Population-level neutral model already explains linguistic patterns.

In customizing the neutral model for language transmission , Reali & Griffiths [1] have added a new, 'Bayesian' learning interpretation to a neutral model that has been used in cultural evolution studies for some time (e.g. [2 –6]). While Reali & Griffiths [1, p. 435] dismiss previous applications of this neutral model as being used merely 'as a metaphor', it has been explored in quantitative detail, and applied even to word frequencies [7]. We therefore question whether this fairly complex description of Bayesian learning is necessary , as it does not change the results of the model, and runs the risk of obscuring the advances made both through careful modifications and wider applications of this powerful model. The Reali & Griffiths [1] version of the model is mathematically equivalent to previous versions, in representing a set of N variants per time step, with the next generation of N variants constructed by repeatedly sampling variants from the previous time step, with some probability of 'mutation', i.e. introduction of a variant of a unique new variant. Reali & Griffiths [1] apply the model in a novel sense to individual cognition, whereas it has previously been considered in terms of a population of fixed size N, which is replaced by N new agents in each time step. In this population version, each new individual either copies an existing variant from the last time step (with probability proportionate to the previous choices of agents), or chooses a new variant. With probability 1 2 m, an incoming agent copies its variant from that of an agent within the previous time step, or else with probability m, the agent innovates by choosing a unique new variant at random. This model has already been shown to yield the inverse power law in the probability of variant frequencies that Reali and Griffiths report, from which the other inverse power law, in word frequency versus replacement rate, also follows. We demonstrate this briefly below, in order to show how the discussion of the model has advanced beyond this, including the incremental addition of a new extra parameter, 'memory' [8]. Before we consider the model predictions, however, we address the question of the psychological plausibility of the assumptions that are made about agent behaviour. The Bayesian learning approach assumes agents use 'a rational procedure for belief updating that explicitly represents the expectations of learners' (Reali & Griffiths [1, p. 430]). …