Adaptation to the cost of resistance in a haploid clonally reproducing organism: The role of mutation, migration and selection

A model of compensatory evolution with respect to fungicide resistance in a haploid clonally reproducing fungus is developed in which compensatory mutations mitigate fitness costs associated with resistance. The role of mutation, migration and selection in invasion of rare genotypes when the environment changes from unsprayed to sprayed and from sprayed to unsprayed is analysed in detail. In some circumstances (ignoring back mutations) stable internal steady-state values for multiple genotypes can be obtained. In these cases a threshold value (f*) for the fraction of the population exposed to the fungicide can be derived for the transition between different steady-state conditions. Conditions are derived for invasion-when-rare of resistant genotypes at boundary equilibria established sometime after the onset of spraying and conversely of sensitive genotypes sometime after the cessation of spraying are derived. In these cases conditions are presented for (a) the invasion of a resistant genotype with a compensatory mutation (resistant-compensated) into a sensitive-uncompensated population that has re-equilibrated following the onset of spraying and (b) the invasion of a susceptible-uncompensated genotype into a resistant-compensated population that has re-equilibrated following the cessation of spraying, provided certain conditions are met. A resistant-compensated genotype may be fixed (or at near-fixation) in the population following a period of spraying, provided the mean intrinsic growth rate of the resistant-compensated genotype in a sprayed environment (over exposed and non-exposed parts of the population) is greater than that of the susceptible-uncompensated genotype. The fraction of the population exposed (the efficiency of spraying) is critical in this respect. However, it is possible for a sensitive-uncompensated genotype to invade provided there is no fitness gain associated with the resistant-compensated genotype, introduction by migration occurs following equilibration of the population to the new environment, and competitive effects are re-imposed when spraying ceases. We further derive a threshold level for the resident resistant-compensated population to reduce to following the cessation of spraying, such that the introduced susceptible-uncompensated genotype will invade. These results will be of use in determining the long-term persistence of resistance in a pathogen population once a fungicide is no longer effective and removed from use.