FIG. A1. At equilibrium, the choice of cell-size and carrying capacity can affect parasite persistence. To test our model and to provide baseline simulations for comparison with scenarios entailing range-expansion, we ran numerous simulations with the population at spatial equilibrium. We ran equilibrium simulations (with ten replicates each over fifty generations) for all combinations of global carrying capacity Kglobal= 8000, 16000, 24000, 32000; grid-cell size = 2, 4, 5, 10 units; and global (frequency independent) transmission rates T = 0.1, 0.2, …, 0.9. Ideally, we wanted a grid-cell size that was small relative to the scale of dispersal, but large enough to accommodate a sufficient number of individuals that parasite prevalence was maintained at the transmission rate at equilibrium. Large carrying-capacity simulations also carry a computational cost (they are slow to run), so we searched for the smallest grid-cell size that gave us stable parasite populations over a wide range of transmission rates at equlibrium, but which was computationally tractable. At a constant dispersal scale, the cell size and carrying capacity we chose had a strong effect on parasite persistence. Carrying capacities below 32000 tended to result in parasite extinction, particularly at low transmission rates, unless cell size was large (ten units). This figure shows observed prevalence versus transmission rate at equilibrium for global carrying capacity K=32000. Cell sizes vary as per the legend. Lines are drawn through mean values from ten simulations. We chose this carrying capacity and a cell size of five units for all following simulations, because this combination allowed parasite persistence across a wide range of transmission rates at spatial equilibrium, but had a cell size only one-third of the maximum dispersal distance.
