Convergence of reputations under indirect reciprocity.

Previous research has shown how indirect reciprocity can promote cooperation through evolutionary game theoretic models. Most work in this field assumes a separation of time-scales: individuals' reputations equilibrate at a fast time scale for given frequencies of strategies while the strategies change slowly according to the replicator dynamics. Much of the previous research has focused on the behaviour and stability of equilibria for the replicator dynamics. Here we focus on the underlying reputational dynamics that occur on a fast time scale. We describe reputational dynamics as systems of differential equations and conduct stability analyses on their equilibria. We prove that reputations converge to a unique equilibrium under a solitary observer model for each of the five standard norms and whether assessments are public or private. These results confirm a crucial but previously understudied assumption underlying the theory of indirect reciprocity for the most studied set of norms.

The floating duck syndrome: biased social learning leads to effort-reward imbalances.

An increasingly common phenomenon in modern work and school settings is individuals taking on too many tasks and spending effort without commensurate rewards. Such an imbalance of efforts and rewards leads to myriad negative consequences, such as burnout, anxiety and disease. Here, we develop a model to explain how such effort-reward imbalances can come about as a result of biased social learning dynamics. Our model is based on a phenomenon that on some US college campuses is called 'the floating duck syndrome'. This phrase refers to the social pressure on individuals to advertise their successes but hide the struggles and the effort put in to achieve them. We show that a bias against revealing the true effort results in social learning dynamics that lead others to underestimate the difficulty of the world. This in turn leads individuals to both invest too much total effort and spread this effort over too many activities, reducing the success rate from each activity and creating effort-reward imbalances. We also consider potential ways to counteract the floating duck effect: we find that solutions other than addressing the root cause, biased observation of effort, are unlikely to work.

Host control and species interactions jointly determine microbiome community structure.

The host microbiome can be considered an ecological community of microbes present inside a complex and dynamic host environment. The host is under selective pressure to ensure that its microbiome remains beneficial. The host can impose a range of ecological filters including the immune response that can influence the assembly and composition of the microbial community. How the host immune response interacts with the within-microbiome community dynamics to affect the assembly of the microbiome has been largely unexplored. We present here a mathematical framework to elucidate the role of host immune response and its interaction with the balance of ecological interactions types within the microbiome community. We find that highly mutualistic microbial communities characteristic of high community density are most susceptible to changes in immune control and become invasion prone as host immune control strength is increased. Whereas highly competitive communities remain relatively stable in resisting invasion to changing host immune control. Our model reveals that the host immune control can interact in unexpected ways with a microbial community depending on the prevalent ecological interactions types for that community. We stress the need to incorporate the role of host-control mechanisms to better understand microbiome community assembly and stability.

Indirect reciprocity with Bayesian reasoning and biases.

Reputations can foster cooperation by indirect reciprocity: if I am good to you then others will be good to me. But this mechanism for cooperation in one-shot interactions only works when people agree on who is good and who is bad. Errors in actions or assessments can produce disagreements about reputations, which can unravel the positive feedback loop between social standing and pro-social behaviour. Cooperators can end up punished and defectors rewarded. Public reputation systems and empathy are two possible mechanisms to promote agreement about reputations. Here we suggest an alternative: Bayesian reasoning by observers. By taking into account the probabilities of errors in action and observation and their prior beliefs about the prevalence of good people in the population, observers can use Bayesian reasoning to determine whether or not someone is good. To study this scenario, we develop an evolutionary game theoretical model in which players use Bayesian reasoning to assess reputations, either publicly or privately. We explore this model analytically and numerically for five social norms (Scoring, Shunning, Simple Standing, Staying, and Stern Judging). We systematically compare results to the case when agents do not use reasoning in determining reputations. We find that Bayesian reasoning reduces cooperation relative to non-reasoning, except in the case of the Scoring norm. Under Scoring, Bayesian reasoning can promote coexistence of three strategic types. Additionally, we study the effects of optimistic or pessimistic biases in individual beliefs about the degree of cooperation in the population. We find that optimism generally undermines cooperation whereas pessimism can, in some cases, promote cooperation.

Indirect reciprocity with abductive reasoning.

Indirect reciprocity is a reputational mechanism through which cooperative behavior can be promoted amongst a group of individuals. However, in order for this mechanism to effectively do so, cheating must be appropriately punished and cooperating appropriately rewarded. Errors in assessments and actions can hinder this process. In such a setting, individuals might try to reason about evidence to assign reputations given the possibility of errors. Here, we consider a well-established theory of reasoning used to combine evidence, abductive reasoning, as a possible means by which such errors can be circumvented. Specifically, we use Dempster-Shafer theory to model individuals who account for possible errors by combining information about their beliefs about the status of the population and the errors rates and then choose the simplest scenario that could explain their observations in the context of these beliefs. We investigate the effectiveness of abductive reasoning at promoting cooperation for five social norms: Scoring, Shunning, Simple Standing, Staying, and Stern Judging. We find that, generally, abductive reasoning can outperform non-reasoning models at ameliorating the effects of the aforementioned challenges and promote higher levels of cooperation under low-error conditions. However, for high-error conditions, we find that abductive reasoning can undermine cooperation. Furthermore, we also find that a degree of bias towards believing previously held reputations can help sustain cooperation.

Pathways to cultural adaptation: the coevolution of cumulative culture and social networks.

Humans have adapted to an immense array of environments by accumulating culturally transmitted knowledge and skills. Adaptive culture can accumulate either via more distinct cultural traits or via improvements of existing cultural traits. The kind of culture that accumulates depends on, and coevolves with, the social structure of societies. Here, we show that the coevolution of learning networks and cumulative culture results in two distinct pathways to cultural adaptation: highly connected populations with high proficiency but low trait diversity vs. sparsely connected populations with low proficiency but higher trait diversity. Importantly, we show there is a conflict between group-level payoffs, which are maximised in highly connected groups that attain high proficiency, and individual level selection, which favours disconnection. This conflict emerges from the interaction of social learning with population structure and causes populations to cycle between the two cultural and network states. The same conflict creates a paradox where increasing innovation rate lowers group payoffs. Finally, we explore how populations navigate these two pathways in environments where payoffs differ among traits and can change over time, showing that high proficiency is favoured when payoffs are stable and vary strongly between traits, while frequent changes in trait payoffs favour more trait diversity. Our results illustrate the complex interplay between networks, learning and the environment, and so inform our understanding of human social evolution.

The impact of threshold decision mechanisms of collective behavior on disease spread.

Humans are a hyper-social species, which greatly impacts the spread of infectious diseases. How do social dynamics impact epidemiology and what are the implications for public health policy? Here, we develop a model of disease transmission that incorporates social dynamics and a behavior that reduces the spread of disease, a voluntary nonpharmaceutical intervention (NPI). We use a "tipping-point" dynamic, previously used in the sociological literature, where individuals adopt a behavior given a sufficient prevalence of the behavior in the population. The thresholds at which individuals adopt the NPI behavior are modulated by the perceived risk of infection, i.e., the disease prevalence and transmission rate, costs to adopt the NPI behavior, and the behavior of others. Social conformity creates a type of "stickiness" whereby individuals are resistant to changing their behavior due to the population's inertia. In this model, we observe a nonmonotonicity in the attack rate as a function of various biological and social parameters such as the transmission rate, efficacy of the NPI, costs of the NPI, weight of social consequences of shirking the social norm, and the degree of heterogeneity in the population. We also observe that the attack rate can be highly sensitive to these parameters due to abrupt shifts in the collective behavior of the population. These results highlight the complex interplay between the dynamics of epidemics and norm-driven collective behaviors.

The evolution of partner specificity in mutualisms.

Mutualistic species vary in their level of partner specificity, which has important evolutionary, ecological, and management implications. Yet, the evolutionary mechanisms which underpin partner specificity are not fully understood. Most work on specialization focuses on the trade-off between generalism and specialism, where specialists receive more benefits from preferred partners at the expense of benefits from non-preferred partners, while generalists receive similar benefits from all partners. Because all mutualisms involve some degree of both cooperation and conflict between partners, we highlight that specialization to a mutualistic partner can be cooperative, increasing benefit to a focal species and a partner, or antagonistic, increasing resource extraction by a focal species from a partner. We devise an evolutionary game theoretic model to assess the evolutionary dynamics of cooperative specialization, antagonistic specialization, and generalism. Our model shows that cooperative specialization leads to bistability: stable equilibria with a specialist host and its preferred partner excluding all others. We also show that under cooperative specialization with spatial effects, generalists can thrive at the boundaries between differing specialist patches. Under antagonistic specialization, generalism is evolutionarily stable. We provide predictions for how a cooperation-antagonism continuum may determine the patterns of partner specificity that develop within mutualistic relationships.

Optimal coordination and reorganization of photosynthetic properties in C4 grasses.

Each of >20 independent evolutions of C4 photosynthesis in grasses required reorganization of the Calvin-Benson-cycle (CB-cycle) within the leaf, along with coordination of C4 -cycle enzymes with the CB-cycle to maximize CO2 assimilation. Considering the vast amount of time over which C4 evolved, we hypothesized (i) trait divergences exist within and across lineages with both C4 and closely related C3 grasses, (ii) trends in traits after C4 evolution yield the optimization of C4 through time, and (iii) the presence/absence of trends in coordination between the CB-cycle and C4 -cycle provides information on the strength of selection. To address these hypotheses, we used a combination of optimality modelling, physiological measurements and phylogenetic-comparative-analysis. Photosynthesis was optimized after the evolution of C4 causing diversification in maximal assimilation, electron transport, Rubisco carboxylation, phosphoenolpyruvate carboxylase and chlorophyll within C4 lineages. Both theory and measurements indicated a higher light-reaction to CB-cycle ratio (Jatpmax /Vcmax ) in C4 than C3 . There were no evolutionary trends with photosynthetic coordination between the CB-cycle, light reactions and the C4 -cycle, suggesting strong initial selection for coordination. The coordination of CB-C4 -cycles (Vpmax /Vcmax ) was optimal for CO2 of 200 ppm, not to current conditions. Our model indicated that a higher than optimal Vpmax /Vcmax affects assimilation minimally, thus lessening recent selection to decrease Vpmax /Vcmax .

Host phenology can drive the evolution of intermediate virulence strategies in some obligate-killer parasites.

Traditional mechanistic trade-offs between transmission and virulence are the foundation of nearly all theory on parasite virulence evolution. For obligate-host killer parasites, evolution toward intermediate virulence depends on a trade-off between virulence (time to death) and transmission (the number of progeny released upon death). Although several ecological factors impact optimal virulence strategies constrained by trade-offs, these factors have been insufficient to explain the intermediate virulence levels observed in nature. The timing of seasonal activity, or phenology, is a factor that commonly influences ecological interactions but is difficult to incorporate into virulence evolution studies. We present a mathematical model of a seasonal obligate-killer parasite to study the impact of host phenology on virulence evolution. The model demonstrates that host phenology can select for intermediate parasite virulence even when a traditional mechanistic trade-off between transmission and virulence is omitted. The optimal virulence strategy is impacted by both the host activity period duration and the host emergence timing variation. Parasites with lower virulence strategies are favored in environments with longer host activity periods and when hosts emerge synchronously. The results demonstrate that host phenology can be sufficient to select for intermediate virulence strategies, providing an alternative driver of virulence evolution in some natural systems.

A Synthesis of Game Theory and Quantitative Genetic Models of Social Evolution.

Two popular approaches for modeling social evolution, evolutionary game theory and quantitative genetics, ask complementary questions but are rarely integrated. Game theory focuses on evolutionary outcomes, with models solving for evolutionarily stable equilibria, whereas quantitative genetics provides insight into evolutionary processes, with models predicting short-term responses to selection. Here we draw parallels between evolutionary game theory and interacting phenotypes theory, which is a quantitative genetic framework for understanding social evolution. First, we show how any evolutionary game may be translated into two quantitative genetic selection gradients, nonsocial and social selection, which may be used to predict evolutionary change from a single round of the game. We show that synergistic fitness effects may alter predicted selection gradients, causing changes in magnitude and sign as the population mean evolves. Second, we show how evolutionary games involving plastic behavioral responses to partners can be modeled using indirect genetic effects, which describe how trait expression changes in response to genes in the social environment. We demonstrate that repeated social interactions in models of reciprocity generate indirect effects and conversely, that estimates of parameters from indirect genetic effect models may be used to predict the evolution of reciprocity. We argue that a pluralistic view incorporating both theoretical approaches will benefit empiricists and theorists studying social evolution. We advocate the measurement of social selection and indirect genetic effects in natural populations to test the predictions from game theory and, in turn, the use of game theory models to aid in the interpretation of quantitative genetic estimates.

A cognitive-evolutionary model for the evolution of teaching.

Mechanisms for social learning have rightly been the focus of much work in cultural evolution. But mechanisms for teaching-mechanisms that determine what information is available for learners to learn in the first place-are equally important to cultural evolution, especially in the case of humans. Here, we propose a simple model of teaching in the context of skill transmission. Our model derives the evolutionary cost and benefit of teaching by explicitly representing cognitive aspects of skill transmission as a dual-inheritance process. We then show that teaching cannot evolve when its direct cost is too high. We also show that there is an "explain-exploit" trade-off inherent to teaching: when payoffs from sharing information are not constant, there can be an indirect cost to teaching. This gives rise to an opportunity cost that goes beyond any direct cost that it may also entail. Finally, we show that evolution limits the strength of teaching provided that the direct cost of teaching is an increasing function of teaching effort. We then discuss how these factors might explain why teaching mechanisms are self-limiting, suggesting that such mechanisms may nevertheless play an important role in the evolution of cumulative culture in humans.

The role of host phenology for parasite transmission.

Phenology is a fundamental determinant of species distributions, abundances, and interactions. In host-parasite interactions, host phenology can affect parasite fitness due to the temporal constraints it imposes on host contact rates. However, it remains unclear how parasite transmission is shaped by the wide range of phenological patterns observed in nature. We develop a mathematical model of the Lyme disease system to study the consequences of differential tick developmental-stage phenology for the transmission of B. burgdorferi. Incorporating seasonal tick activity can increase B. burgdorferi fitness compared to continuous tick activity but can also prevent transmission completely. B. burgdorferi fitness is greatest when the activity period of the infectious nymphal stage slightly precedes the larval activity period. Surprisingly, B. burgdorferi is eradicated if the larval activity period begins long after the end of nymphal activity due to a feedback with mouse population dynamics. These results highlight the importance of phenology, a common driver of species interactions, for the fitness of a parasite.

Rank-dependent social inheritance determines social network structure in spotted hyenas.

The structure of animal social networks influences survival and reproductive success, as well as pathogen and information transmission. However, the general mechanisms determining social structure remain unclear. Using data from 73,767 social interactions among wild spotted hyenas collected over 27 years, we show that the process of social inheritance determines how offspring relationships are formed and maintained. Relationships between offspring and other hyenas bear resemblance to those of their mothers for as long as 6 years, and the degree of similarity increases with maternal social rank. Mother-offspring relationship strength affects social inheritance and is positively correlated with offspring longevity. These results support the hypothesis that social inheritance of relationships can structure animal social networks and be subject to adaptive tradeoffs.

Social finance as cultural evolution, transmission bias, and market dynamics.

The thoughts and behaviors of financial market participants depend upon adopted cultural traits, including information signals, beliefs, strategies, and folk economic models. Financial traits compete to survive in the human population and are modified in the process of being transmitted from one agent to another. These cultural evolutionary processes shape market outcomes, which in turn feed back into the success of competing traits. This evolutionary system is studied in an emerging paradigm, social finance. In this paradigm, social transmission biases determine the evolution of financial traits in the investor population. It considers an enriched set of cultural traits, both selection on traits and mutation pressure, and market equilibrium at different frequencies. Other key ingredients of the paradigm include psychological bias, social network structure, information asymmetries, and institutional environment.

Not by transmission alone: the role of invention in cultural evolution.

Innovation-the combination of invention and social learning-can empower species to invade new niches via cultural adaptation. Social learning has typically been regarded as the fundamental driver for the emergence of traditions and thus culture. Consequently, invention has been relatively understudied outside the human lineage-despite being the source of new traditions. This neglect leaves basic questions unanswered: what factors promote the creation of new ideas and practices? What affects their spread or loss? We critically review the existing literature, focusing on four levels of investigation: traits (what sorts of behaviours are easiest to invent?), individuals (what factors make some individuals more likely to be inventors?), ecological contexts (what aspects of the environment make invention or transmission more likely?), and populations (what features of relationships and societies promote the rise and spread of new inventions?). We aim to inspire new research by highlighting theoretical and empirical gaps in the study of innovation, focusing primarily on inventions in non-humans. Understanding the role of invention and innovation in the history of life requires a well-developed theoretical framework (which embraces cognitive processes) and a taxonomically broad, cross-species dataset that explicitly investigates inventions and their transmission. We outline such an agenda here. This article is part of the theme issue 'Foundations of cultural evolution'.

False beliefs can bootstrap cooperative communities through social norms.

Building cooperative communities is a crucial problem for human societies. Much research suggests that cooperation is facilitated by knowing who the cooperators and defectors are, and being able to respond accordingly. As such, anonymous games are thought to hinder cooperation. Here, we show that this conclusion is altered dramatically in the presence of conditional cooperation norms and heterogeneous beliefs about others' behaviours. Specifically, we show that inaccurate beliefs about other players' behaviours can foster and stabilise cooperation via social norms. To show this, we combine a community's population dynamics with the behavioural dynamics of their members. In our model, individuals can join a community based on beliefs generated by public signals regarding the level of cooperation within, and decide to cooperate or not depending on these beliefs. These signals may overstate how much cooperation there really is. We show that even if individuals eventually learn the true level of cooperation, the initially false beliefs can trigger a dynamic that sustains high levels of cooperation. We also characterise how the rates of joining, leaving and learning in the community affect the cooperation level and community size simultaneously. Our results illustrate how false beliefs and social norms can help build cooperative communities.

Combating climate change with matching-commitment agreements.

Countries generally agree that global greenhouse gas emissions are too high, but prefer other countries reduce emissions rather than reducing their own. The Paris Agreement is intended to solve this collective action problem, but is likely insufficient. One proposed solution is a matching-commitment agreement, through which countries can change each other's incentives by committing to conditional emissions reductions, before countries decide on their unconditional reductions. Here, we study matching-commitment agreements between two heterogeneous countries. We find that such agreements (1) incentivize both countries to make matching commitments that in turn incentivize efficient emissions reductions, (2) reduce emissions from those expected without an agreement, and (3) increase both countries' welfare. Matching-commitment agreements are attractive because they do not require a central enforcing authority and only require countries to fulfil their promises; countries are left to choose their conditional and unconditional emissions reductions according to their own interests.

Evolution of contribution timing in public goods games.

Life-history strategies are a crucial aspect of life, which are complicated in group-living species, where pay-offs additionally depend on others' behaviours. Previous theoretical models of public goods games have generally focused on the amounts individuals contribute to the public good. Yet a much less-studied strategic aspect of public goods games, the timing of contributions, can also have dramatic consequences for individual and collective performance. Here, we develop two stage game theoretical models to explore how the timing of contributions evolves. In the first stage, individuals contribute to a threshold public good based on a performance schedule. The second stage begins once the threshold is met, and the individuals then compete as a function of their performance. We show how contributing rapidly is not necessarily optimal, because delayers can act as 'cheats,' avoiding contributing while reaping the benefits of the public good. However, delaying too long can put the delayers at a disadvantage as they may be ill-equipped to compete. These effects lead to bistability in a single group, and spatial diversity among multiple interacting groups.

The balance of interaction types determines the assembly and stability of ecological communities.

What determines the assembly and stability of complex communities is a central question in ecology. Past work has suggested that mutualistic interactions are inherently destabilizing. However, this conclusion relies on the assumption that benefits from mutualisms never stop increasing. Furthermore, almost all theoretical work focuses on the internal (asymptotic) stability of communities assembled all at once. Here, we present a model with saturating benefits from mutualisms and sequentially assembled communities. We show that such communities are internally stable for any level of diversity and any combination of species interaction types. External stability, or resistance to invasion, is thus an important but overlooked measure of stability. We demonstrate that the balance of different interaction types governs community dynamics. A higher fraction of mutualistic interactions can increase the external stability and diversity of communities as well as species persistence, if mutualistic interactions tend to provide unique benefits. Ecological selection increases the prevalence of mutualisms, and limits on biodiversity emerge from species interactions. Our results help resolve long-standing debates on the stability, saturation and diversity of communities.