In 1979, a lineage of avian-like H1N1 influenza A viruses emerged in European swine populations independently from the classical swine H1N1 virus lineage that had circulated in pigs since the Spanish influenza pandemic of 1918. To determine whether these two distinct lineages of swine-adapted A/H1N1 viruses evolved from avian-like A/H1N1 ancestors in similar ways, as might be expected given their common host species and origin, we compared patterns of nucleotide and amino acid change in whole genome sequences of both groups. An analysis of nucleotide compositional bias across all eight genomic segments for the two swine lineages showed a clear lineage-specific bias, although a segment-specific effect was also apparent. As such, there appears to be only a relatively weak host-specific selection pressure. Strikingly, despite each lineage evolving in the same species of host for decades, amino acid analysis revealed little evidence of either parallel or convergent changes. These findings suggest that although adaptation due to evolutionary lineages can be distinguished, there are functional and structural constraints on all gene segments and that the evolutionary trajectory of each lineage of swine A/H1N1 virus has a strong historical contingency. Thus, in the context of emergence of an influenza A virus strain via a host switch event, it is difficult to predict what specific polygenic changes are needed for mammalian adaptation.