Evolutionary game dynamics is one of the most fruitful frameworks for studying evolution in different disciplines, from Biology to Economics. Within this context, the approach of choice for many researchers is the so-called replicator equation, that describes mathematically the idea that those individuals performing better have more offspring and thus their frequency in the population grows. While very many interesting results have been obtained with this equation in the three decades elapsed since it was first proposed, it is important to realize the limits of its applicability. One particularly relevant issue in this respect is that of non-mean-field effects, that may arise from temporal fluctuations or from spatial correlations, both neglected in the replicator equation. This review discusses these temporal and spatial effects focusing on the non-trivial modifications they induce when compared to the outcome of replicator dynamics. Alongside this question, the hypothesis of linearity and its relation to the choice of the rule for strategy update is also analyzed. The discussion is presented in terms of the emergence of cooperation, as one of the current key problems in Biology and in other disciplines.

Spatial structure is known to have an impact on the evolution of cooperation, and so it has been intensively studied during recent years. Previous work has shown the relevance of some features, such as the synchronicity of the updating, the clustering of the network, or the influence of the update rule. This has been done, however, for concrete settings with particular games, networks, and update rules, with the consequence that some contradictions have arisen and a general understanding of these topics is missing in the broader context of the space of 2 ϫ 2 games. To address this issue, we have performed a systematic and exhaustive simulation in the different degrees of freedom of the problem. In some cases, we generalize previous knowledge to the broader context of our study and explain the apparent contradictions. In other cases, however, our conclusions refute what seems to be established opinions in the field, as for example the robustness of the effect of spatial structure against changes in the update rule, or offer new insights into the subject, e.g., the relation between the intensity of selection and the asymmetry between the effects on games with mixed equilibria.

Summary The brain is a site of relative immune privilege. Although CD4 T cells have been reported in the central nervous system, their presence in the healthy brain remains controversial, and their function remains largely unknown. We used a combination of imaging, single cell, and surgical approaches to identify a CD69 + CD4 T cell population in both the mouse and human brain, distinct from circulating CD4 T cells. The brain-resident population was derived through in situ differentiation from activated circulatory cells and was shaped by self-antigen and the peripheral microbiome. Single-cell sequencing revealed that in the absence of murine CD4 T cells, resident microglia remained suspended between the fetal and adult states. This maturation defect resulted in excess immature neuronal synapses and behavioral abnormalities. These results illuminate a role for CD4 T cells in brain development and a potential interconnected dynamic between the evolution of the immunological and neurological systems. Video Abstract

Human wellbeing in modern societies relies on social cohesion, which can be characterized by high levels of cooperation and a large number of social ties. Both features, however, are frequently challenged by individual self-interest. In fact, the stability of social and economic systems can suddenly break down as the recent financial crisis and outbreaks of civil wars illustrate. To understand the conditions for the emergence and robustness of social cohesion, we simulate the creation of public goods among mobile agents, assuming that behavioral changes are determined by individual satisfaction. Specifically, we study a generalized win-stay-lose-shift learning model, which is only based on previous experience and rules out greenbeard effects that would allow individuals to guess future gains. The most noteworthy aspect of this model is that it promotes cooperation in social dilemma situations despite very low information requirements and without assuming imitation, a shadow of the future, reputation effects, signaling, or punishment. We find that moderate greediness favors social cohesion by a coevolution between cooperation and spatial organization, additionally showing that those cooperation-enforcing levels of greediness can be evolutionarily selected. However, a maladaptive trend of increasing greediness, although enhancing individuals' returns in the beginning, eventually causes cooperation and social relationships to fall apart. Our model is, therefore, expected to shed light on the long-standing problem of the emergence and stability of cooperative behavior. C ontemporary societies are complex systems that are permanently challenged by the selfishness of their members. For example, the recent financial crisis and subsequent turmoil illustrate the vulnerability of modern socioeconomical systems. However, the problem is not new. The history of civilizations displays a recurrent pattern of development and collapse of both medium-sized cultures and large empires. Different theories have been proposed to explain why such systemic failures occur again and again, despite experience gained in the past. Such theories are based, for example, on the growing complexity of societies during their evolution (1) or an overexploitation of the environment (2).Here, we will explore possible psychosocial reasons that may underlie these processes of rise and fall, which are in close relationship with the emergence and stability of social cohesion. Although cooperation and agglomeration provide the fabric that allows civilizations to emerge and thrive (3), they are also subject to strong destabilizing forces. We investigate a twofold operational definition of social cohesion, comprising cooperation (4, 5) and agglomeration (6). By cooperation, we mean contributions of work or goods to achieve a common end (7,8), and by agglomeration, we mean the establishment of relationships between peers. Destabilizing forces are modeled by means of social dilemma situations, particularly public goods games (9, 10) (PGGs), which exemplify th...

Evolutionary game theory has traditionally assumed that all individuals in a population interact with each other between reproduction events. We show that eliminating this restriction by explicitly considering the time scales of interaction and selection leads to dramatic changes in the outcome of evolution. Examples include the selection of the inefficient strategy in the Harmony and Stag-Hunt games, and the disappearance of the coexistence state in the Snowdrift game. Our results hold for any population size and in more general situations with additional factors influencing fitness.Evolutionary game theory is the mathematical framework for modelling evolution in biological, social and economical systems [1,2,3], and is deeply connected to dynamical systems theory and statistical mechanics [4,5,6,7,8,9,10,11]. In the standard setup of evolutionary game theory, strategies available for the game are represented by a fraction of individuals in the population. Individuals then interact according to the rules of the game, and the so earned payoffs determine the frequencies of the next generation (i.e., payoffs represent reproductive fitness). Customarily, most evolutionary game studies make the additional assumption that individuals play many times and with all other players before reproduction takes place, so that payoffs, equivalently fitness, are given by the mean distribution of types in the population. This is also the situation for the so called round-robin tournament, in which each individual plays once with every other. Both hypotheses, common in biological evolution, implies that selection occurs much more slowly than the interaction between individuals. Although recent experimental studies show that this may not always be the case in biology [12,13,14], it is clear that in cultural evolution or social learning the time scale of selection is much closer to the time scale of interaction. The effects of this mixing of scales cannot be disregarded [15], and then it is natural to ask about the consequences of the above assumption and the effect of relaxing it. Though the main field of application of our work is social and cultural evolution, we maintain the usual language of evolutionary biology, to avoid introducing new terminology.In this Letter, we show that rapid selection affects evolutionary dynamics in such a dramatic way that for some games it even changes the stability of equilibria. In order to make explicit the relation between selection and interaction time scales, we use discrete-time dynamics. We follow Moran dynamics [16], as this is the proper way to describe evolution of discrete generations in the field of population dynamics [17]. Specifically, we choose the frequency-dependent version of the Moran dynamics introduced by [18], which allows to consider an evolutionary game in this dynamical context: N individuals interact by playing a game and reproduce by selecting one individual, with probability proportional to the payoff, to duplicate and substitute a randomly chosen individual. The payoff...