Phenotypic diversity and population growth in fluctuating environment: a MBPRE approach

TL;DR

This paper models population growth in fluctuating environments using multitype branching processes, deriving optimal phenotypic strategies to maximize growth rate and analyzing genealogical lineages.

Contribution

It introduces a novel MBPRE framework for phenotypic adaptation, providing exact formulas for growth rate and characterizing optimal strategies in non-hereditary models.

Findings

Exact expression for net growth rate in non-hereditary strategies

Characterization of optimal phenotypic strategies

Analysis of typical genealogies in fluctuating environments

Abstract

Organisms adapt to fluctuating environments by regulating their dynamics, and by adjusting their phenotypes to environmental changes. We model population growth using multitype branching processes in random environments, where the offspring distribution of some organism having trait $t\in\cT$ in environment $e\in\cE$ is given by some (fixed) distribution $\Upsilon_{t,e}$ on $\bbN$. Then, the phenotypes are attributed using a distribution (strategy) $\pi_{t,e}$ on the trait space $\cT$. We look for the optimal strategy $\pi_{t,e}$, $t\in\cT$, $e\in\cE$ maximizing the net growth rate or Lyapounov exponent, and characterize the set of optimal strategies. This is considered for various models of interest in biology: hereditary versus non-hereditary strategies and strategies involving or not involving a sensing mechanism. Our main results are obtained in the setting of non-hereditary strategies: thanks to a reduction to simple branching processes in random environment, we derive an exact expression for the net growth rate and a characterisation of optimal strategies. We also focus on typical genealogies, that is, we consider the problem of finding the typical lineage of a randomly chosen organism.