Although adult brains are malleable and even undergo limited neuorgenesis, the extent of the neuroplasticiy is much lower than in children. This is most obvious in language acquisition, and recovery from brain trauma.

**Are there formal models (computational or mathematical) that explain *why* our brains so drastically reduce in plasticity with age?**

If a highly malleable brain is supposed to help us adapt and deal with a constantly changing environment, then naively one would expect it to be advantageous to maintain a malleable brain for your whole life.

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### Background from critical-period in language acquisition

*This is an example of formal models that I am already familiar with that answer a related question (critical-period in language acquisition). I am interested in answers in this spirit, but that can address not just language-acquisition but the general decrease in neuroplasticity.*

In the case of the critical period for language acquisition there are evolutionary models by Hurford (1991) and Komarova & Nowak (2001). However, neither model generalizes easily to the case of neuralplasticity.

Hurford's model uses neutral drift to explain the upper bound on the critical period of language acquisition because of the need for second language acquisition in life is largely unnecessary. However, the need to adapt to your environment is necessary throughout life, so plasticity should not be under neutral drift.

In the case of Komarova & Nowak, the upper bound is due to a trade-off between the cost of learning (driving critical period down) and the importance of learning a language accurately (driving critical period up). This balances out and allows for an ESS due to dimishing returns: once you've learned a language pretty-well it becomes more costly to invest in learning further than the returns from better learning. However, adapting to a constantly changing environment is not a single static task, and thus it is not clear why your returns would diminish. Further, it is not clear how keeping high plasticity is more costly than maintaining lower plasticity.

### Notes

* This is a question of *why*, not *how*. Although it is very interesting to know *how* the plasticity of adult brains decreases, in this question I am interested in *why* this is the case over the hypothetical "keep as malleable as a baby" alternative.
* Both Hurford (1991) and Komarova & Nowak (2001) provide formal evolutionary models that I do not describe in detail. I am interested in formal models like this, although they need not be evolutionary. An answer on the level of rhetoric (especially if it is evolutionary rhetoric) is not nearly as interesting to me as a formal model.
* Hurford (1991) and Komarova & Nowak (2001) are meant as examples of work that answer the potentially easier question of critical period of language-acquisition. I am interested in the more general question of decrease in neuroplasticity.

### References

Hurford, J. R. (1991). The evolution of critical period for language acquisition. Cognition, 40, 159-201. [FREE PDF](http://www.ling.ed.ac.uk/%7Ejim/crit.per.pdf)

Komarova, N. L. & Nowak, M. A. (2001). Natural selection of the critical period for language acquisition. Proc. R. Soc. London. B, 268(1472), 1189-1196. [FREE PDF](http://rspb.royalsocietypublishing.org/content/268/1472/1189.full.pdf)