JOINT MATHEMATICS COLLOQUIUMUNIVERSITY OF IDAHOWASHINGTON STATE UNIVERSITY |
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Abstract |
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| In relating genotypes to fitness, models of
adaptation need to both be computationally tractable and qualitatively
match observed data. One reason that 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 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 fitness 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 fitness
trajectories, the distribution of fitness achieved, and epistasis.
Stickbreaking is compared to the additive and multiplicative models. We
conclude that the stickbreaking model is qualitatively consistent with
several commonly observed patterns of adaptive evolution. This is
joint work with Craig Miller and Holly Wichman.
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