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'' view point: 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 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 is emphasized.Comment: submitted to EP

Some Effects of Prescribed Fire at Cedar Creek Natural History Area

On four oak savanna restoration compartments with a total area of 100 acres, annual burns (1965-1972) reduced the percent of milacre plots stocked with hazel to 39 compared with 65 on unburned areas. Four growing seasons after one and three fires the hazel distribution was not significantly different from the control. Annual burns increased the density of hazel stems in clones to 19.5 per .0001 acre compared to 11.0 on controls. Stem density four years after 1 and 3 burns averaged 10.0 and 8.0 per .0001 acre. The o.d. weight of live hazel stems per .0001 on annual burn areas was 16 percent of that on controls. Four years after 1 or 3 fires stem weight was not significantly different from the control. Stem height on annual burn areas averaged 17 inches compared with 33 inches on the con1rols. Maximum stem heights on annual burns averaged 24 inches compared wi1h 42 inches on controls. Four growing seasons after 1 or 3 fires average and maximum stem heights were not significantly different from controls

Critical behavior in an evolutionary Ultimatum Game

Experimental studies have shown the ubiquity of altruistic behavior in human societies. The social structure is a fundamental ingredient to understand the degree of altruism displayed by the members of a society, in contrast to individual-based features, like for example age or gender, which have been shown not to be relevant to determine the level of altruistic behavior. We explore an evolutionary model aiming to delve how altruistic behavior is affected by social structure. We investigate the dynamics of interacting individuals playing the Ultimatum Game with their neighbors given by a social network of interaction. We show that a population self-organizes in a critical state where the degree of altruism depends on the topology characterizing the social structure. In general, individuals offering large shares but in turn accepting large shares, are removed from the population. In heterogeneous social networks, individuals offering intermediate shares are strongly selected in contrast to random homogeneous networks where a broad range of offers, below a critical one, is similarly present in the population.Comment: 13 pages, 7 figure

Nonequilibrium phase transition in a model for social influence

We present extensive numerical simulations of the Axelrod's model for social influence, aimed at understanding the formation of cultural domains. This is a nonequilibrium model with short range interactions and a remarkably rich dynamical behavior. We study the phase diagram of the model and uncover a nonequilibrium phase transition separating an ordered (culturally polarized) phase from a disordered (culturally fragmented) one. The nature of the phase transition can be continuous or discontinuous depending on the model parameters. At the transition, the size of cultural regions is power-law distributed.Comment: 5 pages, 4 figure

Freezing and Slow Evolution in a Constrained Opinion Dynamics Model

We study opinion formation in a population that consists of leftists, centrists, and rightist. In an interaction between neighboring agents, a centrist and a leftist can become both centrists or leftists (and similarly for a centrist and a rightist). In contrast, leftists and rightists do not affect each other. The initial density of centrists rho_0 controls the evolution. With probability rho_0 the system reaches a centrist consensus, while with probability 1-rho_0 a frozen population of leftists and rightists results. In one dimension, we determine this frozen state and the opinion dynamics by mapping the system onto a spin-1 Ising model with zero-temperature Glauber kinetics. In the frozen state, the length distribution of single-opinion domains has an algebraic small-size tail x^{-2(1-psi)} and the average domain size grows as L^{2*psi}, where L is the system length. The approach to this frozen state is governed by a t^{-psi} long-time tail with psi-->2*rho_0/pi as rho_0-->0.Comment: 4 pages, 6 figures, 2-column revtex4 format, for submission to J. Phys. A. Revision contains lots of stylistic changes and 1 new result; the main conclusions are the sam

Adaptation and enslavement in endosymbiont-host associations

The evolutionary persistence of symbiotic associations is a puzzle. Adaptation should eliminate cooperative traits if it is possible to enjoy the advantages of cooperation without reciprocating - a facet of cooperation known in game theory as the Prisoner's Dilemma. Despite this barrier, symbioses are widespread, and may have been necessary for the evolution of complex life. The discovery of strategies such as tit-for-tat has been presented as a general solution to the problem of cooperation. However, this only holds for within-species cooperation, where a single strategy will come to dominate the population. In a symbiotic association each species may have a different strategy, and the theoretical analysis of the single species problem is no guide to the outcome. We present basic analysis of two-species cooperation and show that a species with a fast adaptation rate is enslaved by a slowly evolving one. Paradoxically, the rapidly evolving species becomes highly cooperative, whereas the slowly evolving one gives little in return. This helps understand the occurrence of endosymbioses where the host benefits, but the symbionts appear to gain little from the association.Comment: v2: Correction made to equations 5 & 6 v3: Revised version accepted in Phys. Rev. E; New figure adde

Spatial patterns and scale freedom in a Prisoner's Dilemma cellular automata with Pavlovian strategies

A cellular automaton in which cells represent agents playing the Prisoner's Dilemma (PD) game following the simple "win-stay, loose-shift" strategy is studied. Individuals with binary behavior, such as they can either cooperate (C) or defect (D), play repeatedly with their neighbors (Von Neumann's and Moore's neighborhoods). Their utilities in each round of the game are given by a rescaled payoff matrix described by a single parameter Tau, which measures the ratio of 'temptation to defect' to 'reward for cooperation'. Depending on the region of the parameter space Tau, the system self-organizes - after a transient - into dynamical equilibrium states characterized by different definite fractions of C agents (2 states for the Von Neumann neighborhood and 4 for Moore neighborhood). For some ranges of Tau the cluster size distributions, the power spectrums P(f) and the perimeter-area curves follow power-law scalings. Percolation below threshold is also found for D agent clusters. We also analyze the asynchronous dynamics version of this model and compare results.Comment: Accepted for publication in JSTA

Memory-Based Snowdrift Game on Networks

We present a memory-based snowdrift game (MBSG) taking place on networks. We found that, when a lattice is taken to be the underlying structure, the transition of spatial patterns at some critical values of the payoff parameter is observable for both 4 and 8-neighbor lattices. The transition points as well as the styles of spatial patterns can be explained by local stability analysis. In sharp contrast to previously reported results, cooperation is promoted by the spatial structure in the MBSG. Interestingly, we found that the frequency of cooperation of the MBSG on a scale-free network peaks at a specific value of the payoff parameter. This phenomenon indicates that properly encouraging selfish behaviors can optimally enhance the cooperation. The memory effects of individuals are discussed in detail and some non-monotonous phenomena are observed on both lattices and scale-free networks. Our work may shed some new light on the study of evolutionary games over networks.Comment: 6 pages, 6 figures, to be published in Phys. Rev.