Catastrophes and the increased risk of population extinction

Natural populations are vulnerable to extinction, and determining the probability of extinction for a wide range of scenarios is a key theme in population biology. One such scenario is a catastrophic event, i.e. a temporary but marked decrease in the population's time-dependent reproduction rate. Using the (Verhulst) logistic model, Assaf et al. (2009) have recently determined the increase in population extinction risk resulting from such an event.

I will present their results as a pedagogical example of how to calculate first-passage properties from an exact Master equation, using a time-dependent eikonal approximation and carrying out an optimal path (instanton) calculation. This formalism produces asymptotically correct results where van Kampen's system size expansion fails.