One of the most fundamental questions in behavioural biology is why societies can persist for a long period of time. While researchers in animal behaviour have been hindered by a lack of an aggregate measure (such as social mobility) to quantify the dynamics of animal societies, researchers in social sciences have been challenged by the complexity and diversity of human societies. As a result, direct empirical evidence is still lacking for the hypothesized causal relationship between social mobility and social stability. Here we attempt to fill the void by examining a much simpler society in the Tibetan macaque (Macaca thibetana), which we have tracked for 30 consecutive years. By testing two group level hypotheses based on benefit-cost analysis and social stratification, we show the first quantitative evidence that an annual 2-to-1 stay/change ratio in the hierarchy with a 3-to-1 upward/downward ratio in intragenerational social mobility provides a substantive expected benefit for adult members to stay in the group and wait for their chances to advance. Furthermore, using a Markov transition matrix constructed from empirical data, we demonstrate that the 3-to-1 upward/downward ratio could lead to long-term structural stability in Tibetan macaque society
