  Extinction of a long-lived isolated stochastic population can be described as
an exponentially slow decay of quasi-stationary probability distribution of the
population size. We address extinction of a population in a two-population
system in the case when the population turnover -- renewal and removal -- is
much slower than all other processes. In this case there is a time scale
separation in the system which enables one to introduce a short-time
quasi-stationary extinction rate W_1 and a long-time quasi-stationary
extinction rate W_2, and develop a time-dependent theory of the transition
between the two rates. It is shown that W_1 and W_2 coincide with the
extinction rates when the population turnover is absent, and present but very
slow, respectively. The exponentially large disparity between the two rates
reflects fragility of the extinction rate in the population dynamics without
turnover.
