Evolutionary dynamics in structured populations

Evolution of cooperation in social dilemmas with assortment in finite populations

We investigate conditions for the evolution of cooperation in social dilemmas in finite populations with assortment of players by group founders and general payoff functions for cooperation and defection within groups. Using a diffusion approximation in the limit of a large population size that does not depend on the precise updating rule, we show that the first-order effect of selection on the fixation probability of cooperation when represented once can be expressed as the difference between time-averaged payoffs with respect to effective time that cooperators and defectors spend in direct competition in the different group states. Comparing this fixation probability to its value under neutrality and to the corresponding fixation probability for defection, we deduce conditions for the evolution of cooperation. We show that these conditions are generally less stringent as the level of assortment increases under a wide range of assumptions on the payoffs such as additive, synergetic or discounted benefits for cooperation, fixed cost for cooperation and threshold benefit functions. This is not necessarily the case, however, when payoffs in pairwise interactions are multiplicatively compounded within groups.

Networked dynamic systems with higher-order interactions: stability versus complexity

The stability of complex systems is profoundly affected by underlying structures, which are often modeled as networks where nodes indicate system components and edges indicate pairwise interactions between nodes. However, such networks cannot encode the overall complexity of networked systems with higher-order interactions among more than two nodes. Set structures provide a natural description of pairwise and higher-order interactions where nodes are grouped into multiple sets based on their shared traits. Here we derive the stability criteria for networked systems with higher-order interactions by employing set structures. In particular, we provide a simple rule showing that the higher-order interactions play a double-sided role in community stability-networked systems with set structures are stabilized if the expected number of common sets for any two nodes is less than one. Moreover, although previous knowledge suggests that more interactions (i.e. complexity) destabilize networked systems, we report that, with higher-order interactions, networked systems can be stabilized by forming more local sets. Our findings are robust with respect to degree heterogeneous structures, diverse equilibrium states and interaction types.

Pink-noise dynamics in an evolutionary game on a regular graph

We consider a multiplayer prisoner's dilemma game on a square lattice and regular graphs based on the pairwise-Fermi update rule, and we obtain heatmaps of the fraction of cooperators and the correlation of neighboring pairs. In the heatmap, we find a mixed region where cooperators and defectors coexist, and the correlation between neighbors is significantly enhanced. Moreover, we observe pink-noise behavior in the mixed region, where the power spectrum can be fitted by a power-law function of frequency. We also find that the pink-noise behavior can be reproduced in a simple random-walk model. In particular, we propose a modified random-walk model which can reproduce not only the pink-noise behavior but also the deviation from it observed in a low-frequency region.

Temporal interaction and its role in the evolution of cooperation

This research investigates the impact of dynamic, time-varying interactions on cooperative behavior in social dilemmas. Traditional research has focused on deterministic rules governing pairwise interactions, yet the impact of interaction frequency and synchronization in groups on cooperation remains underexplored. Addressing this gap, our work introduces two temporal interaction mechanisms to model the stochastic or periodic participation of individuals in public goods games, acknowledging real-life variances due to exogenous temporal factors and geographical time differences. We consider that the interaction state significantly influences both game payoff calculations and the strategy updating process, offering new insights into the emergence and sustainability of cooperation. Our results indicate that maximum game participation frequency is suboptimal under a stochastic interaction mechanism. Instead, an intermediate activation probability maximizes cooperation, suggesting a vital balance between interaction frequency and inactivity security. Furthermore, local synchronization of interactions within specific areas is shown to be beneficial, as time differences hinder the spread of cross-structures but promote the formation of dense cooperative clusters with smoother boundaries. We also note that stronger clustering in networks, larger group sizes, and lower noise increase cooperation. This research contributes to understanding the role of node-based temporality and probabilistic interactions in social dilemmas, offering insights into fostering cooperation.

The coalescent in finite populations with arbitrary, fixed structure

The coalescent is a stochastic process representing ancestral lineages in a population undergoing neutral genetic drift. Originally defined for a well-mixed population, the coalescent has been adapted in various ways to accommodate spatial, age, and class structure, along with other features of real-world populations. To further extend the range of population structures to which coalescent theory applies, we formulate a coalescent process for a broad class of neutral drift models with arbitrary - but fixed - spatial, age, sex, and class structure, haploid or diploid genetics, and any fixed mating pattern. Here, the coalescent is represented as a random sequence of mappings [Formula: see text] from a finite set G to itself. The set G represents the "sites" (in individuals, in particular locations and/or classes) at which these alleles can live. The state of the coalescent, Ct:G→G, maps each site g∈G to the site containing g's ancestor, t time-steps into the past. Using this representation, we define and analyze coalescence time, coalescence branch length, mutations prior to coalescence, and stationary probabilities of identity-by-descent and identity-by-state. For low mutation, we provide a recipe for computing identity-by-descent and identity-by-state probabilities via the coalescent. Applying our results to a diploid population with arbitrary sex ratio r, we find that measures of genetic dissimilarity, among any set of sites, are scaled by 4r(1-r) relative to the even sex ratio case.

Evolutionary dynamics of any multiplayer game on regular graphs

Multiplayer games on graphs are at the heart of theoretical descriptions of key evolutionary processes that govern vital social and natural systems. However, a comprehensive theoretical framework for solving multiplayer games with an arbitrary number of strategies on graphs is still missing. Here, we solve this by drawing an analogy with the Balls-and-Boxes problem, based on which we show that the local configuration of multiplayer games on graphs is equivalent to distributing k identical co-players among n distinct strategies. We use this to derive the replicator equation for any n-strategy multiplayer game under weak selection, which can be solved in polynomial time. As an example, we revisit the second-order free-riding problem, where costly punishment cannot truly resolve social dilemmas in a well-mixed population. Yet, in structured populations, we derive an accurate threshold for the punishment strength, beyond which punishment can either lead to the extinction of defection or transform the system into a rock-paper-scissors-like cycle. The analytical solution also qualitatively agrees with the phase diagrams that were previously obtained for non-marginal selection strengths. Our framework thus allows an exploration of any multi-strategy multiplayer game on regular graphs.

The Unification of Evolutionary Dynamics through the Bayesian Decay Factor in a Game on a Graph

We unify evolutionary dynamics on graphs in strategic uncertainty through a decaying Bayesian update. Our analysis focuses on the Price theorem of selection, which governs replicator(-mutator) dynamics, based on a stratified interaction mechanism and a composite strategy update rule. Our findings suggest that the replication of a certain mutation in a strategy, leading to a shift from competition to cooperation in a well-mixed population, is equivalent to the replication of a strategy in a Bayesian-structured population without any mutation. Likewise, the replication of a strategy in a Bayesian-structured population with a certain mutation, resulting in a move from competition to cooperation, is equivalent to the replication of a strategy in a well-mixed population without any mutation. This equivalence holds when the transition rate from competition to cooperation is equal to the relative strength of selection acting on either competition or cooperation in relation to the selection differential between cooperators and competitors. Our research allows us to identify situations where cooperation is more likely, irrespective of the specific payoff levels. This approach provides new perspectives into the intended purpose of Price's equation, which was initially not designed for this type of analysis.

Deterministic theory of evolutionary games on temporal networks

Recent empirical studies have revealed that social interactions among agents in realistic networks merely exist intermittently and occur in a particular sequential order. However, it remains unexplored how to theoretically describe evolutionary dynamics of multiple strategies on temporal networks. Herein, we develop a deterministic theory for studying evolutionary dynamics of any [Formula: see text] pairwise games in structured populations where individuals are connected and organized by temporally activated edges. In the limit of weak selection, we derive replicator-like equations with a transformed payoff matrix characterizing how the mean frequency of each strategy varies over time, and then obtain critical conditions for any strategy to be evolutionarily stable on temporal networks. Interestingly, the re-scaled payoff matrix is a linear combination of the original payoff matrix with an additional one describing local competitions between any pair of different strategies, whose weights are solely determined by network topology and selection intensity. As a particular example, we apply the deterministic theory to analysing the impacts of temporal networks in the mini-ultimatum game, and find that temporally networked population structures result in the emergence of fairness. Our work offers theoretical insights into the subtle effects of network temporality on evolutionary game dynamics.

Discipline and punishment in panoptical public goods games

In Public Goods Games (PGG), the temptation to free-ride on others' contributions poses a significant threat to the sustainability of cooperative societies. Therefore, societies strive to mitigate this through incentive systems, employing rewards and punishments to foster cooperative behavior. Thus, peer punishment, in which cooperators sanction defectors, as well as pool punishment, where a centralized punishment institution executes the punishment, is deeply analyzed in previous works. Although the literature indicates that these methods may enhance cooperation on social dilemmas under particular contexts, there are still open questions, for instance, the structural connection between graduated punishment and the monitoring of public goods games. Our investigation proposes a compulsory PGG framework under Panoptical surveillance. Inspired by Foucault's theories on disciplinary mechanisms and biopower, we present a novel mathematical model that scrutinizes the balance between the severity and scope of punishment to catalyze cooperative behavior. By integrating perspectives from evolutionary game theory and Foucault's theories of power and discipline, this research uncovers the theoretical foundations of mathematical frameworks involved in punishment and discipline structures. We show that well-calibrated punishment and discipline schemes, leveraging the panoptical effect for universal oversight, can effectively mitigate the free-rider dilemma, fostering enhanced cooperation. This interdisciplinary approach not only elucidates the dynamics of cooperation in societal constructs but also underscores the importance of integrating diverse methodologies to address the complexities of fostering cooperative evolution.

Imitation dynamics on networks with incomplete information

Imitation is an important learning heuristic in animal and human societies. Previous explorations report that the fate of individuals with cooperative strategies is sensitive to the protocol of imitation, leading to a conundrum about how different styles of imitation quantitatively impact the evolution of cooperation. Here, we take a different perspective on the personal and external social information required by imitation. We develop a general model of imitation dynamics with incomplete information in networked systems, which unifies classical update rules including the death-birth and pairwise-comparison rule on complex networks. Under pairwise interactions, we find that collective cooperation is most promoted if individuals neglect personal information. If personal information is considered, cooperators evolve more readily with more external information. Intriguingly, when interactions take place in groups on networks with low degrees of clustering, using more personal and less external information better facilitates cooperation. Our unifying perspective uncovers intuition by examining the rate and range of competition induced by different information situations.

Fixation probability in evolutionary dynamics on switching temporal networks

Population structure has been known to substantially affect evolutionary dynamics. Networks that promote the spreading of fitter mutants are called amplifiers of selection, and those that suppress the spreading of fitter mutants are called suppressors of selection. Research in the past two decades has found various families of amplifiers while suppressors still remain somewhat elusive. It has also been discovered that most networks are amplifiers of selection under the birth-death updating combined with uniform initialization, which is a standard condition assumed widely in the literature. In the present study, we extend the birth-death processes to temporal (i.e., time-varying) networks. For the sake of tractability, we restrict ourselves to switching temporal networks, in which the network structure deterministically alternates between two static networks at constant time intervals or stochastically in a Markovian manner. We show that, in a majority of cases, switching networks are less amplifying than both of the two static networks constituting the switching networks. Furthermore, most small switching networks, i.e., networks on six nodes or less, are suppressors, which contrasts to the case of static networks.

Nudging cooperation among agents in an experimental social network

We investigate the development of cooperative behavior in networks over time. In our controlled laboratory experiment, subjects can cooperate by sending costly messages that contain valuable information for the receiver or other subjects in the network. Any message sent can increase the chance that subjects find the information they are looking for and consequently their profit. We find that cooperation emerges spontaneously and remains stable over time. In an additional treatment, we provide a non-binding suggestion about who to contact at the beginning of the experiment. We find that subjects partially follow our recommendation, and this increases their own and others' profit. Despite the removal of suggestions, subjects build long-lasting relationships with the suggested contacts.

Supplementary Information

The online version contains supplementary material available at 10.1007/s41109-023-00588-x.

Fixation dynamics on hypergraphs

Hypergraphs have been a useful tool for analyzing population dynamics such as opinion formation and the public goods game occurring in overlapping groups of individuals. In the present study, we propose and analyze evolutionary dynamics on hypergraphs, in which each node takes one of the two types of different but constant fitness values. For the corresponding dynamics on conventional networks, under the birth-death process and uniform initial conditions, most networks are known to be amplifiers of natural selection; amplifiers by definition enhance the difference in the strength of the two competing types in terms of the probability that the mutant type fixates in the population. In contrast, we provide strong computational evidence that a majority of hypergraphs are suppressors of selection under the same conditions by combining theoretical and numerical analyses. We also show that this suppressing effect is not explained by one-mode projection, which is a standard method for expressing hypergraph data as a conventional network. Our results suggest that the modeling framework for structured populations in addition to the specific network structure is an important determinant of evolutionary dynamics, paving a way to studying fixation dynamics on higher-order networks including hypergraphs.

Zealous cooperation does not always promote cooperation in public goods games

There is a conventional belief that prosocial behaviors cannot arise through selfish human nature, because defection always exploits cooperation to achieve a higher payoff at an individual level. Unyieldingly, some people hope to move society to cooperation through their zealous cooperation, regardless of payoffs. From the perspective of spatial evolutionary games, however, such zealous behavior is unnecessary because cooperation can emerge from selfish human nature by aggregating in evolution. Yet, to what extent can zealous cooperation induce others to cooperate? We assume a fraction of zealous agents in spatial public goods games who always cooperate. The results show that a moderate proportion of these zealous cooperators can diminish the cooperation level in the system, and cooperation is only promoted when zealots are many. Regarding spatial behaviors, the areas of zealous cooperation in a medium density can prevent evolutionary cooperation from passing through and aggregating. The phenomenon of zealous cooperation impeding cooperation becomes more pronounced when agents become less random and more selfish. This is because dotted zealous cooperation provides significant payoffs to neighboring defection, making them more solid in fitness. In this way, we also find that when zealous cooperators have low productivity, the neighbors receive fewer benefits by exploitation, thus allowing cooperation to spread. We also study replicator dynamics in unstructured populations where zealous cooperation always promotes cooperation, agreeing that zealous cooperation hindering cooperation is a spatial effect.

Using genetic association data to guide drug discovery and development: Review of methods and applications

Evidence on the validity of drug targets from randomized trials is reliable but typically expensive and slow to obtain. In contrast, evidence from conventional observational epidemiological studies is less reliable because of the potential for bias from confounding and reverse causation. Mendelian randomization is a quasi-experimental approach analogous to a randomized trial that exploits naturally occurring randomization in the transmission of genetic variants. In Mendelian randomization, genetic variants that can be regarded as proxies for an intervention on the proposed drug target are leveraged as instrumental variables to investigate potential effects on biomarkers and disease outcomes in large-scale observational datasets. This approach can be implemented rapidly for a range of drug targets to provide evidence on their effects and thus inform on their priority for further investigation. In this review, we present statistical methods and their applications to showcase the diverse opportunities for applying Mendelian randomization in guiding clinical development efforts, thus enabling interventions to target the right mechanism in the right population group at the right time. These methods can inform investigators on the mechanisms underlying drug effects, their related biomarkers, implications for the timing of interventions, and the population subgroups that stand to gain the most benefit. Most methods can be implemented with publicly available data on summarized genetic associations with traits and diseases, meaning that the only major limitations to their usage are the availability of appropriately powered studies for the exposure and outcome and the existence of a suitable genetic proxy for the proposed intervention.

Optimization of institutional incentives for cooperation in structured populations

The application of incentives, such as reward and punishment, is a frequently applied way for promoting cooperation among interacting individuals in structured populations. However, how to properly use the incentives is still a challenging problem for incentive-providing institutions. In particular, since the implementation of incentive is costly, to explore the optimal incentive protocol, which ensures the desired collective goal at a minimal cost, is worthy of study. In this work, we consider the positive and negative incentives for a structured population of individuals whose conflicting interactions are characterized by a Prisoner's Dilemma game. We establish an index function for quantifying the cumulative cost during the process of incentive implementation, and theoretically derive the optimal positive and negative incentive protocols for cooperation on regular networks. We find that both types of optimal incentive protocols are identical and time-invariant. Moreover, we compare the optimal rewarding and punishing schemes concerning implementation cost and provide a rigorous basis for the usage of incentives in the game-theoretical framework. We further perform computer simulations to support our theoretical results and explore their robustness for different types of population structures, including regular, random, small-world and scale-free networks.

Modelling speciation: Problems and implications

Darwin's and Wallace's 1859 explanation that novel speciation resulted from natural variants that had been subjected to selection was refined over the next 150 years as genetic inheritance and the importance of mutation-induced change were discovered, the quantitative theory of evolutionary population genetics was produced, the speed of genetic change in small populations became apparent and the ramifications of the DNA revolution became clear. This paper first discusses the modern view of speciation in its historical context. It then uses systems-biology approaches to consider the many complex processes that underpin the production of a new species; these extend in scale from genes to populations with the processes of variation, selection and speciation being affected by factors that range from mutation to climate change. Here, events at a particular scale level (e.g. protein network activity) are activated by the output of the level immediately below (i.e. gene expression) and generate a new output that activates the layer above (e.g. embryological development), with this change often being modulated by feedback from higher and lower levels. The analysis shows that activity at each level in the evolution of a new species is marked by stochastic activity, with mutation of course being the key step for variation. The paper examines events at each of these scale levels and particularly considers how the pathway by which mutation leads to phenotypic variants and the wide range of factors that drive selection can be investigated computationally. It concludes that, such is the complexity of speciation, most steps in the process are currently difficult to model and that predictions about future speciation will, apart from a few special cases, be hard to make. The corollary is that opportunities for novel variants to form are maximised.

Social dilemmas of sociality due to beneficial and costly contagion

Levels of sociality in nature vary widely. Some species are solitary; others live in family groups; some form complex multi-family societies. Increased levels of social interaction can allow for the spread of useful innovations and beneficial information, but can also facilitate the spread of harmful contagions, such as infectious diseases. It is natural to assume that these contagion processes shape the evolution of complex social systems, but an explicit account of the dynamics of sociality under selection pressure imposed by contagion remains elusive. We consider a model for the evolution of sociality strategies in the presence of both a beneficial and costly contagion. We study the dynamics of this model at three timescales: using a susceptible-infectious-susceptible (SIS) model to describe contagion spread for given sociality strategies, a replicator equation to study the changing fractions of two different levels of sociality, and an adaptive dynamics approach to study the long-time evolution of the population level of sociality. For a wide range of assumptions about the benefits and costs of infection, we identify a social dilemma: the evolutionarily-stable sociality strategy (ESS) is distinct from the collective optimum—the level of sociality that would be best for all individuals. In particular, the ESS level of social interaction is greater (respectively less) than the social optimum when the good contagion spreads more (respectively less) readily than the bad contagion. Our results shed light on how contagion shapes the evolution of social interaction, but reveals that evolution may not necessarily lead populations to social structures that are good for any or all.

Evolutionary Kuramoto dynamics

Biological systems have a variety of time-keeping mechanisms ranging from molecular clocks within cells to a complex interconnected unit across an entire organism. The suprachiasmatic nucleus, comprising interconnected oscillatory neurons, serves as a master-clock in mammals. The ubiquity of such systems indicates an evolutionary benefit that outweighs the cost of establishing and maintaining them, but little is known about the process of evolutionary development. To begin to address this shortfall, we introduce and analyse a new evolutionary game theoretic framework modelling the behaviour and evolution of systems of coupled oscillators. Each oscillator is characterized by a pair of dynamic behavioural dimensions, a phase and a communication strategy, along which evolution occurs. We measure success of mutations by comparing the benefit of synchronization balanced against the cost of connections between the oscillators. Despite the simple set-up, this model exhibits non-trivial behaviours mimicking several different classical games—the Prisoner’s Dilemma, snowdrift games, coordination games—as the landscape of the oscillators changes over time. Across many situations, we find a surprisingly simple characterization of synchronization through connectivity and communication: if the benefit of synchronization is greater than twice the cost, the system will evolve towards complete communication and phase synchronization.

A game-based approach for designing a collaborative evolution mechanism for unmanned swarms on community networks

Intelligent and coordinated unmanned aerial vehicle (UAV) swarm combat will be the main mode of warfare in the future, and mechanistic design of autonomous cooperation within swarms is the key to enhancing combat effectiveness. Exploration of the essential features and patterns of autonomous collaboration in unmanned swarms has become the focus of scientific research and technological applications, in keeping with the evolving conceptions of the military theatre. However, given the unique attributes of the military and the novelty of the warfare mode of unmanned swarms, few achievements have been reported in the existing research. In this study, we analysed the military requirements of unmanned swarm operations and proposed an analytic framework for autonomous collaboration. Then, a literature review addressing swarm evolution dynamics, game-based swarm collaboration, and collaborative evolution on complex networks was conducted. Next, on the basis of the above work, we designed a community network for unmanned swarm cooperation and constructed a collaborative evolution model based on the multiplayer public goods game (PGG). Furthermore, according to the “network” and “model”, the dynamic evolution process of swarm collaboration was formally deduced. Finally, a simulation was conducted to analyse the influence of relevant parameters (i.e., swarm size, degree distribution, cost, multiplication factor) on the collaborative behaviour of unmanned swarms. According to the simulation results, some reasonable suggestions for collaborative management and control in swarm operation are given, which can provide theoretical reference and decision-making support for the design of coordination mechanisms and improved combat effectiveness in unmanned swarm operation.

Evolution of direct reciprocity in group-structured populations

People tend to have their social interactions with members of their own community. Such group-structured interactions can have a profound impact on the behaviors that evolve. Group structure affects the way people cooperate, and how they reciprocate each other's cooperative actions. Past work has shown that population structure and reciprocity can both promote the evolution of cooperation. Yet the impact of these mechanisms has been typically studied in isolation. In this work, we study how the two mechanisms interact. Using a game-theoretic model, we explore how people engage in reciprocal cooperation in group-structured populations, compared to well-mixed populations of equal size. In this model, the population is subdivided into groups. Individuals engage in pairwise interactions within groups while they also have chances to imitate strategies outside the groups. To derive analytical results, we focus on two scenarios. In the first scenario, we assume a complete separation of time scales. Mutations are rare compared to between-group comparisons, which themselves are rare compared to within-group comparisons. In the second scenario, there is a partial separation of time scales, where mutations and between-group comparisons occur at a comparable rate. In both scenarios, we find that the effect of population structure depends on the benefit of cooperation. When this benefit is small, group-structured populations are more cooperative. But when the benefit is large, well-mixed populations result in more cooperation. Overall, our results reveal how group structure can sometimes enhance and sometimes suppress the evolution of cooperation.

Altruistic behaviors and cooperation among gifted adolescents

The present study is a differential study that describes the nature of the relationship between cooperation and altruistic behavior in a sample of gifted adolescents in three universities in Egypt and Kuwait University. It also identified the differences between males/females, and senior students/junior students in both cooperation and altruism. A total of 237 gifted adolescents—with average age 21.3 ± SD 2.6 years—from three Egyptian universities: Alexandria University, Sadat Academy for Management Sciences, and Suez University (in Egypt), and Kuwait University, were involved in this study. Measures used in the study include the Scales for Rating the Behavioral Characteristics of Superior Students (SRBCSS), Generative Altruism Scale (GAlS), and The Cooperative/Competitive Strategy Scale (CCSS). Results revealed that there is a significant positive relationship between altruism and cooperation among gifted adolescents. Also, findings show that there are statistically significant differences between males and females in both altruism and cooperation. In addition, there are differences statistically significant between senior students and junior students in both altruism and cooperation in favor of senior students. It is recommended that altruism and cooperation intervention-based programs should be designed to increase the adaptive behaviors of adolescents.

The role of evolutionary game theory in spatial and non-spatial models of the survival of cooperation in cancer: a review

Evolutionary game theory (EGT) is a branch of mathematics which considers populations of individuals interacting with each other to receive pay-offs. An individual’s pay-off is dependent on the strategy of its opponent(s) as well as on its own, and the higher its pay-off, the higher its reproductive fitness. Its offspring generally inherit its interaction strategy, subject to random mutation. Over time, the composition of the population shifts as different strategies spread or are driven extinct. In the last 25 years there has been a flood of interest in applying EGT to cancer modelling, with the aim of explaining how cancerous mutations spread through healthy tissue and how intercellular cooperation persists in tumour-cell populations. This review traces this body of work from theoretical analyses of well-mixed infinite populations through to more realistic spatial models of the development of cooperation between epithelial cells. We also consider work in which EGT has been used to make experimental predictions about the evolution of cancer, and discuss work that remains to be done before EGT can make large-scale contributions to clinical treatment and patient outcomes.

Evolutionary instability of selfish learning in repeated games

Across many domains of interaction, both natural and artificial, individuals use past experience to shape future behaviors. The results of such learning processes depend on what individuals wish to maximize. A natural objective is one's own success. However, when two such "selfish" learners interact with each other, the outcome can be detrimental to both, especially when there are conflicts of interest. Here, we explore how a learner can align incentives with a selfish opponent. Moreover, we consider the dynamics that arise when learning rules themselves are subject to evolutionary pressure. By combining extensive simulations and analytical techniques, we demonstrate that selfish learning is unstable in most classical two-player repeated games. If evolution operates on the level of long-run payoffs, selection instead favors learning rules that incorporate social (other-regarding) preferences. To further corroborate these results, we analyze data from a repeated prisoner's dilemma experiment. We find that selfish learning is insufficient to explain human behavior when there is a trade-off between payoff maximization and fairness.

When stochasticity leads to cooperation

The evolution of cooperation has gained more attention after Smith introduced game theory in the study of evolutionary biology. Subsequent works have extensively explained this phenomenon, consistently showing the importance of spatial structure for the evolution of cooperation. Here we analyze the effect of stochasticity on the evolution of cooperation in group-structured populations. We find a simple formula for the fixation probability of cooperators and show that cooperation can be favored by selection if a condition similar to Hamilton's rule is satisfied, which is also valid for strong selection and high migration. In fact, cooperation can be favored even in the absence of population viscosity and in the limit of an infinite number of finite-size groups. We discuss the importance of stochastic fluctuations in helping cooperation. We argue that this may be a general principle because fluctuations favoring the cooperators are often much more impactful than those favoring the defectors.

Spatial patterns in ecological systems: from microbial colonies to landscapes

Self-organized spatial patterns are ubiquitous in ecological systems and allow populations to adopt non-trivial spatial distributions starting from disordered configurations. These patterns form due to diverse nonlinear interactions among organisms and between organisms and their environment, and lead to the emergence of new (eco)system-level properties unique to self-organized systems. Such pattern consequences include higher resilience and resistance to environmental changes, abrupt ecosystem collapse, hysteresis loops, and reversal of competitive exclusion. Here, we review ecological systems exhibiting self-organized patterns. We establish two broad pattern categories depending on whether the self-organizing process is primarily driven by nonlinear density-dependent demographic rates or by nonlinear density-dependent movement. Using this organization, we examine a wide range of observational scales, from microbial colonies to whole ecosystems, and discuss the mechanisms hypothesized to underlie observed patterns and their system-level consequences. For each example, we review both the empirical evidence and the existing theoretical frameworks developed to identify the causes and consequences of patterning. Finally, we trace qualitative similarities across systems and propose possible ways of developing a more quantitative understanding of how self-organization operates across systems and observational scales in ecology.

Population Structure and Genetic Diversity of Chinese Honeybee (Apis Cerana Cerana) in Central China

Central China has a rich terrain with a temperate monsoon climate and varied natural environments for the Chinese honeybee (Apis cerana cerana). However, little comprehensive research on population genetic diversity has been done in this area. A population survey of the structure and genetic diversity of Apis cerana cerana in this area is deeply needed for understanding adaptation to variable environments and providing more references for the protection of honeybee biodiversity. In this study, we present a dataset of 72 populations of Chinese honeybees collected from nine sites by whole genome sequencing in Central China. We obtained 2,790,214,878 clean reads with an average covering a depth of 22×. A total of 27,361,052 single nucleotide polymorphisms (SNPs) were obtained by mapping to the reference genome with an average mapping rate of 93.03%. Genetic evolution analysis was presented via the population structure and genetic diversity based on the datasets of SNPs. It showed that Apis cerana cerana in plains exhibited higher genetic diversity than in mountain areas. The mantel test between Apis cerana cerana groups revealed that some physical obstacles, especially the overurbanization of the plains, contributed to the differentiation. This study is conducive to elucidating the evolution of Apis cerana in different environments and provides a theoretical basis for investigating and protecting the Chinese honeybee.

Population genetics in microchannels

Many microbial populations proliferate in small channels. In such environments, reproducing cells organize in parallel lanes. Reproducing cells shift these lanes, potentially expelling other cells from the channel. In this paper, we combine theory and experiments to understand how these dynamics affects the diversity of a microbial population. We theoretically predict that genetic diversity is quickly lost along lanes of cells. Our experiments confirm that a population of proliferating Escherichia coli in a microchannel organizes into lanes of genetically identical cells within a few generations. Our findings elucidate the effect of lane formation on populations evolution, with potential applications ranging from microbial ecology in soil to dynamics of epithelial tissues in higher organisms.

Spatial constraints, such as rigid barriers, affect the dynamics of cell populations, potentially altering the course of natural evolution. In this paper, we investigate the population genetics of Escherichia coli proliferating in microchannels with open ends. Our analysis is based on a population model, in which reproducing cells shift entire lanes of cells toward the open ends of the channel. The model predicts that diversity is lost very rapidly within lanes but at a much slower pace among lanes. As a consequence, two mixed, neutral E. coli strains competing in a microchannel must organize into an ordered regular stripe pattern in the course of a few generations. These predictions are in quantitative agreement with our experiments. We also demonstrate that random mutations appearing in the middle of the channel are much more likely to reach fixation than those occurring elsewhere. Our results illustrate fundamental mechanisms of microbial evolution in spatially confined space.

Lanza V, Rodríguez-Beltrán J, Galán JC, San Millán A, Cantón R, Coque TM. Evolutionary Pathways and Trajectories in Antibiotic Resistance

Evolution is the hallmark of life. Descriptions of the evolution of microorganisms have provided a wealth of information, but knowledge regarding "what happened" has precluded a deeper understanding of "how" evolution has proceeded, as in the case of antimicrobial resistance. The difficulty in answering the "how" question lies in the multihierarchical dimensions of evolutionary processes, nested in complex networks, encompassing all units of selection, from genes to communities and ecosystems. At the simplest ontological level (as resistance genes), evolution proceeds by random (mutation and drift) and directional (natural selection) processes; however, sequential pathways of adaptive variation can occasionally be observed, and under fixed circumstances (particular fitness landscapes), evolution is predictable. At the highest level (such as that of plasmids, clones, species, microbiotas), the systems' degrees of freedom increase dramatically, related to the variable dispersal, fragmentation, relatedness, or coalescence of bacterial populations, depending on heterogeneous and changing niches and selective gradients in complex environments. Evolutionary trajectories of antibiotic resistance find their way in these changing landscapes subjected to random variations, becoming highly entropic and therefore unpredictable. However, experimental, phylogenetic, and ecogenetic analyses reveal preferential frequented paths (highways) where antibiotic resistance flows and propagates, allowing some understanding of evolutionary dynamics, modeling and designing interventions. Studies on antibiotic resistance have an applied aspect in improving individual health, One Health, and Global Health, as well as an academic value for understanding evolution. Most importantly, they have a heuristic significance as a model to reduce the negative influence of anthropogenic effects on the environment.

Interindividual cooperation mediated by partisanship complicates Madison's cure for "mischiefs of faction"

Political theorists have long argued that enlarging the political sphere to include a greater diversity of interests would cure the ills of factions in a pluralistic society. While the scope of politics has expanded dramatically over the past 75 y, polarization is markedly worse. Motivated by this paradox, we take a bottom-up approach to explore how partisan individual-level dynamics in a diverse (multidimensional) issue space can shape collective-level factionalization via an emergent dimensionality reduction. We extend a model of cultural evolution grounded in evolutionary game theory, in which individuals accumulate benefits through pairwise interactions and imitate (or learn) the strategies of successful others. The degree of partisanship determines the likelihood of learning from individuals of the opposite party. This approach captures the coupling between individual behavior, partisan-mediated opinion dynamics, and an interaction network that changes endogenously according to the evolving interests of individuals. We find that while expanding the diversity of interests can indeed improve both individual and collective outcomes, increasingly high partisan bias promotes a reduction in issue dimensionality via party-based assortment that leads to increasing polarization. When party bias becomes extreme, it also boosts interindividual cooperation, thereby further entrenching extreme polarization and creating a tug-of-war between individual cooperation and societal cohesion. These dangers of extreme partisanship are highest when individuals' interests and opinions are heavily shaped by peers and there is little independent exploration. Overall, our findings highlight the urgency to study polarization in a coupled, multilevel context.

Networks of reliable reputations and cooperation: a review

Reputation has been shown to provide an informal solution to the problem of cooperation in human societies. After reviewing models that connect reputations and cooperation, we address how reputation results from information exchange embedded in a social network that changes endogenously itself. Theoretical studies highlight that network topologies have different effects on the extent of cooperation, since they can foster or hinder the flow of reputational information. Subsequently, we review models and empirical studies that intend to grasp the coevolution of reputations, cooperation and social networks. We identify open questions in the literature concerning how networks affect the accuracy of reputations, the honesty of shared information and the spread of reputational information. Certain network topologies may facilitate biased beliefs and intergroup competition or in-group identity formation that could lead to high cooperation within but conflicts between different subgroups of a network. Our review covers theoretical, experimental and field studies across various disciplines that target these questions and could explain how the dynamics of interactions and reputations help or prevent the establishment and sustainability of cooperation in small- and large-scale societies.

This article is part of the theme issue ‘The language of cooperation: reputation and honest signalling’.

Dying to cooperate: the role of environmental harshness in human collaboration

It has been proposed that environmental stress acted as a selection pressure on the evolution of human cooperation. Through agent-based evolutionary modelling, mathematical analysis, and human experimental data we illuminate the mechanisms by which the environment influences cooperative success and decision making in a Stag Hunt game. The modelling and mathematical results show that only cooperative foraging phenotypes survive the harshest of environments but pay a penalty for miscoordination in favourable environments. When agents are allowed to coordinate their hunting intentions by communicating, cooperative phenotypes outcompete those who pursue individual strategies in almost all environmental and payoff scenarios examined. Data from human participants show flexible decision-making in face of cooperative uncertainty, favouring high-risk, high-reward strategy when environments are harsher and starvation is imminent. Converging lines of evidence from the three approaches indicate a significant role for environmental variability in human cooperative dynamics and the species-unique cognition designed to support it.

The network structure affects the fixation probability when it couples to the birth-death dynamics in finite population

The study of evolutionary dynamics on graphs is an interesting topic for researchers in various fields of science and mathematics. In systems with finite population, different model dynamics are distinguished by their effects on two important quantities: fixation probability and fixation time. The isothermal theorem declares that the fixation probability is the same for a wide range of graphs and it only depends on the population size. This has also been proved for more complex graphs that are called complex networks. In this work, we propose a model that couples the population dynamics to the network structure and show that in this case, the isothermal theorem is being violated. In our model the death rate of a mutant depends on its number of neighbors, and neutral drift holds only in the average. We investigate the fixation probability behavior in terms of the complexity parameter, such as the scale-free exponent for the scale-free network and the rewiring probability for the small-world network.

In this work, we examine an evolutionary model that considers the effect of competition between the mutated individuals for acquiring more resources. This competition has an effect on the death rate of mutants. The model purposes that the death rate of each mutant depends on the number of its neighbors, while the average death rate in the population is equal to one. The birth rate for all individuals is assumed to be the same and equal to one. This situation is called here the ‘neutral drift in average’. We study the dynamics of the model on complex networks to take into account the non-uniformity of the environment. The results show the fixation probability differs from the Moran model. For the construction of this model, we were biologically motivated by the avascular tumour, which consists of a population of normal and cancer cells. The cancer cells likely need more oxygen than normal cells. There is a competition between cells for consuming oxygen, and cancer cells are far more sensitive to the amount of oxygen in the environment than normal cells. This means the death rate of a cancer cell grows by increasing the number of its neighbors.

Modeling pluralism and self-regulation explains the emergence of cooperation in networked societies

Understanding the dynamics of cooperative behavior of individuals in complex societies represents a fundamental research question which puzzles scientists working in heterogeneous fields. Many studies have been developed using the unitary agent assumption, which embeds the idea that when making decisions, individuals share the same socio-cultural parameters. In this paper, we propose the ECHO-EGN model, based on Evolutionary Game Theory, which relaxes this strong assumption by considering the heterogeneity of three fundamental socio-cultural aspects ruling the behavior of groups of people: the propensity to be more cooperative with members of the same group (Endogamic cooperation), the propensity to cooperate with the public domain (Civicness) and the propensity to prefer connections with members of the same group (Homophily). The ECHO-EGN model is shown to have high performance in describing real world behavior of interacting individuals living in complex environments. Extensive numerical experiments allowing the comparison of real data and model simulations confirmed that the introduction of the above mechanisms enhances the realism in the modelling of cooperation dynamics. Additionally, theoretical findings allow us to conclude that endogamic cooperation may limit significantly the emergence of cooperation.

Fixation probabilities in network structured meta-populations

The effect of population structure on evolutionary dynamics is a long-lasting research topic in evolutionary ecology and population genetics. Evolutionary graph theory is a popular approach to this problem, where individuals are located on the nodes of a network and can replace each other via the links. We study the effect of complex network structure on the fixation probability, but instead of networks of individuals, we model a network of sub-populations with a probability of migration between them. We ask how the structure of such a meta-population and the rate of migration affect the fixation probability. Many of the known results for networks of individuals carry over to meta-populations, in particular for regular networks or low symmetric migration probabilities. However, when patch sizes differ we find interesting deviations between structured meta-populations and networks of individuals. For example, a two patch structure with unequal population size suppresses selection for low migration probabilities.

Evolutionary ecology theory - microbial population structure

Microbial populations typically show a large degree of intra-population diversity. This diversity is intertwined with the structure of the population. Here, we discuss endogenous and exogenous drivers of population structure in microbes and how the population structure can affect evolutionary dynamics and vice versa. Endogenous structure, which can be genetic or demographic, is driven by the ecology and evolutionary dynamics within the population. Exogenous structure is typically driven by the spatial and temporal properties of the environment. A particular interesting case arises when also this exogenous structure experiences feedbacks from the microbial population.

Cooperative success in epithelial public goods games

Cancer cells obtain mutations which rely on the production of diffusible growth factors to confer a fitness benefit. These mutations can be considered cooperative, and studied as public goods games within the framework of evolutionary game theory. The population structure, benefit function and update rule all influence the evolutionary success of cooperators. We model the evolution of cooperation in epithelial cells using the Voronoi tessellation model. Unlike traditional evolutionary graph theory, this allows us to implement global updating, for which birth and death events are spatially decoupled. We compare, for a sigmoid benefit function, the conditions for cooperation to be favoured and/or beneficial for well-mixed and structured populations. We find that when population structure is combined with global updating, cooperation is more successful than if there were local updating or the population were well-mixed. Interestingly, the qualitative behaviour for the well-mixed population and the Voronoi tessellation model is remarkably similar, but the latter case requires significantly lower incentives to ensure cooperation.

The role of habitat configuration in shaping animal population processes: a framework to generate quantitative predictions

By shaping where individuals move, habitat configuration can fundamentally structure animal populations. Yet, we currently lack a framework for generating quantitative predictions about the role of habitat configuration in modulating population outcomes. To address this gap, we propose a modelling framework inspired by studies using networks to characterize habitat connectivity. We first define animal habitat networks, explain how they can integrate information about the different configurational features of animal habitats, and highlight the need for a bottom–up generative model that can depict realistic variations in habitat potential connectivity. Second, we describe a model for simulating animal habitat networks (available in the R package AnimalHabitatNetwork), and demonstrate its ability to generate alternative habitat configurations based on empirical data, which forms the basis for exploring the consequences of alternative habitat structures. Finally, we lay out three key research questions and demonstrate how our framework can address them. By simulating the spread of a pathogen within a population, we show how transmission properties can be impacted by both local potential connectivity and landscape-level characteristics of habitats. Our study highlights the importance of considering the underlying habitat configuration in studies linking social structure with population-level outcomes.

Aspiration dynamics generate robust predictions in heterogeneous populations

Update rules, which describe how individuals adjust their behavior over time, affect the outcome of social interactions. Theoretical studies have shown that evolutionary outcomes are sensitive to model details when update rules are imitation-based but are robust when update rules are self-evaluation based. However, studies of self-evaluation based rules have focused on homogeneous population structures where each individual has the same number of neighbors. Here, we consider heterogeneous population structures represented by weighted networks. Under weak selection, we analytically derive the condition for strategy success, which coincides with the classical condition of risk-dominance. This condition holds for all weighted networks and distributions of aspiration levels, and for individualized ways of self-evaluation. Our findings recover previous results as special cases and demonstrate the universality of the robustness property under self-evaluation based rules. Our work thus sheds light on the intrinsic difference between evolutionary dynamics under self-evaluation based and imitation-based update rules.

Social interaction outcomes can depend on the type of information individuals possess and how it is used in decision-making. Here, Zhou et al. find that self-evaluation based decision-making rules lead to evolutionary outcomes that are robust to different population structures and ways of self-evaluation.

Introducing a graph topology for robust cooperation

Identifying the conditions that support cooperation in spatial evolutionary game theory has been the focus of a large body of work. In this paper, the classical Prisoner's Dilemma is adopted as an interaction model; agents are placed on graphs and their interactions are constrained by a graph topology. A simple strategy update mechanism is used where agents copy the best performing strategy of their neighbourhood (including themselves). In this paper, we begin with a fully cooperative population and explore the robustness of the population to the introduction of defectors. We introduce a graph structure that has the property that the initial fully cooperative population is robust to any one perturbation (a change of any cooperator to a defector). We present a proof of this property and specify the necessary constraints on the graph. Furthermore, given the standard game payoffs, we calculate the smallest graph which possesses this property. We present an approach for increasing the size of the graph and we show empirically that this extended graph is robust to an increasing percentage of perturbations. We define a new class of graphs for the purpose of future work.

Anthropological Prosociality via Sub-Group Level Selection

A perennial challenge of evolutionary psychology is explaining prosocial traits such as a preference for fairness rather than inequality, compassion towards suffering, and an instinctive ability to coordinate within small teams. Considering recent fossil evidence and a novel logical test, we deem present explanations insufficiently explanatory of the divergence of hominins. In answering this question, we focus on the divergence of hominins from the last common ancestor (LCA) shared with Pan. We consider recent fossil discoveries that indicate the LCA was bipedal, which reduces the cogency of this explanation for hominin development. We also review evolutionary theory that claims to explain how hominins developed into modern humans, however it is found that no mechanism differentiates hominins from other primates. Either the mechanism was available to the last common ancestor (LCA) (with P. troglodytes as its proxy), or because early hominins had insufficient cognition to utilise the mechanism. A novel mechanism, sub-group level selection (sGLS) is hypothesised by triangulating two pieces of data rarely considered by evolutionary biologists. These are behavioural dimorphism of Pan (chimpanzees and bonobos) that remain identifiable in modern humans, and the social behaviour of primate troops in a savannah ecology. We then contend that sGLS supplied an exponential effect which was available to LCA who left the forest, but was not sufficiently available to any other primates. In conclusion, while only indirectly supported by various evidence, sGLS is found to be singularly and persuasively explanatory of human's unique evolutionary story.

Group Behavior and Emergence of Cancer Drug Resistance

Drug resistance is a major impediment in cancer. Although it is generally thought that acquired drug resistance is due to genetic mutations, emerging evidence indicates that nongenetic mechanisms also play an important role. Resistance emerges through a complex interplay of clonal groups within a heterogeneous tumor and the surrounding microenvironment. Traits such as phenotypic plasticity, intercellular communication, and adaptive stress response, act in concert to ensure survival of intermediate reversible phenotypes, until permanent, resistant clones can emerge. Understanding the role of group behavior, and the underlying nongenetic mechanisms, can lead to more efficacious treatment designs and minimize or delay emergence of resistance.

Graph-structured populations and the Hill-Robertson effect

The Hill-Robertson effect describes how, in a finite panmictic diploid population, selection at one diallelic locus reduces the fixation probability of a selectively favoured allele at a second, linked diallelic locus. Here we investigate the influence of population structure on the Hill-Robertson effect in a population of size N. We model population structure as a network by assuming that individuals occupy nodes on a graph connected by edges that link members who can reproduce with each other. Three regular networks (fully connected, ring and torus), two forms of scale-free network and a star are examined. We find that (i) the effect of population structure on the probability of fixation of the favourable allele is invariant for regular structures, but on some scale-free networks and a star, this probability is greatly reduced; (ii) compared to a panmictic population, the mean time to fixation of the favoured allele is much greater on a ring, torus and linear scale-free network, but much less on power-2 scale-free and star networks; (iii) the likelihood with which each of the four possible haplotypes eventually fix is similar across regular networks, but scale-free populations and the star are consistently less likely and much faster to fix the optimal haplotype; (iv) increasing recombination increases the likelihood of fixing the favoured haplotype across all structures, whereas the time to fixation of that haplotype usually increased, and (v) star-like structures were overwhelmingly likely to fix the least fit haplotype and did so significantly more rapidly than other populations. Last, we find that small (N < 64) panmictic populations do not exhibit the scaling property expected from Hill & Robertson (1966 Genet. Res. 8, 269-294. (doi:10.1017/S0016672300010156)).

A game-theoretical dynamic imitation model on networks

A game-theoretical model is constructed to capture the effect of imitation on the evolution of cooperation. This imitation describes the case where successful individuals are more likely to be imitated by newcomers who will employ their strategies and social networks. Two classical repeated strategies 'always defect (ALLD)' and 'tit-for-tat (TFT)' are adopted. Mathematical analyses are mainly conducted by the method of coalescence theory. Under the assumption of a large population size and weak selection, the results show that the evolution of cooperation is promoted in this dynamic network. As we observed that the critical benefit-to-cost ratio is smaller compared to that in well-mixed populations. The critical benefit-to-cost ratio approaches a specific value which depends on three parameters, the repeated rounds of the game, the effective strategy mutation rate, and the effective link mutation rate. Specifically, for a very high value of the effective link mutation rate, the critical benefit-to-cost ratio approaches 1. Remarkably, for a low value of the effective link mutation rate, by letting the effective strategy mutation is nearly equal to zero, the critical benefit-to-cost ratio approaches [Formula: see text] for the resulting highly connected networks, which allows TFT to be evolutionary stable. It illustrates that dominance of TFTs is associated with more connected networks. This research can enrich the theory of the coevolution of game strategy and network structure with dynamic imitation.

A collective risk dilemma for tourism restrictions under the COVID-19 context

The current COVID-19 pandemic has impacted millions of people and the global economy. Tourism has been one the most affected economic sectors because of the mobility restrictions established by governments and uncoordinated actions from origin and destination regions. The coordination of restrictions and reopening policies could help control the spread of virus and enhance economies, but this is not an easy endeavor since touristic companies, citizens, and local governments have conflicting interests. We propose an evolutionary game model that reflects a collective risk dilemma behind these decisions. To this aim, we represent regions as players, organized in groups; and consider the perceived risk as a strict lock-down and null economic activity. The costs for regions when restricting their mobility are heterogeneous, given that the dependence on tourism of each region is diverse. Our analysis shows that, for both large populations and the EU NUTS2 case study, the existence of heterogeneous costs enhances global agreements. Furthermore, the decision on how to group regions to maximize the regions' agreement of the population is a relevant issue for decision makers to consider. We find out that a layout of groups based on similar costs of cooperation boosts the regions' agreements and avoid the risk of having a total lock-down and a negligible tourism activity. These findings can guide policy makers to facilitate agreements among regions to maximize the tourism recovery.