Studying the role of phenotypic change in biological invasion success through mathematical modeling

When an exotic species is introduced outside its natural range, new interspecific interactions with native species may arise. These interactions can induce phenotypic changes, which may originate from phenotypic plasticity or adaptive processes. Phenotypic change may play an important role in biological invasions, either by promoting or by preventing its success. In this work, a mathematical modeling approach is used to study a native predator-prey system exposed to an exotic species that predates on the native species and that also competes by interference with the native predator. This proposed approach allows to describe the eco-evolutionary dynamics involving the inducible defense of the prey and the inducible offense of both predators. The model is represented by a system of ordinary differential equations (ODEs), analyzed using advanced analytical and numerical methods. Specifically, we applied the qualitative theory of ODEs and developed numerical algorithms for parameter sweeps. Parameter values for the numerical experiments were based on the American mink, one of the most harmful invasive species in Europe and South America. The results show that the role of phenotypic change in invasion success depends on three components: the efficiency of the new trait values, the associated costs, and the speed of trait change. The specific conditions that lead to an unsuccessful invasion are: the prey's defense efficiency against the exotic predator is higher than its defense efficiency against the native predator. The cost imposed by the exotic predator is greater than the cost imposed by the native predator. Lastly, the speed of phenotypic change is faster in the native predator than in the exotic predator.