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The D-statistics analyses find evidence of gene flow between most sister bear species (Fig. 4, Supplementary Tables 4 and 5 and Supplementary Fig. 14). Regardless if spectacled bear or giant panda is used as outgroup, the involved species and relative signal strengths of gene flow in the tested topologies remain the same (Supplementary Table 6). The D-statistics is limited to four-taxon topologies and therefore gene flow signals are difficult to interpret when they occur between distant species, as it cannot determine if it is a direct, indirect, or ancestral signal. For taking more complex gene flow patterns into account, and to determine the direction of gene flow, we applied the recently introduced DFOIL-statistics26. This method uses a symmetric five-taxon topology and has specifically been developed to detect and differentiate gene flow signal among ancestral lineages26.DFOIL analyses estimated the percentage of GFs rejecting the species tree and indicating gene flow. Blue arrows show values >1%, and dashed lavender for <0.1% (Table 1). These percentages do not indicate the amount of introgressed DNA, which can be a fraction of the GF sequence. Green arrows depict significant D-statistics data for gene flow signal. Some gene flow cannot have occurred directly between species, because the species exist in different habitats, but may be remnants of ancestral gene flow or gene flow through a vector species.

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Full size imageIn agreement with the phylogenetic conflict and D-statistics, the DFOIL- statistics finds gene flow between the ancestor of the American black bear/brown/polar bear clade and the Asiatic black bear (Fig. 4, Table 1). The Etruscan bear was geographically overlapping with other bear species and was, like the Asiatic black bear, widely distributed30. It has been identified in fossil layers of Europe 2.5 Ma − 1.0 Ma1,31. The wide geographical distribution would explain the nearly equally strong gene flow from Asiatic black bear into brown bear also observed in the D-statistics (Supplementary Fig. 14). Finally, there is a gene flow signal between the American and Asiatic black bears. The gene flow could have taken place either on the American or Asiatic side of the Bering Strait and is consistent with mitochondrial capture between the species2 (Fig. 3). Most of the weaker gene flow signals in Fig. 4 (dashed-lines) do not necessarily reflect direct species hybridization and are possibly remnants of ancestral gene flow not detected due to allelic loss or signals of indirect gene flow by ghost lineages or intermediate species. Permutations of species for the DFOIL analysis including other polar, sloth and brown bear individuals show that the results are taxon independent (Table 1).