1 Chapter 43 Vowel harmony in computational models of emergence Mark Dras & K. David Harrison 43.1 Introduction This chapter will discuss computational models of the evolution of vowel harmony, of which there are two main approaches, one proposed by Harrison et al. (2002) and Dras & Harrison (2003), and the other by Mailhot (2010, 2013). It will first outline the kinds of harmony phenomena that the models deal with; then it will discuss some general issues involved in computational modeling of complex systems such as language, and relatedly what claims can be made by particular sorts of models. The core of the chapter will then discuss the two alternative approaches to the modeling of vowel harmony. 43.2 Harmony phenomena 43.2.1 Description Harrison et al. (2002) and Dras & Harrison (2003) explore the particular case of Turkic vowel harmony. The facts are discussed in more detail in Chapter 59, this volume, but briefly: In most Turkic (and Altaic) languages, backness (i.e., palatal) harmony is apparent both as an ambient pattern of vowel co-occurrence within word roots, and as a productive pattern of vowel alternations in suffixes. Harmony also determines the quality of epenthetic vowels and the vowels of nonce words, reduplicants and loanwords, in ways that, though systematic, may differ from the patterns attested in root and suffix vowels in the language. A typical Turkic vowel inventory includes four front and four back vowels, neatly divisible into harmonic classes. (1) front back high i y ɯ u non-high e ø ɑ o