A single hematopoietic stem cell (HSC) can generate a clone, consisting of daughter HSCs and differentiated progeny, which can sustain the hematopoietic system of multiple hosts for a long time. At the same time, this massive expansion potential must be restrained to prevent abnormal, leukemic proliferation. We used an interdisciplinary approach, combining transplantation assays with mathematical and computational methods, to systematically analyze the proliferative potential of individual HSCs. We show that all HSC clones examined have an intrinsically limited life span. Daughter HSCs within a clone behaved synchronously in transplantation assays and eventually exhausted at the same time. These results indicate that each HSC is programmed to have a finite life span. This program and the memory of the life span of the mother HSC are inherited by all daughter HSCs. In contrast, there was extensive heterogeneity in life spans between individual HSC clones, ranging from 10 to almost 60 mo. We used model-based machine learning to develop a mathematical model that efficiently predicts the life spans of individual HSC clones on the basis of a few initial measurements of donor type cells in blood. Computer simulations predict that the probability of self-renewal decays with a logistic kinetic over the life span of a normal HSC clone. Other decay functions lead to either graft failure or leukemic proliferation. We propose that dynamical fate probabilities are a crucial condition that leads to self-limiting clonal proliferation.