Game Dynamics with Learning and Evolution of Universal Grammar

We investigate a model of language evolution, based on population game dynamics with learning. First, we examine the case of two genetic variants of universal grammar (UG), the heart of the human language faculty, assuming each admits two possible grammars. The dynamics are driven by a communication game. We prove using dynamical systems techniques that if the payoff matrix obeys certain constraints, then the two UGs are stable against invasion by each other, that is, they are evolutionarily stable. Then, we prove a similar theorem for an arbitrary number of disjoint UGs. In both theorems, the constraints are independent of the learning process. Intuitively, if a mutation in UG results in grammars that are incompatible with the established languages, then the mutation will die out because mutants will be unable to communicate and therefore unable to realize any potential benefit of the mutation. An example for which these theorems do not apply shows that compatible mutations may or may not be able to invade, depending on the population's history and the learning process. These results suggest that the genetic history of language is constrained by the need for compatibility and that mutations in the language faculty may have died out or taken over due more to historical accident than to any straightforward notion of relative fitness. MSC 1991: 37N25 · 92D15 · 91F20     

Viability and Resilience of Languages in Competition

We study the viability and resilience of languages, using a simple dynamical model of two languages in competition. Assuming that public action can modify the prestige of a language in order to avoid language extinction, we analyze two cases: (i) the prestige can only take two values, (ii) it can take any value but its change at each time step is bounded. In both cases, we determine the viability kernel, that is, the set of states for which there exists an action policy maintaining the coexistence of the two languages, and we define such policies. We also study the resilience of the languages and identify configurations from where the system can return to the viability kernel (finite resilience), or where one of the languages is lead to disappear (zero resilience). Within our current framework, the maintenance of a bilingual society is shown to be possible by introducing the prestige of a language as a control variable.     

The evolutionary language game.

We explore how evolutionary game dynamics have to be modified to accomodate a mathematical framework for the evolution of language. In particular, we are interested in the evolution of vocabulary, that is associations between signals and objects. We assume that successful communication contributes to biological fitness: individuals who communicate well leave more offspring. Children inherit from their parents a strategy for language learning (a language acquisition device). We consider three mechanisms whereby language is passed from one generation to the next: (i) parental learning: children learn the language of their parents; (ii) role model learning: children learn the language of individuals with a high payoff; and (iii) random learning: children learn the language of randomly chosen individuals. We show that parental and role model learning outperform random learning. Then we introduce mistakes in language learning and study how this process changes language over time. Mistakes increase the overall efficacy of parental and role model learning: in a world with errors evolutionary adaptation is more efficient. Our model also provides a simple explanation why homonomy is common while synonymy is rare.     

Words as alleles: connecting language evolution with Bayesian learners to models of genetic drift

Scientists studying how languages change over time often make an analogy between biological and cultural evolution, with words or grammars behaving like traits subject to natural selection. Recent work has exploited this analogy by using models of biological evolution to explain the properties of languages and other cultural artefacts. However, the mechanisms of biological and cultural evolution are very different: biological traits are passed between generations by genes, while languages and concepts are transmitted through learning. Here we show that these different mechanisms can have the same results, demonstrating that the transmission of frequency distributions over variants of linguistic forms by Bayesian learners is equivalent to the Wright–Fisher model of genetic drift. This simple learning mechanism thus provides a justification for the use of models of genetic drift in studying language evolution. In addition to providing an explicit connection between biological and cultural evolution, this allows us to define a ‘neutral’ model that indicates how languages can change in the absence of selection at the level of linguistic variants. We demonstrate that this neutral model can account for three phenomena: the s-shaped curve of language change, the distribution of word frequencies, and the relationship between word frequencies and extinction rates.     

Aging in language dynamics

Human languages evolve continuously, and a puzzling problem is how to reconcile the apparent robustness of most of the deep linguistic structures we use with the evidence that they undergo possibly slow, yet ceaseless, changes. Is the state in which we observe languages today closer to what would be a dynamical attractor with statistically stationary properties or rather closer to a non-steady state slowly evolving in time? Here we address this question in the framework of the emergence of shared linguistic categories in a population of individuals interacting through language games. The observed emerging asymptotic categorization, which has been previously tested - with success - against experimental data from human languages, corresponds to a metastable state where global shifts are always possible but progressively more unlikely and the response properties depend on the age of the system. This aging mechanism exhibits striking quantitative analogies to what is observed in the statistical mechanics of glassy systems. We argue that this can be a general scenario in language dynamics where shared linguistic conventions would not emerge as attractors, but rather as metastable states.     

The layer-oriented approach to declarative languages for biological modeling

We present a new approach to modeling languages for computational biology, which we call the layer-oriented approach. The approach stems from the observation that many diverse biological phenomena are described using a small set of mathematical formalisms (e.g. differential equations), while at the same time different domains and subdomains of computational biology require that models are structured according to the accepted terminology and classification of that domain. Our approach uses distinct semantic layers to represent the domain-specific biological concepts and the underlying mathematical formalisms. Additional functionality can be transparently added to the language by adding more layers. This approach is specifically concerned with declarative languages, and throughout the paper we note some of the limitations inherent to declarative approaches. The layer-oriented approach is a way to specify explicitly how high-level biological modeling concepts are mapped to a computational representation, while abstracting away details of particular programming languages and simulation environments. To illustrate this process, we define an example language for describing models of ionic currents, and use a general mathematical notation for semantic transformations to show how to generate model simulation code for various simulation environments. We use the example language to describe a Purkinje neuron model and demonstrate how the layer-oriented approach can be used for solving several practical issues of computational neuroscience model development. We discuss the advantages and limitations of the approach in comparison with other modeling language efforts in the domain of computational biology and outline some principles for extensible, flexible modeling language design. We conclude by describing in detail the semantic transformations defined for our language.     

Agent-Based Models of Strategies for the Emergence and Evolution of Grammatical Agreement

Grammatical agreement means that features associated with one linguistic unit (for example number or gender) become associated with another unit and then possibly overtly expressed, typically with morphological markers. It is one of the key mechanisms used in many languages to show that certain linguistic units within an utterance grammatically depend on each other. Agreement systems are puzzling because they can be highly complex in terms of what features they use and how they are expressed. Moreover, agreement systems have undergone considerable change in the historical evolution of languages. This article presents language game models with populations of agents in order to find out for what reasons and by what cultural processes and cognitive strategies agreement systems arise. It demonstrates that agreement systems are motivated by the need to minimize combinatorial search and semantic ambiguity, and it shows, for the first time, that once a population of agents adopts a strategy to invent, acquire and coordinate meaningful markers through social learning, linguistic self-organization leads to the spontaneous emergence and cultural transmission of an agreement system. The article also demonstrates how attested grammaticalization phenomena, such as phonetic reduction and conventionalized use of agreement markers, happens as a side effect of additional economizing principles, in particular minimization of articulatory effort and reduction of the marker inventory. More generally, the article illustrates a novel approach for studying how key features of human languages might emerge.     

Learning bias, cultural evolution of language, and the biological evolution of the language faculty

The biases of individual language learners act to determine the learnability and cultural stability of languages: learners come to the language learning task with biases which make certain linguistic systems easier to acquire than others. These biases are repeatedly applied during the process of language transmission, and consequently should effect the types of languages we see in human populations. Understanding the cultural evolutionary consequences of particular learning biases is therefore central to understanding the link between language learning in individuals and language universals, common structural properties shared by all the world’s languages. This paper reviews a range of models and experimental studies which show that weak biases in individual learners can have strong effects on the structure of socially learned systems such as language, suggesting that strong universal tendencies in language structure do not require us to postulate strong underlying biases or constraints on language learning. Furthermore, understanding the relationship between learner biases and language design has implications for theories of the evolution of those learning biases: models of gene-culture coevolution suggest that, in situations where a cultural dynamic mediates between properties of individual learners and properties of language in this way, biological evolution is unlikely to lead to the emergence of strong constraints on learning.     

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.     

Effects of Conformism on the Cultural Evolution of Social Behaviour

Models of cultural evolution study how the distribution of cultural traits changes over time. The dynamics of cultural evolution strongly depends on the way these traits are transmitted between individuals by social learning. Two prominent forms of social learning are payoff-based learning (imitating others that have higher payoffs) and conformist learning (imitating locally common behaviours). How payoff-based and conformist learning affect the cultural evolution of cooperation is currently a matter of lively debate, but few studies systematically analyse the interplay of these forms of social learning. Here we perform such a study by investigating how the interaction of payoff-based and conformist learning affects the outcome of cultural evolution in three social contexts. First, we develop a simple argument that provides insights into how the outcome of cultural evolution will change when more and more conformist learning is added to payoff-based learning. In a social dilemma (e.g. a Prisoner’s Dilemma), conformism can turn cooperation into a stable equilibrium; in an evasion game (e.g. a Hawk-Dove game or a Snowdrift game) conformism tends to destabilize the polymorphic equilibrium; and in a coordination game (e.g. a Stag Hunt game), conformism changes the basin of attraction of the two equilibria. Second, we analyse a stochastic event-based model, revealing that conformism increases the speed of cultural evolution towards pure equilibria. Individual-based simulations as well as the analysis of the diffusion approximation of the stochastic model by and large confirm our findings. Third, we investigate the effect of an increasing degree of conformism on cultural group selection in a group-structured population. We conclude that, in contrast to statements in the literature, conformism hinders rather than promotes the evolution of cooperation.     

Adaptive Communication: Languages with More Non-Native Speakers Tend to Have Fewer Word Forms

Explaining the diversity of languages across the world is one of the central aims of typological, historical, and evolutionary linguistics. We consider the effect of language contact-the number of non-native speakers a language has-on the way languages change and evolve. By analysing hundreds of languages within and across language families, regions, and text types, we show that languages with greater levels of contact typically employ fewer word forms to encode the same information content (a property we refer to as lexical diversity). Based on three types of statistical analyses, we demonstrate that this variance can in part be explained by the impact of non-native speakers on information encoding strategies. Finally, we argue that languages are information encoding systems shaped by the varying needs of their speakers. Language evolution and change should be modeled as the co-evolution of multiple intertwined adaptive systems: On one hand, the structure of human societies and human learning capabilities, and on the other, the structure of language.     

The Biological Origin of Linguistic Diversity

In contrast with animal communication systems, diversity is characteristic of almost every aspect of human language. Languages variously employ tones, clicks, or manual signs to signal differences in meaning; some languages lack the noun-verb distinction (e.g., Straits Salish), whereas others have a proliferation of fine-grained syntactic categories (e.g., Tzeltal); and some languages do without morphology (e.g., Mandarin), while others pack a whole sentence into a single word (e.g., Cayuga). A challenge for evolutionary biology is to reconcile the diversity of languages with the high degree of biological uniformity of their speakers. Here, we model processes of language change and geographical dispersion and find a consistent pressure for flexible learning, irrespective of the language being spoken. This pressure arises because flexible learners can best cope with the observed high rates of linguistic change associated with divergent cultural evolution following human migration. Thus, rather than genetic adaptations for specific aspects of language, such as recursion, the coevolution of genes and fast-changing linguistic structure provides the biological basis for linguistic diversity. Only biological adaptations for flexible learning combined with cultural evolution can explain how each child has the potential to learn any human language.     

Language development: breaking the code

This paper reviews the major achievements of the preschool years regarding language acquisition. Although most children appear to master their native language with little apparent effort, learning a language is a complex task. It requires the ability to extract clues from environmental stimuli and to discover how those stimuli convey meanings and are modified according to the meaning conveyed. In general, language learning follows a similar sequence regardless of the language being learned. The major accomplishments in the areas of speech perception, early sound production, phonology, lexicon, syntax, and morphology are described, with specific examples from recent studies of acquisition of French in young children from Québec. These examples confirm major milestones observed in other languages, but also illustrate how comparisons across languages and across children learning the same language can be challenging. For each area, current issues are identified regarding the bases (neurological, genetic) of language development, as well as the processes (social, cognitive, linguistic) involved. Current hypotheses regarding language acquisition and language disorders are briefly discussed.     

Self-selected modular recurrent neural networks with postural and inertial subnetworks applied to complex movements

 It has been shown that dynamic recurrent neural networks are successful in identifying the complex mapping relationship between full-wave-rectified electromyographic (EMG) signals and limb trajectories during complex movements. These connectionist models include two types of adaptive parameters: the interconnection weights between the units and the time constants associated to each neuron-like unit; they are governed by continuous-time equations. Due to their internal structure, these models are particularly appropriate to solve dynamical tasks (with time-varying input and output signals). We show in this paper that the introduction of a modular organization dedicated to different aspects of the dynamical mapping including privileged communication channels can refine the architecture of these recurrent networks. We first divide the initial individual network into two communicating subnetworks. These two modules receive the same EMG signals as input but are involved in different identification tasks related to position and acceleration. We then show that the introduction of an artificial distance in the model (using a Gaussian modulation factor of weights) induces a reduced modular architecture based on a self-elimination of null synaptic weights. Moreover, this self-selected reduced model based on two subnetworks performs the identification task better than the original single network while using fewer free parameters (better learning curve and better identification quality). We also show that this modular network exhibits several features that can be considered as biologically plausible after the learning process: self-selection of a specific inhibitory communicating path between both subnetworks after the learning process, appearance of tonic and phasic neurons, and coherent distribution of the values of the time constants within each subnetwork. Received: 17 September 2001 / Accepted in revised form: 15 January 2002     

Transfer Functions for Protein Signal Transduction: Application to a Model of Striatal Neural Plasticity

We present a novel formulation for biochemical reaction networks in the context of protein signal transduction. The model consists of input-output transfer functions, which are derived from differential equations, using stable equilibria. We select a set of “source” species, which are interpreted as input signals. Signals are transmitted to all other species in the system (the “target” species) with a specific delay and with a specific transmission strength. The delay is computed as the maximal reaction time until a stable equilibrium for the target species is reached, in the context of all other reactions in the system. The transmission strength is the concentration change of the target species. The computed input-output transfer functions can be stored in a matrix, fitted with parameters, and even recalled to build dynamical models on the basis of state changes. By separating the temporal and the magnitudinal domain we can greatly simplify the computational model, circumventing typical problems of complex dynamical systems. The transfer function transformation of biochemical reaction systems can be applied to mass-action kinetic models of signal transduction. The paper shows that this approach yields significant novel insights while remaining a fully testable and executable dynamical model for signal transduction. In particular we can deconstruct the complex system into local transfer functions between individual species. As an example, we examine modularity and signal integration using a published model of striatal neural plasticity. The modularizations that emerge correspond to a known biological distinction between calcium-dependent and cAMP-dependent pathways. Remarkably, we found that overall interconnectedness depends on the magnitude of inputs, with higher connectivity at low input concentrations and significant modularization at moderate to high input concentrations. This general result, which directly follows from the properties of individual transfer functions, contradicts notions of ubiquitous complexity by showing input-dependent signal transmission inactivation.     

Effect of Spatial Dispersion on Evolutionary Stability: A Two-Phenotype and Two-Patch Model

In this paper, we investigate a simple two-phenotype and two-patch model that incorporates both spatial dispersion and density effects in the evolutionary game dynamics. The migration rates from one patch to another are considered to be patch-dependent but independent of individual’s phenotype. Our main goal is to reveal the dynamical properties of the evolutionary game in a heterogeneous patchy environment. By analyzing the equilibria and their stabilities, we find that the dynamical behavior of the evolutionary game dynamics could be very complicated. Numerical analysis shows that the simple model can have twelve equilibria where four of them are stable. This implies that spatial dispersion can significantly complicate the evolutionary game, and the evolutionary outcome in a patchy environment should depend sensitively on the initial state of the patches.     

Learning shapes spontaneous activity itinerating over memorized states

Learning is a process that helps create neural dynamical systems so that an appropriate output pattern is generated for a given input. Often, such a memory is considered to be included in one of the attractors in neural dynamical systems, depending on the initial neural state specified by an input. Neither neural activities observed in the absence of inputs nor changes caused in the neural activity when an input is provided were studied extensively in the past. However, recent experimental studies have reported existence of structured spontaneous neural activity and its changes when an input is provided. With this background, we propose that memory recall occurs when the spontaneous neural activity changes to an appropriate output activity upon the application of an input, and this phenomenon is known as bifurcation in the dynamical systems theory. We introduce a reinforcement-learning-based layered neural network model with two synaptic time scales; in this network, I/O relations are successively memorized when the difference between the time scales is appropriate. After the learning process is complete, the neural dynamics are shaped so that it changes appropriately with each input. As the number of memorized patterns is increased, the generated spontaneous neural activity after learning shows itineration over the previously learned output patterns. This theoretical finding also shows remarkable agreement with recent experimental reports, where spontaneous neural activity in the visual cortex without stimuli itinerate over evoked patterns by previously applied signals. Our results suggest that itinerant spontaneous activity can be a natural outcome of successive learning of several patterns, and it facilitates bifurcation of the network when an input is provided.     

On learning dynamics underlying the evolution of learning rules

In order to understand the development of non-genetically encoded actions during an animal’s lifespan, it is necessary to analyze the dynamics and evolution of learning rules producing behavior. Owing to the intrinsic stochastic and frequency-dependent nature of learning dynamics, these rules are often studied in evolutionary biology via agent-based computer simulations. In this paper, we show that stochastic approximation theory can help to qualitatively understand learning dynamics and formulate analytical models for the evolution of learning rules. We consider a population of individuals repeatedly interacting during their lifespan, and where the stage game faced by the individuals fluctuates according to an environmental stochastic process. Individuals adjust their behavioral actions according to learning rules belonging to the class of experience-weighted attraction learning mechanisms, which includes standard reinforcement and Bayesian learning as special cases. We use stochastic approximation theory in order to derive differential equations governing action play probabilities, which turn out to have qualitative features of mutator-selection equations. We then perform agent-based simulations to find the conditions where the deterministic approximation is closest to the original stochastic learning process for standard 2-action 2-player fluctuating games, where interaction between learning rules and preference reversal may occur. Finally, we analyze a simplified model for the evolution of learning in a producer–scrounger game, which shows that the exploration rate can interact in a non-intuitive way with other features of co-evolving learning rules. Overall, our analyses illustrate the usefulness of applying stochastic approximation theory in the study of animal learning.     

Nash equilibria for an evolutionary language game

We study an evolutionary language game that describes how signals become associated with meaning. In our context, a language, L, is described by two matrices: the P matrix contains the probabilities that for a speaker certain objects are associated with certain signals, while the Q matrix contains the probabilities that for a listener certain signals are associated with certain objects. We define the payoff in our evolutionary language game as the total amount of information exchanged between two individuals. We give a formal classification of all languages, L(P, Q), describing the conditions for Nash equilibria and evolutionarily stable strategies (ESS). We describe an algorithm for generating all languages that are Nash equilibria. Finally, we show that starting from any random language, there exists an evolutionary trajectory using selection and neutral drift that ends up with a strategy that is a strict Nash equilibrium (or very close to a strict Nash equilibrium). Received: 1 March 2000 / Published online: 3 August 2000