Modelling species invasion using a metapopulation model with variable mortality and stochastic birth-death processes

A species entering a novel landscape must overcome several obstacles that inhibit invasion, which often leads invaders to go extinct while populations are still small and made up of relatively young individuals. Here, we investigate a theoretical model of invader population dynamics to explore the effects of demographic structure on invader success. To do so, we extended the classic Levins metapopulation model by allowing mortality to vary across individual life stages, such that smaller individuals have a higher chance of dying. We also allow size to vary across individuals, using an application of the Gillespie algorithm. Thus, unlike in the classic Levins model, for which successful invasions occur deterministically whenever colonisation exceeds the background mortality rate, invasion success in our model depends on the distribution of sizes found across individuals in the population. Nevertheless, the resulting likelihood of successful invasion can be estimated as a function of just two parameters – the colonisation rate, and a derived index representing the time-averaged mortality rate. This time-averaged mortality can be expressed analytically as a function of individual-level growth rates, the initial size of individuals, and of the impact of disturbances. While demographic stochasticity also contributes to some invasion failures in our model, we find that these effects are rare except when landscapes and initial fraction of occupied sites are both small. Our results demonstrate that invasion success in a complex stochastic model with explicit demographic structure can be predicted using a relatively simple, analytically tractable function. Applications of these results may therefore be particularly useful for studying general patterns of invasion success among sessile organisms with size dependant mortality, such as terrestrial plants.