Effective potential reveals evolutionary trajectories in complex fitness landscapes

TL;DR

This paper introduces an effective potential framework based on quasispecies theory to predict evolutionary trajectories in complex fitness landscapes, accounting for different mutation regimes and landscape topographies.

Contribution

It generalizes quasispecies theory to identify metastable states as minima of an effective potential, enabling predictive modeling of evolution across mutation rates.

Findings

Effective potential captures metastable evolutionary states.

Markov model predicts evolution paths under various mutation rates.

Framework links evolutionary dynamics with quantum many-body theory.

Abstract

Growing efforts to measure fitness landscapes in molecular and microbial systems are premised on a tight relationship between landscape topography and evolutionary trajectories. This relationship, however, is far from being straightforward: depending on their mutation rate, Darwinian populations can climb the closest fitness peak (survival of the fittest), settle in lower regions with higher mutational robustness (survival of the flattest), or fail to adapt altogether (error catastrophes). These bifurcations highlight that evolution does not necessarily drive populations "from lower peak to higher peak", as Wright imagined. The problem therefore remains: how exactly does a complex landscape topography constrain evolution, and can we predict where it will go next? Here I introduce a generalization of quasispecies theory which identifies metastable evolutionary states as minima of an effective potential. From this representation I derive a coarse-grained, Markov state model of evolution, which in turn forms a basis for evolutionary predictions across a wide range of mutation rates. Because the effective potential is related to the ground state of a quantum Hamiltonian, my approach could stimulate fruitful interactions between evolutionary dynamics and quantum many-body theory