Extinctions Caused by Host-Range Expansion

Nearly all emerging diseases in humans are a result of host-range expansion, in which a pathogen of one species evolves the ability to infect a new host species. To present a rigorous analysis of pathogen host-range expansion, we derive a Lotka-Volterra dynamical system with two competing host species and a single parasite species; the parasite infects only one of the host species. We provide a stability and bifurcation analysis of this model. We then ask what happens if the parasite evolves the ability to infect the alternate host, extending the model to include a parasite population with an expanded host range. We derive explicit global stability and bifurcation conditions for this four-dimensional model in terms of the system parameters. We demonstrate that only four outcomes may occur following the range expansion of a parasite or pathogen, and provide both local and global asymptotic stability conditions for these outcomes. While three of these outcomes were expected, the fourth is counterintuitive, predicting that host-range expansion can drive the original host species to extinction. For example, a native species could be driven to extinction by a longstanding native parasite if that parasite acquires the ability to infect a cultivated species. We briefly discuss the phenomena driving this unexpected prediction and its implications.