How to reach linguistic consensus: a proof of convergence for the naming game

In this paper we introduce a mathematical model of naming games. Naming games have been widely used within research on the origins and evolution of language. Despite the many interesting empirical results these studies have produced, most of this research lacks a formal elucidating theory. In this paper we show how a population of agents can reach linguistic consensus, i.e. learn to use one common language to communicate with one another. Our approach differs from existing formal work in two important ways: one, we relax the too strong assumption that an agent samples infinitely often during each time interval. This assumption is usually made to guarantee convergence of an empirical learning process to a deterministic dynamical system. Two, we provide a proof that under these new realistic conditions, our model converges to a common language for the entire population of agents. Finally the model is experimentally validated.     

Finite populations choose an optimal language

This paper studies the evolution of a proto-language in a finite population under the frequency-dependent Moran process. A proto-language can be seen as a collection of concept-to-sign mappings. An efficient proto-language is a bijective mapping from objects of communication to used signs and vice versa. Based on the comparison of fixation probabilities, a method for deriving conditions of evolutionary stability in a finite population [Nowak et al., 2004. Emergence of cooperation and evolutionary stability in finite populations. Nature 428, 246-650], it is shown that efficient proto-languages are the only strategies that are protected by selection, which means that no mutant strategy can have a fixation probability that is greater than the inverse population size. In passing, the paper provides interesting results about the comparison of fixation probabilities as well as Maynard Smith's notion of evolutionary stability for finite populations [Maynard Smith, 1988. Can a mixed strategy be stable in a finite population? J. Theor. Biol. 130, 247-251] that are generally true for games with a symmetric payoff function.     

Fixation probabilities in evolutionary game dynamics with a two-strategy game in finite diploid populations

Fixation processes in evolutionary game dynamics in finite diploid populations are investigated. Traditionally, frequency dependent evolutionary dynamics is modeled as deterministic replicator dynamics. This implies that the infinite size of the population is assumed implicitly. In nature, however, population sizes are finite. Recently, stochastic processes in finite populations have been introduced in order to study finite size effects in evolutionary game dynamics. One of the most significant studies on evolutionary dynamics in finite populations was carried out by Nowak et al. which describes “one-third law” [Nowak, et al., 2004. Emergence of cooperation and evolutionary stability in finite populations. Nature 428, 646-650]. It states that under weak selection, if the fitness of strategy α is greater than that of strategy β when α has a frequency , strategy α fixates in a β-population with selective advantage. In their study, it is assumed that the inheritance of strategies is asexual, i.e. the population is haploid. In this study, we apply their framework to a diploid population that plays a two-strategy game with two ESSs (a bistable game). The fixation probability of a mutant allele in this diploid population is derived. A “three-tenth law” for a completely recessive mutant allele and a “two-fifth law” for a completely dominant mutant allele are found; other cases are also discussed.     

The fastest evolutionary trajectory

Given two mutants, A and B, separated by n mutational steps, what is the evolutionary trajectory which allows a homogeneous population of A to reach B in the shortest time? We show that the optimum evolutionary trajectory (fitness landscape) has the property that the relative fitness increase between any two consecutive steps is constant. Hence, the optimum fitness landscape between A and B is given by an exponential function. Our result is precise for small mutation rates and excluding back mutations. We discuss deviations for large mutation rates and including back mutations. For very large mutation rates, the optimum fitness landscape is flat and has a single peak at type B.     

A game theoretical approach to the evolution of structured communication codes

Structured meaning-signal mappings, i.e., mappings that preserve neighborhood relationships by associating similar signals with similar meanings, are advantageous in an environment where signals are corrupted by noise and sub-optimal meaning inferences are rewarded as well. The evolution of these mappings, however, cannot be explained within a traditional language evolutionary game scenario in which individuals meet randomly because the evolutionary dynamics is trapped in local maxima that do not reflect the structure of the meaning and signal spaces. Here we use a simple game theoretical model to show analytically that when individuals adopting the same communication code meet more frequently than individuals using different codes—a result of the spatial organization of the population—then advantageous linguistic innovations can spread and take over the population. In addition, we report results of simulations in which an individual can communicate only with its K nearest neighbors and show that the probability that the lineage of a mutant that uses a more efficient communication code becomes fixed decreases exponentially with increasing K. These findings support the mother tongue hypothesis that human language evolved as a communication system used among kin, especially between mothers and offspring.     

A review of evolutionary graph theory with applications to game theory

Evolutionary graph theory (EGT), studies the ability of a mutant gene to overtake a finite structured population. In this review, we describe the original framework for EGT and the major work that has followed it. This review looks at the calculation of the “fixation probability” - the probability of a mutant taking over a population and focuses on game-theoretic applications. We look at varying topics such as alternate evolutionary dynamics, time to fixation, special topological cases, and game theoretic results. Throughout the review, we examine several interesting open problems that warrant further research.     

The one-third law of evolutionary dynamics

Evolutionary game dynamics in finite populations provide a new framework for studying selection of traits with frequency-dependent fitness. Recently, a "one-third law" of evolutionary dynamics has been described, which states that strategy A fixates in a B-population with selective advantage if the fitness of A is greater than that of B when A has a frequency 13. This relationship holds for all evolutionary processes examined so far, from the Moran process to games on graphs. However, the origin of the "number"13 is not understood. In this paper we provide an intuitive explanation by studying the underlying stochastic processes. We find that in one invasion attempt, an individual interacts on average with B-players twice as often as with A-players, which yields the one-third law. We also show that the one-third law implies that the average Malthusian fitness of A is positive.     

A popular misapplication of evolutionary modeling to the study of human cooperation

To examine the evolutionary basis of a behavior, an established approach (known as the phenotypic gambit) is to assume that the behavior is controlled by a single allele, the fitness effects of which are derived from a consideration of how the behavior interacts, via life-history, with other ecological factors. Here we contrast successful applications of this approach with several examples of an influential and superficially similar line of research on the evolutionary basis of human cooperation. A key difference is identified: in the latter line of research the focal behavior, cooperation, is abstractly defined in terms of immediate fitness costs and benefits. Selection is then assumed to act on strategies in an iterated social context for which fitness effects can be derived by aggregation of the abstractly defined immediate fitness effects over a lifetime. This approach creates a closed theoretical loop, rendering models incapable of making predictions or providing insight into the origin of human cooperation. We conclude with a discussion of how evolutionary approaches might be appropriately used in the study of human social behavior.     

Transitions and transversions in evolutionary descent: An approach to understanding

Summary In this paper I lay a quantitative theoretical groundwork for understanding the proportions of the possible types of base substitutions observed between 12 genes sharing a common ancestor and isolated from extant species. The experimentally observed types of base substitution between two sequenced genes do not give a direct measure of the types of base substitutions that occur during evolutionary descent. However, by use of a statistical assemblage of these observations, we can recover, without the assumption of parsimony, the conditional base substitution probabilities that determine this descent. Three methods—direct count, regression, and informational entropy maximization—are described by which these probabilities can be estimated from experimental data. The methods are complementary in that each is most useful for somewhat different types of experimental data. These methods are used to study the ratio of transversions to transitions during gene divergence. Though this ratio is not constant during divergence, it does approach a stable limiting value that in principle can vary from zero, corresponding to 100% transition differences, to infinity, corresponding to 0% transition differences. In practice the limiting ratio tends to hover around a value of two, which is expected on a random basis. However, base substitution pathways that are very nonrandom also may lead to a limiting ratio of exactly two, so that such a value is not diagnostic for random pathways. The limiting ratio can be directly calculated from a knowledge of the twelve conditional probabilities for each type of base substitution, or from a knowledge of the equilibrium base composition of the DNAs compared. An expression is given for this calculation. Fifteen years ago Jean Derancourt, Andrew Lebor and Emile Zuckerkandl (1967), analyzing the amino acid sequence of globin chains coded by nuclear genes, made the original observation that the proportion of transition differences decreases with increasing evolutionary time. Recently Brown et al. (1982) and Brown and Simpson (1982) have reported a decrease in the observed proportion of transition differences in mitochondrial DNA with increasing evolutionary divergence. The conditions that must be satisfied for this type of behavior to occur at stable base composition and with stable base substitution probabilities are defined. Multiple substitutionsper se do not lead to a decrease in transition differences with increasing evolutionary divergence.     

Graphing evolutionary pattern and process: a history of techniques in archaeology and paleobiology

Graphs displaying evolutionary patterns are common in paleontology and in United States archaeology. Both disciplines subscribed to a transformational theory of evolution and graphed evolution as a sequence of archetypes in the late nineteenth and early twentieth centuries. U.S. archaeologists in the second decade of the twentieth century, and paleontologists shortly thereafter, developed distinct graphic styles that reflected the Darwinian variational model of evolution. Paleobiologists adopted the view of a species as a set of phenotypically variant individuals and graphed those variations either as central tendencies or as histograms of frequencies of variants. Archaeologists presumed their artifact types reflected cultural norms of prehistoric artisans and the frequency of specimens in each type reflected human choice and type popularity. They graphed cultural evolution as shifts in frequencies of specimens representing each of several artifact types. Confusion of pattern and process is exemplified by a paleobiologist misinterpreting the process illustrated by an archaeological graph, and an archaeologist misinterpreting the process illustrated by a paleobiological graph. Each style of graph displays particular evolutionary patterns and implies particular evolutionary processes. Graphs of a multistratum collection of prehistoric mammal remains and a multistratum collection of artifacts demonstrate that many graph styles can be used for both kinds of collections.     

Eavesdropping and language dynamics

Communication in nature is not restricted to the transmitter-receiver pair. Unintended listeners, or eavesdroppers, can intercept the signal and possibly utilize the received information to their benefit, which may confer a certain cost to the communicating pair. In this paper we explore (computationally and mathematically) such situations with the goal of uncovering their effect on language evolution. We find that in the presence of eavesdropping, languages exhibit a tendency to become more complex. On the other hand, if eavesdroppers belong to a different (competing) population, the languages used by the two populations tend to converge, if the cost of eavesdropping is sufficiently high; otherwise the languages synchronize. These findings are discussed in the context of animal communication and human language. In particular, the emergence of synonyms is predicted. We demonstrate that a small associated cost can suppress synonyms in the absence of eavesdropping, but that their likelihood increases strongly with the probability of eavesdropping.     

A novel approach for predicting the evolutionary time of acquisition of foreign genes by bacteria: Application of codon usage analyses

Lysogenic bacteriophages are considered as a major player for the introduction of foreign genes into bacterial strains. At the time of introduction foreign genes do not fit well into the translation system of the recipient host bacterium as they tend to retain the characteristics of the donor bacterium from which they have been transferred. Consequently foreign genes are poorly transcribed at the early phase of their evolution within the host bacterium. This is largely due to the difference in the codon usage pattern between the horizontally transferred genes and the host bacterium. In this study we present detailed analyses of various parameters of the codon usages such as codon adaptation index (CAI), mean difference (MD) of the relative adaptiveness, synonymous substitution rate (SSR) of six different phage encoded toxin genes (cholera toxin, shiga toxin, diphtheria toxin, neurotoxin C1, enterotoxin type A and cytotoxin), and proposed conceptual relationship between the evolutionary time of acquisition of the foreign genes and the selected set of parameters of the codon usage. On the basis of the observed data we hypothesize that CAI, MD and SSR of the phage encoded toxin genes are correlated with the evolutionary time of their acquisition, and have developed a novel approach based on the analyses of these parameters, which can be used to predict the evolutionary time of their acquisition by the corresponding host bacterium.     

Ethics,evolution and culture

Recent work in the fields of evolutionary ethics and moral psychology appears to be converging on a single empirically- and evolutionary-based science of morality or ethics. To date, however, these fields have failed to provide an adequate conceptualisation of how culture affects the content and distribution of moral norms. This is particularly important for a large class of moral norms relating to rapidly changing technological or social environments, such as norms regarding the acceptability of genetically modified organisms. Here we suggest that a science of morality/ethics can benefit from adopting a cultural evolution or gene-culture coevolution approach, which treats culture as a second, separate evolutionary system that acts in parallel to biological/genetic evolution. This cultural evolution approach brings with it a set of established theoretical concepts (e.g. different cultural transmission mechanisms) and empirical methods (e.g. evolutionary game theory) that can significantly improve our understanding of human morality.

The evolution of vocabulary

Human language is unique among the communication systems of the natural world. The vocabulary of human language is unique in being both culturally transmitted and symbolic. In this paper I present an investigation into the factors involved in the evolution of such vocabulary systems. I investigate both the cultural evolution of vocabulary systems and the biological evolution of learning rules for vocabulary acquisition. Firstly, vocabularies are shown to evolve on a cultural time-scale so as to fit the expectations of learners-a population's vocabulary adapts to the biases of the learners in that population. A learning bias in favour of one-to-one mappings between meanings and words leads to the cultural evolution of communicatively optimal vocabulary systems, even in the absence of any explicit pressure for communication. Furthermore, the pressure to conform to the biases of learners is shown to outweigh natural selection acting on cultural transmission. Human language learners appear to bring a one-to-one bias to the acquisition of vocabulary systems. The functionality of human vocabulary may therefore be a consequence of the biases of human language learners. Secondly, the evolutionary stability of genetically transmitted vocabulary learning biases is investigated using both static and dynamic models. A one-to-one learning bias, which leads to the cultural evolution of optimal communication, is shown to be evolutionarily stable. However, the evolution de novo of this bias is complicated by the cumulative nature of the cultural evolution of vocabulary systems. This suggests that the biases of human language learners may not have evolved specifically and exclusively for the acquisition of communicatively functional vocabulary.     

Quantifying cultural macro-evolution: a case study of the hinoeuma fertility drop

Understanding patterns and underlying processes of human cultural diversity has been a major challenge in evolutionary anthropology. Recent developments in the study of cultural macro-evolution have illuminated various novel aspects of cultural phenomena at the population level. However, limitations in data availability have constrained previous analyses to use simplest models ignoring factors that potentially affect cultural evolutionary dynamics. Here, we focus on two such factors: accumulated effects of cultural transmission between populations over time and variation in social influence among populations. As a test case, we analyze data on the hinoeuma fertility drop, the Japanese nation-wide drastic decline in the number of births caused by a culturally-transmitted superstition recurring every sixty years, to show that these factors do play significant roles. Specifically, our results suggest that transmission of the superstition in a short timescale has tended to occur among neighboring populations, while transmission in a long timescale is likely to have occurred between populations culturally close to each other, with the cultural closeness being measured by similarity in dialects. The results also indicate a special role played by a population occupying a center in a language–distance network (the cultural center) in the spread of the superstition.     

Success-biased social learning: Cultural and evolutionary dynamics

Success bias is a social learning strategy whereby learners tend to acquire the cultural variants of successful individuals. I develop a general model of success-biased social learning for discrete cultural traits with stochastic payoffs, and investigate its dynamics when only two variants are present. I find that success bias inherently favors rare variants, and consequently performs worse than unbiased imitation (i.e. random copying) when success payoffs are at least mildly stochastic and the optimal variant is common. Because of this weakness, success bias fails to replace unbiased imitation in an evolutionary model when selection is fairly weak or when the environment is relatively stable, and sometimes fails to invade at all. I briefly discuss the optimal strength of success bias, the complicated nature of defining success in social learning contexts, and the value of variant frequency as an important source of information to social learners. I conclude with predictions regarding the prevalence of success bias in different behavioral domains.     

Evolution as a cognition process: Towards an evolutionary epistemology

Recently, biologist and philosophers have been much attracted by an evolutionary view of knowledge, so-called evolutionary epistemology. Developing this insight, the present paper argues that our cognitive abilities are the outcome of organic evolution, and that, conversely, evolution itself may be described as a cognition process. Furthermore, it is argued that the key to an adequate evolutionary epistemology lies in a system-theoretical approach to evolution which grows from, but goes beyond, Darwin's theory of natural selection.