Fig. 4

a Sampling sites of Gasterosteus aculeatus used for a time-calibrated species tree analysis. b A time-calibrated species tree of representative populations of Gasterosteus aculeatus and G. nipponicus inferred with SNAPP based on 2022 SNPs with the root calibration at 680 ka. The trees recorded in a run are overlaid by the maximum clade credibility tree. Posterior probabilities of each node are shown. Each bar plot indicates the 95% highest posterior density interval of the node height. Individuals from Japanese freshwater populations of G. aculeatus are highlighted in blue. The results of other runs are provided in Additional file 3, Fig. S3