Haematopoiesis is the process by which progenitor cells differentiate into competent mature blood cells. Only those cells in the latter stages of haematopoiesis can be observed in vitro, so theories about the early stages of the process cannot be tested directly. Experimental data of bone marrow samples from Safari cats provides evidence for the clonal succession hypothesis of early haematopoiesis. In this paper, a hidden Markov model is constructed to quantify this support. Recursive updating techniques are derived and are used to calculate the likelihood and to construct fitted values for the model. Inference is based on multimodal likelihood surfaces.