Stochastic population dynamics and time to extinction of a declining population of barn swallows

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Abstract
Summary: Time to extinction was predicted for a declining population of barn swallowHirundo rusticain Denmark, using a model that includes demographic as well as environmental stochasticity and that takes the uncertainties in the parameter estimates into account. We apply the concept of population prediction interval (PPI), which is a stochastic interval that includes the unknown variable that may be the extinction time or the population size at some future point of time, with a given probability (1 − α). The lower bound of the upper one‐sided prediction interval for the extinction time for α = 0·10 was 22 years. Ignoring uncertainties in the parameter estimates led to a 41% increase in this statistic. Although the estimate of the demographic variance was small compared to other passerines (σd2 = 0·180), a sensitivity analysis showed that it strongly influenced the predicted time to extinction compared to the model ignoring demographic stochasticity. A similar effect on the prediction of the time to extinction was found for the environmental variance σe2. In addition, choosing σe2 = 0 strongly reduced the width of the prediction interval. This demonstrates that reliable population projections require modelling of the environmental as well as the demographic stochasticity, and that the uncertainty in the estimates of the model parameters must be taken into account.