Physiological studies of cranial blood flow in humans in reclining vs. upright postures suggest that selection for bipedalism was correlated with the establishment of epigenetic adaptations for delivering blood preferentially to the vertebral plexus of veins, depending upon momentary respiratory and postural constraints. The frequencies of vascular/osteological channels used to deliver blood to the vertebral plexus of veins were determined for samples of African pongids, various taxa of fossil hominids, and extant Homo sapiens. These channels include an enlarged occipital/marginal (O/M) sinus system, multiple hypoglossal canals, and foramina that conduct emissary veins: posterior condyloid, mastoid, occipital, and parietal. The African pongid, and therefore presumably the ancestral prebipedal hominoid, condition is characterized by low frequencies of all of these routes except multiple hypoglossal canals. The earliest known bipeds (Australopithecus afarensis) and robust australopithecines are characterized by fixation of enlarged O/M sinus systems. Robust australopithecines are also characterized by apparently low frequencies of mastoid and parietal foramina, and high frequencies of multiple hypoglossal canals and posterior condyloid foramina. In gracile australopithecines and subsequently living hominids, trends towards increased frequencies of mastoid and (later) parietal emissary foramina coincide with a trend towards decreased frequencies of an enlarged O/M sinus system and multiple hypoglossal canals. These findings suggest that selection for bipedalism initially resulted in epigenetic adaptations for routes to deliver blood to the vertebral plexus including an enlarged O/M sinus system and hypoglossal canals, but that the pressures underlying these adaptations relaxed as bipedalism became established, and other routes for delivering blood to the vertebral plexus of veins were either directly or indirectly selected for, perhaps in conjunction with a changing architecture of the skull. A systematic implication of this study is that robust australopithecines are descendants of A. afarensis rather than of A. africanus.