  It is argued that the present log-normal distribution of language sizes is,
to a large extent, a consequence of demographic dynamics within the population
of speakers of each language. A two-parameter stochastic multiplicative process
is proposed as a model for the population dynamics of individual languages, and
applied over a period spanning the last ten centuries. The model disregards
language birth and death. A straightforward fitting of the two parameters,
which statistically characterize the population growth rate, predicts a
distribution of language sizes in excellent agreement with empirical data.
Numerical simulations, and the study of the size distribution within language
families, validate the assumptions at the basis of the model.
