The interacting effects of parameters uncertainty and demographic stochasticity on the establishment success of introduced species, and our ability to predict them
Invasive species are an important component of global change and a serious threat to biodiversity. Predicting the probability that an introduced species establishes and becomes invasive is therefore of considerable importance. Knowledge of the typical strength of competition between resident and introduced species is one of the ingredients needed to predict the establishment of an introduced species. Many other factors affect the outcome of an introduction, including environmental and demographic stochasticity, Allee effects and spatial effects. Demographic stochasticity is potentially quite important, since introduced species are typically at low abundance. We focus on the competitive interaction between residents and potential invader using a stochastic version of the classic competitive Lotka-Volterra (LV) equations. We assess the effect of demographic stochasticity on inferring the strength of competition and on our ability to predict the probability of an introduced species to establish. Our method is based on a diffusion approximation for the mean and the variance of the population size of the invader and on a linearization of the interaction term of the LV model. Using these approximations we provide a modified single species model describing the dynamics of the introduced species and its interaction with the resident species.
We present a novel method to infer competition parameters during the first stages of an introduction, while the invading species is at low abundance. We show how having a prior knowledge of the single species demographic parameters can improve the precision of the estimates of the competition parameters of at least one order of magnitude. Finally we assess how our ability of predicting the establishment of an introduced species depends on demographic stochasticity. Our results provide a first step in disentangling the combined effects of demographic stochasticity and parameter uncertainty in our ability to predict establishment success.