Journal
JOURNAL OF THEORETICAL BIOLOGY
Volume 249, Issue 3, Pages 606-616Publisher
ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD
DOI: 10.1016/j.jtbi.2007.08.009
Keywords
language evolution; evolutionary stability; Moran process; fixation probabilities
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This paper studies the evolution of a proto-language in a finite population under the frequency-dependent Moran process. A proto-language can be seen as a collection of concept-to-sign mappings. An efficient proto-language is a bijective mapping from objects of communication to used signs and vice versa. Based on the comparison of fixation probabilities, a method for deriving conditions of evolutionary stability in a finite population [Nowak et al., 2004. Emergence of cooperation and evolutionary stability in finite populations. Nature 428, 246-650] it is shown that efficient proto-languages are the only strategies that are protected by selection, which means that no mutant strategy can have a fixation probability that is greater than the inverse population size. In passing, the paper provides interesting results about the comparison of fixation probabilities as well as Maynard Smith's notion of evolutionary stability for finite populations [Maynard Smith, 1988. Can a mixed strategy be stable in a finite population? J. Theor. Biol. 130, 247-251] that are generally, true for games with a symmetric payoff function. (c) 2007 Elsevier Ltd. All rights reserved.
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