Fig. 4

Demographic history and genome-wide patterns of differentiation of major groups (super-populations) of Harmonia axyridis. a The most likely evolutionary demographic history of global invasion of H. axyridis as estimated from FSC26 analyses under the 3-population model, suggesting a recent invasion (~ 14 ybp) of the Europe super-population from an Asian source, with significant yet low continued gene flow from the America super-population. Additionally, the estimated population size of the America super-population is considerably smaller compared to the European and two Asian super-populations, the detailed information was shown in additional file 1: Table S5-S7. b The most likely evolutionary demographic history of global invasion of H. axyridis as estimated from FSC26 analyses under the 4-population model, indicating recent (~ 13 ybp) hybrid origins of the European super-population as a result of admixture between the Eastern China and the America super-populations, which themselves diverged from their common ancestor ~ 24 ybp. The Western China and the Eastern China super-populations were estimated to have diverged around 43 ybp. The America, Europe, and Eastern China super-populations have undergone significant increase in effective population sizes after recovery from bottlenecks, while the Western China has decreased in size since divergence, the detailed information was shown in additional file 2: Table S8-S9. c Historical variation in effective population sizes estimated from the whole genome resequencing data sourced from Chen et al., 2021 (native population from China), and Boyes et al., 2021 (invasive, non-native population from the UK, Europe). All estimates were scaled by a generation time of 1 generation per year, and a mutation rate of 3.5e − 9 per site per generation