Direct reciprocity is a mechanism for the evolution of cooperation in repeated social interactions. According to the literature, individuals naturally learn to adopt conditionally cooperative strategies if they have multiple encounters with their partner. Corresponding models have greatly facilitated our understanding of cooperation, yet they often make strong assumptions on how individuals remember and process payoff information. For example, when strategies are updated through social learning, it is commonly assumed that individuals compare their average payoffs. This would require them to compute (or remember) their payoffs against everyone else in the population. To understand how more realistic constraints influence direct reciprocity, we consider the evolution of conditional behaviours when individuals learn based on more recent experiences. Even in the most extreme case that they only take into account their very last interaction, we find that cooperation can still evolve. However, such individuals adopt less generous strategies, and they cooperate less often than in the classical setup with average payoffs. Interestingly, once individuals remember the payoffs of two or three recent interactions, cooperation rates quickly approach the classical limit. These findings contribute to a literature that explores which kind of cognitive capabilities are required for reciprocal cooperation. While our results suggest that some rudimentary form of payoff memory is necessary, it suffices to remember a few interactions.

Understanding the conditions for maintaining cooperation in groups of unrelated individuals despite the presence of non-cooperative members is a major research topic in contemporary biological, sociological, and economic theory. The N-person snowdrift game models the type of social dilemma where cooperative actions are costly, but there is a reward for performing them. We study this game in a scenario where players move between play groups following the casual group dynamics, where groups grow by recruiting isolates and shrink by losing individuals who then become isolates. This describes the size distribution of spontaneous human groups and also the formation of sleeping groups in monkeys. We consider three scenarios according to the probability of isolates joining a group. We find that for appropriate choices of the cost-benefit ratio of cooperation and the aggregation-disaggregation ratio in the formation of casual groups, free-riders can be completely eliminated from the population. If individuals are more attracted to large groups, we find that cooperators persist in the population even when the mean group size diverges. We also point out the remarkable similarity between the replicator equation approach to public goods games and the trait group formulation of structured demes.

The threshold public goods game is one of the best-known models of non-linear public goods dilemmas. Cooperators and defectors typically coexist in this game when the population is assumed to follow the so-called structured deme model. In this article, we develop a dynamical model of a general N-player game in which there is no deme structure: Individuals interact with randomly chosen neighbours and selection occurs between randomly chosen pairs of individuals. We show that in the deterministic limit, the dynamics in this model leads to the same replicator dynamics as in the structured deme model, i.e., coexistence of cooperators and defectors is typical in threshold public goods game even when the population is completely well mixed. We extend the model to study the effect of density dependence and density fluctuation on the dynamics. We show analytically and numerically that decreasing population density increases the equilibrium frequency of cooperators till the fixation of this strategy, but below a critical density cooperators abruptly disappear from the population. Our numerical investigations show that weak density fluctuations enhance cooperation, while strong fluctuations suppress it.

Direct reciprocity is a powerful mechanism for cooperation in social dilemmas. The very logic of reciprocity, however, seems to require that individuals are symmetric, and that everyone has the same means to influence each others\' payoffs. Yet in many applications, individuals are asymmetric. Herein, we study the effect of asymmetry in linear public good games. Individuals may differ in their endowments (their ability to contribute to a public good) and in their productivities (how effective their contributions are). Given the individuals\' productivities, we ask which allocation of endowments is optimal for cooperation. To this end, we consider two notions of optimality. The first notion focuses on the resilience of cooperation. The respective endowment distribution ensures that full cooperation is feasible even under the most adverse conditions. The second notion focuses on efficiency. The corresponding endowment distribution maximizes group welfare. Using analytical methods, we fully characterize these two endowment distributions. This analysis reveals that both optimality notions favor some endowment inequality: More productive players ought to get higher endowments. Yet the two notions disagree on how unequal endowments are supposed to be. A focus on resilience results in less inequality. With additional simulations, we show that the optimal endowment allocation needs to account for both the resilience and the efficiency of cooperation.

Neanderthals hunted and butchered straight-tusked elephants, the largest terrestrial mammals of the Pleistocene, in a lake landscape on the North European plain, 125,000 years ago, as recently shown by a study of the Last Interglacial elephant assemblage from Neumark-Nord (Germany). With evidence for a remarkable focus on adult males and on their extended utilization, the data from this location are thus far without parallel in the archaeological record. Given their relevance for our knowledge of the Neanderthal niche, we investigated whether the Neumark-Nord subsistence practices were more than a local phenomenon, possibly determined by local characteristics. Analyzing elephant remains from two other Last Interglacial archaeological sites on the North European plain, Gröbern and Taubach, we identified in both assemblages similar butchering patterns as at Neumark-Nord, demonstrating that extended elephant exploitation was a widespread Neanderthal practice during the (early part of the) Last Interglacial. The substantial efforts needed to process these animals, weighing up to 13 metric tons, and the large amounts of food generated suggest that Neanderthals either had ways of storing vast amounts of meat and fat and/or temporarily aggregated in larger groups than commonly acknowledged. The data do not allow us to rule out one of the two explanations, and furthermore both factors, short-term larger group sizes as well as some form of food preservation, may have played a role. What the data do show is that exploitation of large straight-tusked elephants was a widespread and recurring phenomenon amongst Last Interglacial Neanderthals on the North European plain.

Many evolutionary processes occur in phenotype spaces which are continuous. It is therefore of interest to explore how selection operates in continuous spaces. One approach is adaptive dynamics, which assumes that mutants are local. Here we study a different process which also allows non-local mutants. We assume that a resident population is challenged by an invader who uses a strategy chosen from a random distribution on the space of all strategies. We study the repeated donation game of direct reciprocity. We consider reactive strategies given by two probabilities, denoting respectively the probability to cooperate after the co-player has cooperated or defected. The strategy space is the unit square. We derive analytic formulae for the stationary distribution of evolutionary dynamics and for the average cooperation rate as function of the cost-to-benefit ratio. For positive reactive strategies, we prove that cooperation is more abundant than defection if the area of the cooperative region is greater than 1/2 which is equivalent to benefit, b, divided by cost, c, exceeding [Formula: see text]. We introduce the concept of strategies that are stable with probability one. We also study an extended process and discuss other games.

Human ecological success relies on our characteristic ability to flexibly self-organize into cooperative social groups, the most successful of which employ substantial specialization and division of labour. Unlike most other animals, humans learn by trial and error during their lives what role to take on. However, when some critical roles are more attractive than others, and individuals are self-interested, then there is a social dilemma: each individual would prefer others take on the critical but unremunerative roles so they may remain free to take one that pays better. But disaster occurs if all act thus and a critical role goes unfilled. In such situations learning an optimum role distribution may not be possible. Consequently, a fundamental question is: how can division of labour emerge in groups of self-interested lifetime-learning individuals? Here, we show that by introducing a model of social norms, which we regard as emergent patterns of decentralized social sanctioning, it becomes possible for groups of self-interested individuals to learn a productive division of labour involving all critical roles. Such social norms work by redistributing rewards within the population to disincentivize antisocial roles while incentivizing prosocial roles that do not intrinsically pay as well as others.

We study evolutionary game dynamics in a growing habitat with vacancies. Fitness is determined by the global effect of the environment and a local prisoner\'s dilemma among neighbors. We study population growth on a one-dimensional lattice and analyze how the environment affects evolutionary competition. As the environment becomes harsh, an absorbing phase transition from growing populations to extinction occurs. The transition point depends on which strategies are present in the population. In particular, we find a \'cooperative window\' in parameter space, where only cooperators can survive. A mutant defector in a cooperative community might briefly proliferate, but over time naturally occurring vacancies separate cooperators from defectors, thereby driving defectors to extinction. Our model reveals that vacancies provide a strong boost for cooperation by spatial selection.

Most insects harbour influential, yet non-essential heritable microbes in their hemocoel. Communities of these symbionts exhibit low diversity. But their frequent multi-species nature raises intriguing questions on roles for symbiont-symbiont synergies in host adaptation, and on the stability of the symbiont communities, themselves. In this study, we build on knowledge of species-defined symbiont community structure across US populations of the pea aphid, Acyrthosiphon pisum. Through extensive symbiont genotyping, we show that pea aphids\' microbiomes can be more precisely defined at the symbiont strain level, with strain variability shaping five out of nine previously reported co-infection trends. Field data provide a mixture of evidence for synergistic fitness effects and symbiont hitchhiking, revealing causes and consequences of these co-infection trends. To test whether within-host metabolic interactions predict common versus rare strain-defined communities, we leveraged the high relatedness of our dominant, community-defined symbiont strains vs. 12 pea aphid-derived Gammaproteobacteria with sequenced genomes. Genomic inference, using metabolic complementarity indices, revealed high potential for cooperation among one pair of symbionts-Serratia symbiotica and Rickettsiella viridis. Applying the expansion network algorithm, through additional use of pea aphid and obligate Buchnera symbiont genomes, Serratia and Rickettsiella emerged as the only symbiont community requiring both parties to expand holobiont metabolism. Through their joint expansion of the biotin biosynthesis pathway, these symbionts may span missing gaps, creating a multi-party mutualism within their nutrient-limited, phloem-feeding hosts. Recent, complementary gene inactivation, within the biotin pathways of Serratia and Rickettsiella, raises further questions on the origins of mutualisms and host-symbiont interdependencies.

The evolution and long-term sustenance of cooperation has consistently piqued scholarly interest across the disciplines of evolutionary biology and social sciences. Previous theoretical and experimental studies on collective risk social dilemma games have revealed that the risk of collective failure will affect the evolution of cooperation. In the real world, individuals usually adjust their decisions based on environmental factors such as risk intensity and cooperation level. However, it is still not well understood how such conditional behaviours affect the evolution of cooperation in repeated group interactions scenario from a theoretical perspective. Here, we construct an evolutionary game model with repeated interactions, in which defectors decide whether to cooperate in subsequent rounds of the game based on whether the risk exceeds their tolerance threshold and whether the number of cooperators exceeds the collective goal in the early rounds of the game. We find that the introduction of conditional cooperation strategy can effectively promote the emergence of cooperation, especially when the risk is low. In addition, the risk threshold significantly affects the evolutionary outcomes, with a high risk promoting the emergence of cooperation. Importantly, when the risk of failure to reach collective goals exceeds a certain threshold, the timely transition from a defective strategy to a cooperative strategy by conditional cooperators is beneficial for maintaining high-level cooperation.