Invasion , Stability and Evolution to Criticality in SpatiallyExtended Artificial Host - Pathogen Ecologies

Running title: Evolution of spatial individual-based ecologies. Key terms: 1) evolution to criticality; 2) spatial dynamics; 3) individual-based ecologies; 4) critical transmissibility; 5) host-pathogen systems; 6) host-pathogen evolution. Abstract We consider an individual-based spatial model of a generic host-pathogen system and explore the diierences between such models and mean-eld systems. We nd a range of new dynamical and evolutionary phenomena. In particular, (i) in this system selective pressure is substantially reduced compared to the corresponding mean-eld models and artiicial suppression of the pathogen population leads to faster evolution and reduces evolutionary stability; (ii) unlike the mean-eld models, there exists a critical transmissibility c above which the pathogen dies out and (iii) the system displays self-evolved criticality. If the transmissibility is allowed to mutate, it evolves to the critical value c. Thus the system evolves so as to put itself at the boundary of where 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 disconnec-tions. We therefore construct a patch model of this and show that this simpliied model behaves in a similar way to the individual-based spatial model.