  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.
