Hysteresis Can Grant Fitness in Stochastically Varying Environment

Abstract: Hysteresis and bet-hedging (random choice of phenotypes) are two different observations typically linked with multiplicity of phenotypes in biological systems. Hysteresis can be viewed as form of the system's persistent memory of past environmental conditions, while bet-hedging is a diversification strategy not necessarily associated with any memory. It has been shown that bet-hedging can increase population growth when phenotype adjusts its switching probability in response to environmental inputs. Although memory and hysteresis have been used to generate environment dependent phenotype switching probabilities, their exact connection to bet-hedging have remained unclear. In this work, using a simple model that takes into account phenotype switching as well as lag phase in the population growth occurring after the phenotype switching, it is shown that memory and hysteresis emerge naturally and are firmly linked to bet-hedging as organisms attempt to optimize their population growth rate. The optimal ``magnitude'' of hysteresis is explained to be associated with stochastic resonance where the characteristic time between subsequent phenotype switching events is linked to the lag phase delay. Furthermore, hysteretic switching strategy is shown not to confer any additional population growth advantage if the environment varies periodically in a deterministic fashion. This suggests that, while bet-hedging may evolve under some conditions even in deterministic environments, memory and hysteresis is probably the result of environmental uncertainty in the presence of lag phase in the switching of phenotypes.