Fig. 11.

Extinction probabilities, both analytic and simulated, for the choices of $\beta \left(t\right),\delta \left(t\right)$ and $\eta \left(t\right)$ described in the main text. The simulated extinction probabilities were calculated from 10,000 simulations of a birth-death chain both with and without immigration, for which the code can be obtained via the supplementary material.