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 \textit{e.g.} RNA viruses \cite{Sanjuan:2010gs} and likely were in early life, evolutionary success requires more than the discovery of a high-fitness mutant genotype: mutants of the new mutant must also have relatively high fitness, \textit{i.e.} the mutant type must be mutationally \textit{robust}. The effective potential $U$ introduced in this paper combines fitness and flatness into a single number---should it be called  ``flitness"?---which directly determines evolutionary trajectories, precisely in the same way potential energy determines the motion of an overdamped Brownian particle.

Within its domain of applicability, the effective potential $U$ addresses two longstanding questions in evolution, namely $(i)$ On what time scale (individual generation, infinite lineage) should ``fitness" be defined \cite{Rosenberg:2015kd}? and $(ii)$ What quantity does evolution optimize \cite{Smith:1978er}? The answers are, respectively: $(i)$ It is fine to define the fitness $\phi(g)$ of a type $g$ as reproductive success over one generation, which makes it directly measurable, but one should keep in mind that $\phi(g)$ is not necessarily a good predictor for the success of a lineage descending from $g$---this role is played by the derived quantity $U(g)$; and $(ii)$ like other dissipative processes, evolution through selection and mutations minimizes the (Kullback-Leibler) divergence to its Markovian equilibrium. For these reasons, 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.

To implement this approach in practice requires that we are able to compute $U$ from fitness data. For larger genotype spaces, this is a hard computational challenge that cannot be resolved through exact diagonalization of the selection-mutation operator. Instead, approximation methods must be developed, following the example set by quantum many-body theory (Appendix \ref{FWA}). In this context, the problem of computing the ground state of a quantum spin chain---the physics analogue of computing $Q$ for a given fitness landscape \cite{Baake:1997cl}---has been a focus for many years. It is therefore likely that some of the recent analytical progress in this field can be leveraged to advance quantitative evolutionary theory.  

I thank A. Klimek and M. Kenmoe for useful discussions and O. Rivoire for critical comments on an early version of this manuscript. Funding for this work has been 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.