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.

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.

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 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.

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.

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 .

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.

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.

Evolution of social norms and correlated equilibria.

Social norms regulate and coordinate most aspects of human social life, yet they emerge and change as a result of individual behaviors, beliefs, and expectations. A satisfactory account for the evolutionary dynamics of social norms, therefore, has to link individual beliefs and expectations to population-level dynamics, where individual norms change according to their consequences for individuals. Here, we present a model of evolutionary dynamics of social norms that encompasses this objective and addresses the emergence of social norms. In this model, a norm is a set of behavioral prescriptions and a set of environmental descriptions that describe the expected behaviors of those with whom the norm holder will interact. These prescriptions and descriptions are functions of exogenous environmental events. These events have no intrinsic meaning or effect on the payoffs to individuals, yet beliefs/superstitions regarding them can effectuate coordination. Although a norm's prescriptions and descriptions are dependent on one another, we show how they emerge from random accumulations of beliefs. We categorize the space of social norms into several natural classes and study the evolutionary competition between these classes of norms. We apply our model to the Game of Chicken and the Nash Bargaining Game. Furthermore, we show how the space of norms and evolutionary stability are dependent on the correlation structure of the environment and under which such correlation structures social dilemmas can be ameliorated or exacerbated.

C4 photosynthesis and climate through the lens of optimality.

CO2, temperature, water availability, and light intensity were all potential selective pressures that determined the competitive advantage and expansion of the C4 photosynthetic carbon-concentrating mechanism over the last ∼30 My. To tease apart how selective pressures varied along the ecological trajectory of C4 expansion and dominance, we coupled hydraulics to photosynthesis models while optimizing photosynthesis over stomatal resistance and leaf/fine-root allocation. We further examined the importance of nitrogen reallocation from the dark to the light reactions. We show here that the primary selective pressures favoring C4 dominance changed through the course of C4 evolution. The higher stomatal resistance and leaf-to-root ratios enabled by C4 led to an advantage without any initial difference in hydraulic properties. We further predict a reorganization of the hydraulic system leading to higher turgor-loss points and possibly lower hydraulic conductance. Selection on nitrogen reallocation varied with CO2 concentration. Through paleoclimate model simulations, we find that water limitation was the primary driver for a C4 advantage, with atmospheric CO2 as high as 600 ppm, thus confirming molecular-based estimates for C4 evolution in the Oligocene. Under these high-CO2 conditions, nitrogen reallocation was necessary. Low CO2 and high light, but not nitrogen reallocation, were the primary drivers for the mid- to late-Miocene global expansion of C4 We also predicted the timing and spatial distribution for origins of C4 ecological dominance. The predicted origins are broadly consistent with prior estimates, but expand upon them to include a center of origin in northwest Africa and a Miocene-long origin in Australia.

Deconstructing Evolutionary Game Theory: Coevolution of Social Behaviors with Their Evolutionary Setting.

Evolution of social behaviors is one of the most fascinating and active fields of evolutionary biology. During the past half century, social evolution theory developed into a mature field with powerful tools to understand the dynamics of social traits such as cooperation under a wide range of conditions. In this article, I argue that the next stage in the development of social evolution theory should consider the evolution of the setting in which social behaviors evolve. To that end, I propose a conceptual map of the components that make up the evolutionary setting of social behaviors, review existing work that considers the evolution of each component, and discuss potential future directions. The theoretical work reviewed here illustrates how unexpected dynamics can happen when the setting of social evolution itself is evolving, such as cooperation sometimes being self-limiting. I argue that a theory of how the setting of social evolution itself evolves will lead to a deeper understanding of when cooperation and other social behaviors evolve and diversify.

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.

Estimating C4 photosynthesis parameters by fitting intensive A/Ci curves.

Measurements of photosynthetic assimilation rate as a function of intercellular CO2 (A/Ci curves) are widely used to estimate photosynthetic parameters for C3 species, yet few parameters have been reported for C4 plants, because of a lack of estimation methods. Here, we extend the framework of widely used estimation methods for C3 plants to build estimation tools by exclusively fitting intensive A/Ci curves (6-8 more sampling points) for C4 using three versions of photosynthesis models with different assumptions about carbonic anhydrase processes and ATP distribution. We use simulation analysis, out of sample tests, existing in vitro measurements and chlorophyll-fluorescence measurements to validate the new estimation methods. Of the five/six photosynthetic parameters obtained, sensitivity analyses show that maximal-Rubisco-carboxylation-rate, electron-transport-rate, maximal-PEP-carboxylation-rate, and carbonic-anhydrase were robust to variation in the input parameters, while day respiration and mesophyll conductance varied. Our method provides a way to estimate carbonic anhydrase activity, a new parameter, from A/Ci curves, yet also shows that models that do not explicitly consider carbonic anhydrase yield approximate results. The two photosynthesis models, differing in whether ATP could freely transport between RuBP and PEP regeneration processes yielded consistent results under high light, but they may diverge under low light intensities. Modeling results show selection for Rubisco of low specificity and high catalytic rate, low leakage of bundle sheath, and high PEPC affinity, which may further increase C4 efficiency.

Gene-Culture Coinheritance of a Behavioral Trait.

Many physical and behavioral traits in animals, including humans, are inherited both genetically and culturally. The presence of different inheritance systems affecting the same trait can result in complex evolutionary dynamics. Here, we present a general model that elucidates the distinct roles of cultural and genetic inheritance systems and their interaction in driving the evolution of complex phenotypes. In particular, we derive a Price equation that incorporates both cultural and genetic inheritance of a phenotype where the effects of genes and culture are additive. We then use this equation to investigate whether a genetically maladaptive phenotype can evolve under dual transmission. We examine the special case of altruism using an illustrative model and show that cultural selection can overcome genetic selection when the variance in culture is sufficiently high with respect to genes. We also show that the presence of cultural transmission can modify genetic selection itself, making genetic selection more favorable to a trait than under purely genetic inheritance. Last, we consider the effect of different timescales of genetic and cultural transmission. We discuss the implications of our results for understanding the evolution of important coinherited behaviors, including how our framework can be used to generate quantitative estimates of selection pressures required for a genetically maladaptive trait to evolve.

Learning to Cooperate: The Evolution of Social Rewards in Repeated Interactions.

Understanding the behavioral and psychological mechanisms underlying social behaviors is one of the major goals of social evolutionary theory. In particular, a persistent question about animal cooperation is to what extent it is supported by other-regarding preferences-the motivation to increase the welfare of others. In many situations, animals adjust their behaviors through learning by responding to the rewards they experience as a consequence of their actions. Therefore, we may ask whether learning in social situations can be driven by evolved other-regarding rewards. Here we develop a mathematical model in order to ask whether the mere act of cooperating with a social partner will evolve to be inherently rewarding. Individuals interact repeatedly in pairs and adjust their behaviors through reinforcement learning. We assume that individuals associate with each game outcome an internal reward value. These perceived rewards are genetically evolving traits. We find that conditionally cooperative rewards that value mutual cooperation positively but the sucker's outcome negatively tend to be evolutionarily stable. Purely other-regarding rewards can evolve only under special parameter combinations. On the other hand, selfish rewards that always lead to pure defection are also evolutionarily successful. These findings are consistent with empirical observations showing that humans tend to display conditionally cooperative behavior and also exhibit a diversity of preferences. Our model also demonstrates the need to further integrate multiple levels of biological causation of behavior.

Population structure reduces benefits from partner choice in mutualistic symbiosis.

Mutualistic symbioses are key drivers of evolutionary and ecological processes. Understanding how different species can evolve to interact in mutually beneficial ways is an important goal of evolutionary theory, especially when the benefits require costly investments by the partners. For such costly investments to evolve, some sort of fitness feedback mechanism must exist that more than recoups the direct costs. Several such feedback mechanisms have been explored both theoretically and empirically, yet we know relatively little of how they might act together, as they probably do in nature. In this paper, I model the joint action of three of the main mechanisms that can maintain interspecific cooperation in symbioses: partner choice by hosts, population structure amongst symbionts and undirected rewards from hosts to symbionts. The model shows that population structure reduces the benefit from partner choice to hosts. It may help or hinder beneficial symbionts and create positive or negative frequency dependence depending on the nature of host rewards to the symbiont. Strong population structure also makes it less likely that host choosiness and symbiont cooperation will be jointly maintained in a population. The intuition behind these results is that all else being equal, population structure reduces local variation available to the host to choose from. Thus, population structure is not always beneficial for the evolution of cooperation between species. These results also underscore the need to do full analyses of multiple mechanisms of social evolution to uncover the interactions between them.

The genealogical decomposition of a matrix population model with applications to the aggregation of stages.

Matrix projection models are a central tool in many areas of population biology. In most applications, one starts from the projection matrix to quantify the asymptotic growth rate of the population (the dominant eigenvalue), the stable stage distribution, and the reproductive values (the dominant right and left eigenvectors, respectively). Any primitive projection matrix also has an associated ergodic Markov chain that contains information about the genealogy of the population. In this paper, we show that these facts can be used to specify any matrix population model as a triple consisting of the ergodic Markov matrix, the dominant eigenvalue and one of the corresponding eigenvectors. This decomposition of the projection matrix separates properties associated with lineages from those associated with individuals. It also clarifies the relationships between many quantities commonly used to describe such models, including the relationship between eigenvalue sensitivities and elasticities. We illustrate the utility of such a decomposition by introducing a new method for aggregating classes in a matrix population model to produce a simpler model with a smaller number of classes. Unlike the standard method, our method has the advantage of preserving reproductive values and elasticities. It also has conceptually satisfying properties such as commuting with changes of units.

Water stress strengthens mutualism among ants, trees, and scale insects.

Abiotic environmental variables strongly affect the outcomes of species interactions. For example, mutualistic interactions between species are often stronger when resources are limited. The effect might be indirect: water stress on plants can lead to carbon stress, which could alter carbon-mediated plant mutualisms. In mutualistic ant-plant symbioses, plants host ant colonies that defend them against herbivores. Here we show that the partners' investments in a widespread ant-plant symbiosis increase with water stress across 26 sites along a Mesoamerican precipitation gradient. At lower precipitation levels, Cordia alliodora trees invest more carbon in Azteca ants via phloem-feeding scale insects that provide the ants with sugars, and the ants provide better defense of the carbon-producing leaves. Under water stress, the trees have smaller carbon pools. A model of the carbon trade-offs for the mutualistic partners shows that the observed strategies can arise from the carbon costs of rare but extreme events of herbivory in the rainy season. Thus, water limitation, together with the risk of herbivory, increases the strength of a carbon-based mutualism.

Agriculture increases individual fitness.

We question the need to explain the onset of agriculture by appealing to the second type of multilevel selection (MLS2). Unlike eusocial insect colonies, human societies do not exhibit key features of evolutionary individuals. If we avoid the mistake of equating Darwinian fitness with health and quality of life, the adoption of agriculture is almost certainly explicable in terms of individual-level selection and individual rationality.

Cheaters must prosper: reconciling theoretical and empirical perspectives on cheating in mutualism.

Cheating is a focal concept in the study of mutualism, with the majority of researchers considering cheating to be both prevalent and highly damaging. However, current definitions of cheating do not reliably capture the evolutionary threat that has been a central motivation for the study of cheating. We describe the development of the cheating concept and distill a relative-fitness-based definition of cheating that encapsulates the evolutionary threat posed by cheating, i.e. that cheaters will spread and erode the benefits of mutualism. We then describe experiments required to conclude that cheating is occurring and to quantify fitness conflict more generally. Next, we discuss how our definition and methods can generate comparability and integration of theory and experiments, which are currently divided by their respective prioritisations of fitness consequences and traits. To evaluate the current empirical evidence for cheating, we review the literature on several of the best-studied mutualisms. We find that although there are numerous observations of low-quality partners, there is currently very little support from fitness data that any of these meet our criteria to be considered cheaters. Finally, we highlight future directions for research on conflict in mutualisms, including novel research avenues opened by a relative-fitness-based definition of cheating.