Conclusion
A widely shared understanding of the role of mutations in evolution has them feeding raw material to the fitness-maximizing sieve of natural selection. But when mutation rates are high, as they are in e.g. RNA viruses \cite{Drake_1999} and likely were in early life \cite{Eigen_2007}, evolutionary success requires more than the discovery of a high-fitness mutant genotype: the mutants of the new mutant must also have relatively high fitness, i.e. the mutant type must be mutationally robust. The effective potential \(U\) introduced in this paper combines fitness and flatness into a single evolutionary potential—should we call it "flitness"?—which directly determines evolutionary trajectories across the spectrum of mutation rates. I argue that instead of the fitness landscape itself, it is this effective potential that we should analyze, coarse-grain, etc. if we are to predict evolution.
On a conceptual level, the effective potential \(U\) addresses two longstanding questions in evolution: (i) On what time scale (individual generation, infinite lineage) should "fitness" be defined \cite{bouchard2015}? and (ii) What quantity does evolution optimize \cite{Smith_1978}? My proposed answers are, respectively: (i) It is fine to define the fitness\(\ \phi\left(g\right)\) of a type \(g\) as reproductive success over one generation, which makes it directly measurable, but one should keep in mind that\(\ \phi\left(g\right)\) is not necessarily a good predictor for the success of a lineage descending from \(g\)—this role is played by the effective potential \(U\left(g\right)\); and (ii) like other dissipative processes, evolution through selection and mutations minimizes the statistical divergence to its Markovian equilibrium. There is an arrow of time in micro-evolution—just not one that points towards maximal fitness.
Acknowledgements
I am indebted to M. Kenmoe, A. Klimek, M. Lässig, O. Rivoire and D. Saakian for discussions and feedback. Funding for this work was provided by the Alexander von Humboldt Foundation in the framework of the Sofja Kovalevskaja Award endowed by the German Federal Ministry of Education and Research.