Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Baxter, G.J.: A voter model with time dependent flip rates. J. Stat. Mech. 2011, P09005 (2011)
Baxter, G.J., Blythe, R.A., Croft, W., McKane, A.J.: Utterance selection model of language change. Phys. Rev. EÂ 73, 046118 (2006)
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)
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)
Baxter, G.J., Blythe, R.A., McKane, A.J.: Fast fixation with a generic network structure. Phys. Rev. E. 86, 031142 (2012)
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)
Blythe, R.A., Croft, W.: S-curves and the mechanism of propagation in language change. Language 88, 269 (2012)
Bybee, J.L.: Phonology and language use. Cambridge University Press, Cambridge (2001)
Castellano, C., Fortunato, S., Loreto, V.: Statistical physics of social dynamics. Rev. Mod. Phys. 81, 591–646 (2009)
Croft, W.: Explaining Language Change: An Evolutionary Approach. Long-man Linguistics Library. Pearson Education, Harlow (2000)
Crow, J.F., Kimura, M.: An Introduction to Population Genetics Theory. Harper and Row, New York (1970)
Dall’Asta, L., Baronchelli, A., Barrat, A., Loreto, V.: Non-equilibrium dynamics of language games on complex networks. Phys. Rev. E 74, 036105 (2006)
Fagyal, Z., Swarup, S., Escobar, A.M., Gasser, L., Lakkaraju, K.: Centers and peripheries: Network roles in language change. Lingua 120, 2061–2079 (2010)
Gardiner, C.W.: Handbook of Stochastic Methods, 3rd edn. Springer, Berlin (2004)
Gordon, E., Campbell, L., Hey, J., MacLagan, M., Sudbury, A., Trudgill, P.: New Zealand English: its Origins and Evolution. Cambridge University Press, Cambridge (2004)
Hawkins, J.A.: Efficiency and Complexity in Grammars. Oxford University Press, Oxford (2004)
Hubbell, S.: The Unified Neutral Theory of Biodiversity, Princeton (2001)
Hull, D.L.: Science as a Process: An Evolutionary Account of the Social and Conceptual Development of Science. University of Chicago Press, Chicago (1988)
Hull, D.L.: Science and selection: essays on biological evolution and the philosophy of science. Cambridge University Press, Cambridge (2001)
Kandler, A., Steele, J.: Ecological Models of Language Competition. Biol. Theor. 3, 164–173 (2008)
Kirby, S.: Natural Language From Artificial Life. Artif. Life 8, 185 (2002)
Labov, W.: Principles of Linguistic Change: Social Factors. Blackwell, Oxford (2001)
LePage, R.B., Tabouret-Keller, A.: Acts of Identity. Cambridge University Press, Cambridge (1985)
Masuda, N., Gibert, N., Redner, S.: Heterogeneous voter models. Phys. Rev. EÂ 82, 010103(R) (2010)
McMahon, A.M.S.: Understanding Language Change. Cambridge University Press (1994)
Niyogi, P., Berwick, R.C.: Evolutionary consequences of language learning. Linguistics Philos. 20, 697 (1997)
Nowak, M.A., Komarova, N.L., Niyogi, P.: Evolution of universal grammar. Science 291, 114 (2001)
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)
Pierrehumbert, J.: Phonetic diversity, statistical learning, and acquisition of phonology. Language and Speech 45, 115–154 (2003)
Risken, H.: The Fokker-Planck Equation. Study. Springer, Berlin (1989)
Trudgill, P.: New-dialect formation: the inevitability of colonial Englishes. Edinburgh University Press, Edinburgh (2004)
Vogt, P.: Modeling Interactions between Language Evolution and Demography. Human Biology 81, Article 7 (2009)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Baxter, G.J. (2016). Social Networks and Beyond in Language Change. In: Mehler, A., Lücking, A., Banisch, S., Blanchard, P., Job, B. (eds) Towards a Theoretical Framework for Analyzing Complex Linguistic Networks. Understanding Complex Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-47238-5_12
Download citation
DOI: https://doi.org/10.1007/978-3-662-47238-5_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-47237-8
Online ISBN: 978-3-662-47238-5
eBook Packages: EngineeringEngineering (R0)