Bulletin of Mathematical Biology

, Volume 65, Issue 1, pp 67–93 | Cite as

Competitive exclusion and coexistence of universal grammars

  • W. Garrett Mitchener
  • Martin A. Nowak


Universal grammar (UG) is a list of innate constraints that specify the set of grammars that can be learned by the child during primary language acquisition. UG of the human brain has been shaped by evolution. Evolution requires variation. Hence, we have to postulate and study variation of UG. We investigate evolutionary dynamics and language acquisition in the context of multiple UGs. We provide examples for competitive exclusion and stable coexistence of different UGs. More specific UGs admit fewer candidate grammars, and less specific UGs admit more candidate grammars. We will analyze conditions for more specific UGs to outcompete less specific UGs and vice versa. An interesting finding is that less specific UGs can resist invasion by more specific UGs if learning is more accurate. In other words, accurate learning stabilizes UGs that admit large numbers of candidate grammars.


Saddle Point Phase Portrait Base Line Stable Manifold Language Acquisition 
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. Ahlfors, L. V. (1979). Complex Analysis, 3rd edn, McGraw-Hill.Google Scholar
  2. Aitchinson, J. (1987). Words in the Mind: An Introduction to the Mental Lexicon, Oxford: Basil Blackwell.Google Scholar
  3. Andronov, A. A., E. A. Leontovich, I. I. Gordon and A. G. Maier (1971). Theory of Bifurcations of Dynamic Systems on a Plane, Jerusalem: Keter Press.Google Scholar
  4. Bickerton, D. (1990). Language and Species, Chicago: University of Chicago Press.Google Scholar
  5. Cangelosi, A. and D. Parisi (eds) (2001). Simulating the Evolution of Language, Springer.Google Scholar
  6. Chomsky, N. (1965). Aspects of the Theory of Syntax, Cambridge, MA: MIT Press.Google Scholar
  7. Chomsky, N. (1972). Language and Mind, New York: Harcourt Brace Jovanovich.Google Scholar
  8. Ferrer i Cancho, R. and R. V. Solé (2001a). The small world of human language. Proc. R. Soc. Lond. B 268, 2261–2266.CrossRefGoogle Scholar
  9. Ferrer i Cancho, R. and R. V. Solé (2001b). Two regimes in the frequency of words and the origin of complex lexicons: Zipf’s law revisited. J. Quant. Linguistics 8, 165–173.CrossRefGoogle Scholar
  10. Ghazanfar, A. A. and M. D. Hauser (1999). The neuroethology of primate vocal communication: substrates for the evolution of speech. Trend. Cog. Sci. 3, 377–384.CrossRefGoogle Scholar
  11. Gibson, E. and K. Wexler (1994). Triggers. Linguistic Inquiry 25, 407–454.Google Scholar
  12. Gold, E. M. (1967). Language identification in the limit. Information Control 10, 447–474.zbMATHCrossRefGoogle Scholar
  13. Grassly, N., A. von Haesler and D. C. Krakauer (2000). Error, population structure and the origin of diverse sign systems. J. Theor. Biol. 206, 369–378.CrossRefGoogle Scholar
  14. Hauser, M. D. (1996). The Evolution of Communication, Cambridge, MA: Harvard University Press.Google Scholar
  15. Hauser, M. D., E. L. Newport and R. N. Aslin (2001). Segmentation of the speech stream in a nonhuman primate: statistical learning in cotton-top tamarins. Cognition 78, B53–B64.CrossRefGoogle Scholar
  16. Hofbauer, J. and K. Sigmund (1998). Evolutionary Games and Population Dynamics, Cambridge University Press.Google Scholar
  17. Hurford, J. R., M. Studdert-Kennedy and C. Knight (eds) (1998). Approaches to the Evolution of Language, Cambridge University Press.Google Scholar
  18. Jackendoff, R. (1999). Possible stages in the evolution of the language capacity. Trend. Cog. Sci. 3, 272–279.CrossRefGoogle Scholar
  19. Kirby, S. (2001). Spontaneous evolution of linguistic structure: an iterated learning model of the emergence of regularity and irregularity. IEEE Trans. Evol. Comput. 5, 102–110.CrossRefGoogle Scholar
  20. Komarova, N. L., P. Niyogi and M. A. Nowak (2001). The evolutionary dynamics of grammar acquisition. J. Theor. Biol. 209, 43–59.CrossRefGoogle Scholar
  21. Krakauer, D. C. (2001). Kin imitation for a private sign system. J. Theor. Biol. 213, 145–157.CrossRefGoogle Scholar
  22. Lachmann, M., S. Szamado and C. T. Bergstrom (2001). Cost and conflict in animal signals and human language. Proc. Natl. Acad. Sci. USA 98, 13189–13194.Google Scholar
  23. Lai, C. S. L., S. E. Fisher, J. A. Hurst, F. Vargha-Khadem and A. P. Monaco (2001). A forkhead-domain gene is mutated in a severe speech and language disorder. Nature 413, 519–523.CrossRefGoogle Scholar
  24. Lieberman, P. (1984). The Biology and Evolution of Language, Cambridge, MA: Harvard University Press.Google Scholar
  25. Lightfoot, D. (1991). How to Set Parameters: Arguments from Language Change, Cambridge, MA: MIT Press.Google Scholar
  26. Lightfoot, D. (1999). The Development of Language: Acquisition, Changes and Evolution, Blackwell Publishers.Google Scholar
  27. May, R. M. (2001). Stability and Complexity in Model Ecosystems, Princeton, NJ: Princeton University Press.Google Scholar
  28. Mitchener, W. G. (2002). Bifurcation analysis of the fully symmetric language dynamical equation. J. Math. Biol. (accepted).Google Scholar
  29. Niyogi, P. (1998). The Informational Complexity of Learning, Boston: Kluwer Academic Publishers.Google Scholar
  30. Niyogi, P. and R. C. Berwick (1996). A language learning model for finite parameter spaces. Cognition 61, 161–193.CrossRefGoogle Scholar
  31. Nowak, M. A. and D. C. Krakauer (1999). The evolution of language. Proc. Natl. Acad. Sci. USA 96, 8028–8033.CrossRefGoogle Scholar
  32. Nowak, M. A., N. L. Komarova and P. Niyogi (2001). Evolution of universal grammar. Science 291, 114–118.MathSciNetCrossRefGoogle Scholar
  33. Nowak, M. A., N. L. Komarova and P. Niyogi (2002). Computational and evolutionary aspects of language. Nature 417, 611–617.CrossRefGoogle Scholar
  34. Nowak, M. A., J. Plotkin and V. A. A. Jansen (2000). Evolution of syntactic communication. Nature 404, 495–498.CrossRefGoogle Scholar
  35. Pinker, S. (1990). The Language Instinct, New York: W. Morrow and Company.Google Scholar
  36. Pinker, S. and A. Bloom (1990). Natural language and natural selection. Behav. Brain Sci. 13, 707–784.Google Scholar
  37. Ramus, F., M. D. Hauser, C. Miller, D. Morris and J. Mehler (2000). Language discrimination by human newborns and by Cotton-Top tamarin monkeys. Science 288, 349–351.CrossRefGoogle Scholar
  38. Strogatz, S. H. (1994). Nonlinear Dynamics and Chaos, Reading, MA: Perseus Books.Google Scholar
  39. Studdert-Kennedy, M. (2000). Evolutionary implications of the particulate principle: Imitation and the dissociation of phonetic form from semantic function, in The Evolutionary Emergence of Language: Social Function and the Origins of Linguistic Form, C. Knight, J. R. Hurford and M. Studdert-Kennedy (Eds), Cambridge: Cambridge University Press.Google Scholar
  40. Uriagereka, J. (1998). Rhyme and Reason: An Introduction to Minimalist Syntax, Cambridge, MA: MIT Press.Google Scholar
  41. Valiant, L. G. (1984). A theory of the learnable. Commun. ACM 27, 436–445.CrossRefGoogle Scholar
  42. Vapnik, V. (1995). The Nature of Statistical Learning Theory, New York: Springer.Google Scholar
  43. Wexler, K. and P. Culicover (1980). Formal Principles of Language Acquisition, Cambridge, MA: MIT Press.Google Scholar

Copyright information

© Society for Mathematical Biology 2003

Authors and Affiliations

  • W. Garrett Mitchener
    • 1
  • Martin A. Nowak
    • 2
  1. 1.Program in Applied and Computational MathematicsPrincetonUSA
  2. 2.Institute for Advanced StudyPrincetonUSA

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