In 1903 Walter Sutton suggested that chromosomes , which segregate in a Mendelian fashion , are hereditary units . In 1902 and 1903 Walter Sutton suggested that chromosomes , which segregate in a Mendelian fashion , are hereditary units : `` I may finally call attention to the probability that the association of paternal and maternal chromosomes in pairs and their subsequent separation during the reducing division ... may constitute the physical basis of the Mendelian law of heredity '' .