A key feature for development consists of producing sister cells that differ in their potential for cellular differentiation. Following two cell divisions, a haploid Schizosaccharomyces pombe cell produces one cell in four 'granddaughters' with a changed mating cell type, implying nonequivalence of sister cells in each of two consecutive cell divisions. The observed pattern of switching is analogous to the mammalian 'stem cell' lineage by which a cell produces one daughter like itself while the other daughter is advanced in its developmental program. It is tested here whether sisters differ because of unequal distribution of cytoplasmic and/or nuclear components to them or due to inheriting a specific parental DNA chain at the mating type locus. Only the DNA strand-segregation model predicts that those cells engineered to contain an inverted tandem duplication of the mating type locus should produce equivalent sisters. Consequently, two 'cousins' in four related granddaughter cells should switch. The results verified the prediction, thus establishing that all cells otherwise fully possess the potential to switch. Therefore, the program of cell type change in S.pombe cell lineages is determined by the pattern of DNA strand inheritance at the mating type locus. A specific DNA sequence present at the mating type locus is postulated to be the cause of developmental asymmetry between sister cells. A general model for cellular differentiation is proposed in which the act of DNA replication itself is hypothesized to produce developmentally nonequivalent sister genomes.