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I believe motherese exists to teach the infant to discriminate phonemes in the native language. Kuhl et al. (2005) show that during the first year language critical period, infants gain an increased ability to discriminate between phonemes of the native language, while their ability to discriminate between phonemes of non-native languages declines. Additionally, their ability to discriminate phonemes is initially language-neutral. Kuhl (2003) further shows a strong correlation between mother speech clarity and infant phonetic discrimination ability.

So if clarity is so important, why talk to children in semi-gibberish and not normal speech? One possibility is that motherese emphasizes certain sounds to enhance the perceptual discrimination. Karzon (1983) investigates this idea, with positive results. To us motherese sounds odd, but in reality it is providing a clearer phonetic structure for the infant to learn.

It's likely that the mother's desire to talk to her baby in motherese, and the babies appreciation of it are traits that co-evolved. Perhaps, like Falk suggests, motherese is an exapted remnant of some early hominid proto-language.

This type of interaction might also have a role in the larger structure of mother/child bonding. But I feel it's unlikely that it evolved for that particular reason. What's more likely is that it was simply co-opted into that mechanism.

References

Karzon, R.G. (1985) Discrimination of polysyllabic sequences by one- to four-month-old infants Journal of Experimental Child Psychology 39(2): 326-342.

Kuhl, P.K., Conboy, B.T., Padden, D., Nelson, T., & Pruitt, J. (2005) Early Speech Perception and Later Language Development: Implications for the "Critical Period" Language Learning and Development 1(3-4): 237-264.

Liu, H-M., Kuhl, P.K., Tsao, F-M. (2003) An association between mothers’ speech clarity and infants’ speech discrimination skills Developmental Science 6(3): F1-F10.