Phylogeographic studies often infer historical demographic processes underlying species distributions based on patterns of neutral genetic variation, but spatial variation in functionally important genes can provide additional insights about biogeographic history allowing for inferences about the potential role of adaptation in geographic range evolution. Integrating data from neutral markers and genes involved in oxygen (O2)‐transport physiology, we test historical hypotheses about colonization and gene flow across low‐ and high‐altitude regions in the Ruddy Duck (Oxyura jamaicensis), a widely distributed species in the New World. Using multilocus analyses that for the first time include populations from the Colombian Andes, we also examined the hypothesis that Ruddy Duck populations from northern South America are of hybrid origin. We found that neutral and functional genes appear to have moved into the Colombian Andes from both North America and southern South America, and that high‐altitude Colombian populations do not exhibit evidence of adaptation to hypoxia in hemoglobin genes. Therefore, the biogeographic history of Ruddy Ducks is likely more complex than previously inferred. Our new data raise questions about the hypothesis that adaptation via natural selection to high‐altitude conditions through amino acid replacements in the hemoglobin protein allowed Ruddy Ducks to disperse south along the high Andes into southern South America. The existence of shared genetic variation with populations from both North America and southern South America as well as private alleles suggests that the Colombian population of Ruddy Ducks may be of old hybrid origin. This study illustrates the breadth of inferences one can make by combining data from nuclear and functionally important loci in phylogeography, and underscores the importance of complete range‐wide sampling to study species history in complex landscapes.