Luis Mario Floría

Evolutionary dynamics of group interactions on structured populations: a review

Interactions among living organisms, from bacteria colonies to human societies, are inherently more complex than interactions among particles and non-living matter. Group interactions are a particularly important and widespread class, representative of which is the public goods game. In addition, methods of statistical physics have proved valuable for studying pattern formation, equilibrium selection and self-organization in evolutionary games. Here, we review recent advances in the study of evolutionary dynamics of group interactions on top of structured populations, including lattices, complex networks and coevolutionary models. We also compare these results with those obtained on well-mixed populations. The review particularly highlights that the study of the dynamics of group interactions, like several other important equilibrium and non-equilibrium dynamical processes in biological, economical and social sciences, benefits from the synergy between statistical physics, network science and evolutionary game theory.

Evolution of Cooperation in Multiplex Networks

We study evolutionary game dynamics on structured populations in which individuals take part in several layers of networks of interactions simultaneously. This multiplex of interdependent networks accounts for the different kind of social ties each individual has. By coupling the evolutionary dynamics of a Prisoners Dilemma game in each of the networks, we show that the resilience of cooperative behaviors for extremely large values of the temptation to defect is enhanced by the multiplex structure. Furthermore, this resilience is intrinsically related to a non-trivial organization of cooperation across the network layers, thus providing a new way out for cooperation to survive in structured populations.

Complex Cooperative Networks from Evolutionary Preferential Attachment

In spite of its relevance to the origin of complex networks, the interplay between form and function and its role during network formation remains largely unexplored. While recent studies introduce dynamics by considering rewiring processes of a pre-existent network, we study network growth and formation by proposing an evolutionary preferential attachment model, its main feature being that the capacity of a node to attract new links depends on a dynamical variable governed in turn by the node interactions. As a specific example, we focus on the problem of the emergence of cooperation by analyzing the formation of a social network with interactions given by the Prisoners Dilemma. The resulting networks show many features of real systems, such as scale-free degree distributions, cooperative behavior and hierarchical clustering. Interestingly, results such as the cooperators being located mostly on nodes of intermediate degree are very different from the observations of cooperative behavior on static networks. The evolutionary preferential attachment mechanism points to an evolutionary origin of scale-free networks and may help understand similar feedback problems in the dynamics of complex networks by appropriately choosing the game describing the interaction of nodes.

Dissipative dynamics of the Frenkel-Kontorova model

The aim of this review article is to present recent advances in the theory of the dynamics of modulated phases in the Frenkel-Kontorova model. This theory is motivated through two specific condensed matter systems: charge-density wave conductors and Josephson junction arrays. The presentation tries to integrate the existing results into the perspective of the equilibrium theory of the model, which is summarized in the beginning. The issues of defectibility, metastability, pinning and synchronization are discussed in connection with the underlying interplay of continuum and discrete descriptions. Special emphasis is placed on the different transitions between dynamical phases; namely depinning transition, unlocking transition and dynamical Aubry transition.

Robustness of cooperation in the evolutionary prisoner's dilemma on complex networks

Recent studies on the evolutionary dynamics of the prisoners dilemma game in scale-free networks have demonstrated that the heterogeneity of the network interconnections enhances the evolutionary success of cooperation. In this paper we address the issue of how the characterization of the asymptotic states of the evolutionary dynamics depends on the initial concentration of cooperators. We find that the measure and the connectedness properties of the set of nodes where cooperation reaches fixation is largely independent of initial conditions, in contrast with the behaviour of both the set of nodes where defection is fixed, and the fluctuating nodes. We also check for the robustness of these results when varying the degree heterogeneity along a one-parametric family of networks interpolating between the class of Erdős–Renyi graphs and the Barabasi–Albert networks.

Cooperative scale-free networks despite the presence of defector hubs

Recent results have shown that heterogeneous populations are better suited to support cooperation than homogeneous settings when the Prisoners Dilemma drives the evolutionary dynamics of the system. The same occurs when the network growth is coevolving together with the evolutionary dynamics, which also gives rise to highly cooperative scale-free networks. In the latter case, however, the organization of cooperation is radically different with respect to the case in which the underlying network is static. In this paper we study the structure of cooperation in static networks grown together with evolutionary dynamics and show that the general belief that hubs can only be occupied by cooperators does not hold. Moreover, these scale-free networks support high levels of cooperation despite having defector hubs. Our results have several important implications for the explanation of cooperative behavior in scale-free networks and highlight the importance that the formation of complex systems have on its function.

Natural selection of cooperation and degree hierarchy in heterogeneous populations

One of the current theoretical challenges to the explanatory powers of Evolutionary Theory is the understanding of the observed evolutionary survival of cooperative behavior when selfish actions provide higher fitness (reproductive success). In unstructured populations natural selection drives cooperation to extinction. However, when individuals are allowed to interact only with their neighbors, specified by a graph of social contacts, cooperation-promoting mechanisms (known as lattice reciprocity) offer to cooperation the opportunity of evolutionary survival. Recent numerical works on the evolution of Prisoners Dilemma in complex network settings have revealed that graph heterogeneity dramatically enhances the lattice reciprocity. Here we show that in highly heterogeneous populations, under the graph analog of replicator dynamics, the fixation of a strategy in the whole population is in general an impossible event, for there is an asymptotic partition of the population in three subsets, two in which fixation of cooperation or defection has been reached and a third one which experiences cycles of invasion by the competing strategies. We show how the dynamical partition correlates with connectivity classes and characterize the temporal fluctuations of the fluctuating set, unveiling the mechanisms stabilizing cooperation in macroscopic scale-free structures.

Intrinsic localized modes: discrete breathers: existence and linear stability

We present some examples of detailed analysis of intrinsic localized modes in lattices, using the accurate numerical methods derived from the proof of existence of MacKay‐Aubry. We report on some improvements on the methods, which are then used to the fullest to obtain the Floquet analysis of the breather solutions. Such calculations are possible taking into account the whole lattice, without any approximations. This yields an unprecedented detail of the mechanisms that govern instabilities in discrete breathers, giving a complete picture of the interplay between localized (“internal”) and extended (“phonon-like”) instabilities. Copyright

Mobile localization in nonlinear Schrödinger lattices

Abstract Using continuation methods from the integrable Ablowitz–Ladik lattice, we have studied the structure of numerically exact mobile discrete breathers in the standard discrete nonlinear Schrodinger equation. We show that, away from that integrable limit, the mobile pulse is dressed by a background of resonant plane waves with wavevectors given by a certain selection rule. This background is seen to be essential for supporting mobile localization in the absence of integrability. We show how the variations of the localized pulse energy during its motion are balanced by the interaction with this background, allowing the localization mobility along the lattice.

Empathy Emerges Spontaneously in the Ultimatum Game: Small Groups and Networks

The Ultimatum game, in which one subject proposes how to share a pot and the other has veto power on the proposal, in which case both lose everything, is a paradigmatic scenario to probe the degree of cooperation and altruism in human subjects. It has been shown that if individuals are empathic, i.e., they play the game having in mind how their opponent will react by offering an amount that they themselves would accept, then non-rational large offers well above the smallest possible ones are evolutionarily selected. We here show that empathy itself may be selected and need not be exogenously imposed provided that interactions take place only with a fraction of the total population, and that the role of proposer or responder is randomly changed from round to round. These empathic agents, that displace agents with independent (uncorrelated) offers and proposals, behave far from what is expected rationally, offering and accepting sizable fractions of the amount to be shared. Specific values for the typical offer depend on the details of the interacion network and on the existence of hubs, but they are almost always significantly larger than zero, indicating that the mechanism at work here is quite general and could explain the emergence of empathy in very many different contexts.