Spatial heterogeneity promotes coexistence of rock-paper-scissor metacommunities

The rock-paper-scissor game -- which is characterized by three strategies R,P,S, satisfying the non-transitive relations S excludes P, P excludes R, and R excludes S -- serves as a simple prototype for studying more complex non-transitive systems. For well-mixed systems where interactions result in fitness reductions of the losers exceeding fitness gains of the winners, classical theory predicts that two strategies go extinct. The effects of spatial heterogeneity and dispersal rates on this outcome are analyzed using a general framework for evolutionary games in patchy landscapes. The analysis reveals that coexistence is determined by the rates at which dominant strategies invade a landscape occupied by the subordinate strategy (e.g. rock invades a landscape occupied by scissors) and the rates at which subordinate strategies get excluded in a landscape occupied by the dominant strategy (e.g. scissor gets excluded in a landscape occupied by rock). These invasion and exclusion rates correspond to eigenvalues of the linearized dynamics near single strategy equilibria. Coexistence occurs when the product of the invasion rates exceeds the product of the exclusion rates. Provided there is sufficient spatial variation in payoffs, the analysis identifies a critical dispersal rate $d^*$ required for regional persistence. For dispersal rates below $d^*$, the product of the invasion rates exceed the product of the exclusion rates and the rock-paper-scissor metacommunities persist regionally despite being extinction prone locally. For dispersal rates above $d^*$, the product of the exclusion rates exceed the product of the invasion rates and the strategies are extinction prone. These results highlight the delicate interplay between spatial heterogeneity and dispersal in mediating long-term outcomes for evolutionary games.Comment: 31pages, 5 figure

Dynamics and collective phenomena of social systems

This thesis focuses on the study of social systems through methods of theoretical physics, in particular proceedings of statistical physics and complex systems, as well as mathematical tools like game theory and complex networks. There already ex- ists predictive and analysis methods to address these problems in sociology, but the contribution of physics provides new perspectives and complementary and powerful tools. This approach is particularly useful in problems involving stochastic aspects and nonlinear dynamics. The contribution of physics to social systems provides not only prediction procedures, but new insights, especially in the study of emergent properties that arise from holistic approaches. We study social systems by introducing different agent-based models (ABM). When possible, the models are analyzed using mathematical methods of physics, in order to achieve analytical solutions. In addition to a theoretical approach, experi- mental treatment is performed via computer simulations both through Monte Carlo methods and deterministic or mixed procedures. This working method has proved very fruitful for the study of several open problems. The book is structured as follows. This introduction presents the mathematical formalisms used in the investigations, which are structured in two parts: in part I we deal with the emergence of cooperation, while in part II we analyze cultural dynamics under the perspective of tolerance