Time-resolved extinction rates of stochastic populations

TL;DR

This paper develops a time-dependent theory for extinction rates in stochastic populations with slow population turnover, revealing a transition between short-term and long-term extinction dynamics.

Contribution

It introduces a novel framework distinguishing short- and long-time quasi-stationary extinction rates in populations with slow turnover processes.

Findings

W_1 and W_2 match extinction rates without turnover and with slow turnover, respectively.

The disparity between W_1 and W_2 indicates fragility in population extinction dynamics.

The theory explains the transition between different extinction rate regimes over time.

Abstract

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.