  Many biological populations, such as bacterial colonies, have developed
through evolution a protection mechanism, called bet-hedging, to increase their
probability of survival under stressful environmental fluctutation. In this
context, the concept of preadaptation refers to a common type of bet-hedging
protection strategy in which a relatively small number of individuals in a
population stochastically switch their phenotypes to a `dormant' metabolic
state in which they increase their probability of survival against potential
environmental shocks. Hence, if an environmental shock took place at some point
in time, preadapted organisms would be better adapted to survive and
proliferate once the shock is over. In many biological populations, the
mechanisms of preadaptation and proliferation present delays whose influence in
the fitness of the population are not well-understood. In this paper, we
propose a rigorous mathematical framework to analyze the role of delays in both
preadaptation and proliferation mechanisms in the survival of biological
populations, with an emphasis on bacterial colonies. Our theoretical framework
allows us to analytically quantify the average growth rate of a bet-hedging
bacterial colony with stochastically delayed reactions with arbitrary
precision. We verify the accuracy of the proposed method by numerical
simulations and conclude that the growth rate of a bet-hedging population shows
a non-trivial dependency on their preadaptation and proliferation delays.
Contrary to the current belief, our results show that faster reactions do not,
in general, increase the overall fitness of a biological population.
