Alexander J. Stewart

From extortion to generosity, evolution in the Iterated Prisoner's Dilemma

Significance Cooperative behavior seems at odds with the Darwinian principle of survival of the fittest, yet cooperation is abundant in nature. Scientists have used the Prisoner Dilemma game, in which players must choose to cooperate or defect, to study the emergence and stability of cooperation. Recent work has uncovered a remarkable class of extortion strategies that provide one player a disproportionate payoff when facing an unwitting opponent. Extortion strategies perform very well in head-to-head competitions, but they fare poorly in large, evolving populations. Rather we identify a closely related set of generous strategies, which cooperate with others and forgive defection, that replace extortionists and dominate in large populations. Our results help to explain the evolution of cooperation. Recent work has revealed a new class of “zero-determinant” (ZD) strategies for iterated, two-player games. ZD strategies allow a player to unilaterally enforce a linear relationship between her score and her opponent’s score, and thus to achieve an unusual degree of control over both players’ long-term payoffs. Although originally conceived in the context of classical two-player game theory, ZD strategies also have consequences in evolving populations of players. Here, we explore the evolutionary prospects for ZD strategies in the Iterated Prisoner’s Dilemma (IPD). Several recent studies have focused on the evolution of “extortion strategies,” a subset of ZD strategies, and have found them to be unsuccessful in populations. Nevertheless, we identify a different subset of ZD strategies, called “generous ZD strategies,” that forgive defecting opponents but nonetheless dominate in evolving populations. For all but the smallest population sizes, generous ZD strategies are not only robust to being replaced by other strategies but can selectively replace any noncooperative ZD strategy. Generous strategies can be generalized beyond the space of ZD strategies, and they remain robust to invasion. When evolution occurs on the full set of all IPD strategies, selection disproportionately favors these generous strategies. In some regimes, generous strategies outperform even the most successful of the well-known IPD strategies, including win-stay-lose-shift.

Extortion and cooperation in the Prisoner’s Dilemma

Self-serving, rational agents sometimes cooperate to their mutual benefit. However, when and why cooperation emerges is surprisingly hard to pin down. To address this question, scientists from diverse disciplines have used the Prisoner’s Dilemma, a simple two-player game, as a model problem. In PNAS, Press and Dyson (1) dramatically expand our understanding of this classic game by uncovering strategies that provide a unilateral advantage to sentient players pitted against unwitting opponents. By exposing these results, Press and Dyson have fundamentally changed the viewpoint on the Prisoner’s Dilemma, opening a range of new possibilities for the study of cooperation.

Why transcription factor binding sites are ten nucleotides long.

Gene expression is controlled primarily by transcription factors, whose DNA binding sites are typically 10 nt long. We develop a population-genetic model to understand how the length and information content of such binding sites evolve. Our analysis is based on an inherent trade-off between specificity, which is greater in long binding sites, and robustness to mutation, which is greater in short binding sites. The evolutionary stable distribution of binding site lengths predicted by the model agrees with the empirical distribution (5–31 nt, with mean 9.9 nt for eukaryotes), and it is remarkably robust to variation in the underlying parameters of population size, mutation rate, number of transcription factor targets, and strength of selection for proper binding and selection against improper binding. In a systematic data set of eukaryotic and prokaryotic transcription factors we also uncover strong relationships between the length of a binding site and its information content per nucleotide, as well as between the number of targets a transcription factor regulates and the information content in its binding sites. Our analysis explains these features as well as the remarkable conservation of binding site characteristics across diverse taxa.

Collapse of cooperation in evolving games

Significance This study offers a new perspective on an age-old question: When does cooperation emerge in populations? Two-player games used to study this question produce an array of counterintuitive results. And yet a consensus has emerged that, in an evolving population, cooperation tends to triumph over cheating––through reciprocity and generosity. But, what happens when players can influence not only their tendencies to cooperate, but also the rewards they reap for cooperation? We analyze coevolution of strategies and payoffs and find that, as individuals maximize the benefits of cooperation, they often pave the way for its collapse. Our analysis provides a framework for studying the coevolution of games and strategies, and suggests that maintaining cooperation may be more difficult than previously thought. Game theory provides a quantitative framework for analyzing the behavior of rational agents. The Iterated Prisoner’s Dilemma in particular has become a standard model for studying cooperation and cheating, with cooperation often emerging as a robust outcome in evolving populations. Here we extend evolutionary game theory by allowing players’ payoffs as well as their strategies to evolve in response to selection on heritable mutations. In nature, many organisms engage in mutually beneficial interactions and individuals may seek to change the ratio of risk to reward for cooperation by altering the resources they commit to cooperative interactions. To study this, we construct a general framework for the coevolution of strategies and payoffs in arbitrary iterated games. We show that, when there is a tradeoff between the benefits and costs of cooperation, coevolution often leads to a dramatic loss of cooperation in the Iterated Prisoner’s Dilemma. The collapse of cooperation is so extreme that the average payoff in a population can decline even as the potential reward for mutual cooperation increases. Depending upon the form of tradeoffs, evolution may even move away from the Iterated Prisoner’s Dilemma game altogether. Our work offers a new perspective on the Prisoner’s Dilemma and its predictions for cooperation in natural populations; and it provides a general framework to understand the coevolution of strategies and payoffs in iterated interactions.

An Immunological Marker of Tolerance to Infection in Wild Rodents

A large-scale field study in naturally occurring vole populations identified gene expression changes over time and demonstrates how wild mammals exhibit tolerance to chronic parasite infections.

Small groups and long memories promote cooperation.

Complex social behaviors lie at the heart of many of the challenges facing evolutionary biology, sociology, economics, and beyond. For evolutionary biologists the question is often how group behaviors such as collective action, or decision making that accounts for memories of past experience, can emerge and persist in an evolving system. Evolutionary game theory provides a framework for formalizing these questions and admitting them to rigorous study. Here we develop such a framework to study the evolution of sustained collective action in multi-player public-goods games, in which players have arbitrarily long memories of prior rounds of play and can react to their experience in an arbitrary way. We construct a coordinate system for memory-m strategies in iterated n-player games that permits us to characterize all cooperative strategies that resist invasion by any mutant strategy, and stabilize cooperative behavior. We show that, especially when groups are small, longer-memory strategies make cooperation easier to evolve, by increasing the number of ways to stabilize cooperation. We also explore the co-evolution of behavior and memory. We find that even when memory has a cost, longer-memory strategies often evolve, which in turn drives the evolution of cooperation, even when the benefits for cooperation are low.

Degree dependence in rates of transcription factor evolution explains the unusual structure of transcription networks

Transcription networks have an unusual structure. In both prokaryotes and eukaryotes, the number of target genes regulated by each transcription factor, its out-degree, follows a broad tailed distribution. By contrast, the number of transcription factors regulating a target gene, its in-degree, follows a much narrower distribution, which has no broad tail. We constructed a model of transcription network evolution through trans- and cis-mutations, gene duplication and deletion. The effects of these different evolutionary processes on the network structure are enough to produce an asymmetrical in- and out-degree distribution. However, the parameter values required to replicate known in- and out-degree distributions are unrealistic. We then considered variation in the rate of evolution of a gene dependent upon its position in the network. When transcription factors with many regulatory interactions are constrained to evolve more slowly than those with few interactions, the details of the in- and out-degree distributions of transcription networks can be fully reproduced over a range of plausible parameter values. The networks produced by our model depend on the relative rates of the different evolutionary processes. By determining the circumstances under which the networks with the correct degree distributions are produced, we are able to assess the relative importance of the different evolutionary processes in our model during evolution.

Seasonal immunoregulation in a naturally-occurring vertebrate

BackgroundFishes show seasonal patterns of immunity, but such phenomena are imperfectly understood in vertebrates generally, even in humans and mice. As these seasonal patterns may link to infectious disease risk and individual condition, the nature of their control has real practical implications. Here we characterize seasonal dynamics in the expression of conserved vertebrate immunity genes in a naturally-occurring piscine model, the three-spined stickleback.ResultsWe made genome-wide measurements (RNAseq) of whole-fish mRNA pools (n = 36) at the end of summer and winter in contrasting habitats (riverine and lacustrine) and focussed on common trends to filter habitat-specific from overarching temporal responses. We corroborated this analysis with targeted year-round whole-fish gene expression (Q-PCR) studies in a different year (n = 478). We also considered seasonal tissue-specific expression (6 tissues) (n = 15) at a third contrasting (euryhaline) locality by Q-PCR, further validating the generality of the patterns seen in whole fish analyses. Extremes of season were the dominant predictor of immune expression (compared to sex, ontogeny or habitat). Signatures of adaptive immunity were elevated in late summer. In contrast, late winter was accompanied by signatures of innate immunity (including IL-1 signalling and non-classical complement activity) and modulated toll-like receptor signalling. Negative regulators of T-cell activity were prominent amongst winter-biased genes, suggesting that adaptive immunity is actively down-regulated during winter rather than passively tracking ambient temperature. Network analyses identified a small set of immune genes that might lie close to a regulatory axis. These genes acted as hubs linking summer-biased adaptive pathways, winter-biased innate pathways and other organismal processes, including growth, metabolic dynamics and responses to stress and temperature. Seasonal change was most pronounced in the gill, which contains a considerable concentration of T-cell activity in the stickleback.ConclusionsOur results suggest major and predictable seasonal re-adjustments of immunity. Further consideration should be given to the effects of such responses in seasonally-occurring disease.

Under-Dominance Constrains the Evolution of Negative Autoregulation in Diploids

Regulatory networks have evolved to allow gene expression to rapidly track changes in the environment as well as to buffer perturbations and maintain cellular homeostasis in the absence of change. Theoretical work and empirical investigation in Escherichia coli have shown that negative autoregulation confers both rapid response times and reduced intrinsic noise, which is reflected in the fact that almost half of Escherichia coli transcription factors are negatively autoregulated. However, negative autoregulation is rare amongst the transcription factors of Saccharomyces cerevisiae. This difference is surprising because E. coli and S. cerevisiae otherwise have similar profiles of network motifs. In this study we investigate regulatory interactions amongst the transcription factors of Drosophila melanogaster and humans, and show that they have a similar dearth of negative autoregulation to that seen in S. cerevisiae. We then present a model demonstrating that this stiking difference in the noise reduction strategies used amongst species can be explained by constraints on the evolution of negative autoregulation in diploids. We show that regulatory interactions between pairs of homologous genes within the same cell can lead to under-dominance — mutations which result in stronger autoregulation, and decrease noise in homozygotes, paradoxically can cause increased noise in heterozygotes. This severely limits a diploids ability to evolve negative autoregulation as a noise reduction mechanism. Our work offers a simple and general explanation for a previously unexplained difference between the regulatory architectures of E. coli and yeast, Drosophila and humans. It also demonstrates that the effects of diploidy in gene networks can have counter-intuitive consequences that may profoundly influence the course of evolution.

ENVIRONMENTAL ROBUSTNESS AND THE ADAPTABILITY OF POPULATIONS

Recent work has shown that genetic robustness can either facilitate or impede adaptation. But the impact of environmental robustness on adaptation remains unclear. Environmental robustness helps ensure that organisms consistently develop the same phenotype in the face of “environmental noise” during development. Under purifying selection, those genotypes that express the optimal phenotype most reliably will be selectively favored. The resulting reduction in genetic variation tends to slow adaptation when the population is faced with a novel target phenotype. However, environmental noise sometimes induces the expression of an alternative advantageous phenotype, which may speed adaptation by genetic assimilation. Here, we use a population‐genetic model to explore how these two opposing effects of environmental noise influence the capacity of a population to adapt. We analyze how the rate of adaptation depends on the frequency of environmental noise, the degree of environmental robustness in the population, the distribution of environmental robustness across genotypes, the population size, and the strength of selection for a newly adaptive phenotype. Over a broad regime, we find that environmental noise can either facilitate or impede adaptation. Our analysis uncovers several surprising insights about the relationship between environmental noise and adaptation, and it provides a general framework for interpreting empirical studies of both genetic and environmental robustness.