Evolutionary dynamics in structured populations

Fixation probabilities in evolutionary dynamics under weak selection

In evolutionary dynamics, a key measure of a mutant trait's success is the probability that it takes over the population given some initial mutant-appearance distribution. This "fixation probability" is difficult to compute in general, as it depends on the mutation's effect on the organism as well as the population's spatial structure, mating patterns, and other factors. In this study, we consider weak selection, which means that the mutation's effect on the organism is small. We obtain a weak-selection perturbation expansion of a mutant's fixation probability, from an arbitrary initial configuration of mutant and resident types. Our results apply to a broad class of stochastic evolutionary models, in which the size and spatial structure are arbitrary (but fixed). The problem of whether selection favors a given trait is thereby reduced from exponential to polynomial complexity in the population size, when selection is weak. We conclude by applying these methods to obtain new results for evolutionary dynamics on graphs.

Genomic epidemiology of superspreading events in Austria reveals mutational dynamics and transmission properties of SARS-CoV-2

Superspreading events shaped the coronavirus disease 2019 (COVID-19) pandemic, and their rapid identification and containment are essential for disease control. Here, we provide a national-scale analysis of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) superspreading during the first wave of infections in Austria, a country that played a major role in initial virus transmissions in Europe. Capitalizing on Austria's well-developed epidemiological surveillance system, we identified major SARS-CoV-2 clusters during the first wave of infections and performed deep whole-genome sequencing of more than 500 virus samples. Phylogenetic-epidemiological analysis enabled the reconstruction of superspreading events and charts a map of tourism-related viral spread originating from Austria in spring 2020. Moreover, we exploited epidemiologically well-defined clusters to quantify SARS-CoV-2 mutational dynamics, including the observation of low-frequency mutations that progressed to fixation within the infection chain. Time-resolved virus sequencing unveiled viral mutation dynamics within individuals with COVID-19, and epidemiologically validated infector-infectee pairs enabled us to determine an average transmission bottleneck size of 103 SARS-CoV-2 particles. In conclusion, this study illustrates the power of combining epidemiological analysis with deep viral genome sequencing to unravel the spread of SARS-CoV-2 and to gain fundamental insights into mutational dynamics and transmission properties.

The evolution of altruism and the serial rediscovery of the role of relatedness

The genetic evolution of altruism (i.e., a behavior resulting in a net reduction of the survival and/or reproduction of an actor to benefit a recipient) once perplexed biologists because it seemed paradoxical in a Darwinian world. More than half a century ago, W. D. Hamilton explained that when interacting individuals are genetically related, alleles for altruism can be favored by selection because they are carried by individuals more likely to interact with other individuals carrying the alleles for altruism than random individuals in the population ("kin selection"). In recent decades, a substantial number of supposedly alternative pathways to altruism have been published, leading to controversies surrounding explanations for the evolution of altruism. Here, we systematically review the 200 most impactful papers published on the evolution of altruism and identify 43 evolutionary models in which altruism evolves and where the authors attribute the evolution of altruism to a pathway other than kin selection and/or deny the role of relatedness. An analysis of these models reveals that in every case the life cycle assumptions entail local reproduction and local interactions, thereby leading to interacting individuals being genetically related. Thus, contrary to the authors' claims, Hamilton's relatedness drives the evolution to altruism in their models. The fact that several decades of investigating the evolution to altruism have resulted in the systematic and unwitting rediscovery of the same mechanism is testament to the fundamental importance of positive relatedness between actor and recipient for explaining the evolution of altruism.

Trinidadian guppies use a social heuristic that can support cooperation among non-kin

Cooperation among non-kin is well documented in humans and widespread in non-human animals, but explaining the occurrence of cooperation in the absence of inclusive fitness benefits has proven a significant challenge. Current theoretical explanations converge on a single point: cooperators can prevail when they cluster in social space. However, we know very little about the real-world mechanisms that drive such clustering, particularly in systems where cognitive limitations make it unlikely that mechanisms such as score keeping and reputation are at play. Here, we show that Trinidadian guppies (Poecilia reticulata) use a 'walk away' strategy, a simple social heuristic by which assortment by cooperativeness can come about among mobile agents. Guppies cooperate during predator inspection and we found that when experiencing defection in this context, individuals prefer to move to a new social environment, despite having no prior information about this new social group. Our results provide evidence in non-human animals that individuals use a simple social partner updating strategy in response to defection, supporting theoretical work applying heuristics to understanding the proximate mechanisms underpinning the evolution of cooperation among non-kin.

Bogdanov–Takens Bifurcation in a Neutral Delayed Hopfield Neural Network with Bidirectional Connection

In this paper, a neutral Hopfield neural network with bidirectional connection is considered. In the first step, by choosing the connection weights as parameters bifurcation, the critical point at which a zero root of multiplicity two occurs in the characteristic equation associated with the linearized system. In the second step, we studied the zeros of a third degree exponential polynomial in order to make sure that except the double zero root, all the other roots of the characteristic equation have real parts that are negative. Moreover, we find the critical values to guarantee the existence of the Bogdanov–Takens bifurcation. In the third step, the normal form is obtained and its dynamical behaviors are studied after the use of the reduction on the center manifold and the theory of the normal form. Furthermore, for the demonstration of our results, we have given a numerical example.

Globalization and the rise and fall of cognitive control

The scale of human interaction is larger than ever before—people regularly interact with and learn from others around the world, and everyone impacts the global environment. We develop an evolutionary game theory model to ask how the scale of interaction affects the evolution of cognition. Our agents make decisions using automatic (e.g., reflexive) versus controlled (e.g., deliberative) cognition, interact with each other, and influence the environment (i.e., game payoffs). We find that globalized direct contact between agents can either favor or disfavor control, depending on whether controlled agents are harmed or helped by contact with automatic agents; globalized environment disfavors cognitive control, while also promoting strategic diversity and fostering mesoscale communities of more versus less controlled agents; and globalized learning destroys mesoscale communities and homogenizes the population. These results emphasize the importance of the scale of interaction for the evolution of cognition, and help shed light on modern challenges.

Humankind is in a period of unprecedented cognitive sophistication as well as globalization. Here, using an evolutionary game theory model, the authors reveal ways in which the transition from local to global interaction can have both positive and potentially negative consequences for the prevalence of cognitive sophistication in the population.

The robustness of reciprocity: Experimental evidence that each form of reciprocity is robust to the presence of other forms of reciprocity

Prosocial behavior is paradoxical because it often entails a cost to one's own welfare to benefit others. Theoretical models suggest that prosociality is driven by several forms of reciprocity. Although we know a great deal about how each of these forms operates in isolation, they are rarely isolated in the real world. Rather, the topological features of human social networks are such that people are often confronted with multiple types of reciprocity simultaneously. Does our current understanding of human prosociality break down if we account for the fact that the various forms of reciprocity tend to co-occur in nature? Results of a large experiment show that each basis of human reciprocity is remarkably robust to the presence of other bases. This lends strong support to existing models of prosociality and puts theory and research on firmer ground in explaining the high levels of prosociality observed in human social networks.

Evolution of cooperation in an epithelium

Cooperation is prevalent in nature, not only in the context of social interactions within the animal kingdom but also on the cellular level. In cancer, for example, tumour cells can cooperate by producing growth factors. The evolution of cooperation has traditionally been studied for well-mixed populations under the framework of evolutionary game theory, and more recently for structured populations using evolutionary graph theory (EGT). The population structures arising due to cellular arrangement in tissues, however, are dynamic and thus cannot be accurately represented by either of these frameworks. In this work, we compare the conditions for cooperative success in an epithelium modelled using EGT, to those in a mechanical model of an epithelium—the Voronoi tessellation (VT) model. Crucially, in this latter model, cells are able to move, and birth and death are not spatially coupled. We calculate fixation probabilities in the VT model through simulation and an approximate analytic technique and show that this leads to stronger promotion of cooperation in comparison with the EGT model.

High thresholds encouraging the evolution of cooperation in threshold public-good games

For a well-mixed population, we consider a threshold public good game where group members only obtain benefits from a public good if a sufficiently large number of them cooperates. We investigate the effect of an increase in the threshold on the level of cooperation that evolves. It is shown that for sufficiently large participation costs, the level of cooperation is higher for low and for high thresholds, than it is for intermediate thresholds – where in the latter case cooperation may not evolve at all. The counterintuitive effect where an increase in the threshold from an intermediate to a high one decreases the probability of cooperation, is related to the so-called common-enemy hypothesis of the evolution of cooperation. We further apply our analysis to assess the relative weight of different game types across the parameter space, and show that game types where either a small, or a large fraction of the population evolves as cooperators, receive more weight compared to game types where an intermediate fraction of cooperators evolves.

Understanding the evolution of interspecies interactions in microbial communities

Microbial communities are complex multi-species assemblages that are characterized by a multitude of interspecies interactions, which can range from mutualism to competition. The overall sign and strength of interspecies interactions have important consequences for emergent community-level properties such as productivity and stability. It is not well understood how interspecies interactions change over evolutionary timescales. Here, we review the empirical evidence that evolution is an important driver of microbial community properties and dynamics on timescales that have traditionally been regarded as purely ecological. Next, we briefly discuss different modelling approaches to study evolution of communities, emphasizing the similarities and differences between evolutionary and ecological perspectives. We then propose a simple conceptual model for the evolution of interspecies interactions in communities. Specifically, we propose that to understand the evolution of interspecies interactions, it is important to distinguish between direct and indirect fitness effects of a mutation. We predict that in well-mixed environments, traits will be selected exclusively for their direct fitness effects, while in spatially structured environments, traits may also be selected for their indirect fitness effects. Selection of indirectly beneficial traits should result in an increase in interaction strength over time, while selection of directly beneficial traits should not have such a systematic effect. We tested our intuitions using a simple quantitative model and found support for our hypotheses. The next step will be to test these hypotheses experimentally and provide input for a more refined version of the model in turn, thus closing the scientific cycle of models and experiments. This article is part of the theme issue 'Conceptual challenges in microbial community ecology'.

Spatial reciprocity in the evolution of cooperation

Cooperation is key to the survival of all biological systems. The spatial structure of a system constrains who interacts with whom (interaction partner) and who acquires new traits from whom (role model). Understanding when and to what degree a spatial structure affects the evolution of cooperation is an important and challenging topic. Here, we provide an analytical formula to predict when natural selection favours cooperation where the effects of a spatial structure are described by a single parameter. We find that a spatial structure promotes cooperation (spatial reciprocity) when interaction partners overlap role models. When they do not, spatial structure inhibits cooperation even without cooperation dilemmas. Furthermore, a spatial structure in which individuals interact with their role models more often shows stronger reciprocity. Thus, imitating individuals with frequent interactions facilitates cooperation. Our findings are applicable to both pairwise and group interactions and show that strong social ties might hinder, while asymmetric spatial structures for interaction and trait dispersal could promote cooperation.

Coexistence and cooperation in structured habitats

Background

Natural habitats are typically structured, imposing constraints on inhabiting populations and their interactions. Which conditions are important for coexistence of diverse communities, and how cooperative interaction stabilizes in such populations, have been important ecological and evolutionary questions.

Results

We investigate a minimal ecological framework of microbial population dynamics that exhibits crucial features to show coexistence: Populations repeatedly undergo cycles of separation into compartmentalized habitats and mixing with new resources. The characteristic time-scale is longer than that typical of individual growth. Using analytic approximations, averaging techniques and phase-plane methods of dynamical systems, we provide a framework for analyzing various types of microbial interactions. Population composition and population size are both dynamic variables of the model; they are found to be decoupled both in terms of time-scale and parameter dependence. We present specific results for two examples of cooperative interaction by public goods: collective antibiotics resistance, and enhanced iron-availability by pyoverdine. We find stable coexistence to be a likely outcome.

Conclusions

The two simple features of a long mixing time-scale and spatial compartmentalization are enough to enable coexisting strains. In particular, costly social traits are often stabilized in such an environment—and thus cooperation established.

Parent-preferred dispersal promotes cooperation in structured populations

Dispersal is a key process for the emergence of social and biological behaviours. Yet, little attention has been paid to dispersal's effects on the evolution of cooperative behaviour in structured populations. To address this issue, we propose two new dispersal modes, parent-preferred and offspring-preferred dispersal, incorporate them into the birth-death update rule, and consider the resultant strategy evolution in the prisoner's dilemma on random-regular, small-world, and scale-free networks, respectively. We find that parent-preferred dispersal favours the evolution of cooperation in these different types of population structures, while offspring-preferred dispersal inhibits the evolution of cooperation in homogeneous populations. On scale-free networks when the strength of parent-preferred dispersal is weak, cooperation can be enhanced at intermediate strengths of offspring-preferred dispersal, and cooperators can coexist with defectors at high strengths of offspring-preferred dispersal. Moreover, our theoretical analysis based on the pair-approximation method corroborates the evolutionary outcomes on random-regular networks. We also incorporate the two new dispersal modes into three other update rules (death-birth, imitation, and pairwise comparison updating), and find that similar results about the effects of parent-preferred and offspring-preferred dispersal can again be observed in the aforementioned different types of population structures. Our work, thus, unveils robust effects of preferential dispersal modes on the evolution of cooperation in different interactive environments.

The role of spatial structure in the evolution of viral innate immunity evasion: A diffusion-reaction cellular automaton model

Most viruses have evolved strategies for preventing interferon (IFN) secretion and evading innate immunity. Recent work has shown that viral shutdown of IFN secretion can be viewed as a social trait, since the ability of a given virus to evade IFN-mediated immunity depends on the phenotype of neighbor viruses. Following this idea, we investigate the role of spatial structure in the evolution of innate immunity evasion. For this, we model IFN signaling and viral spread using a spatially explicit approximation that combines a diffusion-reaction model and cellular automaton. Our results indicate that the benefits of preventing IFN secretion for a virus are strongly determined by spatial structure through paracrine IFN signaling. Therefore, innate immunity evasion can evolve as a cooperative or even altruistic trait based on indirect fitness effects that IFN shutdown exerts on other members of the viral population. We identify key factors determining whether evasion from IFN-mediated immunity should evolve, such as population bottlenecks occurring during viral transmission, the relative speed of cellular infection and IFN secretion, and the diffusion properties of the medium.

Evolution of egalitarian social norm by resource management

Social organizations, especially human society, rely on egalitarian social norm, which can be characterized by high levels of fairness, empathy and collective conformity. Nevertheless, the evolution of egalitarian social norm remains a conundrum, as it suffers the persistent challenge from individual self-interest. To address this issue, we construct an evolutionary game theoretical model by employing the Ultimatum Game, in which rational individuals are able to perform resource management. We show that resource management drives a population evolving into an oscillatory state with high equilibrium degrees of fairness, empathy and collective conformity and thus constitutes a key mechanism for the evolution of egalitarian social norm in social dilemma situations. Specifically, it results in (1) the formation of egalitarian social norm from diverse individual norms, (2) the emergence of egalitarian social norm in a selfish and unfair world, and (3) the maintenance of egalitarian social norm despite the presence of norm violators. The constructive role of resource management is explained by a mean-field analysis revealing that resource management can effectively enlarge the attraction basin of egalitarian norms or even change the dynamical property of the mini Ultimatum Game from bistability between egalitarian norms and less egalitarian norms to complete-dominance of egalitarian norms over less egalitarian norms. Furthermore, we find that the capacity of resource management can be evolutionarily selected by a coevolution between egalitarian social norm and resource management. Our study suggests that efficiency and equity are linked to each other.

An Evolutionary Game Model with Punishment and Protection to Promote Trust in the Sharing Economy

In this paper, we present an evolutionary trust game, taking punishment and protection into consideration, to investigate the formation of trust in the so-called sharing economy from a population perspective. This sharing economy trust model comprises four types of players: a trustworthy provider, an untrustworthy provider, a trustworthy consumer, and an untrustworthy consumer. Punishment in the form of penalty for untrustworthy providers and protection in the form of insurance for consumers are mechanisms adopted to prevent untrustworthy behaviour. Through comprehensive simulation experiments, we evaluate dynamics of the population for different initial population setups and effects of having penalty and insurance in place. Our results show that each player type influences the ‘existence’ and ‘survival’ of other types of players, and untrustworthy players do not necessarily dominate the population even when the temptation to defect (i.e., to be untrustworthy) is high. Additionally, we observe that imposing a heavier penalty or having insurance for all consumers (trustworthy and untrustworthy) can be counterproductive for promoting trustworthiness in the population and increasing the global net wealth. Our findings have important implications for understanding trust in the context of the sharing economy, and for clarifying the usefulness of protection policies within it.

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.

Evolutionary games on isothermal graphs

Population structure affects the outcome of natural selection. These effects can be modeled using evolutionary games on graphs. Recently, conditions were derived for a trait to be favored under weak selection, on any weighted graph, in terms of coalescence times of random walks. Here we consider isothermal graphs, which have the same total edge weight at each node. The conditions for success on isothermal graphs take a simple form, in which the effects of graph structure are captured in the ‘effective degree’—a measure of the effective number of neighbors per individual. For two update rules (death-Birth and birth-Death), cooperative behavior is favored on a large isothermal graph if the benefit-to-cost ratio exceeds the effective degree. For two other update rules (Birth-death and Death-birth), cooperation is never favored. We relate the effective degree of a graph to its spectral gap, thereby linking evolutionary dynamics to the theory of expander graphs. Surprisingly, we find graphs of infinite average degree that nonetheless provide strong support for cooperation.

The spatial structure of a population is often critical for the evolution of cooperation. Here, Allen and colleagues show that when spatial structure is represented by an isothermal graph, the effective number of neighbors per individual determines whether or not cooperation can evolve.

Diffusion approximation for an age-class-structured population under viability and fertility selection with application to fixation probability of an advantageous mutant

In this paper, we ascertain the validity of a diffusion approximation for the frequencies of different types under recurrent mutation and frequency-dependent viability and fertility selection in a haploid population with a fixed age-class structure in the limit of a large population size. The approximation is used to study, and explain in terms of selection coefficients, reproductive values and population-structure coefficients, the differences in the effects of viability versus fertility selection on the fixation probability of an advantageous mutant.

Motion, fixation probability and the choice of an evolutionary process

Seemingly minor details of mathematical and computational models of evolution are known to change the effect of population structure on the outcome of evolutionary processes. For example, birth-death dynamics often result in amplification of selection, while death-birth processes have been associated with suppression. In many biological populations the interaction structure is not static. Instead, members of the population are in motion and can interact with different individuals at different times. In this work we study populations embedded in a flowing medium; the interaction network is then time dependent. We use computer simulations to investigate how this dynamic structure affects the success of invading mutants, and compare these effects for different coupled birth and death processes. Specifically, we show how the speed of the motion impacts the fixation probability of an invading mutant. Flows of different speeds interpolate between evolutionary dynamics on fixed heterogeneous graphs and well-stirred populations; this allows us to systematically compare against known results for static structured populations. We find that motion has an active role in amplifying or suppressing selection by fragmenting and reconnecting the interaction graph. While increasing flow speeds suppress selection for most evolutionary models, we identify characteristic responses to flow for the different update rules we test. In particular we find that selection can be maximally enhanced or suppressed at intermediate flow speeds.

Whether a mutation spreads in a population or not is one of the most important questions in biology. The evolution of cancer and antibiotic resistance, for example, are mediated by invading mutants. Recent work has shown that population structure can have important consequences for the outcome of evolution. For instance, a mutant can have a higher or a lower chance of invasion than in unstructured populations. These effects can depend on seemingly minor details of the evolutionary model, such as the order of birth and death events. Many biological populations are in motion, for example due to external stirring. Experimentally this is known to be important; the performance of mutants in E. coli populations, for example, depends on the rate of mixing. Here, we focus on simulations of populations in a flowing medium, and compare the success of a mutant for different flow speeds. We contrast different evolutionary models, and identify what features of the evolutionary model affect mutant success for different speeds of the flow. We find that the chance of mutant invasion can be at its highest (or lowest) at intermediate flow speeds, depending on the order in which birth and death events occur in the evolutionary process.

Properties of network structures, structure coefficients, and benefit-to-cost ratios

In structured populations the spatial arrangement of cooperators and defectors on the interaction graph together with the structure of the graph itself determines the game dynamics and particularly whether or not fixation of cooperation (or defection) is favored. For networks described by regular graphs and for a single cooperator (and a single defector) the question of fixation can be addressed by a single parameter, the structure coefficient. This quantity is invariant with respect to the location of the cooperator on the graph and also does not vary over different networks. We may therefore consider it to be generic for regular graphs and call it the generic structure coefficient. For two and more cooperators (or several defectors) fixation properties can also be assigned by structure coefficients. These structure coefficients, however, depend on the arrangement of cooperators and defectors which we may interpret as a configuration of the game. Moreover, the coefficients are specific for a given interaction network modeled as a regular graph, which is why we may call them specific structure coefficients. In this paper, we study how specific structure coefficients vary over interaction graphs and analyze how spectral properties of interaction networks relate to specific structure coefficients. We also discuss implications for the benefit-to-cost ratios of donation games.

Fixation properties of multiple cooperator configurations on regular graphs

Whether or not cooperation is favored in evolutionary games on graphs depends on the population structure and spatial properties of the interaction network. The population structure can be expressed as configurations. Such configurations extend scenarios with a single cooperator among defectors to any number of cooperators and any arrangement of cooperators and defectors on the network. For interaction networks modeled as regular graphs and for weak selection, the emergence of cooperation can be assessed by structure coefficients, which can be specified for each configuration and each regular graph. Thus, as a single cooperator can be interpreted as a lone mutant, the configuration-based structure coefficients also describe fixation properties of multiple mutants. We analyze the structure coefficients and particularly show that under certain conditions, the coefficients strongly correlate to the average shortest path length between cooperators on the evolutionary graph. Thus, for multiple cooperators fixation properties on regular evolutionary graphs can be linked to cooperator path lengths.

The use of multilayer network analysis in animal behaviour

Network analysis has driven key developments in research on animal behaviour by providing quantitative methods to study the social structures of animal groups and populations. A recent formalism, known as multilayer network analysis, has advanced the study of multifaceted networked systems in many disciplines. It offers novel ways to study and quantify animal behaviour through connected 'layers' of interactions. In this article, we review common questions in animal behaviour that can be studied using a multilayer approach, and we link these questions to specific analyses. We outline the types of behavioural data and questions that may be suitable to study using multilayer network analysis. We detail several multilayer methods, which can provide new insights into questions about animal sociality at individual, group, population and evolutionary levels of organization. We give examples for how to implement multilayer methods to demonstrate how taking a multilayer approach can alter inferences about social structure and the positions of individuals within such a structure. Finally, we discuss caveats to undertaking multilayer network analysis in the study of animal social networks, and we call attention to methodological challenges for the application of these approaches. Our aim is to instigate the study of new questions about animal sociality using the new toolbox of multilayer network analysis.

Methods for approximating stochastic evolutionary dynamics on graphs

Population structure can have a significant effect on evolution. For some systems with sufficient symmetry, analytic results can be derived within the mathematical framework of evolutionary graph theory which relate to the outcome of the evolutionary process. However, for more complicated heterogeneous structures, computationally intensive methods are required such as individual-based stochastic simulations. By adapting methods from statistical physics, including moment closure techniques, we first show how to derive existing homogenised pair approximation models and the exact neutral drift model. We then develop node-level approximations to stochastic evolutionary processes on arbitrarily complex structured populations represented by finite graphs, which can capture the different dynamics for individual nodes in the population. Using these approximations, we evaluate the fixation probability of invading mutants for given initial conditions, where the dynamics follow standard evolutionary processes such as the invasion process. Comparisons with the output of stochastic simulations reveal the effectiveness of our approximations in describing the stochastic processes and in predicting the probability of fixation of mutants on a wide range of graphs. Construction of these models facilitates a systematic analysis and is valuable for a greater understanding of the influence of population structure on evolutionary processes.

Ecological feedback on diffusion dynamics

Spatial patterns are ubiquitous across different scales of organization in ecological systems. Animal coat pattern, spatial organization of insect colonies and vegetation in arid areas are prominent examples from such diverse ecologies. Typically, pattern formation has been described by reaction-diffusion equations, which consider individuals dispersing between subpopulations of a global pool. This framework applied to public goods game nicely showed the endurance of populations via diffusion and generation of spatial patterns. However, how the spatial characteristics, such as diffusion, are related to the eco-evolutionary process as well as the nature of the feedback from evolution to ecology and vice versa, has been so far neglected. We present a thorough analysis of the ecologically driven evolutionary dynamics in a spatially extended version of ecological public goods games. Furthermore, we show how these evolutionary dynamics feed back into shaping the ecology, thus together determining the fate of the system.

The impact of truncation selection and diffusion on cooperation in spatial games

Natural Selection is frequently modelled via proportional selection where survival is proportional to the average payoff differential. There has been little attention devoted to modelling truncation selection where replicators below a threshold are culled and survivors reproduce. Here, we systematically explore truncation selection for two strategy games in a spatial setting. We employ two variations of truncation selection: independent, where the threshold is fixed; and dependent, where the proportion culled is fixed. Further, we explore the effects of diffusion with the algorithms: contest-diffusion-offspring (CDO), and diffusion-contest-offspring (DCO). CDO and DCO frequently facilitate and diminish cooperation, respectively. For independent truncation, there are three qualitative regimes determined by the payoff threshold: cooperation decreases as the threshold rises; polymorphisms are stable; and extinction is frequent. Further, an intermediate payoff to cooperators playing defectors can maximize cooperation for the DCO algorithm with a high payoff threshold. Dependent truncation affects games differently; lower levels reduce cooperation for the Hawk Dove game and increase it for the Stag Hunt, and higher levels produce the opposite effects. Comparing these truncation methods to proportional selection, we show how they impact the prevalence of cooperation.

Evolution of non-kin cooperation: social assortment by cooperative phenotype in guppies

Cooperation among non-kin constitutes a conundrum for evolutionary biology. Theory suggests that non-kin cooperation can evolve if individuals differ consistently in their cooperative phenotypes and assort socially by these, such that cooperative individuals interact predominantly with one another. However, our knowledge of the role of cooperative phenotypes in the social structuring of real-world animal populations is minimal. In this study, we investigated cooperative phenotypes and their link to social structure in wild Trinidadian guppies (Poecilia reticulata). We first investigated whether wild guppies are repeatable in their individual levels of cooperativeness (i.e. have cooperative phenotypes) and found evidence for this in seven out of eight populations, a result which was mostly driven by females. We then examined the social network structure of one of these populations where the expected fitness impact of cooperative contexts is relatively high, and found assortment by cooperativeness, but not by genetic relatedness. By contrast, and in accordance with our expectations, we did not find assortment by cooperativeness in a population where the expected fitness impact of cooperative contexts is lower. Our results provide empirical support for current theory and suggest that assortment by cooperativeness is important for the evolution and persistence of non-kin cooperation in real-world populations.

Generalized Social Dilemmas: The Evolution of Cooperation in Populations with Variable Group Size

Evolutionary game theory is an important tool to model animal and human behaviour. A key class of games is the social dilemmas, where cooperation benefits the group but defection benefits the individual within any group. Previous works have considered which games qualify as social dilemmas, and different categories of dilemmas, but have generally concentrated on fixed sizes of interacting groups. In this paper, we develop a systematic investigation of social dilemmas on all group sizes. This allows for a richer definition of social dilemmas. For example, while increasing a group size to include another defector is always bad for all existing group members, extra cooperators can be good or bad, depending upon the particular dilemma and group size. We consider a number of commonly used social dilemmas in this context and in particular show the effect of variability in group sizes for the example of a population comprising negative binomially distributed group sizes. The most striking effect is that increasing the variability in group sizes for non-threshold public goods games is favourable for the evolution of cooperation. The situation for threshold public goods games and commons dilemmas is more complex.

Experimental disturbances reveal group-level costs of social instability

In group-living species, social stability is an important trait associated with the evolution of complex behaviours such as cooperation. While the drivers of stability in small groups are relatively well studied, little is known about the potential impacts of unstable states on animal societies. Temporary changes in group composition, such as a social group splitting and recombining (i.e. a disturbance event), can result in individuals having to re-establish their social relationships, thus taking time away from other tasks such as foraging or vigilance. Here, we experimentally split socially stable groups of captive zebra finches (Taeniopygia guttata), and quantified the effects of repeated disturbance events on (1) group foraging efficiency, and (2) co-feeding associations when subgroups were recombined. We found that the efficiency of groups to deplete a rich, but ephemeral, resource patch decreased after just a single short disturbance event. Automated tracking of individuals showed that repeated disturbances reduced efficiency by causing social relationships to become more differentiated and weaker, resulting in fewer individuals simultaneously accessing the patch. Our experiment highlights how short-term disturbances can severely disrupt social structure and group functionality, revealing potential costs associated with group instability that can have consequences for the evolution of animal societies.

A mathematical formalism for natural selection with arbitrary spatial and genetic structure

We define a general class of models representing natural selection between two alleles. The population size and spatial structure are arbitrary, but fixed. Genetics can be haploid, diploid, or otherwise; reproduction can be asexual or sexual. Biological events (e.g. births, deaths, mating, dispersal) depend in arbitrary fashion on the current population state. Our formalism is based on the idea of genetic sites. Each genetic site resides at a particular locus and houses a single allele. Each individual contains a number of sites equal to its ploidy (one for haploids, two for diploids, etc.). Selection occurs via replacement events, in which alleles in some sites are replaced by copies of others. Replacement events depend stochastically on the population state, leading to a Markov chain representation of natural selection. Within this formalism, we define reproductive value, fitness, neutral drift, and fixation probability, and prove relationships among them. We identify four criteria for evaluating which allele is selected and show that these become equivalent in the limit of low mutation. We then formalize the method of weak selection. The power of our formalism is illustrated with applications to evolutionary games on graphs and to selection in a haplodiploid population.

Stationary frequencies and mixing times for neutral drift processes with spatial structure

We study a general setting of neutral evolution in which the population is of finite, constant size and can have spatial structure. Mutation leads to different genetic types (traits), which can be discrete or continuous. Under minimal assumptions, we show that the marginal trait distributions of the evolutionary process, which specify the probability that any given individual has a certain trait, all converge to the stationary distribution of the mutation process. In particular, the stationary frequencies of traits in the population are independent of its size, spatial structure and evolutionary update rule, and these frequencies can be calculated by evaluating a simple stochastic process describing a population of size one (i.e. the mutation process itself). We conclude by analysing mixing times, which characterize rates of convergence of the mutation process along the lineages, in terms of demographic variables of the evolutionary process.

Cooperation in the spatial prisoner's dilemma game with probabilistic abstention

Research has shown that the addition of abstention as an option transforms social dilemmas to rock-paper-scissor type games, where defectors dominate cooperators, cooperators dominate abstainers (loners), and abstainers (loners), in turn, dominate defectors. In this way, abstention can sustain cooperation even under adverse conditions, although defection also persists due to cyclic dominance. However, to abstain or to act as a loner has, to date, always been considered as an independent, third strategy to complement traditional cooperation and defection. Here we consider probabilistic abstention, where each player is assigned a probability to abstain in a particular instance of the game. In the two limiting cases, the studied game reverts to the prisoner's dilemma game without loners or to the optional prisoner's dilemma game. For intermediate probabilities, we have a new hybrid game, which turns out to be most favorable for the successful evolution of cooperation. We hope this novel hybrid game provides a more realistic view of the dilemma of optional/voluntary participation.

Network Interventions for Changing Physical Activity Behaviour in Preadolescents

Network interventions can help achieve behavioural change by inducing peer-pressure in the network. However, inducing peer-pressure without considering the structure of the existing social network may render the intervention ineffective or weaker. In a 7-week school-based field experiment using preadolescents' physical activity (PA) as a proxy for estimating behavioural change, we test the hypothesis that boys' and girls' distinct networks are susceptible to different social incentives. We run three different social-rewards schemes, in which classmates' rewards depend on the PA of two friends either reciprocally (directly or indirectly) or collectively. Compared to a random-rewards control, social-rewards schemes had an overall significantly positive effect on PA (51.8% increase), with females being more receptive to the direct reciprocity scheme (76.4%) and males to team (collective) rewards (131.5%). Differences in the sex-specific sub-networks can explain these findings. Network interventions adapted to the network-specific characteristics may constitute a powerful tool for behavioural change.

Hunter-Gatherers Maintain Assortativity in Cooperation despite High Levels of Residential Change and Mixing

Widespread cooperation is a defining feature of human societies from hunter-gatherer bands to nation states [1, 2], but explaining its evolution remains a challenge. Although positive assortment of cooperators is recognized as a basic requirement for the evolution of cooperation, the mechanisms governing assortment are debated. Moreover, the social structure of modern hunter-gatherers, characterized by high mobility, residential mixing, and low genetic relatedness [3], undermines assortment and adds to the puzzle of how cooperation evolved. Here, we analyze four years of data (2010, 2013, 2014, 2016) tracking residence and levels of cooperation elicited from a public goods game in Hadza hunter-gatherers of Tanzania. Data were collected from 56 camps, comprising 383 unique individuals, 137 of whom we have data for two or more years. Despite significant residential mixing, we observe a robust pattern of assortment that is necessary for cooperation to evolve; in every year, Hadza camps exhibit high between-camp and low within-camp variation in cooperation. We find little evidence that cooperative behavior within individuals is stable over time or that similarity in cooperation between dyads predicts their future cohabitation. Both sets of findings are inconsistent with models that assume stable cooperative and selfish types, including partner choice models. Consistent with social norms, culture, and reciprocity theories, the strongest predictor of an individual's level of cooperation is the mean cooperation of their current campmates. These findings underscore the adaptive nature of human cooperation-particularly its responsiveness to social contexts-as a feature that is important in generating the assortment necessary for cooperation to evolve.

Replicator equation on networks with degree regular communities

The replicator equation is one of the fundamental tools to study evolutionary dynamics in well-mixed populations. This paper contributes to the literature on evolutionary graph theory, providing a version of the replicator equation for a family of connected networks with communities, where nodes in the same community have the same degree. This replicator equation is applied to the study of different classes of games, exploring the impact of the graph structure on the equilibria of the evolutionary dynamics.

Genetic adaptation as a biological buffer against climate change: Potential and limitations

Climate change profoundly impacts ecosystems and their biota, resulting in range shifts, novel interactions, food web alterations, changed intensities of host-parasite interactions, and extinctions. An increasing number of studies have documented evolutionary changes in traits such as phenology and thermal tolerance. In this opinion paper, we argue that, while evolutionary responses have the potential to provide a buffer against extinctions or range shifts, a number of constraints and complexities blur this simple prediction. First, there are limits to evolutionary potential both in terms of genetic variation and demographic effects, and these limits differ strongly among taxa and populations. Second, there can be costs associated with genetic adaptation, such as a reduced evolutionary potential towards other (human-induced) environmental stressors or direct fitness costs due to tradeoffs. Third, the differential capacity of taxa to genetically respond to climate change results in novel interactions because different organism groups respond to a different degree with local compared to regional (dispersal and range shift) responses. These complexities result in additional changes in the selection pressures on populations. We conclude that evolution can provide an initial buffer against climate change for some taxa and populations but does not guarantee their survival. It does not necessarily result in reduced extinction risks across the range of taxa in a region or continent. Yet, considering evolution is crucial, as it is likely to strongly change how biota will respond to climate change and will impact which taxa will be the winners or losers at the local, metacommunity and regional scales.

Hypothesis: Cancer Is a Disease of Evolved Trade-Offs Between Neoplastic Virulence and Transmission

Virulence is defined as the ability of a pathogen to cause morbidity and/or mortality in infected hosts. The relationship between virulence and transmissibility is complex; natural selection may promote decreased virulence to enhance host mobility and increase the probability for transmission, or transmissibility may be enhanced by increased virulence, leading to higher pathogen load and, in some cases, superior evasion from host defenses. An evolutionary trade-off exists between the ability of pathogens to maintain opportunities for long-term transmission via suppressed virulence and increased short-term transmission via enhanced virulence. We propose an analogy between transmissibility and virulence in microbial pathogens and in cancer. Thus, in the latter case, the outcome of invasive growth and metastasis is analogous to transmissibility, and virulence is defined by high rates of proliferation, invasiveness and motility, potential for metastasis, and the extent to which the cancer contributes to patient morbidity and mortality. Horizontal and vertical transmission, associated with increased or decreased pathogen virulence respectively, can also be utilized to model the neoplastic process and factors that would increase or decrease tumor aggressiveness. Concepts of soft vs. hard selection and evolutionary game theory can optimize our understanding of carcinogenesis and therapeutic strategies. Therefore, the language of transmissibility, horizontal vs. vertical transmission, selection, and virulence can be used to inform approaches to inhibit tumorigenic progression, and, more generally, for cancer prevention and treatment.

Population Structure Promotes the Evolution of Intuitive Cooperation and Inhibits Deliberation

Spatial structure is one of the most studied mechanisms in evolutionary game theory. Here, we explore the consequences of spatial structure for a question which has received considerable empirical and theoretical attention in recent years, but has not yet been studied from a network perspective: whether cooperation relies on intuitive predispositions or deliberative self-control. We examine this question using a model which integrates the “dual-process” framework from cognitive science with evolutionary game theory, and considers the evolution of agents who are embedded within a social network and only interact with their neighbors. In line with past work in well-mixed populations, we find that selection favors either the intuitive defector strategy which never deliberates, or the dual-process cooperator strategy which intuitively cooperates but uses deliberation to switch to defection when doing so is payoff-maximizing. We find that sparser networks (i.e., smaller average degree) facilitate the success of dual-process cooperators over intuitive defectors, while also reducing the level of deliberation that dual-process cooperators engage in; and that these results generalize across different kinds of networks. These observations demonstrate the important role that spatial structure can have not just on the evolution of cooperation, but on the co-evolution of cooperation and cognition.

Stirring does not make populations well mixed

In evolutionary dynamics, the notion of a ‘well-mixed’ population is usually associated with all-to-all interactions at all times. This assumption simplifies the mathematics of evolutionary processes, and makes analytical solutions possible. At the same time the term ‘well-mixed’ suggests that this situation can be achieved by physically stirring the population. Using simulations of populations in chaotic flows, we show that in most cases this is not true: conventional well-mixed theories do not predict fixation probabilities correctly, regardless of how fast or thorough the stirring is. We propose a new analytical description in the fast-flow limit. This approach is valid for processes with global and local selection, and accurately predicts the suppression of selection as competition becomes more local. It provides a modelling tool for biological or social systems with individuals in motion.

Public goods games in populations with fluctuating size

Many mathematical frameworks of evolutionary game dynamics assume that the total population size is constant and that selection affects only the relative frequency of strategies. Here, we consider evolutionary game dynamics in an extended Wright-Fisher process with variable population size. In such a scenario, it is possible that the entire population becomes extinct. Survival of the population may depend on which strategy prevails in the game dynamics. Studying cooperative dilemmas, it is a natural feature of such a model that cooperators enable survival, while defectors drive extinction. Although defectors are favored for any mixed population, random drift could lead to their elimination and the resulting pure-cooperator population could survive. On the other hand, if the defectors remain, then the population will quickly go extinct because the frequency of cooperators steadily declines and defectors alone cannot survive. In a mutation-selection model, we find that (i) a steady supply of cooperators can enable long-term population survival, provided selection is sufficiently strong, and (ii) selection can increase the abundance of cooperators but reduce their relative frequency. Thus, evolutionary game dynamics in populations with variable size generate a multifaceted notion of what constitutes a trait's long-term success.

Evolving synergetic interactions

Cooperators forgo their own interests to benefit others. This reduces their fitness and thus cooperators are not likely to spread based on natural selection. Nonetheless, cooperation is widespread on every level of biological organization ranging from bacterial communities to human society. Mathematical models can help to explain under which circumstances cooperation evolves. Evolutionary game theory is a powerful mathematical tool to depict the interactions between cooperators and defectors. Classical models typically involve either pairwise interactions between individuals or a linear superposition of these interactions. For interactions within groups, however, synergetic effects may arise: their outcome is not just the sum of its parts. This is because the payoffs via a single group interaction can be different from the sum of any collection of two-player interactions. Assuming that all interactions start from pairs, how can such synergetic multiplayer games emerge from simpler pairwise interactions? Here, we present a mathematical model that captures the transition from pairwise interactions to synergetic multiplayer ones. We assume that different social groups have different breaking rates. We show that non-uniform breaking rates do foster the emergence of synergy, even though individuals always interact in pairs. Our work sheds new light on the mechanisms underlying such synergetic interactions.