Information and fitness in two-state systems: self-replicating individuals in a fluctuating environment

A population of individuals with the same genes can present heterogeneous traits (phenotypes). The prevalence of this heterogeneity can be explained as a bet-hedging strategy that improves the population proliferation rate (fitness) in fluctuating environments. The phenotype distribution is influenced by factors such as competition between phenotypes, the duration of environmental states, and the rate of phenotype-switching. We illustrate these effects in a system where both the environment and the phenotype can adopt two states. This system includes scenarios such as symmetric bet-hedging and dormant-proliferating phenotypes. We examine how environmental and phenotypic states share mutual information, measured in bits, and explore the relationship between this information and population fitness. We propose that when fitness is measured relative to the case where phenotype and environment are independent, information and fitness can be treated as equivalent measures. We investigate strategies that individuals can use to improve this information, such as adjusting the rates of proliferation and phenotype-switching relative to the environmental fluctuation rate. Through these strategies, with fixed marginal distributions, an increase in information implies an increase in population fitness. We also identify limits to the maximum achievable fitness and information and discuss the value of the information in terms of this new normalized fitness. Our framework offers new insights into how organisms adapt to fluctuating environmental conditions.