A Mathematical Model Supporting a Hyperpredation Effect in the Apparent Competition Between Invasive Eastern Cottontail and Native European Hare

Exploring the effects of competition and predation on the success of biological invasion through mathematical modeling

Biological invasions are a major cause of species extinction and biodiversity loss. Exotic predators are the type of introduced species that have the greatest negative impact, causing the extinction of hundreds of native species. Despite this, they continue to be intentionally introduced by humans. Understanding the causes that determine the success of these invasions is a challenge within the field of invasion biology. Mathematical models play a crucial role in understanding and predicting the behavior of exotic species in different ecosystems. This study examines the effect of predation and competition on the invasion success of an exotic generalist predator in a native predator-prey system. Considering that the exotic predator both consumes the native prey and competes with the native predator, it is necessary to study the interplay between predation and competition, as one of these interspecific interactions may either counteract or contribute to the impact of the other on the success of a biological invasion. Through a mathematical model, represented by a system of ordinary differential equations, it is possible to describe four different scenarios upon the arrival of the exotic predator in a native predator-prey system. The conditions for each of these scenarios are described analytically and numerically. The numerical simulations are performed considering the American mink (Mustela vison), an invasive generalist predator. The results highlight the importance of considering the interplay between interspecific interactions for understanding biological invasion success.

Biological control for predation invasion based on pair approximation

Biological invasions have been paid more attention since invasive species may cause certain threats to local ecosystems. When biological control is adopted, selecting control species for effect better becomes the focus of latest studies. A food web system, with one native species, one invasive species as predator, and one introduced control species preying on both native and invasive species, is established based on pair approximation, in which the spatial landscape of biological invasion and control is concerned, and the local and global dispersal strategies of invasive species, in addition to the predation preferences of control species for native and invasive species, are considered. The influence of the initial density and initial spatial structures of the control species is investigated and the effects of control species releasing time are analyzed. Generally, the earlier the species introduction, the better the control effect, especially for invasive species dispersing globally. Interestingly, too low control species predation preference for native species can lead to unsuccessful introduction, while too much predation preference will have a weak control effect. The larger the control species predatory preference for invasive species is, the more conducive it is to biological control. The extinction of the invasive species is closely related to the initial density and concentration of the control species. This study gives some insights on selecting control species, its appropriate releasing time, and the density and spatial aggregation of it. Some real-life examples are elaborated on, which provides references for biological invasion control.