RT Journal Article SR Electronic T1 Exploiting evolutionary non-commutativity to prevent the emergence of bacterial antibiotic resistance JF bioRxiv FD Cold Spring Harbor Laboratory Press SP 007542 DO 10.1101/007542 A1 Daniel Nichol A1 Peter Jeavons A1 Alexander G Fletcher A1 Robert A Bonomo A1 Philip K Maini A1 Jerome L Paul A1 Robert A Gatenby A1 Alexander RA Anderson A1 Jacob G Scott YR 2014 UL http://biorxiv.org/content/early/2014/08/03/007542.abstract AB The increasing rate of antibiotic resistance and slowing discovery of novel antibiotic treatments presents a growing threat to public health. In the present study we develop a Markov Chain model of evolution in asexually reproducing populations which we use to illustrate that different selection pressures do not commute. We demonstrate that the emergence of resistant individuals can be both hindered and promoted by careful orderings of drug application. This suggests a new strategy in the war against antibiotic therapy resistant organisms: rational drug ordering to shepherd evolution through genotype space to states corresponding to greater sensitivity to antibiotic treatment. The model we present is an encoding of the `Strong Selection Weak Mutation' model of evolution on fitness landscapes within a Markov Chain, which associates the global properties of the fitness landscape with the algebraic properties of the Markov Chain transition matrix. Through this association we derive results on the non-commutativity and irreversibility of natural selection.