Cost of antibiotic resistance and the geometry of adaptation

The distribution of effects of beneficial mutations is key to our understanding of biological adaptation. Yet, empirical estimates of this distribution are scarce, and its functional form is largely unknown. Theoretical models of adaptation predict that the functional form of this distribution should depend on the distance to the optimum. Here, we estimate the rate and distribution of adaptive mutations that compensate for the effect of a single deleterious mutation, which causes antibiotic resistance. Using a system with multiple molecular markers, we estimate the distribution of fitness effects of mutations at two distances from the adaptive peak in 60 populations of Escherichia coli. We find that beneficial mutations, which can contribute to compensatory evolution, occur at very high rates, of the order of 10(-5) per genome per generation and can be detected within a few tens of generations. They cause an average fitness increase of 2.5% and 3.6%, depending on the cost of resistance, which is expected under Fisher's geometrical model of adaptation. Moreover, we provide the first description of the distribution of beneficial mutations, segregating during the process of compensatory evolution, to antibiotic resistances bearing different costs. Hence, these results have important implications to understanding the spread and maintenance of antibiotic resistance in bacteria.