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Pastoralists who depend on their herds for their livelihoods need a minimum number of animals to support their household. Due to the dynamics of herd growth, pastoralists may find themselves at times below that minimum number. Previous studies have shown that there is a herd-size threshold below which households are unlikely to escape poverty. We explore the concept of a herd-size threshold using an agent-based model to examine the role of scale and stochasticity in family herd dynamics. The model was parametrized with data from the literature. The results from the computer simulations show (1) that offtake rates significantly limit herd growth; and (2) that herd-size threshold is better understood as a range of probabilities. We discuss the methodological and conceptual advantages of using agent-based modeling to examine demographic dynamics, including the possibility of conducting multiple experiments in silico to examine the dynamics of herd growth.