Information Theoretic Models in Language Evolution

  • R. Ahlswede
  • E. Arikan
  • L. Bäumer
  • C. Deppe
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4123)


We study a model for language evolution which was introduced by Nowak and Krakauer ([12]). We analyze discrete distance spaces and prove a conjecture of Nowak for all metrics with a positive semidefinite associated matrix. This natural class of metrics includes all metrics studied by different authors in this connection. In particular it includes all ultra-metric spaces.

Furthermore, the role of feedback is explored and multi-user scenarios are studied. In all models we give lower and upper bounds for the fitness.


Language Evolution Distance Space Noisy Channel Ultrametric Space Weight Enumerator 
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  1. 1.
    Ahlswede, R.: Multi-way communication channels. In: Proceedings of 2nd International Symposium on Information Theory, Thakadsor, Armenian SSR, Akademiai Kiado, Budapest, September 1971, pp. 23–52 (1973)Google Scholar
  2. 2.
    Ahlswede, R., Wegener, I.: Suchprobleme, Teubner (1979), English translation: Wiley (1987), Russian translation: MIR (1982)Google Scholar
  3. 3.
    Berlekamp, E.R.: Block coding for the binary symmetric channel with noiseless, delayless feedback in H.B.Mann, Error Correcting Codes, Wiley, pp. 61–85 (1968)Google Scholar
  4. 4.
    Cover, T.M.: Broadcast channels. IEEE Trans. Inform. Theory 18, 2–14 (1972)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Dress, A.: The information storage capacity of a metric space (preprint)Google Scholar
  6. 6.
    Fichet, B.: Dimensionality problems in l 1-norm representations. In: Classification and Dissimilarity Analysis. Lecture Notes in Statistics, vol. 93, pp. 201–224. Springer, Berlin (1994)Google Scholar
  7. 7.
    Gallager, R.G.: Information Theory and Reliable Communication. Wiley, New York (1968)MATHGoogle Scholar
  8. 8.
    Hamming, R.V.: Error detecting and error correcting codes. Bell Sys. Tech. Journal 29, 147–160 (1950)MathSciNetGoogle Scholar
  9. 9.
    MacWilliams, F.J.: Combinatorial problems of elementary group theory, Ph.D. Thesis, Harvard University (1962)Google Scholar
  10. 10.
    MacWilliams, F.J.: A theorem on the distribution of weights in a systematic code. Bell syst. Tech. J. 42, 79–94 (1963)MathSciNetGoogle Scholar
  11. 11.
    MacWilliams, F.J., Sloane, N.J.A.: The Theory of Error-Correcting Codes. Elsevier Science Publishers B.V, Amsterdam (1977)MATHGoogle Scholar
  12. 12.
    Nowak, M.A., Krakauer, D.C.: The evolution of language. PNAS 96(14), 8028–8033 (1999)Google Scholar
  13. 13.
    Nowak, M.A., Krakauer, D.C., Dress, A.: An error limit for the evolution of language. Proceedings of the Royal Society Biological Sciences Series B 266(1433), 2131–2136 (1999)CrossRefGoogle Scholar
  14. 14.
    Plotkin, J.B., Nowak, M.A.: Language evolution and information theory. J. theor. Biol. 205, 147–159 (2000)CrossRefGoogle Scholar
  15. 15.
    Shannon, C.E.: The zero-error capacity of a noisy channel. IRE Trans. Inform. Theory E, 8–19 (1956)Google Scholar
  16. 16.
    Timan, A.F., Vestfried, I.A.: Any seperable ultrametric space is isometrically embeddable in l 2. Funk. Anal. Pri. 17(1), 85–86 (1983)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • R. Ahlswede
    • 1
  • E. Arikan
    • 2
  • L. Bäumer
    • 1
  • C. Deppe
    • 1
  1. 1.Fakultät für MathematikUniversität BielefeldBielefeldGermany
  2. 2. 

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