TY - JOUR T1 - Exploiting evolutionary non-commutativity to prevent the emergence of bacterial antibiotic resistance JF - bioRxiv DO - 10.1101/007542 SP - 007542 AU - Daniel Nichol AU - Peter Jeavons AU - Alexander G Fletcher AU - Robert A Bonomo AU - Philip K Maini AU - Jerome L Paul AU - Robert A Gatenby AU - Alexander RA Anderson AU - Jacob G Scott Y1 - 2014/01/01 UR - http://biorxiv.org/content/early/2014/08/03/007542.abstract N2 - 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. ER -