Fitness in time-dependent environments includes a geometric contribution

TL;DR

This paper reveals that in time-dependent environments, the relative fitness of mutants includes a geometric term related to the environment trajectory, impacting phenotypic evolution and fixation speed.

Contribution

It introduces a geometric component to fitness in dynamic environments, linking evolutionary dynamics to geometric phases known from physics.

Findings

Fitness in changing environments has a geometric contribution.

The geometric term depends on the trajectory in environment space.

Implications for evolution of stress-resistant functions.

Abstract

Phenotypic evolution implies sequential fixations of new genomic sequences. The speed at which these mutations fixate depends, in part, on the relative fitness (selection coefficient) of the mutant vs. the ancestor. Using a simple population dynamics model we show that the relative fitness in dynamical environments is not equal to the fitness averaged over individual environments. Instead it includes a term that explicitly depends on the sequence of the environments. This term is geometric in nature and depends only on the oriented area enclosed by the trajectory taken by the system in the environment state space. It is related to the well-studied geometric phases in classical and quantum physical systems. We discuss possible biological implications of these observations, focusing on evolution of novel metabolic or stress-resistant functions.