Predicting language diversity with complex network

TL;DR

This paper models language diversity evolution in societies using complex network theory, emphasizing the role of local interactions, network topology, and rewiring mechanisms in capturing empirical language diversity data.

Contribution

It introduces a social interaction model based on network topology and rewiring, explaining the growth of language diversity with population size and resolving previous model contradictions.

Findings

Local interactions are crucial for empirical data accuracy.

High clustering and network disintegration characterize effective models.

Rewiring mechanisms significantly influence language change dynamics.

Abstract

Evolution and propagation of the world's languages is a complex phenomenon, driven, to a large extent, by social interactions. Multilingual society can be seen as a system of interacting agents, where the interaction leads to a modification of the language spoken by the individuals. Two people can reach the state of full linguistic compatibility due to the positive interactions, like transfer of loanwords. But, on the other hand, if they speak entirely different languages, they will separate from each other. These simple observations make the network science the most suitable framework to describe and analyze dynamics of language change. Although many mechanisms have been explained, we lack a qualitative description of the scaling behavior for different sizes of a population. Here we address the issue of the language diversity in societies of different sizes, and we show that local interactions are crucial to capture characteristics of the empirical data. We propose a model of social interactions, extending the idea from, that explains the growth of the language diversity with the size of a population of country or society. We argue that high clustering and network disintegration are the most important characteristics of models properly describing empirical data. Furthermore, we cancel the contradiction between previous models and the Solomon Islands case. Our results demonstrate the importance of the topology of the network, and the rewiring mechanism in the process of language change.

Full text

Predicting language diversity with complex networks

Tomasz Raducha

tomasz.raducha@fuw.edu.pl

Institute of Experimental Physics, Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland

  

Tomasz Gubiec

Institute of Experimental Physics, Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland

Center for Polymer Studies, Boston University, Boston, MA 02215 USA

**Evolution and propagation of the world’s languages is a complex phenomenon, driven, to a large extent, by social interactions beckner2009language ; mufwene2002competition ; tomasello2010origins . Multilingual society can be seen as a system of interacting agents eckert2000language ; baxter2009modeling ; carro2016coupled , where the interaction leads to a modification of the language spoken by the individuals lieberman2007quantifying ; bybee2006usage . Two people can reach the state of full linguistic compatibility due to the positive interactions, like transfer of loanwords. But, on the other hand, if they speak entirely different languages, they will separate from each other. These simple observations make the network science albert2002statistical the most suitable framework to describe and analyze dynamics of language change castello2008modelling ; schulze2008birth ; hruschka2009building . Although many mechanisms have been explained abrams2003linguistics ; loreto2007social ; patriarca2012modeling ; sutherland2003parallel , we lack a qualitative description of the scaling behavior for different sizes of a population. Here we address the issue of the language diversity in societies of different sizes, and we show that local interactions are crucial to capture characteristics of the empirical data. We propose a model of social interactions, extending the idea from raducha2017coevolving , that explains the growth of the language diversity with the size of a population of country or society. We argue that high clustering and network disintegration are the most important characteristics of models properly describing empirical data. Furthermore, we cancel the contradiction between previous models axelrod1997dissemination ; sanmiguel2007 and the Solomon Islands case. Our results demonstrate the importance of the topology of the network, and the rewiring mechanism in the process of language change. **

Consider a system of $N$ individuals, each using language described by a set of $F$ traits. Individuals are connected by links, indicating social interactions enabling language transfer. Two agents can speak very similar dialects or completely different languages, what is reflected in $q$ different values of every trait. Traits should be interpreted as groups of words, or grammar rules, rather than single words. During the interaction people tend to adapt their languages to each other, if they have anything in common (see FIG. 1). The more similar languages they speak, the more probable is the positive interaction and learning from each other, leading to a further increase of the similarity. On the other hand, people using languages with all traits different have no possibility to communicate and will cut the connection and look for a new neighbor. After disconnecting from a neighbor, active node will choose a new one from a set of vertices distant by two edges (see FIG. 2), i.e. neighbors of neighbors. This rewiring mechanism assumes only local interactions, what is intuitive for every-day use of language. It was shown that social networks are characterized by high value of the clustering coefficient newman2003social ; dorogovtsev2002evolution ; foster2011clustering ; palla2007quantifying . This rewiring mechanism increases the value of the clustering coefficient by the definition. Parameters $F$ and $q$ reflects the diversity of language. One trait can stand for a vocabulary in a given field. Than, different values of $q$ indicate different words used to describe the same objects.

It was shown that the model defined as above displays three significantly different phases raducha2017coevolving . In the first phase, for small values of $q$, we observe death of most of the dialects. In this phase, when the system reaches the final configuration almost all agents speak the same language, and the graph is connected. In the second phase the network disintegrates into many small components, each with a different language. Society is polarized and different clusters use different languages. In the third phase a partial recombination occurs, but the number of languages increases further, resulting in existence of links between individuals speaking different languages. For that reason, the two first phases are more suitable for the explanation of the language change. Additionally, it is a reasonable assumption that languages can vary to a finite extent.

Despite the fact that this simple usage-based model of language manages to capture the essence of social interactions, its interpretation considering languages was abandoned after very first publication axelrod1997dissemination , due to the contradiction with the empirical data. Anthropological study of Solomon Islands in the late 70’s terrell1977human showed that the number of languages functioning on an island grows with the size of the island. As noted in the original paper, results of the first model defined on a static square lattice were exactly opposite – the number of domains was decreasing with increasing size of the lattice. Moreover, the first adaptive model sanmiguel2007 , taking into account coevolution of the nodes’ states and the topology of the network, did not solve this issue – the number of domains was approximately constant for different sizes of the network.

In FIG. 3 we analyze behavior of two variants of the model – local rewiring with a uniform probability and local rewiring with a preferential attachment. It is clear that the number of domains, indicating number of languages, increase with the system size. This result is qualitatively consistent with the empirical data for Solomon Islands given in terrell1977human . It is worth noting that this dependency is also valid, yet weaker, for different models described in raducha2017coevolving , but only for a certain range of values of the parameter $q$.

Based on our findings, we should expect larger number of languages for countries with bigger population. To validate this prediction we analyze two databases. The first one form 1996 consisting information about 6866 languages and their 9130 dialects from 209 different countries grimes1996ethnologue , and the second one from 2013 (regularly updated) consisting information about 2679 languages in 188 countries wals2013 . In FIG. 4 we plot the number of languages against the size of a population for countries from six continents. The trend seems to be increasing in every example, but fluctuations darken the picture. Obviously, language diversity on a scale of continents is driven not only by social interactions. There are many factors influencing the linguistic structure of the society, for example language policy and legislation, colonization, border changes, demolition of the population during wars or epidemics, compulsory resettlement etc. Nevertheless, we expect our findings to hold on average. To eliminate fluctuations we aggregate data for consecutive intervals. Results are shown in FIG. 5, excluding, for the sake of clarity, four countries that have either the population size (China, India) or the number of languages (Indonesia, Papua New Guinea) grater by almost order of magnitude from the others. We obtain growing number of languages with the population size for both databases. Moreover, this dependency is even more pronounced in the data set of dialects. Again, results of the simulations are qualitatively consistent with the empirical data.

In our study we showed that even complex description of nodes’ states in social networks is not sufficient to explain real-world phenomena. Furthermore, even sophisticated dynamics of states can be not enough when the structure of the network is divergent to empirical examples. Topology and its transformations are crucial in a proper description of the language change due to social interactions. In this field, models with only local rewiring, leading to high clustering and frequent disintegration, most accurately reproduce empirical data. Here we have taken steps towards understanding the process of the language change and its foundations, although its full structure is undiscovered. Nevertheless, comprehensive model of language should take into account proper dynamics of the network topology.

I Methods

Algorithm. The model we use is described in details in raducha2017coevolving . We start every simulation with a random graph with $N$ vertices, each representing one agent. We set the number of links $M$ to obtain a certain value of the average degree $\langle k\rangle$. Every node $i$ is described by a vector of traits $\sigma_{i}=(\sigma_{i,1},\sigma_{i,2},...,\sigma_{i,F})$. Every trait can initially adopt one of $q$ discrete values $\sigma_{i,f}\in\{1,2,...,q\},f=1,2,...,F$, what gives $q^{F}$ possible different states. At the beginning, we draw a set of $F$ traits for each node with equal probability for every value form $1$ to $q$. Then, every time step consists of following rules:

Draw an active node $i$ and one of its neighbors $j$. 2. 2.

Compare vectors $\sigma$ of chosen vertices and determine the number $m$ of identical traits (overlap), such that $\sigma_{i,f}=\sigma_{j,f}$.

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If all traits are equal i. e. $m=F$, nothing happens.

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If none of the traits are equal $m=0$, disconnect the edge $(i,j)$ from node $j$, draw a new node $l$, and attach a link to it, creating an edge $(i,l)$.

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In other cases, with probability equal $m/F$ the positive interaction occurs, in which we randomly select one of not-shared traits $f^{\prime}$ (from among $F-m$) and the active node $i$ adopts its value from the node $j$, i. e. $\sigma_{i,f^{\prime}}\to\sigma^{\prime}_{i,f^{\prime}}=\sigma_{j,f^{\prime}}$. 3. 3.

Go to the next time step.

The method of selecting new neighbors is crucial. We allow to create a new connection only within a set of nodes distant by two edges (neighbors of neighbors). Multiple connections and auto-connections are prohibited. We analyze two possibilities: uniform probability for every node in the set, and preferential attachment with probability $P(i)\sim(k_{i}+1)^{2}$. Simulation is ran until frozen configuration is obtained or thermalization is reached. In order to describe behavior of the system we use several quantities and coefficients, which are defined as follows.

Component $s$: two vertices $i$ and $j$ belong to the same component $s$, if they are connected, or vertex $k$ exists such that vertex $i$ belongs to the same component as vertex $k$ and vertex $k$ belongs to the same component as vertex $j$. Then, by the largest component of the network we mean the biggest connected subgraph of the network.

Domain $d$: two vertices $i$ and $j$ belong to the same domain $d$, if they are connected and share all traits $\sigma_{i}=\sigma_{j}$, or vertex $k$ exists such that vertex $i$ belongs to the same domain as vertex $k$ and vertex $k$ belongs to the same domain as vertex $j$. By definition, a given domain cannot exceed the size of the component it shares nodes with. On the other hand, the number of components cannot be superior to the number of domains.

Local clustering coefficient $c_{i}$: for undirected graphs it can be defined as the number of connections between neighbors of the node $i$ divided by $k_{i}(k_{i}-1)/2$, i.e. the number of links that could possibly exist between them.

Global clustering coefficient $C$: it is defined as three times the number of triangles in the network divided by the number of connected triplets of vertices (one triangle consists three connected triplets).

Average path length $\langle l\rangle$: it is the shortest distance between two vertices, averaged over all pairs of vertices in the network. If there is no path between two vertices (network has many components), this pair is not taken into account.

Data Availability. The data about languages in different countries that support the findings of this study are available in two online databases: Ethnologue www.ethnologue.com/13/names grimes1996ethnologue and WALS www.wals.info wals2013 . The data about population sizes that support the findings of this study are available from United Nations World Population Prospects https://esa.un.org/unpd/wpp united2015world

Acknowledgements.

The authors would like to thank Mateusz Wilinski for discussions and corrections.