The effect of gene flow and thalassaemia start frequencies on the spread of sickle cell, with and without epistasis. Panels (a) and (b) illustrate the results of a scenario where βS was first introduced 100 generations ago, into a population containing fixed (and identical) frequencies of both α and β thalassaemia (y axis). Malaria selection is applied to every deme at a level of 0.005 years−1, and after its first introduction, βS is assumed to re-challenge the population in 30% of subsequent generations, chosen at random. The colour of each cell in the heatmap indicates the mean proportion of demes where the frequency of βS is <0.005 after 100 generations. 100 repeated simulations were used to generate each cell. Supplementary Fig. S5 offers a detailed illustration of the data underlying this figure for thalassaemia starting frequencies of 0.04 and 0.08. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)