Fitness value of information with delayed phenotype switching: Optimal performance with imperfect sensing

The ability of organisms to accurately sense their environment and respond accordingly is critical for evolutionary success. However, exactly how the sensory ability influences fitness is a topic of active research, while the necessity of a time delay between when unreliable environmental cues are sensed and when organisms can mount a response has yet to be explored at any length. Accounting for this delay in phenotype response in models of population growth, we find that a critical error probability can exist under certain environmental conditions: An organism with a sensory system with any error probability less than the critical value can achieve the same long-term growth rate as an organism with a perfect sensing system. We also observe a tradeoff between the evolutionary value of sensory information and robustness to error, mediated by the rate at which the phenotype distribution relaxes to steady state. The existence of the critical error probability could have several important evolutionary consequences, primarily that sensory systems operating at the nonzero critical error probability may be evolutionarily optimal.