title: Dynamics of social group competition: modeling the decline of religious affiliation.
abstract: When social groups compete for members, the resulting dynamics may be understandable with mathematical models. We demonstrate that a simple ordinary differential equation (ODE) model is a good fit for religious shift by comparing it to a new international data set tracking religious nonaffiliation. We then generalize the model to include the possibility of nontrivial social interaction networks and examine the limiting case of a continuous system. Analytical and numerical predictions of this generalized system, which is robust to polarizing perturbations, match those of the original ODE model and justify its agreement with real-world data. The resulting predictions highlight possible causes of social shift and suggest future lines of research in both physics and sociology.
authors.affiliation: Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, Illinois 60208, USA.
authors.forename: Daniel M
authors.initials: DM
authors.lastname: Abrams
authors.forename: Haley A
authors.initials: HA
authors.lastname: Yaple
authors.forename: Richard J
authors.initials: RJ
authors.lastname: Wiener
mesh_terms: D003163:Competitive Behavior; D006801:Humans; D015233:Models, Statistical; D008962:Models, Theoretical; D012067:Religion; D012933:Social Identification