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Finite populations choose an optimal language
Freitag, 02.11.2007 10:00 - 11:00
Christina Pawlowitsch
Harvard, Program of Evolutionary Dynamics

Finite populations choose an optimal language

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, Nature), 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, J. theor.
Biol.) that are generally true for games with a symmetric payoff function.
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