Wave pinning in competition-diffusion models in variable environments

Disease-induced chaos, coexistence, oscillations, and invasion failure in a competition-model with strong Allee effect

Biological invasions have impacts on diverse social, ecological, and economic issues. Among others, invasion success can be determined by epidemiological aspects, intraspecific dynamics as, e.g., Allee effects, and interspecific interactions as, e.g., competition. In this study, a process-based model describing competitive eco-epidemiological dynamics of two species, which are both subject to an Allee effect, is developed. Only one of the species can be infected by an infectious disease which is transmitted both, horizontally and vertically. The local dynamics of the disease-free competition model, the competition-free SI-model, and the full eco-epidemiological model are considered. In particular, it is shown that an outbreak of a disease is more likely in the absence of a competitor. Thus, competition and species richness can increase disease resistance of particular species in a community. The complete partial differential equation model is investigated both, analytically and numerically in order to determine possible impacts of the disease on the invasion dynamics. It is shown that in case of strong competition, invasion fronts are always slowed down or even reversed due to the infection for parameter regimes in which the invader is the stronger competitor in the absence of the disease while in case of weak competitive pressure, the dynamics are more complex. Besides slowing down of the invasion front, disease-induced chaos, coexistence (i.e., coexistence in a regime in which coexistence without disease would not be possible), and oscillations can occur. Furthermore, spatial spread can temporarily prevent an infected population from going extinct with potentially detrimental impacts for the resident. This happens via a (replicating) traveling pulse which pushes the competitor out of the domain. The results are discussed in order to enhance the understanding of mechanisms underlying biological invasions and to develop better management strategies for biological invasions as, e.g., selective infections.