Fitness effects of fixed beneficial mutations in microbial populations

Beneficial mutations are intuitively relevant to understanding adaptation [1-3], yet not all beneficial mutations are of consequence to the long-term evolutionary outcome of adaptation. Many beneficial mutations - mostly those of small effect - are lost due either to (1) genetic drift [4, 5] or to (2) competition among clones carrying different beneficial mutations, a phenomenon called the "Hill-Robertson effect" for sexual populations [6] and "clonal interference" for asexual populations [7]. Competition among clones becomes more prevalent with increasing genetic linkage and increasing population size, and it is thus generally characteristic of microbial populations [8, 9]. Together, these two phenomena suggest that only those beneficial mutations of large fitness effect should achieve fixation, despite the fact that most beneficial mutations produced are predicted to have very small fitness effects [10,11]. Here, we confirm this prediction - both empirically and theoretically - by showing that fitness effects of fixed beneficial mutations follow a distribution whose mode is positive