Modeling language evolution and feature dynamics in a realistic geographic environment (2020)

Abstract: Recent, innovative efforts to understand the uneven distribution of languages and linguistic feature values in time and space attest to both the challenge these issues pose and the value in solving them. In this paper, we introduce a model for simulating languages and their features over time in a realistic geographic environment. At its core is a model of language phylogeny and migration whose parameters are chosen to reproduce known language family sizes and geographic dispersions. This foundation in turn is used to explore the dynamics of linguistic features. Languages are assigned feature values that can change randomly or under the influence of nearby languages according to predetermined probabilities. We assess the effects of these settings on resulting geographic and genealogical patterns using homogeneity measures defined in the literature. The resulting model is both flexible and realistic, and it can be employed to answer a wide range of related questions.

## introduction the distribution of linguistic feature values across time and space is uneven. the overall frequencies of particular feature values can be skewed with some highly frequent and others vanishingly rare, and many feature values have been observed to cluster geographically or within particular language families. such patterns are most commonly explained in terms of the competing influences of inheritance, diffusion, universal tendencies of language drift, and chance. understanding these dynamics has long been a goal of linguists, and it has important implications for historical linguistics, areal linguistics, and linguistic typology. despite growing attention to these issues and advances in comparative and quantitative methods, many questions remain unanswered. the well-known problem of spatial autocorrelation limits the usefulness of a direct statistical approach to disentangling geography from genealogy, and as a result various other approaches have been innovated. there are a number of studies exploring the stability or biases of typological features within language families @xcite @xcite . of these approaches, those that account for geography are limited to comparisons within families or between families. other successful approaches which account for both genealogy and geography are limited to a particular region @xcite , use typological distance measures that do not allow for the comparison of features separately (e.g. @xcite , or apply a ratio of genealogical and geographic measures that reduces independently varying factors to their quotient @xcite . computer simulations have also emerged as a promising method by which to explore these and related issues (e.g., @xcite . however, nearly all of these models employ abstract representations of space, such as a lattice. a recent exception is @xcite , which uses 'populated places' from the geonames database to add geographic realism to its simulations of language family expansions. however, wichmann's simulations are limited to individual language families, so they do not model interactions between language families. in this paper, we introduce a model for simulating languages and their features over time in a realistic geographic environment. the foundation of this model-and a prerequisite for exploring feature dynamics-is a reliable model of language speciation, migration, and death. we will collectively refer to these aspects of the model as phylogeny, and we compare the output of our phylogeny model to real language family data in order to demonstrate its validity. this model is then equipped with a flexible mechanism for representing linguistic features. feature values are allowed to change randomly or under the influence of nearby languages according to pre-set probabilities, and we use various homogeneity measures from the literature to explore how these settings interact to produce feature value distributions. this model can be employed to answer a wide range of questions related to the distributions of languages and features. ## foundations of the model implemented in r 3.6.0 (r core team, 2019), our simulations operate over a fixed number of discrete timesteps, where each timestep is intended to represent 20 years. unless otherwise specified, the simulations presented in this paper run for 500 timesteps (10,000 years), and event probabilities apply to each language at each timestep. we start with a list of 1.8 million populated places in eurasia from the geonames database foot_0 . using data on populated places has been shown to be useful when simulating language phylogeny and migration, as it introduces elements of geographical realism @xcite . for purposes of computational efficiency, we randomly sample 50,000 of the 1.8 million coordinates for use in our simulations. to begin a simulation, unrelated languages are randomly placed at 300 of the populated places. each of these 300 languages are assigned values of a feature of any number of values. these values can be assigned randomly (such as the simulations presented in this paper) or according to a pre-determined frequency distribution. at each timestep in the simulation, languages undergo phylogenetic simulation-they can either speciate, die, migrate, or remain unchanged-and feature simulation-they can obtain a new feature value via diffusion or internal change. ## modeling languages the utility of a model for investigating language feature dynamics is limited by its realism with regard to language phylogeny and migration. put another way, our simulations must accurately model languages before they can be expected to accurately model the features of those languages. in this section, we describe the simulation of language speciation, extinction, and migration. then, we test the validity of our phylogenetic model against characteristics of real language families and their geographic dispersions. in order to accurately model language evolution in time and space, it is essential for languages to undergo real-world changes to their phylogeny: namely, speciation, death, and migration. these phylogenetic aspects of the simulation are critical to consider to establish a realistic basis before examining feature dynamics. we first discuss their details and validations, and then delve into features. ## modeling features equipped with a reliable model of language phylogeny, we turn to the simulation of linguistic features. our model is intended to explore one feature at a time, but it is flexible with regard to the characteristics of that feature. features can have any number of values, and they can be structured or unstructured. ## assessing model output to explore feature dynamics in the model, we ran a series of simulations varying the probabilities for diffusion and internal change. four different settings were used, representing the combinations of relatively low and high values of each of these parameters. the exact probabilities for each setting are reflected in ## case study: transitional probabilities there is tremendous potential in the simulation of feature dynamics, and we have barely scratched the surface of it in this paper. as we mentioned earlier, the model can handle structured features. to what extent do structured features behave differently from unstructured features? furthermore, consider the possibility that transitional probabilities for diffusion and/or internal change might be different for each value of a feature. in other words, the probability of changing from value a to value b may be different than the probability of changing from value b to value a. the model is already equipped with an adjacency matrix to represent a directed graph with connections from each feature to every other, where weights on the edges are the transitional probabilities. with structured features at play, the model also recalculates the chances of diffusion and internal change from the general transitional probabilities, dividing them up in a 3:1 ratio to allow for the necessary dependent values. we present here a preliminary exploration into structured feature dynamics, examined in the context of a two-valued feature. we ran a series of simulations reflecting three sets of transitional probabilities. exact values for each setting are detailed in figure 6 illustrates the change in the percentage of the dominant feature value (favored as result of change) over the course of simulations for each of the three transitional probability settings. these results reveal an amplified skew in the distribution of resulting feature values relative to the preset transitional probabilities. for example, transitional probabilities of 70%-30% result in a feature value distribution in the vicinity of 85%-15%. these findings demonstrate how even relatively minor differences in the underlying stability of feature values can be amplified significantly by the dynamics of languages in space in time. in particular, diffusion plays an important role in magnifying these feature value inequalities. this is just one of many potential explorations into the complex ways in which language feature dynamics produce particular feature value distributions, all of which require a model of suitable flexibility and realism. ## further applications the primary contribution of this paper is a tool which can be used to investigate a myriad of unresolved issues concerning the distribution of languages and their features across time and space. a few further extensions and applications of the model are discussed here. the realistic geographic environment featured in the model make explorations into spatial phenomena an obvious area for extension. for example, much is unknown about how local diffusion events and/or deep genealogical relationships can conspire to create long-distance areal effects. similarly, the existence of linguistic areas presents a nice challenge for our model. which settings can result in the development of such areas? the model of phylogeny at the heart of our simulations also invites investigations into the social/cultural and geographic factors that may affect competition between languages and language families. for example, the model could easily be adapted with a mechanism of temporary speciation 'momentum' bestowed upon language families with a political or technological advantage. alternatively, the model could be equipped with information about climate or terrain to constrain the movements of and influences among different language groups. ## conclusion in this paper, we have presented a new model which brings a realistic geographic environment to the simulation of languages and linguistic features over time. this model is realistic, producing plausible language family sizes and dispersions. at the same time, it is also flexible, constructed with adaptability in mind and equipped to model features of various structures and properties. we have also shown how our model can be utilized to address a wide range of related issues with implications for historical linguistics, areal linguistics, and linguistic typology. it opens the door for further discoveries in the evolution of language and patterns of human migration and interaction.