Competition and fragmentation: a simple model generating lognormal-like   distributions
  The current distribution of language size in terms of speaker population is generally described using a lognormal distribution. Analyzing the original real data we show how the double-Pareto lognormal distribution can give an alternative fit that indicates the existence of a power law tail. A simple Monte Carlo model is constructed based on the processes of competition and fragmentation. The results reproduce the power law tails of the real distribution well and give better results for a poorly connected topology of interactions. 
V. Schw\"ammle, Silvio M. D. Queir\'os, E. Brigatti and T.   Tchumatchenko