Fisher's geometrical model and the mutational patterns of antibiotic resistance across dose gradients

Abstract

Fisher's geometrical model (FGM) has been widely used to depict the fitness effects of mutations. It is a general model with few underlying assumptions that gives a large and comprehensive view of adaptive processes. It is thus attractive in several situations, for example adaptation to antibiotics, but comes with limitations, so that more mechanistic approaches are often preferred to interpret experimental data. It might be possible however to extend FGM assumptions to better account for mutational data. This is theoretically challenging in the context of antibiotic resistance because resistance mutations are assumed to be rare. In this article, we show with Escherichia coli how the fitness effects of resistance mutations screened at different doses of nalidixic acid vary across a dose-gradient. We found experimental patterns qualitatively consistent with the basic FGM (rate of resistance across doses, gamma distributed costs) but also unexpected patterns such as a decreasing mean cost of resistance with increasing screen dose. We show how different extensions involving mutational modules and variations in trait covariance across environments, can be discriminated based on these data. Overall, simple extensions of the FGM accounted well for complex mutational effects of resistance mutations across antibiotic doses.

Surfing on the seascape: Adaptation in a changing environment

“…In the recent years, Fisher's geometric model (FGM) has been a popular choice for investigating adaptation in changing environments (Matuszewski et al 2014;Martin and Lenormand 2015;Harmand et al 2017). Our model assumes that we have k independent traits.…”

What doesn’t kill us makes us stronger: can Fisher’s Geometric model predict antibiotic resistance evolution?

“…The results obtained in Harmand et al [4] indicate a potential shortcoming of studying these small fitness landscapes: rather than having a constrained evolutionary path to a resistant phenotype, as previously observed, their results suggest that antibiotic resistance can be the product of mutations in different regions of the genome. Returning to the fitness landscape perspective, this indicates that there are many alternative paths that can lead to the evolution of antibiotic resistance.…”

“…Harmand et al [4] incorporated three extensions to the FGM, which allowed them to match the mutational patterns of antibiotic resistance that they obtained from a screen across a gradient of drug concentrations. The implemented extensions took into account that: 1) only a subset of mutations may contribute to traits under selection, reflecting that not all regions in the genome affect the ability to resist antibiotics; 2) mutations that confer a fitness increase in one environment may not reflect a similar increase in others, if the selective constraints are different; and 3) different antibiotic concentrations may either constrain the maximum fitness that populations can reach (changing the height of the fitness peak) or change the rate of fitness increase with each mutation (changing the width/slope of the peak).…”

“…This comparison points at a difficult challenge when aiming at developing a predictive framework for evolution: real-time experiments may indicate that evolution is likely to take similar and predictable paths because the strongest and most frequent mutations dictate the outcome, whereas systematic screens of mutants potentially indicate several paths, that may, however, not be relevant in nature. Only a combination of different experimental approaches with motivated theory as presented in Harmand et al [4] will allow for a better understanding of where in this continuum evolution is taking place in nature, and to which degree we are able to interfere with it in order to slow down adaptation.…”

Nonlinear frequency‐dependent selection promotes long‐term coexistence between bacteria species

“…; Harmand et al . , ) and one C. freundii strain ( C ) at very low starting frequency resulting from contamination of E glycerol stocks. Hence, E is well adapted to the experimental conditions in the absence of C whereas these conditions are new for C .…”