Effects of dispersal and stochasticity on the presence–absence of multiple species

• Deterministic model and IBM with dispersal are used to predict priority effects (PE).
• Moderate dispersal enhances PE and causes species range overlap to increase.
• Strong dispersal causes the reduction of PE and leads to species exclusion.
• PE are more prevalent in the IBM than the deterministic model for large populations.
• Fewer occurrences of PE are observed in the IBM with small populations.

A key problem in ecology is to predict the presence–absence of species across a geographical region. Dispersal is thought to have an important influence on the range limits of species, and understanding this problem in a multi-species community with priority effects (i.e. initial abundances determine the presence–absence of species) is a challenging task because dispersal interacts with biotic and abiotic factors as well as demographic stochasticity. By using stochastic individual-based models (IBM) and deterministic models consisting of biotic interactions and environmental gradients, we investigate the joint effects of dispersal and stochasticity on the occurrence of priority effects that can shape the presence–absence of multiple species. Our analysis shows the conditions under which priority effects occur and disappear as dispersal intensity changes. Without dispersal, priority effects emerge in the presence of intense biotic interactions; only one species surviving at any given location, with no overlap in their ranges. Inclusion of dispersal first reduces the prevalence of priority effects (i.e. for weak dispersal), and then leads to their increase (i.e. for moderate dispersal); consequently, dispersal enhances the possibility for species ranges to overlap. Increasing dispersal strength above a threshold value leads to the disappearance of priority effects and causes extinction of some species. We also demonstrate contrasting observations of stochasticity on priority effects: while this phenomenon is more prevalent in the stochastic IBM than in the deterministic models for large populations, we observe fewer occurrences of priority effects in IBM for small populations; in particular, our IBM results show that priority effects are eliminated by weaker values of dispersal when population sizes are small than when they are large. This situation can induce an uncertainty in the predictions of species presence–absence. Overall, our results demonstrate how the interplay of dispersal and stochasticity can combine to result in the (dis-)appearance of priority effects that strongly determine the presence–absence of species.