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

We consider an individual-based spatial model of a generic host-pathogen system and explore the differences between such models and mean-field systems. We find a range of new dynamical and evolutionary phenomena, in particular: (i) in this system, selective pressure is substantially reduced compared with the corresponding mean-field models, and artificial suppression of the pathogen population leads to faster evolution and reduces evolutionary stability; (ii) unlike the mean-field models, there exists a critical transmissibility tau(c) above which the pathogen dies out; and (iii) the system displays self-evolved criticality. 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 boundary at which it can exist. Observations of the individual-based spatial model motivate an explanation for these phenomena in terms of the dynamics of host patches involving their connections and disconnections. We therefore construct a patch model of this and show that this simplified model behaves in a similar way to the individual-based spatial model.