  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 trade off 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
non-zero critical error probability may be evolutionarily optimal.
