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Appendix S1 Sampling information of RWA worldwide.

Appendix S2 Invasion scenarios for the New World and the Middle East RWAs used in ABC analyses.

Appendix S3 Model specification, prior distributions for demographic parameters and locus-specific mutation model parameters of Set 1 & Set 2.

Appendix S4 Network of worldwide RWA mtDNA haplotypes.

Appendix S5 FST values and significance of pairwise comparisons among worldwide populations. Black values indicate significance after Bonferroni correction at 0.05 level. The bold highlight the FST of nonsignificance.

Appendix S6 amova for RWAs worldwide based on microsatellite loci and analysed in two groups: native and introduced populations.

Appendix S7 Factorial correspondence analysis of worldwide RWAs. The circles indicate populations that cluster according to native geography and introduced ranges.

Appendix S8 Network of worldwide RWA endosymbiont LeuBC protein-coding genes.

Appendix S9 Principle component analysis (PCA) of six evolutionary scenarios. The scenario labelled in dark blue (scenario 3) is that with the highest posterior probability. The observed data set is among the posterior distribution.

Appendix S10 Model checking and probability of observed S. S. in the 5% (light grey) and 1% (dark grey) tail of simulated ranges using Prior Set 1.

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