Critical Processes

As described in Section 3.2, a threshold exists between colonies completing growth in a finite number of generations and colonies with a positive probability of growing without bound. The condition defining this threshold is that a colony contains cell types for which the maximum branching probability is 0.5 (see Theorem 1). The branching process is then defined as critical. We have already seen that a colony with p _m , p _s ≤ 0.5 has probability 1 of completion of growth. However, if any of the cell types in the colony have a branching probability equal to 0.5, then the expected time for the colony to complete growth is infinite. Thus, aspects of finite and infinite growth are observed in a critical process. One might expect that, biologically, the critical case is important, for it possibly approximates the equilibrium situation in vivo.