The dynamics of adaptation on correlated fitness landscapes

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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.