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Appendix S1 Methods.

Fig. S1 The probability of dispersal as a function of distance from the focal deme in the centre was based on a discretized Gaussian distribution with a standard deviation of α = 1 km and deme size = 0.75 × 0.75 km.

Fig. S2 The starting location of populations on the landscape for the one-refugium (1R) and two-refugia (2R) demographies.

Fig. S3 Selective environments for the first replicate of data sets (a new set was generated for each replicate of data sets).

Fig. S4 Sampling scheme on the landscape used for all data sets.

Fig. S5FST for an infinite sample from all demes on the landscape vs. FST for the sample of 20 individuals from each of 75 locations.

Fig. S6 Definition of false-positive rate, true-positive rate and false discovery rate.

Fig. S7P-values from the FDIST2 implementation in r vs. P-values from LOSITAN.

Fig. S8FST distributions with selected loci.

Fig. S9 The correlation between allele frequencies and the environment across the landscape vs. FST for the island model.

Fig. S10 The correlation between allele frequencies and the environment across the landscape vs. FST for isolation by distance.

Fig. S11 The correlation between allele frequencies and the environment across the landscape vs. FST for the one-refuge model.

Fig. S12 The correlation between allele frequencies and the environment across the landscape vs. FST for the two-refugia model.

Fig. S13 Error rates based on ranking the top 1% of loci in each data set (i.e. top 100 loci).

Fig. S14 Effect of prior odds parameter on the distribution of FST from BayeScan for the island model (IM) and expansion from two refugia (2R).

Fig. S15 False-positive rates, power and false discovery rates based on different parameter-izations in FDIST2: default settings (using the entire data set to estimate mean FST); neutral parameterization (using only neutral loci to estimate mean FST); and empirical P-values (using a large neutral set to calculate empirical P-values of all loci in the data set based on FST).

Fig. S16 False-positive rates, power and false discovery rates based on different parameterizations in FLK: default settings (using the entire data set to estimate the coancestry matrix Fij); neutral parameterization (using only neutral loci to estimate the coancestry matrix Fij); and empirical P-values (using a large neutral set to calculate empirical P-values of all loci in the data set based on the statistic TF–LK).

Fig. S17 Examples of coancestry and covariance matrices estimated by FLK and Bayenv2, respectively, for the 10 000-N and 9000-N:1000-S data sets.

Fig. S18 Effect of using the ‘Use “neutral” mean FST’ option in LOSITAN on power (TPR: true-positive rate) and false-positive rates (FPR) in both tails of the FST distribution.

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