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Appendix S1-S5Derivations as a Mathematica notebook (reader available from http://www.wolfram.com/products/player/).

Figure S1 The proportion of time contributed by MT2 to model one, as a function of the effective number of demes D' (red line). The 5% cut-off line is denoted by the blue dashed line. Results are plotted for ND m = 0.1; results are similar for ND m = 2.

Figure S2 Fixation time of an advantageous allele where the population is divided over a one-dimension structure with 5 demes (D' = 3). Results are plotted for the first model (red dots), second model (blue dots), simulation results (black crosses, standard errors lie within the markers) and Fisher’s approximation (red dotted line). ND = 2000, and (a) ND m = 0.1, (b) ND m = 0.5, (c) ND m = 1 and (d) ND m = 2.

Figure S3 Fixation time of an advantageous allele where the population is divided over a one-dimension structure with 11 demes (D' = 6; (a) and (b)), and with 101 demes (D' = 51; (c) and (d)). Results are plotted for the first model (light gray squares), second model (dark gray diamonds), simulation results (black crosses joined by a line, standard errors lie within the markers) and Fisher’s approximation (black dotted line). ND = 2000 (a and b) or N = 500 (c and d), and ND m = 0.5 (a and c) or ND m = 1 (b and d).

Figure S4 Fixation time of an advantageous allele where the population is divided over a two-dimension structure with 9 demes (so D' = 3). ND = 2000, and (a) ND m = 0.1, (b) ND m = 0.5, (c) ND m = 1 and (d) ND m = 2.

Figure S5 Fixation time of an advantageous allele where the population is divided over a two-dimension structure with 25 demes (D' = 5; (a) and (b)), and 100 demes (D' = 10; (c) and (d)). As well as plotting the simulation data and two model results, the corrected version of model 2 that accounts for the different ways in which an advantageous allele can reach a target deme is also shown (light gray circles). ND = 2000 (a and b) or N = 500 (c and d), and ND m = 0.5 (a and c) or ND m = 1 (b and d).

Figure S6 Fixation time of an advantageous allele as a function of the migration rate ND m, where the population is divided over a one-dimension structure with 101 demes (D' = 51, a and b), or a two-dimensional torus with 100 demes (D' = 10, c and d). ND = 500, and ND s = 10 (a and c) or ND s = 50 (b and d).

Figure S7 Fixation time of an advantageous allele for ND = 2000 and ND m = 5. The population is divided over a one-dimensional structure with 5 demes (a), 11 demes (b) or 101 demes (c), or a two-dimension structure with 9 demes (d), 25 demes (e), or 100 demes (f).

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