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The soybean aphid, Aphis glycines (Hemiptera: Aphididae), is an invasive pest that can cause severe yield loss to soybeans in the North Central United States. A tactic to counter this pest is the use of aphid-resistant soybean varieties. However, the frequency of virulent biotypes that can survive on resistant varieties is expected to increase as more farmers use these varieties. Soybean aphids can alter soybean physiology primarily by two mechanisms, feeding facilitation, and the obviation of resistance, favoring subsequent colonization by additional conspecifics. We developed a nonlocal, differential equation population model to explore the dynamics of these biological mechanisms on soybean plants coinfested with virulent and avirulent aphids. We then use demographic parameters from laboratory experiments to perform numerical simulations via the model. We used this model to determine that initial conditions are an important factor in the season-long cooccurrence of both biotypes. The initial population of both biotypes above the resistance threshold or avirulent aphid close to resistance threshold and high virulent aphid population results in coexistence of the aphids throughout the season. These simulations successfully mimicked aphid dynamics observed in the field- and laboratory-based microcosms. The model showed an increase in colonization of virulent aphids increases the likelihood that aphid resistance is suppressed, subsequently increasing the survival of avirulent aphids. This interaction produced an indirect, positive interaction between the biotypes. These results suggest the potential for a ‘within plant’ refuge that could contribute to the sustainable use of aphid-resistant soybeans.

 

The Trojan Y Chromosome strategy (TYC) is a promising eradication method for biological control of nonnative species. The strategy works by manipulating the sex ratio of a population through the introduction ofsupermalesthat guarantee male offspring. In the current study, we compare the TYC method with a pure harvesting strategy. We also analyze a hybrid harvesting model that mirrors the TYC strategy. The dynamic analysis leads to results on stability of solutions and bifurcations of the model. Several conclusions about the different strategies are established via optimal control methods. In particular, the results affirm that either a pure harvesting or hybrid strategy may work better than the TYC method at controlling a nonnative species population.

Recommendations for resource managers

Where harvesting is feasible, it is as effective if not more effective than the classical TYC method. Therein managers may attempt harvesting female fish while stocking males or harvesting both male and female fishes.

Managers may attempt linear harvesting, saturating density‐dependent harvesting, and unbounded density‐dependent harvesting. Linear harvesting is seen to be the most effective.

We caution against the outright use of harvesting due to various density‐dependent effects that may arise. To this end hybrid models that involve a combination of harvesting and TYC‐type methods might be a better strategy.

One may also use harvesting as a tool in mesocosm settings to predict the efficacy of the TYC strategy in the wild.

 

Blue mussels (Mytilus edulis) are important keystone species that have been declining in the Gulf of Maine. This could be attributed to a variety of complex factors such as indirect effects due to invasion by epibionts, which remains unexplored mathematically. Based on classical optimal foraging theory (OFT) and anti-fouling defense mechanisms of mussels, we derive an ODE model for crab–mussel interactions in the presence of an invasive epibiont, Didemnum vexillum. The dynamical analysis leads to results on stability, global boundedness and bifurcations of the model. Next, via optimal control methods, we predict various ecological outcomes. Our results have key implications for preserving mussel populations in the advent of invasion by non-native epibionts. In particular, they help us understand the changing popluation dynamics of local predator–prey communities, due to indirect effects that epibionts confer.