Fluctuation Domains in Adaptive Evolution

TL;DR

This paper introduces the concept of fluctuation domains in adaptive evolution, linking the predictability of evolutionary paths to the curvature of the fitness landscape, with implications for understanding evolutionary dynamics.

Contribution

It derives a new expression for phenotypic variation in evolution, connecting fluctuation behavior to landscape curvature, and explores ecological scenarios of competition.

Findings

Fluctuation domains are determined by the curvature of the fitness landscape.

Positive curvature regions show fluctuation enhancement, negative curvature regions show dissipation.

The framework applies to ecological scenarios involving resource competition.

Abstract

We derive an expression for the variation between parallel trajectories in phenotypic evolution, extending the well known result that predicts the mean evolutionary path in adaptive dynamics or quantitative genetics. We show how this expression gives rise to the notion of fluctuation domains - parts of the fitness landscape where the rate of evolution is very predictable (due to fluctuation dissipation) and parts where it is highly variable (due to fluctuation enhancement). These fluctuation domains are determined by the curvature of the fitness landscape. Regions of the fitness landscape with positive curvature, such as adaptive valleys or branching points, experience enhancement. Regions with negative curvature, such as adaptive peaks, experience dissipation. We explore these dynamics in the ecological scenarios of implicit and explicit competition for a limiting resource.