Phenotypic heterogeneity in temporally fluctuating environments

TL;DR

This paper develops a continuous model for phenotypic heterogeneity in fluctuating environments, analyzing how different environmental stochastic processes influence the evolution of diverse phenotypes and their growth advantages.

Contribution

It extends existing models to include a continuous spectrum of phenotypes and analyzes their evolution under correlated and uncorrelated environmental fluctuations.

Findings

Phenotypic heterogeneity can be evolutionarily advantageous in certain fluctuating environments.

Analytical expressions identify conditions favoring phenotypic diversity.

Correlated environmental fluctuations influence the optimal distribution of phenotypes.

Abstract

Many biological systems regulate phenotypic heterogeneity as a fitness-maximising strategy in uncertain and dynamic environments. Analysis of such strategies is typically confined both to a discrete set of environmental conditions, and to a discrete (often binary) set of phenotypes specialised to each condition. In this work, we extend theory on both fronts to encapsulate a potentially continuous spectrum of phenotypes arising in response to environmental fluctuations that drive changes in the phenotype-dependent growth rate. We consider two broad classes of stochastic environment: those that are temporally uncorrelated (modelled by white-noise processes), and those that are correlated (modelled by Poisson and Ornstein-Uhlenbeck processes). For tractability, we restrict analysis to an exponential growth model, and consider biologically relevant simplifications that pertain to the timescale of phenotype switching relative to fluctuations in the environment. These assumptions yield a series of analytical and semi-analytical expressions that reveal environments in which phenotypic heterogeneity is evolutionarily advantageous.