Identifying stages in the lifespan of dynamic groups

Dynamic groups, characterized by their evolving memberships, present unique challenges in understanding group behavior and performance. Traditional models often overlook the fluidity of group composition, focusing instead on static memberships. In this paper, we introduce a comprehensive framework to empirically measure and analyze changes in group composition over time, offering new insights into group dynamics. We propose key metrics, including Growth Rate, Churn, and Revitalization, that quantify the movement of members in and out of groups. Further, we define distinct stages of group development, such as organic growth, dynamic growth, fluid stability, and erosion, which capture the evolving nature of group composition. A data-driven method is presented to systematically identify these stages across a group's lifespan. As a case study, we apply our methodology to a dataset from the massively multiplayer online game Travian, involving nearly 900 alliances and over 17,000 players, revealing common patterns of group evolution and frequent transitions between growth and decline. Our findings underscore the value of understanding group stages, offering practical implications for managing dynamic groups in various organizational settings.