The spontaneous emergence of conventions: An experimental study of cultural evolution

How do shared conventions emerge in complex decentralized social systems? This question engages fields as diverse as linguistics, sociology, and cognitive science. Previous empirical attempts to solve this puzzle all presuppose that formal or informal institutions, such as incentives for global agreement, coordinated leadership, or aggregated information about the population, are needed to facilitate a solution. Evolutionary theories of social conventions, by contrast, hypothesize that such institutions are not necessary in order for social conventions to form. However, empirical tests of this hypothesis have been hindered by the difficulties of evaluating the real-time creation of new collective behaviors in large decentralized populations. Here, we present experimental results—replicated at several scales—that demonstrate the spontaneous creation of universally adopted social conventions and show how simple changes in a population’s network structure can direct the dynamics of norm formation, driving human populations with no ambition for large scale coordination to rapidly evolve shared social conventions.Social conventions are the foundation for social and economic life (1–7), However, it remains a central question in the social, behavioral, and cognitive sciences to understand how these patterns of collective behavior can emerge from seemingly arbitrary initial conditions (2–4, 8, 9). Large populations frequently manage to coordinate on shared conventions despite a continuously evolving stream of alternatives to choose from and no a priori differences in the expected value of the options (1, 3, 4, 10). For instance, populations are able to produce linguistic conventions on accepted names for children and pets (11), on common names for colors (12), and on popular terms for novel cultural artifacts, such as referring to junk email as “SPAM” (13, 14). Similarly, economic conventions, such as bartering systems (2), beliefs about fairness (3), and consensus regarding the exchangeability of goods and services (15), emerge with clear and widespread agreement within economic communities yet vary broadly across them (3, 16).Prominent theories of social conventions suggest that institutional mechanisms—such as centralized authority (14), incentives for collective agreement (15), social leadership (16), or aggregated information (17)—can explain global coordination. However, these theories do not explain whether, or how, it is possible for conventions to emerge when social institutions are not already in place to guide the process. A compelling alternative approach comes from theories of social evolution (2, 18–20). Social evolutionary theories maintain that networks of locally interacting individuals can spontaneously self-organize to produce global coordination (21, 22). Although there is widespread interest in this approach to social norms (6, 7, 14, 18, 23–26), the complexity of the social process has prevented systematic empirical insight into the thesis that these local dynamics are sufficient to explain universally adopted conventions (27, 28).Several difficulties have limited prior empirical research in this area. The most notable of these limitations is scale. Although compelling experiments have successfully shown the creation of new social conventions in dyadic and small group interactions (29–31), the results in small group settings can be qualitatively different from the dynamics in larger groups (Model), indicating that small group experiments are insufficient for demonstrating whether or how new conventions endogenously form in larger populations (32, 33). Important progress on this issue has been made using network-based laboratory experiments on larger groups (15, 24). However, this research has been restricted to studying coordination among players presented with two or three options with known payoffs. Natural convention formation, by contrast, is significantly complicated by the capacity of individuals to continuously innovate, which endogenously expands the “ecology” of alternatives under evaluation (23, 29, 31). Moreover, prior experimental studies have typically assumed the existence of either an explicit reward for universal coordination (15) or a mechanism that aggregates and reports the collective state of the population (17, 24), which has made it impossible to evaluate the hypothesis that global coordination is the result of purely local incentives.More recently, data science approaches to studying norms have addressed many of these issues by analyzing behavior change in large online networks (34). However, these observational studies are limited by familiar problems of identification that arise from the inability to eliminate the confounding influences of institutional mechanisms. As a result, previous empirical research has been unable to identify the collective dynamics through which social conventions can spontaneously emerge (8, 34–36).We addressed these issues by adopting a web-based experimental approach. We studied the effects of social network structure on the spontaneous evolution of social conventions in populations without any resources to facilitate global coordination (9, 37). Participants in our study were rewarded for coordinating locally, however they had neither incentives nor information for achieving large scale agreement. Further, to eliminate any preexisting bias in the evolutionary process, we studied the emergence of arbitrary linguistic conventions, in which none of the options had any a priori value or advantage over the others (3, 23). In particular, we considered the prototypical problem of whether purely local interactions can trigger the emergence of a universal naming convention (38, 39).     

Obstacles to integrated pest management adoption in developing countries

Despite its theoretical prominence and sound principles, integrated pest management (IPM) continues to suffer from anemic adoption rates in developing countries. To shed light on the reasons, we surveyed the opinions of a large and diverse pool of IPM professionals and practitioners from 96 countries by using structured concept mapping. The first phase of this method elicited 413 open-ended responses on perceived obstacles to IPM. Analysis of responses revealed 51 unique statements on obstacles, the most frequent of which was “insufficient training and technical support to farmers.” Cluster analyses, based on participant opinions, grouped these unique statements into six themes: research weaknesses, outreach weaknesses, IPM weaknesses, farmer weaknesses, pesticide industry interference, and weak adoption incentives. Subsequently, 163 participants rated the obstacles expressed in the 51 unique statements according to importance and remediation difficulty. Respondents from developing countries and high-income countries rated the obstacles differently. As a group, developing-country respondents rated “IPM requires collective action within a farming community” as their top obstacle to IPM adoption. Respondents from high-income countries prioritized instead the “shortage of well-qualified IPM experts and extensionists.” Differential prioritization was also evident among developing-country regions, and when obstacle statements were grouped into themes. Results highlighted the need to improve the participation of stakeholders from developing countries in the IPM adoption debate, and also to situate the debate within specific regional contexts.Feeding the 9,000 million people expected to inhabit Earth by 2050 will present a constant and significant challenge in terms of agricultural pest management (1–3). Despite a 15- to 20-fold increase in pesticide use since the 1960s, global crop losses to pests—arthropods, diseases, and weeds—have remained unsustainably high, even increasing in some cases (4). These losses tend to be highest in developing countries, averaging 40–50%, compared with 25–30% in high-income countries (5). Alarmingly, crop pest problems are projected to increase because of agricultural intensification (4, 6), trade globalization (7), and, potentially, climate change (8).Since the 1960s, integrated pest management (IPM) has become the dominant crop protection paradigm, being endorsed globally by scientists, policymakers, and international development agencies (2, 9–15). The definitions of IPM are numerous, but all involve the coordinated integration of multiple complementary methods to suppress pests in a safe, cost-effective, and environmentally friendly manner (9, 11). These definitions also recognize IPM as a dynamic process in terms of design, implementation, and evaluation (11). In practice, however, there is a continuum of interpretations of IPM (e.g., refs. 14, 16, 17), but bounded by those that emphasize pesticide management (i.e., “tactical IPM”) and those that emphasize agroecosystem management (i.e., “strategic IPM,” also known as “ecologically based pest management”) (16, 18, 19). Despite apparently solid conceptual grounding and substantial promotion by the aforementioned groups, IPM has a discouragingly poor adoption record, particularly in developing-country settings (9, 10, 15–23), raising questions over its applicability as it is presently conceived (15, 16, 22, 24).The possible reasons behind the developing countries’ poor adoption of IPM have been the subject of considerable discussion since the 1980s (9, 15, 16, 22, 25–31), but this debate has been notable for the limited direct involvement from developing-country stakeholders. Most of the literature exploring poor adoption of IPM in the developing world has originated in the developed world (e.g., refs. 15, 16, 22). An international workshop, entitled “IPM in Developing Countries,” was held at the Pontificia Universidad Católica del Ecuador (PUCE) from October 31 to November 3, 2011. Poor IPM adoption spontaneously became a central discussion point, creating an opportunity to address the apparent participation bias in the IPM adoption debate.It was therefore decided to explore the topic further by eliciting and mapping the opinions of a large and diverse pool of IPM professionals and practitioners from around the world, including many based in developing countries. The objective was to generate and prioritize a broad list of hypotheses to explain poor IPM adoption in developing-country agriculture. We also wanted to explore differences as influenced by respondents’ characteristics, particularly their region of practice. To achieve these objectives, we used structured concept mapping (32), an empirical survey method often used to quantify and give thematic structure to open-ended opinions (33).We know of only one other similar study that characterizes obstacles to IPM. It was based on the structured responses of 153 experts, all from high-income countries (30). Our survey was designed to progress from unstructured to structured responses, and to reach a much larger and diverse pool of participants, particularly those from the “Global South.” Considering that the vast majority of farmers live in developing countries (34), it would seem imperative that the voices from this region be heard.     

Empirical social triad statistics can be explained with dyadic homophylic interactions

The remarkable robustness of many social systems has been associated with a peculiar triangular structure in the underlying social networks. Triples of people that have three positive relations (e.g., friendship) between each other are strongly overrepresented. Triples with two negative relations (e.g., enmity) and one positive relation are also overrepresented, and triples with one or three negative relations are drastically suppressed. For almost a century, the mechanism behind these very specific (“balanced”) triad statistics remained elusive. Here, we propose a simple realistic adaptive network model, where agents tend to minimize social tension that arises from dyadic interactions. Both opinions of agents and their signed links (positive or negative relations) are updated in the dynamics. The key aspect of the model resides in the fact that agents only need information about their local neighbors in the network and do not require (often unrealistic) higher-order network information for their relation and opinion updates. We demonstrate the quality of the model on detailed temporal relation data of a society of thousands of players of a massive multiplayer online game where we can observe triangle formation directly. It not only successfully predicts the distribution of triangle types but also explains empirical group size distributions, which are essential for social cohesion. We discuss the details of the phase diagrams behind the model and their parameter dependence, and we comment on to what extent the results might apply universally in societies.

Recognizing the fundamental role of triadic interactions in shaping social structures, Heider (1) introduced the notion of balanced and unbalanced triads. A triad (triangle) of individuals is balanced if it includes zero or two negative links; otherwise, it is unbalanced. Heider (1) hypothesized that social networks have a tendency to reduce the number of unbalanced triangles over time such that balanced triads would dominate in a stationary situation. This theory of “social balance” has been confirmed empirically in many different contexts, such as schools (2), monasteries (3), social media (4), or computer games (5). Social balance theory and its generalizations (6–8) have been studied extensively for more than a half century for their importance in understanding polarization of societies (9), global organization of social networks (10), evolution of the network of international relations (11), opinion formation (12, 13), epidemic spreading (14, 15), government formation (16), and decision-making processes (17).Following Heider’s intuition (18–41), current approaches toward social balance often account for the effect of triangles on social network formation in one way or another. For example, the models in refs. 22 and 23 consider a reduction of the number of unbalanced triads either in the neighborhood of a node or in the whole network. The latter process sometimes leads to imbalance due to the existence of so-called jammed states (42). In order to reach social balance, individuals can also update their links according to their relations to common neighbors (18–21) or adjust link weights via opinion updates (24, 25) or via a minimization of social stress based on triadic interactions (37–44). These works not only ignore the difficulty of individuals to know the social interactions beyond their direct neighbors in reality, so far, they also have not considered the detailed statistical properties of the over- or underrepresentation of the different types of triads, such as those reported in refs. 4 and 5, with the exception of refs. 43 and 44.It is generally believed that the similarity of individuals plays a crucial role in the formation of social ties in social networks, something that has been called homophily (45–48). This means that to form a positive or negative tie with another person, people compare only pairwise overlaps in their individual opinions (dyadic interaction). It has also been argued that social link formation takes into account a tendency in people to balance their local interaction networks in the sense that they introduce friends to each other, that they do give up friendships if two mutual friends have negative attitudes toward each other, and that they tend to avoid situations where everyone feels negatively about the others. This is the essence of social balance theory (1). Obviously, link formation following social balance is cognitively much more challenging than homophily-based link formation since in the former, one has to keep in mind the many mutual relations between all your neighbors in a social network. While social balance–driven link formation certainly occurs in the context of close friendships, it is less realistic to assume that this mechanism is at work in social link formation in general. In Fig. 1, we schematically show the situation in a portion of a social network. It is generally hard for node i to know all the relations between his neighbors j, k, and l.Open in a separate windowFig. 1.Schematic view of opinion and link updates in a society. Every individual has an opinion vector whose components represent (binary) opinions on G=5 different subjects. Red (blue) links denote positive (negative) relationships. The question marks denote unknown relationships between i’s neighbors. As an agent i flips one of its opinions (red circle), si1, from 1 to –1, i can either decrease or increase its individual stress, H(i), depending on the value of the parameter α (Eq. 1). For instance, H(i) would increase if α=1 but would decrease for α=0. For high “rationality” values of individuals w.r.t. social stress, as quantified by β, the latter is more likely to be accepted, resulting in a reduction of the number of unbalanced triads in i’s neighborhood.Here, assuming that it is generally unrealistic for individuals to know their social networks at the triadic level, we aim to understand the emergence and the concrete statistics of balanced triads on the basis of dyadic or one-to-one interactions. Therefore, we use a classic homophily rule (45, 46) to define a “stress level” between any pair of individuals based on the similarity (or overlap) of their individual opinions. Here, the opinions of an individual i are represented by a vector with G components, si, that we show in Fig. 1. Homophily implies that i and j tend to become friends if the overlap (e.g., scalar product of their opinion vectors) is positive, and they become enemies if the overlap is negative. Such a specification of homophily is often referred to as an attraction–repulsion or assimilation–differentiation rule (49, 50). Assuming that, generally, social relations rearrange such as to minimize individual social stress on average, we will show that balanced triads naturally emerge from purely dyadic homophilic interactions without any explicit selection mechanisms for specific triads. We formulate the opinion link dynamics leading to social balance within a transparent physics-inspired framework. In particular, we observe a dynamic transition between two different types of balanced steady states that correspond to different compositions of balanced triads.Explaining the empirical statistics of triangles in social systems is a challenge. Early works considered groups of a few monks in a monastery (3) or a few students in classrooms (51). The studies suffered from limited data and small network sizes. Large-scale studies were first performed in online platforms (4) and in the society of players of the massive multiplayer online game (MMOG) Pardus. Players in Pardus engage in a form of economic life, such as trade and mining, and in social activities, such as communication on a number of channels, forming friendships and enmities (details are in refs. 5, 52, and 53). In the social networks of this game, balanced triads were once more confirmed to be overrepresented compared with what is expected by chance. Similar patterns of triad statistics were also observed in Epinion, Slashdot, and Wikipedia (4). More details on the Pardus society are in Materials and Methods. This dataset gives us the unique possibility to validate the model and compare the predictions with actual triangle statistics and formation of positively connected groups that are foundational to social cohesion.     

Scaling identity connects human mobility and social interactions

Massive datasets that capture human movements and social interactions have catalyzed rapid advances in our quantitative understanding of human behavior during the past years. One important aspect affecting both areas is the critical role space plays. Indeed, growing evidence suggests both our movements and communication patterns are associated with spatial costs that follow reproducible scaling laws, each characterized by its specific critical exponents. Although human mobility and social networks develop concomitantly as two prolific yet largely separated fields, we lack any known relationships between the critical exponents explored by them, despite the fact that they often study the same datasets. Here, by exploiting three different mobile phone datasets that capture simultaneously these two aspects, we discovered a new scaling relationship, mediated by a universal flux distribution, which links the critical exponents characterizing the spatial dependencies in human mobility and social networks. Therefore, the widely studied scaling laws uncovered in these two areas are not independent but connected through a deeper underlying reality.Over the past few years, we have witnessed tremendous progress in uncovering patterns behind human mobility (1–7) and social networks (8–10), owing partly to the increasing availability of large-scale datasets capturing human behavior in a new level of detail, resolution, and scale (11, 12). Building on rich, fundamental literature from the social sciences (13–19), these data offer a huge opportunity for research, fueling concomitant advances in areas of both human mobility and social networks with profound consequences in broad domains. One important aspect affecting both areas is the critical role space plays. Indeed, growing evidence suggests both our movements and communication patterns are associated with spatial costs that follow reproducible scaling laws. Indeed, previous studies have shown that human travels adhere to spatial constraints (20), characterized by levy flights and continuous time random walk models (1, 2, 4), a scaling law that has proven to be critical in various phenomena driven by human mobility, from spread of viruses (21–23) to migrations (2, 6) and emergency response (24–26). In another related yet distinct area, there has been much empirical evidence about the geographic effect on communication patterns (20), documenting that the probability for two individuals to communicate decays with distance, following power law distributions (20, 27–30). This robust pattern plays an important role in navigating the social network (31), from routing (32, 33) to search of experts (34, 35) to spread of information (27, 36) and innovations (37). Although human movements and social interactions bear high-level similarities in the role spatial distance plays, and are often referred to as two prominent examples of spatial networks (20), they remain as largely separate lines of inquiry, lacking any known connections between their critical exponents. This is particularly perplexing given the fact that they often exploit the same datasets (5, 20, 38–40) and are treated similarly in most modeling frameworks (6, 41).In this paper, we test the hypothesis that previously observed spatial dependency captures a convolution of geographical propensity and a popularity-based heterogeneity among locations, by exploiting three large-scale mobile phone datasets from different countries across two continents (see Datasets for more details). By separating these two factors, we discovered a scaling relationship linking the critical exponents associated with the spatial effect on movement and communication patterns, effectively reducing the number of independent parameters characterizing human behavior. The uncovered scaling theory not only allows us to derive human movements from communication volumes, or vice versa, it also hints for a deeper connection that may exist among all networked systems where space plays a role, from transportations (2, 6, 42) and communications (27, 29, 30) to the internet (32, 33) and human brains (43).     

Changing climates of conflict: A social network experiment in 56 schools

Theories of human behavior suggest that individuals attend to the behavior of certain people in their community to understand what is socially normative and adjust their own behavior in response. An experiment tested these theories by randomizing an anticonflict intervention across 56 schools with 24,191 students. After comprehensively measuring every school’s social network, randomly selected seed groups of 20–32 students from randomly selected schools were assigned to an intervention that encouraged their public stance against conflict at school. Compared with control schools, disciplinary reports of student conflict at treatment schools were reduced by 30% over 1 year. The effect was stronger when the seed group contained more “social referent” students who, as network measures reveal, attract more student attention. Network analyses of peer-to-peer influence show that social referents spread perceptions of conflict as less socially normative.One of the most elusive and important goals in the behavioral sciences is to understand how community-wide patterns of behavior can be changed (1–8). In some cases, social scientists seek to reduce widespread and persistent patterns of negative behavior like corruption or conflict; in others, to promote positive behavior like healthy eating or environmental conservation. Research on changing individual behavior provides many intervention strategies targeted to the psychology of the individual, such as attitudinal persuasion, situational cues, and peer influence (9–12). Another body of research focuses on scaling up behavior change interventions to the community level, studying attempts to reach every individual in a population with mass education or persuasion messaging (13), or with institutional regulation or defaults (14). A third strategy has been to seed a social network with individuals who demonstrate new behaviors, and to rely on processes of social influence to spread the behavior through the channel of structural features of the network (15–18).The present paper incorporates all three approaches. We implemented a social influence strategy designed to change individual behavior, and we tested whether, as a result, new behaviors and norms are transmitted through a social network and also whether they scale up to shift overall levels of behavior within a community. Specifically, we randomized the selection of students within a comprehensively measured social network to determine the relative power of certain individuals to influence the behavior of others. We randomly assigned the presence of this treatment to some community networks and not others. This approach allowed us to determine whether influence from a small group of influential people is enough to shift a community’s behavioral climate, which we define as a widespread and persistent behavioral pattern across the community.Our experimental design is motivated by theoretical debates about how social norms emerge and are transmitted within communities (1, 19–23). At the community level, it is believed that social norms, or perceptions of typical or desirable behavior, emerge when they support the survival of the group (24) or because of arbitrary historical precedent (23). Once formed, these informal rules for behavior are transmitted by the survival of those who follow them, or through the punishment of deviants and the social success of followers. For these reasons, theory suggests that most individual community members strive to understand the social norms of a group and adjust their own behavior accordingly (21, 25). When many individuals in a community perceive a similar norm and adjust their behavior, then a community-wide behavioral pattern may emerge.Social norms may be explained directly to community members through storytelling or advice, but small-scale experiments and theory suggest that individuals often infer which behaviors are typical and desirable through observation of other community members’ behavior (1, 21, 22). A large literature attempts to identify which community members are effective at transmitting social information across a community (16, 18, 26–28). Theories of norm perception predict that individuals infer community social norms by observing the behavior of community members who have many connections within the community’s social network (29). Sometimes called “social referents” (20), individuals may view these community members as important sources of normative information, in part because their many connections imply a comparatively greater knowledge of typical or desirable behavioral patterns in the community. In fact, social referents may have many connections for numerous reasons: they may have a higher status, they may be more popular, or they may have a greater capacity for socialization. Social referents may be different on many dimensions, but what they share is a comparatively greater amount of attention from their peers. Theory and evidence point to the prediction, supported by recent experimental evidence (20, 30), that social referents are particularly influential over perceptions of community norms and behavior in their network.However, despite the large theoretical and empirical literature devoted to ideas about how social norms and behavioral patterns emerge and persist, the central question of which individual level interventions can shift a community’s behavioral climate remains open. We pose this question in the context of adolescent school conflict, such as verbal and physical aggression, rumor mongering, and social exclusion. Although the term “conflict” lacks a consensus definition (31), we follow other social scientists (32, 33) who define conflict broadly, as characterized by antagonistic relations or interactions, or behavioral opposition, respectively, between two or more social entities. This broad definition includes harassment or antagonism from a high-power or high-status person aimed at a person with lower power or status (i.e., bullying), but also conflict between or among people with relatively balanced levels of social power and status.Within many middle and secondary schools in the United States, student conflict is part of the schools’ behavioral climate; that is, conflict is widespread and persistent (34, 35). In contrast to claims that conflict is driven by a minority group of student “bullies” (36), evidence suggests a majority of students contribute to conflicts at their school (37), and these conflicts persist over time because of cyclical patterns of offense and retaliation (38).Student conflict, and in particular bullying, has recently attracted research and policy attention as online social media have brought face-to-face student conflicts into adult view (34, 39). New laws and school policies have been introduced to improve school climate, along with many school programs targeting students’ character and empathy. However, basic research illustrates that students perceive social constraints on reporting or intervening in peer conflict (40). That is, students may perpetuate and tolerate conflict not because of their personal character or level of empathy, but because they perceive conflict behaviors to be typical or desirable: that is, normative within their school’s social network. In such a context, reporting or intervening in peer conflict could be perceived by peers as deviant.     

Evolution of cooperation with asymmetric social interactions

How cooperation emerges in human societies is both an evolutionary enigma and a practical problem with tangible implications for societal health. Population structure has long been recognized as a catalyst for cooperation because local interactions facilitate reciprocity. Analysis of population structure typically assumes bidirectional social interactions. But human social interactions are often unidirectional—where one individual has the opportunity to contribute altruistically to another, but not conversely—as the result of organizational hierarchies, social stratification, popularity effects, and endogenous mechanisms of network growth. Here we expand the theory of cooperation in structured populations to account for both uni- and bidirectional social interactions. Even though unidirectional interactions remove the opportunity for reciprocity, we find that cooperation can nonetheless be favored in directed social networks and that cooperation is provably maximized for networks with an intermediate proportion of unidirectional interactions, as observed in many empirical settings. We also identify two simple structural motifs that allow efficient modification of interaction directions to promote cooperation by orders of magnitude. We discuss how our results relate to the concepts of generalized and indirect reciprocity.

The past year has crystallized the real-life importance of a long-standing enigma: When will individuals incur personal costs for the benefit of others? Confronted with a global pandemic, some individuals and societies have responded with prosocial behavior, such as volunteering as frontline workers, donating protective materials and supplies, and adhering to strict quarantine policies (1, 2). Whereas in other groups or at other times defection has dominated, as individuals chose to forgo face masks, to refuse readily available vaccination, or to flaunt travel restrictions and other measures for public health. Understanding the spread and maintenance of cooperation is now widely recognized as an important practical problem with tangible benefits, especially as we tackle global problems of collective action in public health, resource management, and climate change (3).The last few decades have seen a proliferation of theoretical research into the evolutionary origins of cooperation and the dynamics of its spread. The literature has revealed several key insights into this enigma (4). Population structure is perhaps the most widely discussed mechanism that can promote cooperation (5, 6), and it has been studied by computer simulation (7–9), mathematical analysis (10–21), and experiments with human subjects (22). In structured populations individuals interact only with their neighbors—through either physical or social ties—and behaviors also spread locally. Population structure has the potential to favor the evolution of cooperative behaviors that would otherwise be disfavored in well-mixed populations (5–7, 11, 16, 17). In network-structured populations, for example, nodes represent individuals and edges typically represent social interactions between connected individuals (9–12, 14–19); in set-structured populations, each individual is located in one or more social circles (23); and in multilayer-structured populations, social interactions occur in multiple different domains, such as online and offline interactions, and payoffs to an individual are summed across domains (20, 24).Despite different approaches to describing population structure, nearly all research on this topic has assumed that social interactions and behavioral spread are bidirectional (7–20, 22). That is, if Alice provides a benefit to Bob when behaving altruistically, Bob is presumed to provide a benefit to Alice when behaving altruistically; moreover, if Alice has a chance to imitate Bob’s behavior, then so too can Bob imitate Alice’s behavior. The assumption of bidirectionality simplifies analysis and enables simple intuitions for how population structure permits the spread of cooperation (11).But bidirectional models neglect the prevalence of asymmetric relationships in human social interactions (25). An asymmetric relationship arises when one individual has the opportunity to act altruistically toward another, but there is no opportunity for any reciprocal action. Asymmetric relationships also constrain the spread of behavior: One individual has the opportunity to copy the strategic behavior of another, but not conversely. Such asymmetries are commonly found across diverse domains of human social interactions, arising from social stratification, organizational hierarchies, popularity effects, and endogenous mechanisms of network growth (26–40). For example, in the empirical friendship network of an Australian National University campus, more than half of the relationships are unidirectional: One student regards another as a friend, but not conversely (41). In the network of Twitter followers (based on a snowball sample crawl across “quality” users in 2009), more than 99% of follower relationships are unidirectional (42). Other examples include email networks (34) and trust and advice networks (35, 43)—which all exhibit a high proportion of unidirectional social interactions. Asymmetric interactions are also widespread outside of the human social domain, in systems such as international trade (trade volumes and tariffs between countries) (25) and river and stream flow (movement of microorganisms, nutrients, and organic matter) (44–46).Recent advances in network science have established that edge directionality can qualitatively alter dynamics across a range of systems, including in disease spread (47) and synchronization (48). The empirical prevalence of directed social interactions, and its remarkable impact on dynamics in other settings, leaves an open question: How does directionality affect the evolution of cooperation?Asymmetric relationships are likely to fundamentally alter the evolution of cooperation, compared to the classic case of bidirectional relationships. A bidirectional relationship allows for (but does not guarantee) reciprocal cooperation between a pair of individuals, which occurs when both individuals choose an altruistic behavior. Moreover, a bidirectional relationship enables the spread of cooperative behavior: If one individual imitates a neighbor’s altruistic behavior, then the neighbor will subsequently experience reciprocity—so that two altruistic neighbors help each other, and two defecting neighbors harm each other. This phenomenon of “network reciprocity” (4) along bidirectional edges is known to facilitate the local spread of cooperation and retard the spread of defection. But prosocial spread and reciprocity cannot occur along a unidirectional edge, because only one individual has the opportunity to contribute toward another, and not conversely. Since reciprocity is disrupted, unidirectional interactions may make it difficult, or even impossible, for cooperation to emerge in structured populations.Here we study the evolution of cooperation in structured populations with directed interactions. We uncover a surprising and general result: Directionality can actually facilitate cooperation, even though it disrupts reciprocity. We prove analytically that cooperation can evolve in populations with directional interactions and that an intermediate level of directionality is most beneficial for cooperation. In fact, converting a portion of links to be unidirectional can even promote cooperation on a bidirectional network whose topology otherwise disfavors the emergence of cooperation. Furthermore, we identify two simple network motifs that are critical to determining the evolution of cooperation and that provide insights into how best to optimize edge directions to stimulate cooperation, by orders of magnitude. Our analysis reveals a profound effect of asymmetric social interactions for the evolution of behavior in structured populations.     

Responses to social and environmental stress are attenuated by strong male bonds in wild macaques

In humans and obligatory social animals, individuals with weak social ties experience negative health and fitness consequences. The social buffering hypothesis conceptualizes one possible mediating mechanism: During stressful situations the presence of close social partners buffers against the adverse effects of increased physiological stress levels. We tested this hypothesis using data on social (rate of aggression received) and environmental (low temperatures) stressors in wild male Barbary macaques (Macaca sylvanus) in Morocco. These males form strong, enduring, and equitable affiliative relationships similar to human friendships. We tested the effect of the strength of a male’s top three social bonds on his fecal glucocorticoid metabolite (fGCM) levels as a function of the stressors’ intensity. The attenuating effect of stronger social bonds on physiological stress increased both with increasing rates of aggression received and with decreasing minimum daily temperature. Ruling out thermoregulatory and immediate effects of social interactions on fGCM levels, our results indicate that male Barbary macaques employ a tend-and-befriend coping strategy in the face of increased environmental as well as social day-to-day stressors. This evidence of a stress-ameliorating effect of social bonding among males under natural conditions and beyond the mother–offspring, kin or pair bond broadens the generality of the social buffering hypothesis.Strong affiliative social relationships exert powerful beneficial effects on an individual’s health and fitness in both humans and nonhuman animals (1–5). One well-studied mediating mechanism, conceptualized in the social buffering hypothesis, is that the presence of a close social partner attenuates the reactivity of the hypothalamic–pituitary–adrenal (HPA) axis (apart from other positive effects on physiological responses) and thus buffers against the potentially adverse effects of physiological stress (4, 6, 7). Evidence for the social buffering hypothesis rests primarily on experimental studies exposing subjects to stressful situations when a close social partner is present or absent (6–8). In that sense, previous studies on the social buffering effect captured an interaction effect of social bonding and a stressor, usually via exposure to a novel environment or, in humans, psychological stress on the stress response (4).The individual functioning as a social buffer against stress is usually a pair-bonded partner [in humans and nonhuman animals (6, 8–11)] or mother [in infant nonhuman animals (11–13)]. The “tend-and-befriend” stress-coping-mechanism (i.e., turning to close affiliates and kin), when under stress, has been linked to the attachment–caregiving system partly regulated by the oxytocinergic system (14–16). Possibly as a direct consequence of this, humans exhibit a strong sex difference in behavioral coping mechanisms to perceived stressful events; women are more likely to seek social support in stressful situations compared with men (ref. 17, but see ref. 18). Stress alleviation via social support has also been shown in nonhuman primates where females with stronger bonds or a tighter social network showed an attenuated response to stressors compared with those with weaker social ties (19, 20). For example, the death of a close female partner (catastrophic stressor), usually kin, in baboons led to increased physiological stress, and the bereaved partner attempted to alleviate this response by strengthening existing bonds (21). After a conflict event in chimpanzees (Pan troglodytes) and bonobos (Pan paniscus) closely bonded bystanders can actively console recipients of aggression, thereby reducing behavioral measures of stress (22–24). Many nonhuman primate females live in closely interwoven matrilineal networks of mutual affiliation and support (25–27) that generate strong fitness advantages in terms of increased reproductive rates and survival (1, 28, 29).Because most males compete for opportunities to fertilize females (30) the focus of studies investigating correlates of male physiological stress have historically been on reproductive competition and hierarchical status (31–33). Nevertheless, recent and increasing evidence has shown that males of some vertebrate species also form strong social bonds that can enhance their fitness (refs. 34–38 and reviewed in ref. 39). However, to date social buffering effects on acute HPA responses in adult male vertebrates have been investigated predominantly in pair-living species (or pair-housed animals) in response to the female pair partner’s presence (reviewed in ref. 6). It remains to be shown whether the human sex difference in behavioral stress-coping mechanisms is exhibited by other mammals as well or whether males, like females, experience social buffering responses under stress when they have strong social ties to other same-sex individuals in their group.Similar to philopatric female baboons and male chimpanzees (38, 40, 41) macaque males of some species, including Barbary macaques (Macaca sylvanus), form strong social relationships with a few male partners (35, 36, 39, 42) that are stable over consecutive years and characterized by equitability in exchanges of affiliation (37). The mechanisms guiding partner selection for the formation of social bonds in male macaques are currently unknown. Parallel dispersal has been observed (43), and in large provisioned groups maternal relatedness partly drives agonistic support (44), but the strength of male social bonds is not decreased in maternally unrelated males in the wild (35). Males vary in the number and strength of social bonds they form (37), which may partly be guided by age (36, 45) and may additionally be affected by personality (46, 47).Barbary macaque males frequently experience noncatastrophic stressful situations in their daily lives that may be social or environmental. Within-group conflicts resulting in aggression represent a social stressor that is positively correlated to glucocorticoid levels (a measure of physiological stress) across many primates (19, 48–51). Within-group aggressive conflicts also vary between individuals (50, 52) and between seasons, with peaks during the mating season (36). An annually recurring environmental stressor in the study population of Barbary macaques is cold stress during the winter months. Winter survival probability was found to be predicted by the number of affiliative relationships an individual formed (53). In baboons temperature stress is associated with increased glucocorticoid levels (54, 55).Here we took advantage of this macaque system of strong male bonding and the occurrence of several stressors in an individual’s daily life to test the social buffering hypothesis in a natural situation and within the male sex. As the buffering hypothesis proposes that social support or bonding is related to well-being only during stressful situations (4), we predicted an interaction effect: As stressor intensity increases (i.e., rate of aggression received increases or minimum temperature declines), the attenuating effect of an individual''s social bond strength on faecal glucocorticoid metabolite (fGCM) levels becomes stronger. We also controlled for an alternative, not mutually exclusive, hypothesis, the “immediate effects hypothesis,” stating that affiliative social behavior directly alleviates physiological stress irrespective of the social relationship the partners feature (20, 56, 57). For this, we tested the proximate effects of rates of grooming given and received by all group members, grooming with the top three male partners, or frequency of male–infant–male triadic interactions on fGCMs.     

Drinking alcohol has sex-dependent effects on pair bond formation in prairie voles

Alcohol use and abuse profoundly influences a variety of behaviors, including social interactions. In some cases, it erodes social relationships; in others, it facilitates sociality. Here, we show that voluntary alcohol consumption can inhibit male partner preference (PP) formation (a laboratory proxy for pair bonding) in socially monogamous prairie voles (Microtus ochrogaster). Conversely, female PP is not inhibited, and may be facilitated by alcohol. Behavior and neurochemical analysis suggests that the effects of alcohol on social bonding are mediated by neural mechanisms regulating pair bond formation and not alcohol’s effects on mating, locomotor, or aggressive behaviors. Several neuropeptide systems involved in the regulation of social behavior (especially neuropeptide Y and corticotropin-releasing factor) are modulated by alcohol drinking during cohabitation. These findings provide the first evidence to our knowledge that alcohol has a direct impact on the neural systems involved in social bonding in a sex-specific manner, providing an opportunity to explore the mechanisms by which alcohol affects social relationships.Prairie voles are a valuable animal model of social monogamy. Males and female mates form durable bonds in the wild and in the laboratory (1, 2), and the neural mechanisms of social bonding delineated in this model species have translated with high predictive validity to humans (3, 4). In both species, social reward and drug reward show striking parallels at the behavioral and neurobiological levels (5–9). Prairie voles are now being used to explore the interactions between social relationships and drug abuse (10–19).We previously demonstrated that prairie voles voluntarily self-administer substantial amounts of alcohol (ethanol) and can influence the drinking patterns of a social partner (16–19), similar to social drinking in humans (20). Because alcohol is known to influence social bonds in humans (21–24), we asked here whether alcohol consumption can affect the formation of adult social attachments in prairie voles. Adult male and female prairie voles were paired for 24 h and simultaneously given access to alcohol (10% ethanol by volume in water) and water or only water. They were then tested in the 3-h partner preference (PP) test (PPT), which has proved to be a remarkably sensitive assay for assessing the effects of genetics (25, 26), early social environment (27), and a range of pharmacological agents on social bond formation (28, 29).     

miR-182 targeting reprograms tumor-associated macrophages and limits breast cancer progression

The protumor roles of alternatively activated (M2) tumor-associated macrophages (TAMs) have been well established, and macrophage reprogramming is an important therapeutic goal. However, the mechanisms of TAM polarization remain incompletely understood, and effective strategies for macrophage targeting are lacking. Here, we show that miR-182 in macrophages mediates tumor-induced M2 polarization and can be targeted for therapeutic macrophage reprogramming. Constitutive miR-182 knockout in host mice and conditional knockout in macrophages impair M2-like TAMs and breast tumor development. Targeted depletion of macrophages in mice blocks the effect of miR-182 deficiency in tumor progression while reconstitution of miR-182-expressing macrophages promotes tumor growth. Mechanistically, cancer cells induce miR-182 expression in macrophages by TGFβ signaling, and miR-182 directly suppresses TLR4, leading to NFκb inactivation and M2 polarization of TAMs. Importantly, therapeutic delivery of antagomiR-182 with cationized mannan-modified extracellular vesicles effectively targets macrophages, leading to miR-182 inhibition, macrophage reprogramming, and tumor suppression in multiple breast cancer models of mice. Overall, our findings reveal a crucial TGFβ/miR-182/TLR4 axis for TAM polarization and provide rationale for RNA-based therapeutics of TAM targeting in cancer.

It is well known that the nonmalignant stromal components in tumors play pivotal roles in tumor progression and therapeutic responses (1, 2). Macrophages are a major component of tumor microenvironment and display considerable phenotypic plasticity in their effects toward tumor progression (3–5). Classically activated (M1) macrophages often exert direct tumor cytotoxic effects or induce antitumor immune responses by helping present tumor-related antigens (6, 7). In contrast, tumoral cues can polarize macrophages toward alternative activation with immunosuppressive M2 properties (6–8). Numerous studies have firmly established the protumor effects of M2-like tumor-associated macrophages (TAMs) and the association of TAMs with poor prognosis of human cancer (9–11). However, how tumors induce the coordinated molecular and phenotypic changes in TAMs for M2 polarization remains incompletely understood, impeding the designing of TAM-targeting strategies for cancer intervention. In addition, drug delivery also represents a hurdle for therapeutic macrophage reprogramming.Noncoding RNAs, including microRNAs, have been shown to play vital roles in various pathological processes of cancer (12). The microRNA miR-182 has been implicated in various developmental processes and disease conditions (13–15). Particularly, it receives extensive attention in cancer studies. Prevalent chromosomal amplification of miR-182 locus and up-regulation of its expression in tumors have been observed in numerous cancer types including breast cancer, gastric cancer, lung adenocarcinoma, colorectal adenocarcinoma, ovarian carcinoma, and melanoma (16–21). miR-182 expression is also linked to higher risk of metastasis and shorter survival of patients (20, 22–24). Functional studies showed that miR-182 expression in cancer cells plays vital roles in various aspects of cancer malignancy, including tumor proliferation (25–29), migration (30, 31), invasion (16, 32, 33), epithelial-mesenchymal transition (34–36), metastasis (21, 37, 38), stemness (30, 39, 40), and therapy resistance (41, 42). A number of target genes, including FOXO1/3 (18, 21, 43–45), CYLD (46), CADM1 (47), BRCA1 (27, 48), MTSS1 (34), PDK4 (49), and SMAD7 (35), were reported to be suppressed by miR-182 in cancer cells. Our previous work also proved that tumoral miR-182 regulates lipogenesis in lung adenocarcinoma and promotes metastasis of breast cancer (34, 35, 49). Although miR-182 was established as an important regulator of cancer cell malignancy, previous studies were limited, with analyses of miR-182 in cultured cancer cells and transplanted tumors. Thus, the consequences of miR-182 regulation in physiologically relevant tumor models, such as genetically modified mice, have not been shown. More importantly, whether miR-182 also plays a role in tumor microenvironmental cell components is unknown.In this study, we show that miR-182 expression in macrophages can be induced by breast cancer cells and regulates TAM polarization in various tumor models of mice. In addition, miR-182 inhibition with TAM-targeting exosomes demonstrates promising efficacy for cancer treatment.     

Indirect influence in social networks as an induced percolation phenomenon

Percolation theory has been widely used to study phase transitions in network systems. It has also successfully explained various macroscopic spreading phenomena across different fields. Yet, the theoretical frameworks have been focusing on direct interactions among nodes, while recent empirical observations have shown that indirect interactions are common in many network systems like social and ecological networks, among others. By investigating the detailed mechanism of both direct and indirect influence on scientific collaboration networks, here we show that indirect influence can play the dominant role in behavioral influence. To address the lack of theoretical understanding of such indirect influence on the macroscopic behavior of the system, we propose a percolation mechanism of indirect interactions called induced percolation. Surprisingly, our model exhibits a unique anisotropy property. Specifically, directed networks show first-order abrupt transitions as opposed to the second-order continuous transition in the same network structure but with undirected links. A mix of directed and undirected links leads to rich hybrid phase transitions. Furthermore, a unique feature of the nonmonotonic pattern is observed in network connectivities near the critical point. We also present an analytical framework to characterize the proposed induced percolation, paving the way to further understanding network dynamics with indirect interactions.

Percolation theory (1) is one of the most prominent frameworks within statistical physics. Initially developed (2, 3) to explain the chemical formation of large macromolecules, it has been recently used to study various dynamical processes in complex networks (4–9). Examples include the use of bond percolation (9, 10) to study the wide spread of rumors over online social media and outbreaks of infectious diseases on structured populations. Site percolation (4, 5, 11) has been employed to study the cascading failures of infrastructure networks (6, 12–16) and the resilience of protein–protein interaction networks (17). Likewise, bootstrap percolation (18), k-core (19–21), and linear threshold percolation (7, 22–24) have enabled the study of the spreading of behaviors over social networks. Finally, the so-called explosive percolation (25) has allowed a better characterization of systems’ structural transitions when they are growing or can adapt, whereas core percolation (26, 27) has contributed significantly to insights into nondeterministic polynomial problems. Common to all these percolation models is that they have successfully described various important dynamical phenomena by considering different direct interactions (8, 9, 28) among network nodes; in particular, they have captured the behavior of network systems as given by phase transitions (4, 8, 9, 28, 29).Our study is motivated by recent evidence that there are many systems in which indirect interactions play a major role in their spreading dynamics (30–35). Such underlying indirect interactions have important implications not only on the dynamics of the system but also on the evolution and the emergence of network structures. For example, Christakis and Fowler (30, 31) found that for the spreading of many social behaviors, such as drug (36) and alcohol addictions (37) and obesity (30), an individual can span their influence to their friends around three degrees of separation (friend of a friend’s friend). This phenomenon is also widely known as “three degrees of influence” in social science. In ecological networks, Guimarães et al. (32, 33) discovered in 2017 that indirect effects contribute strongly to the trait coevolution among reciprocal species, which can alter environmental selection and promote the evolution of species.Despite the ubiquity of indirect influence in various real-world systems, few studies have examined the exact mechanisms by which the indirect influences occur, or the relative strengths between direct and indirect influences. Here, based on empirical analyses of scientific collaboration networks, we reveal that indirect influence occurs through next-nearest neighbors and can be the dominant mechanism through which research interests change; on the contrary, evidence of direct (nearest) influence is relatively weak.However, on the theoretical front, up to now there has been no percolation-based theoretical model to describe the underlying mechanism of indirect influence or its distinctions with existing percolation models in terms of the macroscopic behaviors. For either regular networks or complex networks, various percolation models like bond, site, bootstrap, k-core, linear threshold and core, etc., are always based on direct interactions (8, 9, 28) among nodes. In essence, all of these models only take into account the existence and the strength of directly connected nodes, regardless of any indirect influences of other nodes. Hence, they are not suitable for describing the indirect mechanism. Here, we propose a percolation framework called induced percolation to theoretically study the impact of such an indirect mechanism on the whole system.Our results show that indirect interactions lead to a unique macroscopic behavior characterized by anisotropy and phase transitions and different spreading outcomes compared to the direct influence mechanisms. Specifically, we study the most general scenario in which links can have directions and report that varying the links’ directionality could change the order of the phase transition. This is in sharp contrast to previous percolation models, for which the nature of the phase transitions is not affected by the directionality of links. Such rich phase transition behavior is further illustrated in our simulations on empirical networks. To the best of our knowledge, the phenomenon of directionality-related order of the phase transitions only exists in some special cases of core percolation (27), whereas it is shown to be a generic feature in our indirect interaction model.     

Detecting affiliation in colaughter across 24 societies

Laughter is a nonverbal vocal expression that often communicates positive affect and cooperative intent in humans. Temporally coincident laughter occurring within groups is a potentially rich cue of affiliation to overhearers. We examined listeners’ judgments of affiliation based on brief, decontextualized instances of colaughter between either established friends or recently acquainted strangers. In a sample of 966 participants from 24 societies, people reliably distinguished friends from strangers with an accuracy of 53–67%. Acoustic analyses of the individual laughter segments revealed that, across cultures, listeners’ judgments were consistently predicted by voicing dynamics, suggesting perceptual sensitivity to emotionally triggered spontaneous production. Colaughter affords rapid and accurate appraisals of affiliation that transcend cultural and linguistic boundaries, and may constitute a universal means of signaling cooperative relationships.Humans exhibit extensive cooperation between unrelated individuals, managed behaviorally by a suite of elaborate communication systems. Social coordination relies heavily on language, but nonverbal behaviors also play a crucial role in forming and maintaining cooperative relationships (1). Laughter is a common nonverbal vocalization that universally manifests across a broad range of contexts, and is often associated with prosocial intent and positive emotions (2–5), although it can also be used in a threatening or aggressive manner (2). That laughter is inherently social is evident in the fact that people are up to 30 times more likely to laugh in social contexts than when alone (6). Despite the ubiquity and similarity of laughter across all cultures, its communicative functions remain largely unknown. Colaughter is simultaneous laughter between individuals in social interactions, and occurs with varying frequency as a function of the sex and relationship composition of the group: friends laugh together more than strangers, and groups of female friends tend to laugh more than groups of male friends or mixed-sex groups (7, 8). Colaughter can indicate interest in mating contexts (9), especially if it is synchronized (10), and is a potent stimulus for further laughter (i.e., it is contagious) (11). Researchers have focused on laughter within groups, but colaughter potentially provides rich social information to those outside of the group. Against this backdrop, we examined (i) whether listeners around the world can determine the degree of social closeness and familiarity between pairs of people solely on the basis of very brief decontextualized recordings of colaughter, and (ii) which acoustic features in the laughs might influence such judgments.Laughter is characterized by neuromechanical oscillations involving rhythmic laryngeal and superlaryngeal activity (12, 13). It often features a series of bursts or calls, collectively referred to as bouts. Laugh acoustics vary dramatically both between and within speakers across bouts (14), but laughter appears to follow a variety of production rules (15). Comparative acoustic analyses examining play vocalizations across several primate species suggest that human laughter is derived from a homolog dating back at least 20 Mya (16, 17). Humans evolved species-specific sound features in laughs involving higher proportions of periodic components (i.e., increasingly voiced), and a predominantly egressive airflow. This pattern is different from laugh-like vocalizations of our closest nonhuman relative, Pan troglodytes, which incorporate alternating airflow and mostly noisy, aperiodic structure (2, 16). In humans, relatively greater voicing in laughs is judged to be more emotionally positive than unvoiced laughs (18), as is greater variability in pitch and loudness (19). People produce different perceivable laugh types [e.g., spontaneous (or Duchenne) versus volitional (or non-Duchenne)] that correspond to different communicative functions and underlying vocal production systems (3, 20–22), with spontaneous laughter produced by an emotional vocal system shared by many mammals (23, 24). Recent evidence suggests that spontaneous laughter is often associated with relatively greater arousal in production (e.g., increased pitch and loudness) than volitional laughter, and contains relatively more features in common with nonhuman animal vocalizations (20) (Audios S1–S6). These acoustic differences might be important for making social judgments if the presence of spontaneous (i.e., genuine) laughter predicts cooperative social affiliation, but the presence of volitional laughter does not.All perceptual studies to date have examined individual laughs, but laughter typically occurs in social groups, often with multiple simultaneous laughers. Both because social dynamics can change rapidly and because newcomers will often need to quickly assess the membership and boundaries of coalitions, listeners frequently must make rapid judgments about the affiliative status obtaining within small groups of interacting individuals; laughter may provide an efficient and reliable cue of affiliation. If so, we should expect humans to exhibit perceptual adaptations sensitive to colaughter dynamics between speakers. However, to date no study has examined listeners’ judgments of the degree of affiliation between laughers engaged in spontaneous social interactions.We conducted a cross-cultural study across 24 societies (Fig. 1) examining listeners’ judgments of colaughter produced by American English-speaking dyads composed either of friends or newly acquainted strangers, with listeners hearing only extremely brief decontextualized recordings of colaughter. This “thin slice” approach is useful because listeners receive no extraneous information that could inform their judgments, and success with such limited information indicates particular sensitivity to the stimulus (25). A broadly cross-cultural sample is important if we are to demonstrate the independence of this perceptual sensitivity from the influences of language and culture (26). Although cultural factors likely shape pragmatic considerations driving human laughter behavior, we expect that many aspects of this phylogenetically ancient behavior will transcend cultural differences between disparate societies.Open in a separate windowFig. 1.Map of the 24 study site locations.     

Link recommendation algorithms and dynamics of polarization in online social networks

The level of antagonism between political groups has risen in the past years. Supporters of a given party increasingly dislike members of the opposing group and avoid intergroup interactions, leading to homophilic social networks. While new connections offline are driven largely by human decisions, new connections on online social platforms are intermediated by link recommendation algorithms, e.g., “People you may know” or “Whom to follow” suggestions. The long-term impacts of link recommendation in polarization are unclear, particularly as exposure to opposing viewpoints has a dual effect: Connections with out-group members can lead to opinion convergence and prevent group polarization or further separate opinions. Here, we provide a complex adaptive–systems perspective on the effects of link recommendation algorithms. While several models justify polarization through rewiring based on opinion similarity, here we explain it through rewiring grounded in structural similarity—defined as similarity based on network properties. We observe that preferentially establishing links with structurally similar nodes (i.e., sharing many neighbors) results in network topologies that are amenable to opinion polarization. Hence, polarization occurs not because of a desire to shield oneself from disagreeable attitudes but, instead, due to the creation of inadvertent echo chambers. When networks are composed of nodes that react differently to out-group contacts, either converging or polarizing, we find that connecting structurally dissimilar nodes moderates opinions. Overall, our study sheds light on the impacts of social-network algorithms and unveils avenues to steer dynamics of radicalization and polarization in online social networks.

Online social networks are increasingly used to access political information (1), engage with political elites, and discuss politics (2). These new communication platforms can benefit democratic processes in several ways: They reduce barriers to information and, subsequently, increase citizen engagement, allow individuals to voice their concerns, help debunk false information, and improve accountability and transparency in political decision-making (3). In principle, individuals can use social media to access ideologically diverse viewpoints and make better-informed decisions (4, 5).At the same time, internet and online social networks reveal a dark side. There are mounting concerns over possible linkages between social media and affective polarization (6, 7). Other than healthy political deliberation, social networks can foster so-called “echo chambers” (8, 9) and “information cocoons” (3, 10) where individuals are only exposed to like-minded peers and homogeneous sources of information, which polarizes attitudes (for counterevidence, see ref. 5). As a result, social media can trigger political sectarianism (6, 7, 11–13) and fuel misinformation (14, 15). Averting the risks of online social networks for political institutions, and potentiating their advantages, requires multidisciplinary approaches and novel methods to understand long-term dynamics on social platforms.That is not an easy task. As pointed out by Woolley and Howard, “to understand contemporary political communication we must now investigate the politics of algorithms and automation” (16). While traditional media outlets are curated by humans, online social media resorts to computer algorithms to personalize contents through automatic filtering. To understand information dynamics in online social networks, one needs to take into account the interrelated subtleties of human decision making [e.g., only share specific contents (17), actively engage with other users, follow or befriend particular individuals, interact offline] and the outcomes of automated decisions (e.g., news sorting and recommendation systems) (18, 19). In this regard, much attention has been placed on the role of news filters and sorting (1, 18, 19). Shmargad and Klar (20) provide evidence that algorithms sorting news impact the way users engage with and evaluate political news, likely exacerbating political polarization. Likewise, Levy (21) notes that social media algorithms can substantially affect users’ news consumption habits.While past studies have examined how algorithms may affect which information appears on a person’s newsfeed, and subsequent polarization, social matching (22) or link recommendation (23) algorithms [also called user, contact, or people recommender systems (24, 25)] constitute another class of algorithms that can affect the way users engage in (and with) online social networks (examples of such systems in SI Appendix, Fig. S13). These algorithms are implemented to recommend new online connections—“friends” or “followees”—to social network users, based on supposed offline familiarity, likelihood of establishing a future relation, similar interests, or the potential to serve as a source of useful information. Current data provide evidence that link recommendation algorithms impact network topologies and increase network clustering: Daly et al. (26) show that an algorithm recommending friends-of-friends, in an IBM internal social network platform, increases clustering and network modularity. Su et al. (27) analyzed the Twitter graph before and after this platform implemented link recommendation algorithms and show that the “Who To Follow” feature led to a sudden increase in edge growth and the network clustering coefficient. Similarly, Zignani et al. (28) show that, on a small sample of the Facebook graph, the introduction of the “People You May Know” (PYMK) feature led to a sudden increase in the number of links and triangles [i.e., motifs comprising three nodes (A, B, C) where the links AB, AC, and BC exist] in the network. The fact that PYMK is responsible for a significant fraction of link creations is alluded to in other works (29). Furthermore, recent work shows, through experiments with real social media users (30) and simulations (31), that link recommendation algorithms can effectively be used as an intervention mechanism to increase networks’ structural diversity (30, 31) and minimize disagreements (32). It is thereby relevant to understand, 1) How do algorithmic link recommendations interplay with opinion formation? and 2) What are the long-term impacts of such algorithms on opinion polarization?Here, we tackle the previous questions from a complex adaptive–systems perspective (33), designing and analyzing a simple model where individuals interact in a dynamic social network. While several models explain the emergence of polarization through link formation based on opinion similarity (34–41) and information exchange (42), here we focus instead on rewiring based on “structural similarity,” which is defined as similarity based on common features that exclusively depend on the network structure (43). This contrasts with the broader concept of homophily, which typically refers to similarity based on common characteristics besides network properties (e.g., opinions, taste, age, background). Compared with rewiring based on homophily—which can also contribute to network fragmentation—rewiring based on structural similarity can be less restrictive in contexts where information about opinions and beliefs is not readily available to individuals before the connection is established. Furthermore, rewiring based on structural similarity is a backbone of link recommendation algorithms [e.g., “People you may know” or “Whom to follow” (25) suggestions], which rely on link prediction methods to suggest connections to users (43, 44). Importantly, our model combines three key ingredients: 1) Links are formed according to structural similarity, based on common neighbors, which is one of the simplest link prediction methods (43); this way, we do not assume a priori that individuals with similar opinions are likely to become connected [as recent works underline, sorting can be incidental to politics (45, 46)]. 2) Then, to examine opinion updating, we adapt a recent model that covers the interplay of social reinforcement and issue controversy to promote radicalization on social networks (39). 3) Last, we explicitly consider that nodes can react differently to out-group links, either converging in their opinions (10, 47) or polarizing further (48–50).We find that establishing links based on structural similarity alone [a process that is likely to be reinforced by link recommendation algorithms—see SI Appendix, Fig. S10 and previous work pointing that such algorithms affect a social network topology and increase their clustering coefficient (26–28)] contributes to opinion polarization. While our model sheds light on the effect of link recommendation algorithms on opinion formation and polarization dynamics, we also offer a justification for polarization to emerge through structural similarity-based rewiring, in the absence of explicit opinion-similarity rewiring (34, 36, 39, 51), confidence-bounds (37, 38, 40), or rewiring based on concordant messages (42).^* Second, we find that the effects of structural similarity-based rewiring are exacerbated if even moderate opinions have high social influence. Finally, we combine nodes that react differently to out-group contacts: “converging” nodes, which converge if exposed to different opinions (10, 21, 52), and “polarizing” nodes, which diverge when exposed to different viewpoints (48–50). We observe that the coexistence of both types of nodes can contribute to moderate opinions. Polarizing nodes develop radical opinions, and converging nodes, influenced by opposing viewpoints, yield more temperate ones. However, again, link recommendation algorithms impact this process: Given the existence of communities isolated to a greater degree through link recommendation, converging nodes may find it harder to access diverse viewpoints, which, in general, contributes to increasing the adoption of extreme opinions.     

The evolution of self-control

Cognition presents evolutionary research with one of its greatest challenges. Cognitive evolution has been explained at the proximate level by shifts in absolute and relative brain volume and at the ultimate level by differences in social and dietary complexity. However, no study has integrated the experimental and phylogenetic approach at the scale required to rigorously test these explanations. Instead, previous research has largely relied on various measures of brain size as proxies for cognitive abilities. We experimentally evaluated these major evolutionary explanations by quantitatively comparing the cognitive performance of 567 individuals representing 36 species on two problem-solving tasks measuring self-control. Phylogenetic analysis revealed that absolute brain volume best predicted performance across species and accounted for considerably more variance than brain volume controlling for body mass. This result corroborates recent advances in evolutionary neurobiology and illustrates the cognitive consequences of cortical reorganization through increases in brain volume. Within primates, dietary breadth but not social group size was a strong predictor of species differences in self-control. Our results implicate robust evolutionary relationships between dietary breadth, absolute brain volume, and self-control. These findings provide a significant first step toward quantifying the primate cognitive phenome and explaining the process of cognitive evolution.Since Darwin, understanding the evolution of cognition has been widely regarded as one of the greatest challenges for evolutionary research (1). Although researchers have identified surprising cognitive flexibility in a range of species (2–40) and potentially derived features of human psychology (41–61), we know much less about the major forces shaping cognitive evolution (62–71). With the notable exception of Bitterman’s landmark studies conducted several decades ago (63, 72–74), most research comparing cognition across species has been limited to small taxonomic samples (70, 75). With limited comparable experimental data on how cognition varies across species, previous research has largely relied on proxies for cognition (e.g., brain size) or metaanalyses when testing hypotheses about cognitive evolution (76–92). The lack of cognitive data collected with similar methods across large samples of species precludes meaningful species comparisons that can reveal the major forces shaping cognitive evolution across species, including humans (48, 70, 89, 93–98).To address these challenges we measured cognitive skills for self-control in 36 species of mammals and birds (Fig. 1 and Tables S1–S4) tested using the same experimental procedures, and evaluated the leading hypotheses for the neuroanatomical underpinnings and ecological drivers of variance in animal cognition. At the proximate level, both absolute (77, 99–107) and relative brain size (108–112) have been proposed as mechanisms supporting cognitive evolution. Evolutionary increases in brain size (both absolute and relative) and cortical reorganization are hallmarks of the human lineage and are believed to index commensurate changes in cognitive abilities (52, 105, 113–115). Further, given the high metabolic costs of brain tissue (116–121) and remarkable variance in brain size across species (108, 122), it is expected that the energetic costs of large brains are offset by the advantages of improved cognition. The cortical reorganization hypothesis suggests that selection for absolutely larger brains—and concomitant cortical reorganization—was the predominant mechanism supporting cognitive evolution (77, 91, 100–106, 120). In contrast, the encephalization hypothesis argues that an increase in brain volume relative to body size was of primary importance (108, 110, 111, 123). Both of these hypotheses have received support through analyses aggregating data from published studies of primate cognition and reports of “intelligent” behavior in nature—both of which correlate with measures of brain size (76, 77, 84, 92, 110, 124).Open in a separate windowFig. 1.A phylogeny of the species included in this study. Branch lengths are proportional to time except where long branches have been truncated by parallel diagonal lines (split between mammals and birds ∼292 Mya).With respect to selective pressures, both social and dietary complexities have been proposed as ultimate causes of cognitive evolution. The social intelligence hypothesis proposes that increased social complexity (frequently indexed by social group size) was the major selective pressure in primate cognitive evolution (6, 44, 48, 50, 87, 115, 120, 125–141). This hypothesis is supported by studies showing a positive correlation between a species’ typical group size and the neocortex ratio (80, 81, 85–87, 129, 142–145), cognitive differences between closely related species with different group sizes (130, 137, 146, 147), and evidence for cognitive convergence between highly social species (26, 31, 148–150). The foraging hypothesis posits that dietary complexity, indexed by field reports of dietary breadth and reliance on fruit (a spatiotemporally distributed resource), was the primary driver of primate cognitive evolution (151–154). This hypothesis is supported by studies linking diet quality and brain size in primates (79, 81, 86, 142, 155), and experimental studies documenting species differences in cognition that relate to feeding ecology (94, 156–166).Although each of these hypotheses has received empirical support, a comparison of the relative contributions of the different proximate and ultimate explanations requires (i) a cognitive dataset covering a large number of species tested using comparable experimental procedures; (ii) cognitive tasks that allow valid measurement across a range of species with differing morphology, perception, and temperament; (iii) a representative sample within each species to obtain accurate estimates of species-typical cognition; (iv) phylogenetic comparative methods appropriate for testing evolutionary hypotheses; and (v) unprecedented collaboration to collect these data from populations of animals around the world (70).Here, we present, to our knowledge, the first large-scale collaborative dataset and comparative analysis of this kind, focusing on the evolution of self-control. We chose to measure self-control—the ability to inhibit a prepotent but ultimately counterproductive behavior—because it is a crucial and well-studied component of executive function and is involved in diverse decision-making processes (167–169). For example, animals require self-control when avoiding feeding or mating in view of a higher-ranking individual, sharing food with kin, or searching for food in a new area rather than a previously rewarding foraging site. In humans, self-control has been linked to health, economic, social, and academic achievement, and is known to be heritable (170–172). In song sparrows, a study using one of the tasks reported here found a correlation between self-control and song repertoire size, a predictor of fitness in this species (173). In primates, performance on a series of nonsocial self-control control tasks was related to variability in social systems (174), illustrating the potential link between these skills and socioecology. Thus, tasks that quantify self-control are ideal for comparison across taxa given its robust behavioral correlates, heritable basis, and potential impact on reproductive success.In this study we tested subjects on two previously implemented self-control tasks. In the A-not-B task (27 species, n = 344), subjects were first familiarized with finding food in one location (container A) for three consecutive trials. In the test trial, subjects initially saw the food hidden in the same location (container A), but then moved to a new location (container B) before they were allowed to search (Movie S1). In the cylinder task (32 species, n = 439), subjects were first familiarized with finding a piece of food hidden inside an opaque cylinder. In the following 10 test trials, a transparent cylinder was substituted for the opaque cylinder. To successfully retrieve the food, subjects needed to inhibit the impulse to reach for the food directly (bumping into the cylinder) in favor of the detour response they had used during the familiarization phase (Movie S2).Thus, the test trials in both tasks required subjects to inhibit a prepotent motor response (searching in the previously rewarded location or reaching directly for the visible food), but the nature of the correct response varied between tasks. Specifically, in the A-not-B task subjects were required to inhibit the response that was previously successful (searching in location A) whereas in the cylinder task subjects were required to perform the same response as in familiarization trials (detour response), but in the context of novel task demands (visible food directly in front of the subject).     

The long-run effects of religious persecution: Evidence from the Spanish Inquisition

Religious persecution is common in many countries around the globe. There is little evidence on its long-term effects. We collect data from all across Spain, using information from more than 67,000 trials held by the Spanish Inquisition between 1480 and 1820. This comprehensive database allows us to demonstrate that municipalities of Spain with a history of a stronger inquisitorial presence show lower economic performance, educational attainment, and trust today. The effects persist after controlling for historical indicators of religiosity and wealth, ruling out potential selection bias.

Religious freedom is a basic human right, but it is under threat in many parts of the world. Some countries like Saudi Arabia expressly forbid all religions except one; others, like North Korea, do not permit any religion at all. The 2018 annual report of the United States Commission on International Religious Freedom lists 28 countries—home to 57% percent of the world population—as actively persecuting citizens for their religious views (1). Religious intolerance is not new. From the Roman Emperor Nero’s outlawing of Christians to the Armenian genocide in Turkey after WWI and attacks on the Rohingya in modern-day Myanmar, religious factors have played an important role in the persecution of minorities, social upheavals, civil war, and interstate conflict (2–4).Beginning with Max Weber’s work on Protestantism and modern growth, a rich literature has examined the relationship between religion and economic performance (5–7). On the one hand, monotheistic religions may contribute to the evolution of pro-social norms, fostering the idea of omniscient, all-powerful “Big Gods” (5) while breaking down growth-impeding social structures (7). At the same time, many religions discourage education and science (8) and view economic success with skepticism. In the cross-section of countries, church attendance is associated with lower growth, while beliefs in heaven and hell correlate positively with economic performance (9). What has received less attention are the long-run consequences of religious persecution and state-imposed religious homogeneity and in particular, how religion in the hands of a powerful state can become a tool for totalitarian rule, affecting every aspect of people’s lives (10). Many state religions persecute nonbelievers and those who deviate from doctrinal orthodoxy. Religion is often opposed to scientific inquiry and can be associated with low educational attainment (11); where persecuted minorities are more educated than the population in general, the associated loss of human capital may be particularly severe (4, 12). Religious uniformity as a means of supporting the legitimacy of the ruler may also be an obstacle to the development of state capacity, resulting in slower development (13). Persecution often relies on denunciations from local neighbors, colleagues, and friends, undermining trust. Instrumentalized religion can therefore become part and parcel of totalitarian control of people’s lives, with severe repercussions for how society functions, destroying trust and social cooperation (14). For example, regions with high trust have happier populations, more financial intermediation, higher life expectancy, and lower infant mortality (15–18). Education, trust, and state capacity facilitate economic exchange and are positively correlated with per capita income around the globe (19–22).In this paper, we investigate the long-run impact of religious persecution on economic performance, education, and trust. The Spanish Inquisition is among the most iconic examples of a state-sponsored apparatus enforcing religious homogeneity. The Inquisition was “one of the most effective means of thought control that Europe has ever known” (10). Recent analyses have highlighted its focus on social control (23–25), its role as a repressive tool of the state (26, 27), and innovations in judicial procedure (28). Histories of Spain’s decline and fall as an economic power frequently emphasize the role of the Inquisition (29), and sociological studies have argued for a “persistence of the inquisitorial mind” in modern-day Spanish thought (30). At the same time, there are questions about its contemporary and modern-day consequences: some in-depth historical accounts of the Inquisition argue that it had a limited impact on social interactions, economic development, and intellectual life (31, 32). The notion that religious persecution leads to poor economic, social, and educational outcomes is not new, but it has largely remained beyond the reach of formal measurement and documentation of concrete mechanisms [one exception is recent work by Squicciarini (11)]. By shedding light on the mechanism responsible for the Inquisition''s long-term impact, we also contribute to the literature on historical persistence (33).     

How social and genetic factors predict friendship networks

Recent research suggests that the genotype of one individual in a friendship pair is predictive of the genotype of his/her friend. These results provide tentative support for the genetic homophily perspective, which has important implications for social and genetic epidemiology because it substantiates a particular form of gene–environment correlation. This process may also have important implications for social scientists who study the social factors related to health and health-related behaviors. We extend this work by considering the ways in which school context shapes genetically similar friendships. Using the network, school, and genetic information from the National Longitudinal Study of Adolescent Health, we show that genetic homophily for the TaqI A polymorphism within the DRD2 gene is stronger in schools with greater levels of inequality. Our results suggest that individuals with similar genotypes may not actively select into friendships; rather, they may be placed into these contexts by institutional mechanisms outside of their control. Our work highlights the fundamental role played by broad social structures in the extent to which genetic factors explain complex behaviors, such as friendships.There is very little question in the social and medical sciences that “birds of a feather” are far more likely to “flock together” compared with differently feathered birds (1). The likelihood of phenotypically similar individuals having social ties has been observed for race, age, education, religion, personality, political views, and health outcomes and behaviors (1, 2). Social connections among persons with similar characteristics are important because these connections may be linked to the reproduction of current social contexts including concentrated socioeconomic disadvantage or the maintenance of health-related social norms (3, 4).To date, the bulk of the research on dyadic ties (connections between two people) has stressed the selective and influential roles of social and behavioral factors (5). New evidence suggests that the genotype of one individual is predictive of the genotype of his/her friends (6). The “genetic similarity theory” (7–9) hypothesizes that people maximize their inclusive fitness not only by their mate selection but also by making friends with and helping their most genetically proximate neighbors. As such, the likelihood of genetic homophily in social networks is straightforward to motivate. Further, friends are similar along many traits and behaviors and there is strong evidence that many of these traits and behaviors have large genetic components (10–13). Most friendships are geographically clustered and, to the extent that variation in genotype is also clustered due to historical migration patterns, residential choices, and social policies, social structure may affect the likelihood of genetic homophily.In a recent publication (6), Fowler et al. used the sibling and twin pair data from the National Longitudinal Study of Adolescent Health to examine the presence of genetic homophily or heterophily among friends. They found evidence for genetic homophily for the TaqI A polymorphism within DRD2. Specifically, when they regressed the respondent’s genotype on the genotype of his/her friends, net of age, race, and sex characteristics of the respondent and his/her friends, they observed a positive and statistically significant regression coefficient (b = 0.11, P < 0.008), which suggests a concordance of genotype among friends within mutually nominated friendships. This is an important finding because, as the authors argue, “homophily and heterophily in friendships, expressed at the genetic level, may have notable implications for our understanding both of the way that our genes can shape our environmental exposures and the way that our social environment can shape our behavior” (ref. 6, p. 3).     

H-ferritin–nanocaged doxorubicin nanoparticles specifically target and kill tumors with a single-dose injection

An ideal nanocarrier for efficient drug delivery must be able to target specific cells and carry high doses of therapeutic drugs and should also exhibit optimized physicochemical properties and biocompatibility. However, it is a tremendous challenge to engineer all of the above characteristics into a single carrier particle. Here, we show that natural H-ferritin (HFn) nanocages can carry high doses of doxorubicin (Dox) for tumor-specific targeting and killing without any targeting ligand functionalization or property modulation. Dox-loaded HFn (HFn-Dox) specifically bound and subsequently internalized into tumor cells via interaction with overexpressed transferrin receptor 1 and released Dox in the lysosomes. In vivo in the mouse, HFn-Dox exhibited more than 10-fold higher intratumoral drug concentration than free Dox and significantly inhibited tumor growth after a single-dose injection. Importantly, HFn-Dox displayed an excellent safety profile that significantly reduced healthy organ drug exposure and improved the maximum tolerated dose by fourfold compared with free Dox. Moreover, because the HFn nanocarrier has well-defined morphology and does not need any ligand modification or property modulation it can be easily produced with high purity and yield, which are requirements for drugs used in clinical trials. Thus, these unique properties make the HFn nanocage an ideal vehicle for efficient anticancer drug delivery.An ideal nanocarrier for efficient drug delivery must be able to target specific cells and carry high doses of therapeutic drugs and should also exhibit optimized physicochemical properties and biocompatibility (1–3). However, it is a tremendous challenge to engineer all of the above characteristics into a single carrier particle (4–6). Ferritin is a spherical iron storage protein composed of 24 subunits of two types, heavy-chain ferritin (HFn) and light-chain ferritin (LFn). Ferritin protein self-assembles naturally into a hollow nanocage with an outer diameter of 12 nm and an interior cavity 8 nm in diameter (7). The cavity is a useful template for synthesizing highly crystalline and monodisperse nanoparticles (NPs) (8–10). Recently, it was reported that HFn binds to human cells via interacting with the transferrin receptor 1 (TfR1) (11). Although it is well known that TfR1 is highly expressed on human cancer cells and has long been used as a targeting marker for tumor diagnosis and therapy, current HFn-based methods for tumor detection and treatment still rely on functionalization of HFn with recognition ligands to achieve tumor-specific targeting (12–16).By using the intrinsic tumor-targeting properties of HFn, we recently reported that iron-encapsulated HFn NPs specifically target and visualize tumor tissues without the use of additional targeting ligands or signal molecules (17). In the present study, we loaded HFn nanocage with doxorubicin (Dox) for tumor-specific drug delivery. HFn nanocages can encapsulate large amounts of foreign molecules (18–24), bind specifically to tumor cells that overexpress TfR1 (17), and should be able to efficiently deliver high doses of therapeutic drugs to tumors. In particular, natural HFn nanocarriers are expected to possess an outstanding biocompatibility and safety profile, because they exist naturally in the human body and are composed of nontoxic elements that therefore would not activate inflammatory or immunological responses (25). In addition, HFn can be produced economically in Escherichia coli and can be purified easily by exploiting their heat-resistant property (17, 26). The production and purification characteristics of the HFn nanocarriers are effective for scale-up of the manufacturing process with robust and reproducible procedures.Although ferritin-based drug delivery has been recently developed for cancer treatment, in almost all published studies ferritin was modified with recognition ligands to achieve tumor-specific targeting (12–15). These extra surface modifications destroy the intrinsic tumor-specific binding of natural ferritin and disturb its in vivo performance and biocompatibility because of the altered surface physicochemical properties of ferritin. In addition, it was shown recently that the foreign ligands introduced by genetic engineering affect the self-assembling process of ferritin during their expression in E. coli, and thus result in a low yield of the final products (27–29) [e.g., the typical yields of RGD-modified HFn are less than 1/10 those of free HFn (26)].In addition, many currently available methods for drug loading into ferritin involves disassembling ferritin nanocages in severe acidic pH (18–22), which irreversibly damages ferritin protein cages and forms hole defects on the spherical protein surface (30). The irreversible damages to ferritin will seriously affect their in vivo stability and drug delivery efficiency. So far, most of the published work on ferritin-based drug delivery only reported in vitro results (18–21), reflecting that the drug-loaded ferritin prepared using the acidic pH method might not be suitable for in vivo applications.     

Evolution in leaps: The punctuated accumulation and loss of cultural innovations

Archaeological accounts of cultural change reveal a fundamental conflict: Some suggest that change is gradual, accelerating over time, whereas others indicate that it is punctuated, with long periods of stasis interspersed by sudden gains or losses of multiple traits. Existing models of cultural evolution, inspired by models of genetic evolution, lend support to the former and do not generate trajectories that include large-scale punctuated change. We propose a simple model that can give rise to both exponential and punctuated patterns of gain and loss of cultural traits. In it, cultural innovation comprises several realistic interdependent processes that occur at different rates. The model also takes into account two properties intrinsic to cultural evolution: the differential distribution of traits among social groups and the impact of environmental change. In our model, a population may be subdivided into groups with different cultural repertoires leading to increased susceptibility to cultural loss, whereas environmental change may lead to rapid loss of traits that are not useful in a new environment. Taken together, our results suggest the usefulness of a concept of an effective cultural population size.The breadth and diversity of cultural traits and their rates of accumulation have received a great deal of scholarly attention. Scientific knowledge in many fields appears to accumulate exponentially (1, 2). However, although the number of tool types in the archaeological record also seems to fit this pattern of exponential increase broadly (3), the number of tools and other cultural traits does not increase steadily and monotonically over time. Depending on the timescale studied, change in tool repertoire may appear punctuated and stepwise. Long, seemingly static, periods are interspersed between “cultural explosions,” periods of sudden cultural accumulation (3–13). Further, in some populations, there is evidence that whole suites of cultural traits, such as the ability to make tools, clothing, and fire (14–16), may be lost, defying the general trend of cultural accumulation over time (4, 7, 8).Reasons for the sudden changes in hominid material culture in the archaeological record continue to be debated; they could be related to demographic factors (17), rapid cognitive change (18–21), relatively sudden changes in hand morphology (22, 23), or dramatic climatic shifts (10, 24–28). Further, intermediate-scale environmental change or migration to a new environment also could affect the accumulation and loss of traits that are primarily useful in specific environments (29–33). In addition, the relationship between the number of cultural traits in a population and population size has been debated (4, 14, 29, 34–41); this relationship also might depend on the social learning strategies of the population (42, 43). Further, there could be a feedback process between the number of tools in a population and the population size: A larger population might be able to invent and retain more tools, but certain innovations also might support a larger population (44, 45). Finally, the distribution of traits in the population (as a result, for example, of social stratification) might affect both stochastic and environmentally mediated cultural losses.Several models of the dynamics of cultural evolution explicitly incorporate appearance, transmission, and in some cases disappearance of cultural traits (14, 35, 40, 45–53). Sudden dramatic changes in cognition, morphology, or climate are not invoked in these models as a precursor to cultural change; instead, cultural change derives from endogenous properties of the models.Most models of cultural evolution focus on the dynamics of the transmission of cultural traits (40, 50, 51), often omitting the details of the creative processes underlying the origin of these traits (e.g., refs. 14, 35, and 54). The source of cultural traits is represented as a random process occurring at a constant rate, analogous to a genetic mutation rate (40, 46, 48, 50, 51, 55). This representation has proven useful but differs from realistic human innovation (56). For example, a particular genetic mutation occurs independently of previous mutations, whereas a cultural trait’s likelihood of invention could depend on the configuration or frequency of existing traits. For example, the invention of a snaring method enabling new kinds of game hunting may lead to the invention of specialized tools for processing this novel food source. This dependence is one sense in which culture is fundamentally cumulative. A second intriguing difference is the cost of failed attempts at adaptation; although deleterious mutations are costly to the organism, the invention of a useless tool typically would not have long-lasting effects: it simply would be discarded and forgotten. A few models do not assume a constant rate of creative invention: as the existing repertoire becomes larger, they allow an increase (47, 57) or decrease (e.g., ref. 54) in the invention rate, or more subtle dependencies among particular traits (49, 52); other models allow cultural traits to influence the dynamics of cultural transmission and homophily (58–63).Large-scale cultural loss has been observed in human populations; however, most existing models lack a mechanism to account for this process. Many represent cultural loss as a Poisson process (47, 49, 51, 52, 57), but, as with cultural accumulation, this assumption of a constant rate may be an over-simplification. In reality, factors such as population size (taken into account in some of these models) and environmental change (7) likely affect the rate and nature of cultural loss. Finally, existing models also implicitly assume a uniform distribution of knowledge in the population. This assumption is unrealistic in human populations, where some knowledge may be concentrated in specific subgroups, such as medicine-women and -men who know the uses and risks of medicinal plants. We suggest that a concept of effective cultural population size as a cultural analog to effective population size in genetics could be highly useful in this context. Notably, Shennan (35) and Premo (64) have suggested the use of an effective population size in the context of cultural evolution for different reasons, stemming from the details of the transmission process or from the geographical substructure of the population.Existing models of cultural evolution cannot reproduce many features of archaeological and anthropological observations of cultural accumulation in hominids. Few models show an exponential increase in the number of cultural traits (47, 49, 57) or large-scale cultural losses (14, 45, 46), and we are unaware of any that reproduce a pattern of cultural accumulation with punctuated bursts of innovation separated by periods of relative stasis (although ref. 45 suggests the possibility of bistability: a sudden shift between two levels of cultural diversity).We suggest that the assumption that all cultural traits originate via a single process cannot generate an accurate representation of human cultural accumulation. Indeed, researchers in fields such as psychology and cognitive science often divide creativity into multiple types or processes, such as everyday and genius-level creativity (65–67, see also ref. 57). Other categorizations reflect properties of the underlying cognitive processes (68, 69). Both approaches suggest that some creative events are rare and somewhat unpredictable and others are more everyday occurrences that depend on the current environment and preexisting knowledge in a population.