Dynamics of adaptation : role of extreme value domains, initial fitness and fitness correlations

Abstract

The adaptation dynamics of a population depends on the size and frequency of beneficial mutations, or in other words, the distribution of beneficial fitness effects (DBFE).Whether adaptation happens via many mutations conferring small fitness advantage, or a few producing large fitness changes depends on the nature of DBFE. Although initial theoretical works suggested that adaptation occurs mostly by mutations that provide small benefits [3], recent works suggest that large effect mutations are also possible [4]. The basic idea governing the shape of the DBFE is due to Gillespie [5], who suggested that the mutations conferring higher fitness than the wild type must lie in the right tail of the fitness distribution and so the statistical properties of such extreme fitnesses can be described by an extreme value theory (EVT) which states that the extreme value distribution of independent random variables can be of three types: Weibull which occurs when the fitnesses are right-truncated, Gumbel for distributions decaying faster than a power law and Fr´echet for distributions with algebraic tails [6]. because beneficial mutations are rare, accounting for less than 15% of the total mutations and occur at a rate between 10−9 to 10−8 per cell per generation [7–9], it is a challenging task to measure them experimentally. But, in recent times some success has been achieved and interestingly, all the three EVT distributions have been observed [10–13].