Rules and Exceptions in Language Dynamics

In all languages, rules have exceptions in the form of irregularities. Since rules make a language efficient, the persistence of irregularity is an anomaly. How language systems become rule governed, how and why they sustain exceptions to rules? Frequent words are unlikely to change over time (e.g., frequent verbs tend to maintain an irregular past tense form). What is the role of frequency in maintaining exceptions to rules?

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F. Colaiori , C. Castellano, C.Cuskley, M.  Pugliese, V. Loreto, and F. Tria (2015). General three-state model with biased population replacement: Analytical solution and application to language dynamics. Phys. Rev. E 91, 012808 (2015).

M. Pugliese, V. Loreto, C. Cuskley, C. Castellano, F. Colaiori, F. Tria (2014). The role of coordination in regularization. The Evolution of Language: Proceedings of the 10th International Conference Evolang 10, Vienna 2014, 260-261

C. Cuskley, C. Castellano, F. Colaiori, V. Loreto, M. Pugliese, F. Tria (2014). Frequency and stability of linguistic variants. The Evolution of Language: Proceedings of the 10th International Conference Evolang 10, Vienna 2014, 417-418