted by theory [16].…”

The dynamics of molecular evolution over 60,000 generations

“…These studies reveal complex dynamics, characterized by rapid adaptation, competition between beneficial mutations, diminishing-returns epistasis, and extensive genetic parallelism. These forces alter patterns of polymorphism 11 and influence which mutations ultimately fix 12–15 . However, it is unclear whether these dynamics are general or, instead, reflect the short timescales and novel environmental conditions of previous studies.…”