Figure 2.

Time-dependent probability of extinction. We show the analytical approximations based on equations (2.3)–(2.5) and simulations for N = 100 (circles with error bars given by the standard error of the binomial distribution) and for N = 10 000 (line). Time has been re-scaled to generations, one generation consists of N time steps. For the simulations, the population size has a marginal influence only for N > 100. While the approximation with three transitions, equation (2.4) is a significant improvement over the approximation with only one transition, equation (2.3), taking into account five transitions (equation (2.5)) does not improve the approximation much further. This indicates that for a better approximation for long times, many terms have to be taken into account (simulations averaged over 100 realizations). (Online version in colour.)