  Theoretical ecologists have long sought to understand how the persistence of
populations depends on biotic and abiotic factors. Classical work showed that
demographic stochasticity causes the mean time to extinction to increase
exponentially with population size, whereas variation in environmental
conditions can lead to a power law scaling. Recent work has focused especially
on the influence of the autocorrelation structure ("color") of environmental
noise. In theoretical physics, there is a burst of research activity in
analyzing large fluctuations in stochastic population dynamics. This research
provides powerful tools for determining extinction times and characterizing the
pathway to extinction. It yields, therefore, sharp insights into extinction
processes and has great potential for further applications in theoretical
biology.
