Two species competition with a "non-smooth" Allee mechanism: applications to soybean aphid population dynamics under climate change.

The soybean aphid (Aphis glycines) is an invasive insect pest that continues to cause large-scale damage to soybean crops in the North Central United States. Recent empirical evidence points to differential fitness in the pestiferous aphid biotypes under abiotic stresses such as flooding. As climate change predicts increased flooding in the North Central United States, mathematical models that incorporate such factors are required to better inform pest management strategies. Motivated by these empirical results, we considered the effect of non-smooth Allee type mechanisms, for the two species Lotka-Volterra competition model. We showed that this mechanism can alter classical competitive dynamics in both the ordinary differential equation (ODE) as well as the spatially explicit setting. In particular, an Allee effect present in the weaker competitor could lead to bi-stability dynamics, as well as competitive exclusion reversal. We discuss applications of our results to pest management strategies for soybean aphids in the context of a changing climate.