  Bet-hedging is a phenotype diversification strategy that combines a
fast-growing vulnerable phenotype with a slow-growing resistant phenotype. In
environments switching between favorable and unfavorable conditions,
bet-hedging optimizes growth and reduces fluctuations over a long time, which
is expected to reduce extinction risk. Here, we address directly how
bet-hedging can reduce extinction probability in an agent-based model. An
agent-based model is appropriate for studying extinction due to the low number
of individuals close to extinction. We also show that the agent-based model
converges to the collective model behavior for populations of $100$ individuals
or more. However, the collective model provides relevant qualitative insight
even for low populations. The collective model provides expressions for
extinction that stress the relevance of the population number, showing that a
factor four increase in the total population has a greater effect than a change
of strategy from maximum growth to minimal extinction. This work provides
further insight into the impact of finite population effects on the bet-hedging
strategy's success.
