Immigration events dispersed in space and time: Factors affecting invasion success

Classical models of biological invasions generally assume that introductions consist of single releases of organisms, whereas in nature successful invasions are usually the result of repeated immigration events. A straightforward consequence of such repeated events is that they are likely to increase invasion success. In this article, we consider a less-obvious consequence, namely how repeated immigration events interact with the spatial dispersion of immigration. We construct a spatially explicit model that includes Allee effects and population diffusion, so that repeated introductions must be concentrated in order for the population to exceed the Allee threshold over a critical minimum area and successfully invade. We use this model to show that the spatial dispersion of immigration events is of key importance in determining invasion success. Specifically, invasion risks decline when immigration events are dispersed more widely. Because of this effect, immigration events that occur close to habitat boundaries are likely to lead to higher invasion risks, as dispersing organisms are forced back towards the source of immigrants. These results have important implications for efforts to reduce the risk of aquatic invasions due to discharges of ballast-water by commercial ships. When ballast discharge occurs either far from port, and thus far from habitat boundaries, or far from other ballast discharge events, and thus with wider dispersion, then invasion risks should be greatly reduced. Our work demonstrates the importance of spatial structure for understanding ecological problems, and shows how mathematical models can be useful in guiding environmental management.