Burkett & Griffiths (2010) go a long way to applying populaitonal thinking to language evolution. They describe a Bayesian model of language acquisition that takes into consideration multiple teachers and multiple languages. They point out that a learner who is trying to settle on a single grammar which fits data from multiple speakers violates the principle of Bayesian rational analysis. Burkett & Griffiths rectify this problem by defining a model in which a learner takes into account that the data it receives may be generated by different speakers who may speak more than one language.

Doing this involves a lot of complications. Here’s a list of things I had to look up before coming close to understanding the paper:

• Bernoulli distributions
• Beta distributions
• Hyperparameters
• Wright-Fisher model of genetic drift
• Kroenecker’s delta function
• Dirichlet process
• Gibbs Sampler
• Chinese Restaurant Process

Yes, probably dirt basic for mathematicians, but terrifying to us mere linguists. This took me about a month to get to grips with...

(Learning Multiple Languages from Multiple Teachers, at replicated typo
ht MR)