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The dynamical analysis of fitness landscapes
  • Matteo Smerlak
Matteo Smerlak
Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany
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Abstract

Growing efforts to measure fitness landscapes in molecular and microbial systems aim to enlighten, and eventually predict, evolutionary trajectories. As in other instances of non-equilibrium dynamics, this task is complicated by the lack of a general optimization principle: depending on their mutation rate, Darwinian populations can alternatively 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). Here I establish an equivalence between selection-mutation dynamics in infinite populations and a certain driven diffusion process in type space, from which I derive (i) a general prescription to identify metastable evolutionary states in a complex fitness landscape, as local minima of the effective potential, (ii) a predictive coarse-graining of evolutionary dynamics, based on their basins of attractions and saddles between them, and (iii) a natural evolutionary Lyapunov function. These results apply to any model of evolutionary dynamics, including Eigen’s “quasispecies” and Crow and Kimura’s “paramuse” models. Because the effective potential is computed from the ground state of a quantum Hamiltonian, my approach could stimulate fruitful interactions between evolutionary dynamics, non-equilibrium statistical mechanics and quantum many-body theory.