How to detect and visualize extinction thresholds for structured PVA models

An extinction thresholdis a population sizebelow which extinctionrisk increases to beyond critical values. However, detecting extinction thresholdsfor structured population modelsis not straightforward because many different populationstructures may correspond to the same population size. Moreover, the precise structure of real populationsusually is not known. We therefore introduce a simple but effective protocol that allows the detection and visualization of extinction thresholdsfor models of structured populationswithout having to refer to populationstructure. The basic idea of this protocol is to record extinctionrisk “on the fly”: every time a certain population sizeoccurs during simulation, the remaining time to extinctionis stored in a frequency distribution. Thus, the simulation model, not the modeller, generates the typical range of populationstructures 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 extinctionrisks.