Exact Results for the Evolution of Stochastic Switching in Variable Asymmetric Environments

TY - JOUR

T1 - Exact Results for the Evolution of Stochastic Switching in Variable Asymmetric Environments

AU - Gaál, Bernadett

AU - Pitchford, Jonathan W.

AU - Wood, A. Jamie

PY - 2010/4

Y1 - 2010/4

N2 - The ability of bacteria to spontaneously switch their expressed phenotype from an identical underlying genotype is now widely acknowledged. Mechanisms behind these switches have been shown to be evolvable. Important questions thus arise: In a fluctuating environment, under what conditions can stochastic switching evolve and how is the evolutionarily optimal switching rate related to the environmental changes? Here we derive exact analytical results for the long-term exponential population growth rate in a two-state periodically changing environment, where the environmental states vary in both their duration and in their impact on the fitness of each phenotype. Using methods from statistical physics we derive conditions under which nonswitching is evolutionarily optimal, and we furthermore demonstrate that the transition between the nonswitching and switching regimes is discontinuous (a first-order phase transition). Our general analytical method allows the evolutionary effects of asymmetries in selection pressures and environmental growth rates to be quantified. The evolutionary implications of our findings are discussed in relation to their to real-world applications in the light of recent experimental evidence.

AB - The ability of bacteria to spontaneously switch their expressed phenotype from an identical underlying genotype is now widely acknowledged. Mechanisms behind these switches have been shown to be evolvable. Important questions thus arise: In a fluctuating environment, under what conditions can stochastic switching evolve and how is the evolutionarily optimal switching rate related to the environmental changes? Here we derive exact analytical results for the long-term exponential population growth rate in a two-state periodically changing environment, where the environmental states vary in both their duration and in their impact on the fitness of each phenotype. Using methods from statistical physics we derive conditions under which nonswitching is evolutionarily optimal, and we furthermore demonstrate that the transition between the nonswitching and switching regimes is discontinuous (a first-order phase transition). Our general analytical method allows the evolutionary effects of asymmetries in selection pressures and environmental growth rates to be quantified. The evolutionary implications of our findings are discussed in relation to their to real-world applications in the light of recent experimental evidence.

KW - GENE-EXPRESSION

KW - FLUCTUATING ENVIRONMENTS

KW - SURVIVAL

KW - BACTERIA

KW - NOISE

KW - INHERITANCE

KW - TOLERANCE

KW - DIVERSITY

KW - CELLS

UR - http://www.scopus.com/inward/record.url?scp=77955916902&partnerID=8YFLogxK

U2 - 10.1534/genetics.109.113431

DO - 10.1534/genetics.109.113431

M3 - Article

SN - 0016-6731

VL - 184

SP - 1113

EP - 1119

JO - Genetics

JF - Genetics

IS - 4

ER -