As the key mechanism of the cultural evolution of language, the aforementioned models are largely based on iterated learning.
Iterated learning refers to the process by which an individual acquires a behavior by observing a similar behavior in another individual who acquired it in the same way.
Early studies of iterated learning that observed human behaviour in a laboratory setting were designed to learn about cultural transmission. One of the pioneer studies in iterated learning is Bartlett’s (1937) ‘serial reproduction’ experiment, in which participants were exposed to some stimulus (such as drawings) and were then asked to reproduce the same material from memory. Their reproduced work served as the stimulus for a second participant, and so on. Bartlett observed that the material that was transmitted in this manner had changed as participants impressed their expectations about what they deemed was the right and appropriate content onto the material, thus causing it to be restructured. For example, if one was shown a picture of an apple and told to draw it, another would observe the resultant drawing and produce a new drawing of an apple (as pictured below). An interesting observation that came out of the study was that drawings could change toward conventional, prototypical forms of the object drawn. (Bartlett, 1932)
Spoken and signed languages, birdsong, and music are transmitted via iterated learning as opposed to explicit teaching. One’s linguistic behavior is thus a product of one’s observation of others’ similar behavior, which was induced by that of those who came before. The chain of diffusion occurs in not only cultural transmission, but also horizontal negotiation of conventions between peers of the same generation. Iterated learning is thus manifested both along a cross-generational chain of different individuals and back-and-forth within a dyad.
Iterated learning can have profound effects on linguistic structure. A study on such effects involved the learning of an artificial language by participants who were organized into diffusion chains. Such studies show that iterated is an adaptive process, in which the linguistic behavior being transmitted gains input from each generation to overcome key constraints. Some constraints to a language’s transmission over time include error rate and ambiguity.
More details on studies based on the theory of iterated learning can be read here and here.