  Understanding the coexistence of diverse species in a changing environment is
an important problem in community ecology. Bet-hedging is a strategy that helps
species survive in such changing environments. However, studies of bet-hedging
have often focused on the expected long-term growth rate of the species by
itself, neglecting competition with other coexisting species. Here we study the
extinction risk of a bet-hedging species in competition with others. We show
that there are three contributions to the extinction risk. The first is the
usual demographic fluctuation due to stochastic reproduction and selection
processes in finite populations. The second, due to the fluctuation of
population growth rate caused by environmental changes, may counterintuitively
reduce the extinction risk for small populations. Besides those two, we reveal
a third contribution, which is unique to bet-hedging species that diversify
into multiple phenotypes: The phenotype composition of the population will
fluctuate over time, resulting in increased extinction risk. We compare such
compositional fluctuation to the demographic and environmental contributions,
showing how they have different effects on the extinction risk depending on the
population size, generation overlap, and environmental correlation.
