Optimality Theory (OT) has been one of the dominant approaches within the field of phonology for some time now, and in recent years optimality-based approaches have been extended to address other levels of linguistic description, with applications in the fields of syntax and morphology. Given the close relationship between morphology and phonology, it is not surprising that OT accounts of morphology should have emerged. Matthew Wolf’s doctoral dissertation (Wolf Reference Wolf2008), for example, provides an OT account of what he describes as interleaving processes at the interface of morphology and phonology. Jochen Trommer’s doctoral dissertation (Trommer Reference Trommer2001), on the other hand, focuses on the interaction between morphology and syntax, offering a hybrid of OT and Distributed Morphology (DM). These two authors both contribute chapters to the volume. Linguists working in OT have extended and refined their theoretical specifications as the framework has been applied to more and varied linguistic phenomena. This is fully reflected in this book, which provides a collection that not only embraces a range of developments of the original framework but debates between authors and chapters the relative merits of many of these developments.

The apparently narrow focus on allomorphy is similarly well motivated. The question of allomorph determination is at the very point of interaction between different levels of linguistic analysis. In its simplest form, the phonological realisation of an affix such as the English nominal plural -s, for example, is determined by fully predictable morphophonological rules. It is [s] when it follows a voiceless non-sibilant, [z] when it follows a voiced non-sibilant and [ɪz] when it follows a sibilant. Although fully phonologically determined, this is not a phonological rule, since English allows the occurrence of [s] after voiced sounds, as in monomorphemic words like dance. Suppletive allomorphy, on the other hand, (often) has no phonological motivation. Suppletive past tense forms of verbs in English (go ${\sim}$ went) are determined lexically. A hybrid of these occurs in what is termed Phonologically Conditioned Suppletive Allomorphy, where the phonological form of a stem, for example, determines which allomorph of an affix is used, but the allomorphs are not phonologically related or derivable from a single underlying form.

This collection demonstrates that there is much more variety in both the types of allomorphy and the determining factors than these two extreme cases suggest. There are examples of allomorphy determined by etymology (the German diminutive -lein versus -chen, for example), by syntactic position (pre- or post-nominal adjectives in Catalan, solució dolenta ‘bad solution’, versus mala solució ‘bad solution’) or even semantic/pragmatic factors (Burushaski plural allomorphs for stems denoting humans). Working out how to incorporate all of these factors within a theory that specifies universal constraints is bound to pose challenges.

Another crucial factor in allomorphy is the question of language change. Many synchronic cases of allomorphy can be traced to earlier phonological processes. The English irregular plurals man/men and tooth/teeth, for example, are traces of a vowel harmony process. It is not possible to account for them in a synchronic analysis of English by reference to that process, though, because the process doesn’t function in English today. Complexity is added by the process of analogical levelling. When realisational irregularities, in the form of allomorphy, are left behind by a former phonological process, many languages will rectify the situation by levelling, thereby eliminating the allomorphy. However, these levelling processes are rarely completely consistent, leaving behind unpredictable irregularities.

The chapters in this book describe a wide range of types of allomorphy and illuminate many of the key issues for debate that they give rise to. To what extent can different linguistic levels (phonology, morphology, syntax, etc.) be kept separate? To what extent can rule-governed approaches explain allomorphy and to what extent is it necessary to make use of lexical listing or subcategorization? What can approaches to synchronic allomorphy tell us about processes of language change? What can they tell us about linguistic processing and storage (i.e. the extent to which polymorphemic words are stored whole and to what extent computed online)? These questions and more are addressed in this book.

Several chapters give in depth analyses of one language or a group of languages, while others aim to provide more wide-ranging arguments about the fundamental question of how best to handle the differing degrees of irregularity in allomorphy. The broad distinction here is between accounts that make recourse to phonological constraints and those that rely on lexical determination. Three of the chapters – by the editors, by Trommer and by Wolf – take the view that phonological constraints, such as the emergence of the unmarked, can account for the allomorphy. Two chapters take the opposing view, that lexical determination is required.

The chapters that focus on detailed case studies address a wide range of questions that arise as a result of the specific requirements of the languages addressed. The chapter by Geert Booij & Bert van der Veer, ‘Allomorphy in OT: The Italian mobile diphthongs’, for example, provides an analysis of the so-called ‘mobile diphthongs’ of Italian, where the stressed diphthongs [jɛ] and [wɔ] alternate with the unstressed monophthongs [e] and [o]. It takes into account the influence of diachronic levelling on the synchronic allomorphy. This leads them to consider the roles of storage of forms versus online computation. Since levelling can only feasibly happen when forms are computed online, they argue that the fact that some forms are stored rather than computed can be used to account for apparent irregularity in allomorphy. The chapter by Sharon Hargus, Noel Rude & Virginia Beavert, ‘Obviative prefix allomorphy in Sahaptin and Nez Perce’, similarly appeals to diachronic considerations and argues that their analysis of prefix allomorphy in Sahaptin has implications for theories of language change. They state that, whereas Kiparsky (Reference Kiparsky and Dingwall1978: 41) predicts that levelling will occur and Ohala (Reference Ohala, Downing, Lima and Noonan1992: 229) predicts that extension will occur, their analysis suggests that neither has happened in the development of Sahaptin going right back to Pre-Proto-Sahaptin.

Mary Paster and Wolf both address Phonologically Conditioned Suppletive Allomorphy (PCSA). Paster’s chapter, ‘Phonologically conditioned suppletive allomorphy: Cross-linguistic results and theoretical consequences’, provides a survey of the phenomenon across languages. She surveyed 600 grammars and found 137 examples of PCSA in 67 languages from 29 language families. She compares the two approaches, ranking of phonological and morphological constraints and lexical subcategorization, and concludes that the latter accounts most accurately for the examples she found. Wolf, in ‘Lexical insertion occurs in the phonological component’, directs his attention to two languages: Moroccan Arabic and Dyirbal, examining examples of enclitic and suffix allomorphy where the realisation of the morpheme is determined by the phonological form of the stem to which it attaches. As in his doctoral work (Wolf Reference Wolf2008), he concludes that it is necessary to interleave phonological and morphological constraints.

Patrik Bye’s chapter, ‘The nature of allomorphy and exceptionality: Evidence from Burushaski plurals’, also follows Paster’s view that lexical selection is required to account for the data presented. The case of plural allomorphy in Burushaski (a language isolate spoken in northwestern Pakistan) is a complex case determined by semantic/pragmatic, phonological and lexical factors. He argues that examples such as this suggest a more complex approach to the dichotomies of rule-governed/listed and motivated/arbitrary, especially highlighting the presence of phonologically arbitrary but rule-governed allomorph choice. Bye’s chapter also includes a lengthy appendix providing the data from which his conclusions are drawn – undoubtedly a useful resource in its own right.

Offering an opposing view to that of Paster, Trommer, in ‘Syllable-counting allomorphy by prosodic templates’, suggests that cases that were claimed by Paster to be non-optimizing are actually optimizing, if a stratal organisation of grammar is assumed. Thus, he demonstrates that, if certain extensions to OT are assumed, then recourse to lexical subcategorization is not necessary. This is based on analysis of a subset of the examples presented by Paster. He further suggests other possible analyses taking advantage of a range of developments and extensions of OT.

The chapter by the editors, ‘The prenominal allomorphy syndrome’, offers an examination of allomorphy in pre- and post-nominal position within the DP in Catalan and Spanish. The data they examine involve cases where one allomorph appears in pre-nominal adjectives or determiners but another appears in post-nominal forms. They follow Trommer in claiming that the allomorphy here can be accounted for by means of universal constraints but, like Wolf, they state the need for an interaction between phonological, morphological and syntactic factors. The syntactic position of the forms governs the choice of allomorph.

Donka Steriade & Igor Yanovich’s chapter, ‘Accentual allomorphs in East Slavic: An argument for inflection dependence’, which examines stress patterns of derivatives in Ukrainian and Russian, also proposes that it is necessary to take something of a hybrid view. Their argument is that most OT approaches map relationships between either base and derivative or between input and output. The stress phenomena they aim to account for, however, require a combination of these, since the stress patterns of derivative forms are dependent on the patterns of the allomorphs in the inflectional paradigms of the base. They propose a set of constraints, such as Match Stem Stress, which depend on this interaction.

Finally, Gilles Boyé & Marc Plénat’s chapter, ‘L’allomorphie radicale dans les lexèmes adjectivaux en franc¸ais. Le cas des adverbs en -ment’, gives a detailed analysis of the allomorphy of the adverb forming suffix in French. They present the case that apparent irregularity in the choice of allomorph can be accounted for by appealing to a phonological dissimilation process.

This edited collection of papers describing Optimality Theoretic approaches to allomorphy had a long and difficult gestation. The original editor began the process back in 2006 and after several years of inactivity the reins were picked up by the eventual editing team in 2011, who completed the process in 2015. The result is a collection of nine chapters, one added and two omitted from the original selection. The length of the chapters varies from 25 to 60 pages, but the presence of extensive example datasets in most makes it difficult to judge whether this reflects genuine differences in the length of the text.

The book is not an easy read. The introduction says that the book is aimed at upper level undergraduates or postgraduates. Certainly undergraduates who have a good grounding in OT should be able to follow most of the papers, but it is unlikely that they would want to read the whole book. A solid knowledge of OT as well as earlier frameworks and some familiarity with the phenomena collected here under the umbrella of allomorphy are necessary. Most of the papers are in English, but one is in French. Although I have a reasonably good grasp of French, my knowledge of technical French is not good enough to be able to follow all of the argument, so my summary of it above is based on the summary in the editors’ introduction.

Having said that, the book works well as a collection. The chapters are not isolated, but give the impression of a well-coordinated set of workshop presentations in which the authors refer and respond to each other’s arguments and examples. The very varied datasets give an excellent flavour of the range of phenomena that come under the heading of allomorphy. The analyses also give a good indication of the many and varied extensions to and developments of OT.

There are several chapters which suggest a solution to the problems posed, but on the whole the reflection on the advantages of the solutions and their limitations is well balanced. There are explicit statements of the many questions that still remain to be answered. Refreshingly, there is also calm reflection on the ways in which OT and related frameworks both improve on earlier approaches, such as Generative Phonology, and share some of their limitations. The main takeaway message is that there is still much more work to do.