In light of this agreement, how does the critical average number of commuters vary with the adapted reproductive number? While for R 0~2 ten average commuters are sufficient to dissolve spatial heterogeneity, this changes dramatically for smaller average reproductive numbers (see Figure 7) . If a well-adapted strain is only just pandemic capable (i.e. R 0 just above 1) villages with only ten commuters are only 50% likely to seed an epidemic in their local city, and spatial structure becomes important again. For example, the critical number of commuters is close to 100 for R 0~1 :2. For R 0~2 the spatial homogeneity coefficient is approximately 0:42 for one commuter. This agrees with what we find in Figure 4 using simulated results.