How to detect and visualize extinction thresholds for structured PVA models

An extinction threshold is a population size below which extinction risk increases to beyond critical values. However, detecting extinction thresholds for structured population models is not straightforward because many different population structures may correspond to the same population size. Moreover, the precise structure of real populations usually is not known. We therefore introduce a simple but effective protocol that allows the detection and visualization of extinction thresholds for models of structured populations without having to refer to population structure. The basic idea of this protocol is to record extinction risk “on the fly”: every time a certain population size occurs during simulation, the remaining time to extinction is stored in a frequency distribution. Thus, the simulation model, not the modeller, generates the typical range of population structures linked to a certain population size. We apply the protocol to two examples to demonstrate the specific and general insights that can be gained. We argue that the protocol might also be useful for overcoming PVA's undue concentration on individual extinction risks.