Modelling the effects of leaky predator-exclusion fences and their surrounding halo

Terrestrial fauna of the southern hemisphere, particularly Australia and New Zealand, have suffered significant declines and extinctions due to predation by introduced red foxes Vulpes vulpes and cats Felis catus. Predator-exclusion fences offer protection to these threatened species and allow their populations to persist and even flourish within their boundaries. These fences have traditionally been designed to stop the movement of both the invasive predators (into the fence), and the native animals (out of the fence). However, recent theory and evidence suggest that when native animals are able to move across the fence, they can create a population beyond the fence boundary. This phenomena has been called a \"halo effect\", and has the potential to both expand the direct and indirect benefits of predator-exclusion fences, and to reduce their negative effects. However, the conditions under which such an effect can be achieved are uncertain. They include questions about which native species could support a meaningful halo, what levels of predation outside the fence can be tolerated, and how permeable the fence would need to be. Here, we formulate this problem as both a simple two-patch model and a spatial partial differential equation model. We use the two approaches to explore the conditions under which a halo can deliver conservation benefits, and offer clear insights into the problem.