اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدCyclic dominance in evolutionary games: A review
188
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Rock is wrapped by paper, paper is cut by scissors, and scissors are crushed by rock. This simple game is popular among children and adults to decide on trivial disputes that have no obvious winner, but cyclic dominance is also at the heart of predator-prey interactions, the mating strategy of side-blotched lizards, the overgrowth of marine sessile organisms, and the competition in microbial populations. Cyclical interactions also emerge spontaneously in evolutionary games entailing volunteering, reward, punishment, and in fact are common when the competing strategies are three or more regardless of the particularities of the game. Here we review recent advances on the rock-paper-scissors and related evolutionary games, focusing in particular on pattern formation, the impact of mobility, and the spontaneous emergence of cyclic dominance. We also review mean-field and zero-dimensional rock-paper-scissors models and the application of the complex Ginzburg-Landau equation, and we highlight the importance and usefulness of statistical physics for the successful study of large-scale ecological systems. Directions for future research, related for example to dynamical effects of coevolutionary rules and invasion reversals due to multi-point interactions, are outlined as well.
قيم البحث
اقرأ أيضاً
Lotkas seminal work (A.J. Lotka A., Proc. Natl. Acad. Sci. U.S.A. 6 (1920) 410) on certain rhythmic relations is already one hundred years old, but the research activity about pattern formations due to cyclical dominance is more vibrant than ever. It
is because non-transitive interactions have paramount role on maintaining biodiversity and adequate human intervention into ecological systems requires deeper understanding of related dynamical processes. In this perspective article we overview different aspects of biodiversity, with focus on how it can be maintained based on mathematical modeling of last years. We also briefly discuss the potential links to evolutionary game models of social systems, and finally, give an overview about potential prospects for future research.
How cooperation can evolve between players is an unsolved problem of biology. Here we use Hamiltonian dynamics of models of the Ising type to describe populations of cooperating and defecting players to show that the equilibrium fraction of cooperato
rs is given by the expectation value of a thermal observable akin to a magnetization. We apply the formalism to the Public Goods game with three players, and show that a phase transition between cooperation and defection occurs that is equivalent to a transition in one-dimensional Ising crystals with long-range interactions. We then investigate the effect of punishment on cooperation and find that punishment plays the role of a magnetic field that leads to an alignment between players, thus encouraging cooperation. We suggest that a thermal Hamiltonian picture of the evolution of cooperation can generate other insights about the dynamics of evolving groups by mining the rich literature of critical dynamics in low-dimensional spin systems.
The Letter presents a novel way to connect random walks, stochastic differential equations, and evolutionary game theory. We introduce a new concept of potential function for discrete-space stochastic systems. It is based on a correspondence between
one-dimensional stochastic differential equations and random walks, which may be exact not only in the continuous limit but also in finite-state spaces. Our method is useful for computation of fixation probabilities in discrete stochastic dynamical systems with two absorbing states. We apply it to evolutionary games, formulating two simple and intuitive criteria for evolutionary stability of pure Nash equilibria in finite populations. In particular, we show that the $1/3$ law of evolutionary games, introduced by Nowak et al [Nature, 2004], follows from a more general mean-potential law.
Species diversity in ecosystems is often accompanied by the self-organisation of the population into fascinating spatio-temporal patterns. Here, we consider a two-dimensional three-species population model and study the spiralling patterns arising fr
om the combined effects of generic cyclic dominance, mutation, pair-exchange and hopping of the individuals. The dynamics is characterised by nonlinear mobility and a Hopf bifurcation around which the systems phase diagram is inferred from the underlying complex Ginzburg-Landau equation derived using a perturbative multiscale expansion. While the dynamics is generally characterised by spiralling patterns, we show that spiral waves are stable in only one of the four phases. Furthermore, we characterise a phase where nonlinearity leads to the annihilation of spirals and to the spatially uniform dominance of each species in turn. Away from the Hopf bifurcation, when the coexistence fixed point is unstable, the spiralling patterns are also affected by nonlinear diffusion.
The evolution of cooperation in social dilemmas in structured populations has been studied extensively in recent years. Whereas many theoretical studies have found that a heterogeneous network of contacts favors cooperation, the impact of spatial eff
ects in scale-free networks is still not well understood. In addition to being heterogeneous, real contact networks exhibit a high mean local clustering coefficient, which implies the existence of an underlying metric space. Here, we show that evolutionary dynamics in scale-free networks self-organize into spatial patterns in the underlying metric space. The resulting metric clusters of cooperators are able to survive in social dilemmas as their spatial organization shields them from surrounding defectors, similar to spatial selection in Euclidean space. We show that under certain conditions these metric clusters are more efficient than the most connected nodes at sustaining cooperation and that heterogeneity does not always favor--but can even hinder--cooperation in social dilemmas. Our findings provide a new perspective to understand the emergence of cooperation in evolutionary games in realistic structured populations.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
