“…Among toothed whales, however, unusually low mitochondrial DNA (mtDNA) diversity in some of the social odontocetes (e.g., sperm, pilot, killer and false‐killer whales; Alexander et al., , ; Hoelzel et al., ; Martien et al., ; Van Cise et al., ) has limited power to infer population structure, phylogeography and historical demography using traditional genetic tools. The sperm whale ( Physeter macrocephalus ) is particularly enigmatic in this respect, as it is one of the most cosmopolitan and abundant of the large odontocetes, and known to move over large ranges of up to thousands of kilometres over annual or longer time periods (Mizroch & Rice, ; Steiner et al., ; Straley et al., ), yet it exhibits low mtDNA diversity and evidence of female philopatry (Alexander et al., ; Lyrholm & Gyllensten, ; Lyrholm, Leimar, Johanneson, & Gyllensten, ; Mesnick et al., ).…”