Threshold dynamics for periodically forced ecological systems: the control of population invasion and exclusion

Abstract

Ecosystems are under increasing threat as a result of anthropogenic activity, through pollution, unregulated harvesting, habitat destruction and the inadvertent spread of pathogens and vertebrate and non-vertebrate species through global transportation links. Many of the necessary interventions to restore or restructure natural ecosystems require the exclusion of a population from the ecosystem or the inclusion of a population if robust biodiversity is the objective. The problem of how best to bring this about is not easy to solve in highly nonlinear systems, especially if the system is exposed to significant time varying external forces. We wish here to build on the understanding gained from previous work by developing an algebraic methodology that yields explicit formulae to analyse the effect of moderate multi-component forcing on the invasion/exclusion process. This can be of assistance to management in designing suitable intervention strategies if one or more of the forcing components is under management control. We apply this methodology to look at three important issues, involving the relationships between resonance and control, between vaccination policy and the stage structure of a disease and between apparent competition and coexistence.