| Abstract | One of the most pressing problems with continuing climate change and natural habitat erosion is the invasion of undesirable plant and animal species and virulent pathogens. To study the conditions whereby such invasions can occur it is important to take into account the major impact that environmental forcing can have, especially when the ecological system is overcompensating and therefore vulnerable to resonance. The underlying theory, developed both algebraically and numerically, is presented and applied to eco-epidemiological systems and their subcomponents. It is clear from the analysis that the response of the system to forcing is highly sensitive both to the pathways taken by the disturbance through the system and to the configuration of the external forcing components, in particular the strengths and periods of and the lags between these components. The analysis addresses the key issues of (i) whether forcing helps or hinders invasion and (ii) whether the interaction between multiple forcing components leads to reinforcement or destructive interference. The theory can be used to solve the problem of how to design control strategies to prevent or (with biodiversity) allow invasion using anthropogenically managed countercyclical measures, exploiting the lag structure and the positive or negative reinforcement. The interference effect can also be used to address the biodiversity problem of how to reduce the risk of species exclusion when large amplitude oscillations force a population to dangerously low levels. The general point that ill-informed intervention can worsen the situation is well illustrated by the analysis. |
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