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].
