Social Networks and Beyond in Language Change

  • Gareth J. BaxterEmail author
Part of the Understanding Complex Systems book series (UCS)


We examine the effects of heterogeneous social interactions in a numerical model of language change based on the evolutionary utterance based theory developed by Croft. Two or more variants of a linguistic variable compete in the population. Social interactions can be separated into a symmetric weighted network of social contact probabilities, and asymmetric weightings given by speakers to each other’s utterances, that is, social influence. Remarkably, when interactions are symmetric between speakers, the network structure has no effect on the mean time to consensus. On the other hand large disparities in social influence, even in rather homogeneous networks, can dramatically affect mean time to reach consensus (fixation). We explore a range of representative scenarios, to give a general picture of both aspects of social interactions, in the absence of explicit selection for any particular variant.


Social Network Degree Distribution Linguistic Variable Voter Model Speech Community 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. [Baxter(2011)]
    Baxter, G.J.: A voter model with time dependent flip rates. J. Stat. Mech. 2011, P09005 (2011)Google Scholar
  2. [Baxter et al.(2006)Baxter, Blythe, Croft, and McKane]
    Baxter, G.J., Blythe, R.A., Croft, W., McKane, A.J.: Utterance selection model of language change. Phys. Rev. E 73, 046118 (2006)Google Scholar
  3. [Baxter et al.(2009)Baxter, Blythe, Croft, and McKane]
    Baxter, G.J., Blythe, R.A., Croft, W., McKane, A.J.: Modeling language change: An evaluation of Trudgill’s theory for the emergence of New Zealand English. Language Variation and Change 21, 257–296 (2009)CrossRefGoogle Scholar
  4. [Baxter et al.(2008)Baxter, Blythe, and McKane]
    Baxter, G.J., Blythe, R.A., McKane, A.J.: Fixation and consensus times on a network: a unified approach. Phys. Rev. Lett. 101, 258701 (2008)CrossRefGoogle Scholar
  5. [Baxter et al.(2012)Baxter, Blythe, and McKane]
    Baxter, G.J., Blythe, R.A., McKane, A.J.: Fast fixation with a generic network structure. Phys. Rev. E. 86, 031142 (2012)Google Scholar
  6. [Blythe(2010)]
    Blythe, R.A.: Ordering in voter models on networks: exact reduction to a single-coordinate diffusion. J. Phys. A: Math. Theor. 43(38), 385003 (2010)MathSciNetCrossRefGoogle Scholar
  7. [Blythe and Croft(2012)]
    Blythe, R.A., Croft, W.: S-curves and the mechanism of propagation in language change. Language 88, 269 (2012)CrossRefGoogle Scholar
  8. [Bybee(2001)]
    Bybee, J.L.: Phonology and language use. Cambridge University Press, Cambridge (2001)CrossRefGoogle Scholar
  9. [Castellano et al.(2009)Castellano, Fortunato, and Loreto]
    Castellano, C., Fortunato, S., Loreto, V.: Statistical physics of social dynamics. Rev. Mod. Phys. 81, 591–646 (2009)CrossRefGoogle Scholar
  10. [Croft(2000)]
    Croft, W.: Explaining Language Change: An Evolutionary Approach. Long-man Linguistics Library. Pearson Education, Harlow (2000)Google Scholar
  11. [Crow and Kimura(1970)]
    Crow, J.F., Kimura, M.: An Introduction to Population Genetics Theory. Harper and Row, New York (1970)zbMATHGoogle Scholar
  12. [Dall’Asta et al.(2006)Dall’Asta, Baronchelli, Barrat, and Loreto]
    Dall’Asta, L., Baronchelli, A., Barrat, A., Loreto, V.: Non-equilibrium dynamics of language games on complex networks. Phys. Rev. E 74, 036105 (2006)Google Scholar
  13. [Fagyal et al.(2010)Fagyal, Swarup, Escobar, Gasser, and Lakkaraju]
    Fagyal, Z., Swarup, S., Escobar, A.M., Gasser, L., Lakkaraju, K.: Centers and peripheries: Network roles in language change. Lingua 120, 2061–2079 (2010)CrossRefzbMATHGoogle Scholar
  14. [Gardiner(2004)]
    Gardiner, C.W.: Handbook of Stochastic Methods, 3rd edn. Springer, Berlin (2004)CrossRefGoogle Scholar
  15. [Gordon et al.(2004)Gordon, Campbell, Hey, MacLagan, Sudbury, and Trudgill]
    Gordon, E., Campbell, L., Hey, J., MacLagan, M., Sudbury, A., Trudgill, P.: New Zealand English: its Origins and Evolution. Cambridge University Press, Cambridge (2004)CrossRefGoogle Scholar
  16. [Hawkins(2004)]
    Hawkins, J.A.: Efficiency and Complexity in Grammars. Oxford University Press, Oxford (2004)CrossRefGoogle Scholar
  17. [Hubbell(2001)]
    Hubbell, S.: The Unified Neutral Theory of Biodiversity, Princeton (2001)Google Scholar
  18. [Hull(1988)]
    Hull, D.L.: Science as a Process: An Evolutionary Account of the Social and Conceptual Development of Science. University of Chicago Press, Chicago (1988)CrossRefGoogle Scholar
  19. [Hull(2001)]
    Hull, D.L.: Science and selection: essays on biological evolution and the philosophy of science. Cambridge University Press, Cambridge (2001)Google Scholar
  20. [Kandler and Steele(2008)]
    Kandler, A., Steele, J.: Ecological Models of Language Competition. Biol. Theor. 3, 164–173 (2008)CrossRefGoogle Scholar
  21. [Kirby(2002)]
    Kirby, S.: Natural Language From Artificial Life. Artif. Life 8, 185 (2002)CrossRefGoogle Scholar
  22. [Labov(2001)]
    Labov, W.: Principles of Linguistic Change: Social Factors. Blackwell, Oxford (2001)Google Scholar
  23. [LePage and Tabouret-Keller(1985)]
    LePage, R.B., Tabouret-Keller, A.: Acts of Identity. Cambridge University Press, Cambridge (1985)Google Scholar
  24. [Masuda et al.(2010)Masuda, Gibert, and Redner]
    Masuda, N., Gibert, N., Redner, S.: Heterogeneous voter models. Phys. Rev. E 82, 010103(R) (2010)Google Scholar
  25. [McMahon(1994)]
    McMahon, A.M.S.: Understanding Language Change. Cambridge University Press (1994)Google Scholar
  26. [Niyogi and Berwick(1997)]
    Niyogi, P., Berwick, R.C.: Evolutionary consequences of language learning. Linguistics Philos. 20, 697 (1997)CrossRefGoogle Scholar
  27. [Nowak et al.(2001)Nowak, Komarova, and Niyogi]
    Nowak, M.A., Komarova, N.L., Niyogi, P.: Evolution of universal grammar. Science 291, 114 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  28. [Ohala(1983)]
    Ohala, J.: The origin of sound patterns in vocal tract constraints. In: MacNeilage, P.F. (ed.) The Production of Speech, pp. 189–216. Springer, New York (1983)CrossRefGoogle Scholar
  29. [Pierrehumbert(2003)]
    Pierrehumbert, J.: Phonetic diversity, statistical learning, and acquisition of phonology. Language and Speech 45, 115–154 (2003)CrossRefGoogle Scholar
  30. [Risken(1989)]
    Risken, H.: The Fokker-Planck Equation. Study. Springer, Berlin (1989)CrossRefGoogle Scholar
  31. [Trudgill(2004)]
    Trudgill, P.: New-dialect formation: the inevitability of colonial Englishes. Edinburgh University Press, Edinburgh (2004)zbMATHGoogle Scholar
  32. [Vogt(2009)]
    Vogt, P.: Modeling Interactions between Language Evolution and Demography. Human Biology 81, Article 7 (2009)Google Scholar

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© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.University of AveiroAveiroPortugal

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