Information theoretic models in language evolution

We study a model for language evolution which was introduced by Nowak and Krakauer ([M.A. Nowak and D.C. Krakauer, The evolution of language, PNAS 96 (14) (1999) 8028-8033]). We analyze discrete distance spaces and prove a conjecture of Nowak for all metrics with a positive semidefinite associated matrix. This natural class of metrics includes all metrics studied by different authors in this connection. In particular it includes all ultra-metric spaces. rmore, the role of feedback is explored and multi-user scenarios are studied. In all models we give lower and upper bounds for the fitness.