The evolutionary dynamics of grammar acquisition

Grammar is the computational system of language. It is a set of rules that specifies how to construct sentences out of words. Grammar is the basis of the unlimited expressibility of human language. Children acquire the gramma r of their native language without formal education simply by hearing a num ber of sample sentences. Children could not solve this learning task if the y did not have some pre-formed expectations. In other words, children have to evaluate the sample sentences and choose one grammar out of a limited se t of candidate grammars. The restricted search space and the mechanism whic h allows to evaluate the sample sentences is called universal grammar. Univ ersal grammar cannot be learned; it must be in place when the learning proc ess starts. In this paper, we design a mathematical theory that places the problem of language acquisition into an evolutionary context. We formulate equations for the population dynamics of communication and grammar learning . We ask how accurate children have to learn the grammar of their parents' language for a population of individuals to evolve and maintain a coherent grammatical system. It turns out that there is a maximum error tolerance fo r which a predominant grammar is stable. We calculate the maximum size of t he search space that is compatible with coherent communication in a populat ion. Thus, we specify the conditions for the evolution of universal grammar . (C) 2001 Academic Press.