Statistical dynamics of religions and adherents

Religiosity is one of the most important sociological aspects of populations. All religions may evolve in their beliefs and adapt to the society developments. A religion is a social variable, like a language or wealth, to be studied like any other organizational parameter. Several questions can be raised, as considered in this study; e.g.: i) From a "macroscopic" point of view: How many religions exist at a given time? ii) From a "microscopic" viewpoint: How many adherents belong to one religion? Does the number of adherents increase or not, and how? No need to say that if quantitative answers and mathematical laws are found, agent-based models can be imagined to describe such non-equilibrium processes. It is found that empirical laws can be deduced and related to preferential attachment processes, like on an evolving network; we propose two different algorithmic models reproducing as well the data. Moreover, a population growth-death equation is shown to be a plausible modeling of evolution dynamics in a continuous-time framework. Differences with language dynamic competition are emphasized.