Computation of PPI
We compute the PPI following the simulation approach by Engen et al. (2001). We first estimate the parameters (see eqn 7). Secondly, the process with these parameters is simulated in such a way that it ends up with the same population size as the one recorded at the last year of observation. The same process is then simulated further until it first reaches extinction or a predefined upper time, tmax. From each simulation we estimate the population parameters as for the real data and perform parametric bootstrapping. We then simulate the process for each bootstrap replicate to extinction or tmax and check whether extinction occurs before the simulated ‘real’ extinction time, using the last parameter estimates, or have smaller population size at tmax if extinction is not reached. Writing Q for the proportion of simulations giving smaller values, the simulations would give prediction intervals with exact coverage if Q was distributed uniformly between 0 and 1. We perform this procedure a large number of times and fit a beta-distribution to the simulated Q-values and use this fitted distribution to obtain a prediction method with improved coverage. For further details, see Engen et al. (2001).