Three compatible models of S-curves in language change
Angus Grieve-Smith
Sign up for access to the world's latest research
checkGet notified about relevant papers
checkSave papers to use in your research
checkJoin the discussion with peers
checkTrack your impact
Abstract
Over the years, a number of models have been proposed to account for widespread observations of S-shaped curves in language change. In all instances there are at least two competing variants for expressing the same meaning or function, and the frequency of one rises slowly at first, then more quickly, and finally tapers off in the direction of full use. Niyogi and Berwick (1997) and others propose a model where a child chooses between two competing grammars during acquisition. In earlier work (Grieve-Smith 2009) I suggest two models, both based on type frequency. Most recently, Baxter et al. (2009) put forth a detailed model with differential weighting, and Blythe and Croft (2012) apply it to S-curves. Croft (2000) and Bybee (2010) compile data from several studies showing that the learning patterns of small children do not correspond to patterns of language change. Lifelong models like those of Grieve-Smith (2009) and Blythe and Croft (2012) are more consistent with this data. These three lifelong models are in fact compatible with each other, and we can make the choice of model based on the situation at hand. In my study (Grieve-Smith 2009), I begin with the logistic model proposed by Kroch (1989), and motivate it through the relative type frequencies of the variants. I then observe that in its original field of population modeling, the logistic was extended by Lotka (1925) and Volterra (1926), who both added a term αij to indicate an advantage that term i may have over term j. Conversely, Blythe and Croft (2012) focus on the differential weighting that language users may apply to the two variants, with a "sampling rule" f(u) that allows the model to take type frequency into account. All three models produce satisfactory S-curves. Grieve-Smith (2009) examined corpus data from the evolution of ne … pas in French theatrical texts and found that the logistic model (R2 = 0.899) and the Lotka-Volterra model (r = 0.978). fit the data closely. Blythe and Croft (2012) do not test their model's predictions against the data, but they do use their model to generate idealized data and report that it generates "an S-shaped trajectory." They observe that it is not necessary to incorporate frequency effects because "the simplest choice of the sampling rule f(u) that implements replicator selection is sufficient to obtain an S-curve," but their model does not preclude taking frequency into account. When examining S-curves in language change, then, we have three models to choose from. The logistic (Kroch 1989), which only uses frequency data, is the simplest and the easiest to implement, and will be sufficient for many datasets. The Lotka-Volterra model (Grieve-Smith 2009), which assigns a different competitive advantage to each variant, can be used when focusing on such advantages. The interactive model of Blythe and Croft (2012) can be used when we want to examine the interactions between language users in greater detail.
Related papers
Modeling frequency effects in language change
Rosemeyer, Malte (In press): Modelling frequency effects in language change. In Behrens, Heike and Stefan Pfänder (eds.), Again on Frequency. Effects in Language. Berlin: Mouton de Gruyter., 2014
Processes of language change in which a grammatical construction decreases in usage frequency should be modeled in terms of both type and token frequency. This paper analyzes Spanish compound tense auxiliary selection, suggesting that the replacement of ser 'be' with haber 'have' was affected by (a) the salience of haber + participle in usage contexts previously associated with the use of ser + participle, and (b) the general token frequency of specific verbs and of the ser + participle syntagms that form from these verbs. I argue that it is necessary to account for both historical processes in order to explain the synchronic gradience in auxiliary selection posited in influential Auxiliary Selection Hierarchy (ASH), and propose statistical methodology to model these frequency effects in language change. The findings suggest both type and token frequency effects. The former is an actualization process due to the prototypicality of use of ser + participle with telic predicates implying a change of state (e.g. morir 'die'), which are affected by the replacement with haber + participle at a later point in the process of change, whereas the latter is a conservation process evident in ser + participle syntagms formed from highly frequent verbs that, due to their high token frequency, are less affected by the ongoing change. This skewed frequency distribution in the verb population and the resulting conserving effect leads to further changes in auxiliary selection rules.
Extracting information from S-curves of language change
Journal of the Royal Society, Interface / the Royal Society, 2014
It is well accepted that adoption of innovations are described by S-curves (slow start, accelerating period and slow end). In this paper, we analyse how much information on the dynamics of innovation spreading can be obtained from a quantitative description of S-curves. We focus on the adoption of linguistic innovations for which detailed databases of written texts from the last 200 years allow for an unprecedented statistical precision. Combining data analysis with simulations of simple models (e.g. the Bass dynamics on complex networks), we identify signatures of endogenous and exogenous factors in the S-curves of adoption. We propose a measure to quantify the strength of these factors and three different methods to estimate it from S-curves. We obtain cases in which the exogenous factors are dominant (in the adoption of German orthographic reforms and of one irregular verb) and cases in which endogenous factors are dominant (in the adoption of conventions for romanization of Russ...
Mathematical models meet linguistic data and vice versa: an introduction to this special issue
International Journal of the Sociology of Language, 2000
Linguistics in the 21st century is faced with a series of methodological innovations that have opened up new ways of describing language: experimental methods allow us to measure the activity of the human brain and to relate this activity to linguistic behavior and ability (Bornkessel-Schlesewsky and Schlesewsky 2009); new discoveries in genetics and in evolutionary biology show how certain genes play crucial roles in our language faculty and allow for a more precise definition of the moment when human language emerged (e.g. Benítez-Burraco et al. 2008); and the analysis of large amounts of data allow for the modeling of linguistic phenomena on a scale impossible to achieve in the past (e.g. Köhler 2012). Surprisingly, many of these innovations have emerged outside the discipline itself. Articles on linguistic issues are now being published in journals such as Nature, Science and Physica A by authors who work in the fields of statistical physics, evolutionary biology, cybernetics and mathematics. The reaction of "genuine" linguists, theoretical and empirical, is often rather skeptical and frequently leads to such studies being viewed with suspicion, or rejected altogether. And indeed, a general tendency in current "scientific" approaches to linguistics is to concentrate principally on the method and to impress with sophisticated experiments or quantitative analysis. However methodologically convincing, though, these studies sometimes belie shortcomings of both an empirical and a theoretical nature. This general observation also holds true for sociolinguistics and for the sociology of language, where a considerable number of recent studies have been published with exciting new proposals on the possibility of modeling individual behavior in a social context and on visualizations of phenomena such as language shift, language change and language death. Of course, as with any other scientific discipline, sociolinguistics has always dealt with models: models of societal stratification, models that link social constellations to linguistic attitudes and linguistic behavior, and even quantitative models that establish correlations
Variation in Language: System- and Usage-based Approaches
2015
The aim of this paper is to focus on the so-called no man's land where sociolinguistics and grammatical theory interact. It is argued that E-language as a social and I-language as a psychological construct do not exist independently, but influence each other. In other words, syntactic variation and change are driven by social factors but constrained by the nature of possible grammars. The interaction between the social meanings of linguistic forms on the one hand and grammar on the other brings about complex and multi-layered relationships between the individual and the group's or societal grammar. This paper emphasizes how individuals are restricted by grammar but, at the same time, able to overcome these restrictions in specific situated contexts through interactions. This combined approach enables us to predict why some structures are more resistant or vulnerable to syntactic variation and change than others and the route(s) individuals may take to overcome syntactic "restrictions". In this process of interdependent relations between the I-and E-languages, the interpretation and evaluation of linguistic forms through interaction is of crucial importance in the realization of so-called "impossible" or "unrealized" constructions.
The a-Curve and Personally Patterned Variation: More Tools for Investigating Language Variation and Change
American Speech, 2012
This article explores two variables that largely have been ignored in studies of language variation and language change: frequency and individual speaker. In doing so, it demonstrates the usefulness of the A-curve, an asymptotic hyperbolic graphic representation of language variation based on usage. Data are drawn from varieties of English: two Afro-Caribbean vernaculars (Antiguan and Negerhollands) and East Sutherland Gaelic. Because both Negerhollands and East Sutherland Gaelic were moribund when the data discussed here were collected and both are characterized by personally patterned variation, the histories of these varieties are briefly considered. The article concludes that both frequency and individual speaker are essential for a full understanding of the ways in which language users deploy their linguistic resources and, thus, are critical for our understanding of human language.
The Y-Model. A Synopsis of Lectures in Linguistics: Reading List and Topics on Language Structure, Phonology, and Syntax
Overview This brief survey is organized to help students target specific themes and topics of research as related to the three core subdisciplines of general linguistics: Structure, Phonology, and Syntax. These three core subdisciplines also may filter through secondary fields which relate to the following (see Y-model below): ·Child Language Acquisition (L1), ·Second Language Development (L2) (e.g., topics which include distinctions between 'acquisition' vs 'learning', the Critical Period Hypothesis, L2-Interferences, L2 methods and Learning strategies, etc.), ·Language in Special Populations/Language Impairment (e.g., Specific Language Impairment (SLI), Autism, Broca's Aphasia, and other language disabilities). Reading List/CSUN~Linguistics/galasso (2020) In other words, cross-over research often combines the three core studies and their subfields binding together, say, Child Language + Phonology, or Interference of 'Second language + Syntax', or lack of language structure + special populations, etc. (For example, the latter could be investigatory research into the lack of full-fledge template structures due to brain anomalies, stroke, or abnormal birth defects). Even within a core study itself, for example say the study of language types, Contrastive Analyses may be employed as part of any research project which looks to gathering language-specific comparisons of, for example, English to ASL (American Sign Language), Spanish to English, L1 versus L2 knowledge, etc. Other studies regarding vernacular modes of English such as African American English, or Pidgin & Creoles, as well as language fusion/mixing (e.g. Spanglish Chicano English) are often trending topics of inquiry, as well as any methods/pedagogical references made to the nature of learning a second/foreign language leading to bilingualism.
Modelling language evolution: Examples and predictions (target article, commentaries and authors' replies)
We survey recent computer modelling research of language evolution, focusing on a rule-based model simulating the lexiconsyntax coevolution and an equation-based model quantifying the language competition dynamics. We discuss four predictions of these models: (a) correlation between domain-general abilities (e.g. sequential learning) and language-specific mechanisms (e.g. word order processing); (b) coevolution of language and relevant competences (e.g. joint attention); (c) effects of cultural transmission and social structure on linguistic understandability; and (d) commonalities between linguistic, biological, and physical phenomena. All these contribute significantly to our understanding of the evolutions of language structures, individual learning mechanisms, and relevant biological and socio-cultural factors. We conclude the survey by highlighting three future directions of modelling studies of language evolution: (a) adopting experimental approaches for model evaluation; (b) consolidating empirical foundations of models; and (c) multi-disciplinary collaboration among modelling, linguistics, and other relevant disciplines.
Modelling transient states in language change
Oxford Scholarship Online
Models of language change may include, apart from the initial and terminal state, an intermediate state T. Building further on Postma (2010), who observed that the dynamics of the transient state T (’failed change’) is algebraically related to the overall change A → B (the former is the first derivative of the latter), we present a generalized algebraic model that includes both the failed change A → B and the successful change A → B. We first generalize the two-state logistic function of A → B to a differential equation (DE) that represents the underlying processes. This DE has a bundle of time shifted logistic curves as its solution. This derives Kroch’s Constant Rate Effect. By modifying this DE, we describe the dynamics of the entire A → T → B process, i.e. we develop a model that includes both the successful and the failed change. The algebraic link between failed change and successful change turns out to be an approximation.
A Dynamical Systems Model for Language Change
1995
This paper formalizes linguists' intuitions about language change, proposing a dynamical systems model for language change derived from a model for language acquisition. Linguists must explain not only how languages are learned but also how and why they have evolved along certain trajectories and not others. While the language learning problem has focused on the behavior of individuals and how they acquire a particular grammar from a class of grammars G, here we consider a population of such learners and investigate the emergent, global population characteristics of linguistic communities over several generations. We argue that language change follows logically from specific assumptions about grammatical theories and learning paradigms. Roughly, as the end product of two types of learning misconvergence over several generations, individual language learner behavior leads to emergent, population language community characteristics. In particular, we show that any triple {G, A, P} of grammatical theory, learning algorithm, and initial sentence distributions can be transformed into a dynamical system whose evolution depicts a population's evolving linguistic composition. We explicitly show how this transformation can be carried out for memoryless learning algorithms and parameterized grammatical theories. As the simplest case, we formalize the example of two grammars (languages) differing by exactly one binary parameter, and show that even this situation leads directly to a quadratic (nonlinear) dynamical system, including regions with chaotic behavior. We next apply the computational model to some
Modeling Transient States in Language Change
2015
Models of language change may include, apart from an initial state and a terminal state, an intermediate state T. Building further on Postma (2010), who observed that the dynamics of the transient state T ("failed change") has an algebraic linking of the dynamics of the overall change A → B, we present a generalized algebraic model that includes both the failed change 0 → T → 0 and the successful change A → B. As a preparatory step, we generalize the algebraic function (logist) of a two-state change A → B to a differential equation (DE), which represents the law that rules the change. This DE has a bundle of time shifted logistic curves as its solution. This is identified as Kroch's Constant Rate Hypothesis. By modifying this DE, it is possible to describe the dynamics of the entire A → T→ B process, i.e. we have a model that includes both the successful and the failed change. The algebraic link between failed change and successful change (the former is the first derivative of the latter) turns out to be an approximation.
What frequency variations tell us about linguistic change: the case of en plein N
Langue française, 2022
Token frequency variation across time is a key empirical quantity for quantitative diachronic linguistics. In particular, the S-curve pattern has been identified as a clear sign of a language change. Yet, there is no single interpretation of this pattern: social diffusion, lexical diffusion, between-variants competition, have all been invoked. Moreover, the special status of the S-curve as the most entrenched pattern for language change has been criticized. To grasp what the different frequency measurements (token frequency, type frequency, prevalence) reveal us on language change, we study the en plein N construction and show that the S-curve pattern reveals two phases in the construction entrenchment, the first phase corresponding to a social diffusion, the second to a semantic expansion. We also evidence that the same S-curve is followed both at the individual types level and at the whole construction level, which highlights the consistency of the construction organization through its dynamics over time.
Lexical frequency as a scalar variable in explaining variation
Canadian Journal of Linguistics-revue Canadienne De Linguistique, 2010
Modeling Language Change: The Pitfall of Grammaticalization
In F. La Mantia, I. Licata & P. Perconti (eds), Language in Complexity – The Emerging Meaning. New York : Springer, 49-72., 2017
Language evolution is the subject of various theoretical studies, following two main paths: one, where language is viewed as a code between meanings and forms to express them, with a focus on language as a social convention; and the other defining language as a set of grammatical rules governing the production of utterances, evolution being the outcome of mistakes in the acquisition process. We claim that none of the current models provides a satisfactory account of the grammaticalization phenomenon, a linguistic process by which words acquire a grammatical status. We argue that this limitation is mainly due to the way these models represent language and communication mechanisms. We therefore introduce a new framework, the “grammatheme,” as a tool which formalizes in an unambiguous way different concepts and mechanisms involved in grammaticalization. The model especially includes an inference mechanism triggering new grammaticalization processes. We present promising preliminary results of a numerical implementation and discuss a possible research program based on this framework.
Tily, H. and Jaeger, T.F. 2011. Complementing quantitative typology with behavioral approaches: Evidence for typological universals. Linguistic Typology 15(2), 497-508.
Dunn et al. (2011) employ computational phylogenetic methods to test whether certain pairs of languages features are universally related in that they co-develop over time (Greenbergian implicational universals). They nd little evidence for universal word-order correlations, contrary to both generative and functional accounts of language. Other commentaries in this issue point to potential problems with the approach employed by Dunn and colleagues (e.g. Croft et al, this issue). Some of these are inherent to quantitative typology: in particular, sparsity of available data and uncertainty about language history. There are, however alternative methods for creating new data to test universal biases for certain word orders. Here we discuss two methods that we take to be of particular promise: Arti cial Language Learning, which has been used to study language acquisition, and Iterative Arti cial Language Learning, which extends the former method to the study of language change over generations. We discuss recent work within these two paradigms that suggests language learners exhibit universal biases that might cause universals like those discussed by Dunn et al. to emerge over time.
Models of language evolution and change
Wiley Interdisciplinary Reviews Cognitive Science, 2014
In the absence of direct evidence of the emergence of language, the explicitness of formal models which allow the exploration of interactions between multiple complex adaptive systems has proven to be an important tool. Computational simulations have been at the heart of the field of evolutionary linguistics for the past two decades, particularly through the language game and iterated learning paradigms, but these are now being extended and complemented in a number of directions, through formal mathematical models, language-ready robotic agents, and experimental simulations in the laboratory.For further resources related to this article, please visit the WIREs website.Conflict of interest: The author has declared no conflicts of interest for this article.
Introduction to special issue on morphosyntactic variation within the individual language user
Nordic Journal of Linguistics
This thematic issue of the Nordic Journal of Linguistics focuses on morphosyntactic variation within the individual language user. The phenomenon of intraspeaker (micro)variation raises questions which arguably go to the heart of linguistic theory, especially in formal/generative perspective. Chomsky famously argued that '[l]inguistic theory is concerned primarily with an ideal speaker-listener, in a completely homogeneous speech community' (Chomsky 1965:3). Significant progress in formal/generative linguistics has been made on the basis of this idealization, but it has always been clear that it is an idealization. A great number of language users are bi-or multidialectal: that is, their linguistic competence encompasses two or more closely related systems which might pretheoretically be seen as 'variants of the same language'. And the great majority of (perhaps all) language users can (consciously or unconsciously) alter their register use depending on context, a choice which can manifest in sociolinguistic variables such as the realization of phonemes and lexical choice, and alsocruciallydiffering morphosyntactic structures. Chomsky (2000:59) has stated that 'everyone grows up in a multilingual environment' and that '[w]hatever the language faculty is it can assume many different states in parallel'. Sociolinguists have of course been concerned with investigating intraspeaker variability at least since the pioneering studies of Labov (e.g. Labov 1969), but such intraspeaker optionality and variation has received somewhat less attention from linguists in the formal or generative tradition. By now, 55 years after 'Aspects', the generative framework has advanced to the extent that more complicated cases of language competence and performance could and should receive more attention and, ideally, a formal description within one and the same model. The papers in this volume aim to provide empirical investigations of the phenomenon, formulate relevant generalizations, and ultimately contribute to our understanding of what such a model should look like. The Scandinavian countries, and Norway in particular, are especially interesting testing grounds for the investigation of morphosyntactic variation in the individual,
Loading Preview
Sorry, preview is currently unavailable. You can download the paper by clicking the button above.