A simple mutational model that produces diminishing returns epistasis and decelerating fitness trajectories in adaptive walks

Paul Joyce (September 14, 2011)

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In relating genotypes to fitness, models of adaptation need to be both computation- ally tractable and to qualitatively match observed data. One reason tractability is not a trivial problem comes from a combinatoric problem whereby no matter in what order a set of mutations occurs, it must yield the same fitness. We refer to this problem as the bookkeeping problem. Because of their commutative property, the simple additive and multiplicative models naturally solve the bookkeeping problem. However, the fitness trajectories and epistatic patterns they predict are inconsistent with the patterns commonly observed in experimental evolution. This motivates us to propose a new and equally simple model that we call stickbreaking. Under the stickbreaking model, the intrinsic fittness effects of mutations scale by the distance of the current background to a hypothesized boundary. We use simulations and theoretical analyses to explore the basic properties of the stickbreaking model such as the distribution of fitness effects, fitness trajectories, and epistasis. Stickbreaking is compared to the additive and multiplicative models using a number of novel likelihood based approaches to account for error in the predictions. We apply or statistical methodology to a number recently published data sets and conclude the stickbreaking model is consistent with several commonly observed patterns of adaptive evolution.