[IEEE-bhpjobs] Wednesday, October 5, 2005, 11:00am Schiciano Auditorium

[Walter Heger]

Duke Institute for Genome Sciences & Policy
Center for Bioinformatics & Computational Biology Seminar Series
Wednesday, October 5, 2005,
11:00am Schiciano Auditorium, Fitzpatrick Center - CIEMAS Bldg. W.
Garrett Mitchener,PhD
Duke University Department of Mathematics “Game Dynamics with Learning and 
Evolution of Universal Grammar” I will present a model of language 
evolution, based on population game dynamics with learning. Specifically, we 
consider the case of two genetic variants of universal grammar (UG), the 
heart of the human language faculty, assuming each admits two possible 
grammars. The dynamics are driven by a communication game. We prove using 
dynamical systems techniques that if the payoff matrix obeys certain 
constraints, then the two UGs are stable against invasion by each other, 
that is, they are evolutionarily stable. These constraints are independent 
of the learning process. Intuitively, if a mutation in UG results in 
grammars that are incompatible with the established languages, then it will 
die out because individuals with the mutation will be unable to communicate 
and therefore unable to realize any potential benefit of the mutation. An 
example for which the proofs do not apply shows that compatible mutations 
may or may not be able to invade, depending on the population's history and 
the learning process. These results suggest that the genetic history of 
language is constrained by the need for compatibility and that mutations in 
the language faculty may have died out or taken over depending more on 
historical accident than on any simple notion of relative fitness.

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