Explore the importance of multiple intermediate compartments in maintaining cell populations through this lecture from the Santa Fe Institute. Delve into the challenges of maintaining product cells from progenitor cells, examining how a single intermediate compartment can lead to undesirable outcomes such as clonal dominance and excessive cell divisions. Discover why a sequence of compartments offers a more efficient approach, minimizing clonality and optimizing the number of division rounds. Gain insights into T cell activation, cellular organization, stochastic elimination, and T cell development exhaustion. Examine the stochastic rules of cellular fate and analyze probability distributions related to compartment numbers. Enhance your understanding of complex biological systems and their implications for cell population maintenance.