INVASION, STABILITY AND EVOLUTION TO CRITICALITY IN SPATIALLY EXTENDED, ARTIFICIAL HOST-PATHOGEN ECOLOGIES

We consider an individual-based spatial model of a generic host-pathog en system and explore the differences between such models and mean-fie ld systems. We find a range of new dynamical and evolutionary phenomen a, in particular: (i) in this system, selective pressure is substantia lly reduced compared with the corresponding mean-field models, and art ificial suppression of the pathogen population leads to faster evoluti on and reduces evolutionary stability; (ii) unlike the mean-field mode ls, there exists a critical transmissibility tau(c) above which the pa thogen dies out; and (iii) the system displays self-evolved criticalit y. If the transmissibility tau is allowed to mutate, it evolves to the critical value tau(c). Thus the system evolves to put itself at the b oundary at which it can exist. Observations of the individual-based sp atial model motivate an explanation for these phenomena in terms of th e dynamics of host patches involving their connections and disconnecti ons. We therefore construct a patch model of this and show that this s implified model behaves in a similar way to the individual-based spati al model.