Evol Ecol Res 11: 433-445 (2009)     Full PDF if your library subscribes.

Simplicity from complexity: emergence of cohesion in the evolutionary dynamics of grammar networks

Yoosook Lee1, Travis C. Collier1, Charles E. Taylor1, and Reza Olfati-Saber2

1Department of Ecology and Evolutionary Biology, UCLA, Los Angeles, California and  2Thayer School of Engineering, Dartmouth College, Hanover, New Hampshire, USA

Correspondence: Y. Lee, Department of Ecology and Evolutionary Biology, UCLA, 621 Charles Young Dr. South (LS 3109), Los Angeles, CA 90095, USA.
e-mail: yoslee@ucdavis.edu


Question: Under what conditions will a group of adaptive, communicating agents converge on a single language, and when will there instead be a multiplicity of languages? This is sometimes termed the ‘Tower of Babel problem’, and is similar to those addressed in Slobodkin’s book on simplicity and complexity.

Features of the model: Agents learn to speak a language from those around them locally, or from those with whom they communicate. Learning fidelity can vary, as can connectedness. Populations of learning agents are simulated and the equilibrium properties deduced.

Range of key variables: Populations of agents are arranged in a regular ring lattice, with varying degrees of connectivity. Languages are not all equally related, as studied in the past, but rather some languages are more closely related than others.

Conclusions: If a grammar has limited mutational transitions to other grammars, one expects three, rather than two, distinctive grammar distributions at equilibrium. In line with previous studies, our model exhibits a bifurcation from the symmetric state, where all grammars are in equal frequency, to an asymmetric state under dense grammar networks. However, different patterns of convergence, including a weak cohesion phase where the distribution of grammar frequencies is roughly Gaussian and centred on the most frequent grammar, emerge in more sparse grammar networks. Weak cohesion is of particular interest from an adaptation standpoint, since there is both linguistic coherence and standing heritable variation.

Keywords: evolutionary dynamics, grammar networks, language evolution.

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