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Phenotypic heterogeneity in temporally fluctuating environments

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 both a discrete and continuous spectrum of phenotypes arising in response to two broad classes of environmental efluctuations that drive changes in the phenotype-dependent growth rates; specifically, stochastic environments that are temporally uncorrelated (specifically, white-noise processes) and correlated (specifically, Poisson and Ornstein-Uhlenbeck processes). For tractability, we restrict analysis to an exponential growth model, and consider biologically relevant simplifications that pertain to the relative timescale of phenotype switching. These assumptions yield a series of analytical and semi-analytical expressions that reveal environments in which both discrete and continuous phenotypic heterogeneity is evolutionary advantageous.

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