Howbet-hedging species survive competition in fluctuating environments

Understanding the coexistence of species in a changing environment is an important problem in ecology. Bet-hedging is a strategy that helps species survive in such changing environments. However, studies of bet-hedging have often focused on unlimited growth of a single species, neglecting competition with other coexisting species. To account for competition, it is important to study the extinction risk of one species in the presence of others. We show that, when both environmental and demographic fluctuations are considered, there are three contributions to the extinction risk. The first is the usual demographic contribution 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. This is a manifestation of the "storage effect" studied in community ecology. The third contribution, unique to bet-hedging species that diversify into multiple phenotypes, comes as the phenotype composition fluctuates with time. We illustrate all three contributions and examine how they depend on environmental correlations and population sizes.