The evolutionary dynamics of the lexical matrix

The lexical matrix is an integral part of the human language system. It pro vides the link between word form and word meaning. A simple lexical matrix is also at the center of any animal communication system, where it defines the associations between form and meaning of animal signals. We study the e volution and population dynamics of the lexical matrix. We assume that chil dren learn the lexical matrix of their parents. This learning process is su bject to mistakes: (i) children may not acquire all lexical items of their parents (incomplete learning); and (ii) children might acquire associations between word forms and word meanings that differ from their parents' lexic al items (incorrect learning). We derive an analytic framework that deals w ith incomplete learning. We calculate the maximum error rate that is compat ible with a population maintaining a coherent lexical matrix of a given siz e. We calculate the equilibrium distribution of the number of lexical items known to individuals. Our analytic investigations are supplemented by nume rical simulations that describe both incomplete and incorrect learning, and other extensions. (C) 2001 Society for Mathematical Biology.