Nominal and verbal plurality in the Mandara and Ɓata subgroups of Central Chadic

This paper contrasts the strategies for marking nominal and verbal plurality in the Mandara and Ɓata subgroups of Central Chadic, and of-fers some thoughts on their possible origin and development. The Mandara subgroup generally uses an /-a-/ infix for verbs, and the suffix /-ak/-ax/-ah/ for nouns. The Ɓata subgroup uses an /-ə-/ infix for both nouns and verbs, as well as a suffix /-j/ (or /-n/ ) for nouns. In both groups, the strategies used also depend upon the structure of the verb root. Data is provided for several languages, including little-documented languages such as Nzanyi, Bacama and Glavda. The data suggests that vowel infixes may originally have been used for both nominal and verbal plurals throughout Chadic, but the development of specific nominal plural suffixes gradually made the use of vowel infix plurals redundant in nouns. The nominal suffix /- ak/-ax/-ah/ would then have been a sub-sequent innovation in the verbal system for verb roots in the Mandara whose structure was incompatible with an infix strategy.


Introduction
One of the striking features of many Chadic languages is an /-a-/ or /-aa-/ infix which is inserted between adjacent consonants of a lexical root to form a plural of a noun or verb, sometimes in conjunction with certain suffixes (e.g. Hausa /gúlb-íí/ 'stream ', /gúl-àà-b-éé/ 'streams'). This so-called 'internal a' is similar in some respects to the well-known vocalisation patterns of other branches of the Afroasiatic phylum, such as Semitic, Cushitic and Berber, leading some scholars (e.g. Greenberg 1955, Diakonoff 1965 to propose it as a feature of Proto-Afroasiatic. Certainly, it is generally agreed to go back as far as Proto-Chadic as a marker of verbal plurality (Frajzyngier 1977: 52, Newman 1990: 134, Wolff 2009, and possibly also of nominal plurality (Ratcliffe 1996: 302, Newman 2006, although the latter function is less widespread throughout Chadic and has been challenged by Wolff (2009), who suggests that so called 'internal vowels' in nouns are a result of Semitic-like vocalisation patterns with or without various additional (morpho)phonological processes.
As Newman (1990: 38) and Wolff (2009: 161) point out, the phenomenon known as 'internal a' is sometimes used to refer to two distinct types of process: morphological processes (e.g. ablaut, apophony, infixation) and phonological processes (e.g. assimilation/ umlaut). Infixation (a morphological process) occurs when a vowel is inserted between two adjacent underlying consonants, whereas vowel lowering (a phonological process) occurs when an underlying high or mid central vowel (/ɨ/ or /ə/) is lowered to /a/ as an assimilatory effect of a root-final /a/. However, as is shown in this paper, there is good reason to suppose that many reported cases of vowel lowering are actually cases of vowel insertion, since the underlying high vowel can often be analysed as epenthetic. 1 The Central Chadic (Biu-Mandara) languages provide a further variation of the vowel infix strategy in that for some groups, the infix is /-ə-/ rather than /-a-/, although it is quite possible that both infixes share a common origin. Thus it is preferable to talk about vowel infix plurals rather than just 'internal a' plurals. This paper examines plural formations in two of the larger subgroups within Central Chadic: the Mandara (A4) subgroup, which uses an /-a-/ infix, and the Ɓata (A8) subgroup, which uses an /-ə-/ infix. In the Mandara subgroup, the vowel [ə] is typically epenthetic and non-phonemic, whereas in the Ɓata subgroup, /ə/ is typically phonemic, and the epenthetic vowel is [ɨ]. As these two subgroups come from different main branches (North and South) of the whole Central Chadic family, it is possible that they may turn out to be somewhat representative of their respective branches. It is shown that both subgroups use internal vowel strategies in conjunction with other strategies such as reduplication, suffixes and suppletives, with the particular strategy used being largely dependent on the root structure. There are, however, also some important differences between the two subgroups, the main one being that the Ɓata subgroup uses internal vowel plurals frequently for both nouns and verbs, whereas the Mandara subgroup uses it mainly for verbs, although traces of it remain in a subset of kinship terms, suggesting that it was perhaps once more widespread.
The term 'plurality' applied to nouns refers to reference to more than one entity. When applied to verbs, it encompasses various notions of multiplicity of action, including multiple participants (multiple subjects of intransitive verbs or multiple objects of transitive verbs), multiple occasions (e.g. iterative, habitual), and multiple locations (distributive), as well as variations in degree or intensity of action. Newman (1980) coined the term 'pluractional' to refer to any of these senses of verbal plurality, and there has been widespread adoption of the term, particularly in Chadic linguistics. As is shown in the case of Podoko in section 3.6, some languages have developed multiple plural verb forms, which are used to express different types of plurality.

The Central Chadic languages
The Central Chadic languages are geographically clustered around the Mandara mountains along the far northern border between Nigeria and Cameroon, just to the south of Lake Chad. Eberhard et al. (2020) currently list 79 Biu-Mandara languages and classify them using Newman's (1977) proposal, which splits Biu-Mandara into three main branches (A, B and C) with the A branch divided into eight subgroups. Hammarström, Forkel & Haspelmath (2019), on the other hand list 81 languages, and largely follow Gravina's (2011) more recent arrangement, given in Figure   The Mandara languages are all quite closely related, having more than 50% internal lexical similarity, whereas the Ɓata group is less so, with Ɓata and Ɓacama having a rather low lexical similarity with the rest of the group, a likely reflection of their geographical separation to the south, which has led to a different environment for contact-induced change (Gravina 2014: 34-35). Previous research into the languages of both subgroups is somewhat varied, with only Wandala/Malgwa (Löhr 2002), Guɗe (Hoskison 1983), Dghweɗe (Frick 1978), Parkwa (Jarvis 1989), and Glavda (Nghagyiya 2011) having any kind of moderately detailed grammatical description. A couple of others, such as Ɓacama (Pweddon 2001) and Jimi (Djibi n.d.) have published dictionaries, but with little or no grammatical data, and most of the others have shorter unpublished wordlists or basic phonological sketches. This paper brings new data on several languages, including Ɓacama, Nzanyi, Guduf-Gava, and Glavda, so that the analysis is based on roughly half the languages from the two subgroups. Data from Ɓacama, Nzanyi and Glavda was collected between 2005 and 2020, whilst working with speakers of these languages who were students at the Theological College of Northern Nigeria in Jos. Some data was elicited by the author directly from the students, whilst some was collected by the students during their fieldwork, which is referenced at the relevant places in the paper. The students in question were: Kaduwe Ornan and Wama Gabriel (Ɓacama), Ishaya Benson (Nzanyi) and Gulla Nghagyiya (Glavda). Data from Glavda was supplemented by data from a short trilingual phrase book (Nghagyiya 2012). Data from Guduf-Gava was provided by Hak-Soo Kim (personal communication) in September 2019. In most cases, the analysis presented here, particularly with respect to morpheme breaks, is my own, and often differs from that which has been previously reported. Tones were not always marked in the sources consulted, or were marked only sporadically without explanation. In this paper they have been marked when available and relevant to the discussion. In some languages, many of the morphemes concerned, including many verb roots, are inherently toneless and receive their tone from the wider context.

The Mandara subgroup
I start with the Mandara subgroup because this is the group that uses an /-a-/ infix rather than an /-ə-/ infix, and the plural formatives are more phonologically transparent. Nominal and verbal plural strategies are discussed for each language in turn.

Glavda
The general strategy for forming nominal plurals in Glavda is the suffix /-ax/ 5 , as shown in Table 1. Final-vowel deletion: (2) a. ɗaag-ar dauda name-poss.1sg Dauda-fv 'My name is Dauda' b. daud ɗaag-ar-a Dauda name-poss.1sg-fv 'My name is Dauda' From comparative data, it has been shown that most words in Proto-Central Chadic have been reconstructed without final vowels, with just a few words ending in a vowel, which is typically /a/ (Gravina 2014: 354). Therefore in Glavda, it seems preferable to assume that in most cases, final vowels are not part of the root. For those few nouns for which a final /a/ has been reconstructed as part of the root (e.g. /ɬa/ 'cow'), one of the adjacent vowels is deleted when the plural suffix is added. As Nghagyiya (2011: 12) notes, the plural suffix /-ax/ can be reduplicated on nouns, usually indicating sets or groups of items, as shown in example (3): (3) a. ɬ-ax-a b. ɬ-ax-ax-a cow-pl-fv cow-pl-pl-fv 'cows' 'groups of cows' A few nouns, mostly wild animals, can take the plural prefix /jaa-/ (< [jaχa] 'family') instead of the suffix /-ax/, as shown in Table 2. It is possible to analyse /jaa-/ as a separate word rather than a prefix, on the grounds that when it co-occurs with vowel-initial nouns, none of the adjacent vowels are deleted, and such sequences are not attested elsewhere within words. Nouns that take /jaa-/ in the plural can all optionally take /-ax/ instead, with no difference in meaning. It is even possible to use both affixes on the same word, which typically gives the sense of sets or groups of items, just as when the /-ax/ suffix is reduplicated, as shown in example (4), taken from Nghagyiya (2011: 12-13): pl-hare-pl-fv 'groups of hares' As in many languages, a few kinship terms take irregular plurals (e.g. [zra] / [zarχa] 'child' / 'children', [uusa] / [ŋɣʷasaχa] 'wife, woman' / 'wives, women', although they usually still show traces of the /-ax/ suffix, as well as an /-a-/ infix, which becomes more apparent in the light of the Guduf-Gava data. Some agentive nouns appear to take a /li-/ prefix in the plural, but like the /jaa-/ prefix, this likely has a nominal origin, since the corresponding singular forms use the prefix /dada-/, derived (via shortening of the first vowel) from /daad-a/ 'father', as in [dadaɣalga] 'beggar' (lit. 'father of begging') / [li-ɣalga] 'beggars'. It is not clear which nominal /li-/ is derived from, as the plural of 'father' is /daad-ax-a/, but cognate pluralisers are found in the neighbouring languages Lamang and also in Hdi (Wolff 2015, Vol. 1: 121, 389).
Plural verbs in Glavda are formed using an /-a-/ infix, inserted between adjacent root consonants, as shown in Table 3. If the root contains just a single consonant, then the nominal suffix /-ax/ is used. For tri-consonantal roots, some roots contain two /-a-/ infixes in the plural, whereas other roots just have one. A few verb roots contain the vowel /a/, but so far, I haven't come across any such verbs that have distinct plural forms, so it may be that these verbs are considered inherently plural.

Guduf-Gava
Guduf-Gava is closely related to Glavda and uses virtually identical plural morphemes, although not with exactly the same distribution. Hak-Soo Kim (personal communication) reports that the prefix /ja-/ and the suffix /-ax/ are interchangeable on most nouns, and they can also co-occur on the same noun, as in Glavda. His impression is that the /-ax/ suffix is used more for individual plurality, whilst /ja-/ is used more for collectives. The prefixes /dad-/ and /li-/ are again used for some agentive nouns. Plural marking is optional on the noun if there is some other indicator of plurality within the clause (e.g. a quantifier or a plural verb), suggesting that the singular form is actually unmarked for number, as is the case in some other languages of this subgroup. Many nouns in the Guduf dialect of Guduf-Gava 7 end in [e] prepausally, rather than [a], although this is thought to be a dialectal innovation, since /e/ is not a phoneme, and in the Gava and Chikide dialects of Guduf-Gava, most nouns end in [a]. Also, in the plural form, the final vowel is /a/, rather than [e]. Again, this vowel is not considered to be part of the root, and it always takes a low tone, unlike other vowels, which can be either high or low. As far as I am aware, all examples given in this section are from the Guduf dialect. Examples of Guduf-Gava nominal plurals are given in Table 4: Table 4. Guduf-Gava nominal plurals Gloss Singular Plural /sʲg-áx-à/ A few kinship terms use an /-a-/ infix plural strategy, as shown in Table 5. Comparing these with the corresponding Glavda kinship terms which use irregular plurals (Table 6), it can be seen that there are traces of the /-a-/ infix in Glavda as well.
Thus it is possible that the /-a-/ infix in nominal plurals were once more common in both Glavda and Guduf-Gava, but now traces of it only remain in a few kinship terms. At first sight, plural verbs in Guduf-Gava are formed in much the same way as they are in Glavda, with monoconsonantal roots taking the /-ax/ suffix, and other roots using an /-a-/ infix, as shown in Table 7. The citation form of monoconsonantal verbs usually involves a [-gè] or [-ga] suffix, although it is not currently known what determines when each suffix is used.  However, unlike Glavda, several Guduf-Gava verb roots contain vowels (/a/, /i/ or /u/), and these are pluralised with the /-ax/ suffix, like monoconsonantal roots, as shown in Table 8:  Table 9.

Dghweɗe
There is very little data on nominal pluralisation is Dghweɗe, but from what is available (Frick 1977(Frick , 1978, it is possible to see some similarities with both Glavda and Guduf-Gava. Firstly, an /-x/ suffix is used for at least some nominal plurals, and traces of an /-a-/ infix is seen for some kinship terms, as shown in Table 10. Secondly, plural marking on nouns seems to be optional in many cases, and relatively rare in natural texts, again suggesting that the singular form is unmarked for number. There is more data on Dghweɗe plural verbs, and again it is clear that the particular plural strategy used is dependent to a large extent upon root structure. Dghweɗe has three main ways of pluralising verbs: the suffix /-àɗ/, the /-a-/ infix, and reduplication of the last VC segment of the verb root, as shown in Table 11.  For a few monosyllabic verbs, the imperfective suffix [-gè] is also used to express verbal plurality, as shown in Table 12: Thus although Dghweɗe has more variation in verb plural formation than both Glavda and Guduf-Gava, once again, it is verbs with monoconsonantal roots or roots containing a vowel that don't take an /-a-/ infix.

Malgwa
Nominal plurals in Malgwa also resemble those in other languages of the group. The most common strategy involves the suffix /-áh/, in which the voiceless velar fricative /x/ has been weakened (from the perspective of the languages so far discussed) to a glottal fricative. Löhr (2002: 98)  , and as [e] mostly appears to occur only in this position (excluding loan words and words where it is adjacent to a palatalised consonant), I consider it a product of either borrowing or a vestigial trace of a word-level palatalisation prosody, which has been reconstructed for Malgwa and its closest genetic relatives (Gravina 2014: 189). Examples of noun plurals are given in  Malgwa also has a collective plural for people and animals, formed using the suffix /-á/, as shown in Table 14:  As with other languages of the group, most plural verbs in Malgwa are formed using an /-a-/ infix, with monoconsonantal verbs requiring a reduplication of the consonant, as shown in Table 16:  There is currently no data available as to how Malgwa pluralises verbs which contain a vowel phoneme, or contain more than two consonants.

Wandala
Nominal plurals in Wandala are formed using the suffix /-ah/, as shown in Table 17: The plural morpheme is reduced to /a/ when followed by certain modifiers such as determiners, quantifiers and possessive adjectives (e.g. [gʲál-àh-à] 'girls', [gʲál-a-nà] 'the girls'). Traces of /-a-/ infix plural forms are again limited to a few human nouns, as shown in Table 18, which may sometimes also carry the plural suffix /-ah/. on nouns occurs prepausally, and elsewhere indicates that "the constituent that follows, although not part of the same grammaticalized construction should nevertheless be interpreted in connection with the preceding constituent" (e.g. topicalised noun phrases). An alternative explanation is given by Wolff and Naumann (2004) who suggest a final [e] on nouns may have arisen from a monophthongisation of */a-y/ involving the frozen Proto-Chadic determiner */-i/ (see also Wolff 2006Wolff , 2009Wolff , 2019. Frajzyngier also notes that plural marking is optional on nouns if the noun is followed by a numeral (as in Guduf-Gava), although human nouns are more likely to be marked for plurality than non-human nouns.
For verbal plurality, Wandala, like Malgwa, uses an /-a-/ infix for most roots, although some monoconsonantal roots are not reduplicated (c.f. Table 16) and take an /-a/ suffix, as shown in Table 19. For those monoconsonantal roots which appear to have homophonic citation forms for singular and plural (e.g. [và] 'give (sg)' / [và] 'give (pl)'), evidence for the /-a/ suffix in the plural comes from the fact that the final vowel is deleted clause-internally for the singular forms, but remains in the plural. Significantly, all verb roots which contain an /a/ vowel underlyingly (e.g. /pal/ 'pound with hammer or stone', /hal/ 'gather') are inherently plural, although sometimes, in order to make the plurality more specific, an /-à/ suffix is used (e.g. /hàl-à/), as in the case of monoconsonantal roots. As with nouns, the majority of verbs end in /a/ in prepausal position, with a small number ending in /e/. Once again, Frajzyngier (2012: 167-169) makes a perceptive observation about such verbs. He notes that all /e/-final verbs share the semantic characterisation of separation of an entity from its source (e.g. [t͡ sè] 'stand, rise', [plè] 'detach', [fjè] 'peel'). As in the case of nouns, since /e/ is not phonemic, it is most likely either epenthetic or the realisation of an underlying /i/. Evidence for the latter comes from comparative data from Hdi, which has a verbal extension /-i/ which encodes separation from source.

Podoko
In Podoko, as in most other languages of the Mandara group, the bare form of the noun is unmarked for number, with plural marking only present when deemed pragmatically necessary. The main plural marker is the suffix /-aki/, which possibly consists of two different suffixes, /-ak/ and /-i/, as the latter can occur without the former. Some nouns (e.g. [nawə] 'goat') take just /-ak/ and /-i/. Several nouns referring to family members (e.g.
[nəwalə] 'man, husband' and other nouns in the middle section of  The marking of palatalisation before the initial consonant in these examples indicates a word-level palatalisation prosody that fronts all the vowels in a word, although the full application of the prosody depends upon the particular consonants and vowels in the word (Gravina 2014: 185 Verbal plurality in Podoko is also marked in two distinct ways (by an /-a-/ infix, and with an /-aw/ suffix), which may combine on the same lexical item, but are also somewhat dependent upon root structure, as shown in Table 21. For example, monoconsonantal verbs and verbs with a /CaC/ root structure only have plurals with the /-aw/ suffix. Most other verbs use the /-aw/ suffix with or without an /-a-/ infix. A few verbs use suppletive plurals (e.g. [kəɗ] 'kill (sg)', [paɬ] 'kill (pl)', although it appears that most suppletive plurals contain the vowel /a/. Interestingly, some verbs use each of these strategies to form two distinct plural forms, with a functional difference between them: an /-a-/ infix strategy alone is used for multiple subjects of intransitive verbs and multiple objects of transitive verbs, but both strategies are used together when the plurality or repetition of the action is highlighted (e.g. habituality).

The Ɓata subgroup
Much of the existing literature on internal vowel plurals in Chadic languages discusses only languages which use an /-a-/ infix or a vowel lowering or vowel lengthening strategy (Newman 1990: 37-41 (nouns), 72-76 (verbs)). The idea of an /-ə-/ infix strategy has often been overlooked because it is harder to spot. This section hopes to show that it is relatively common in both nominal and verbal plurals, at least in the languages of the Ɓata subgroup. The difficulty in noticing it stems from the fact that the pronunciation of the phonemic vowel /ə/ and the epenthetic vowel /ɨ/ are affected by neighbouring palatalised and labialised segments in ways in which an /a/ vowel is not. However, once the phonological rules of consonant-vowel interaction are properly understood, the use of the /-ə-/ infix becomes clear, and avoids the need to posit a lot of seemingly random vowel change rules. It also links pluralisation strategies across the whole of the Central Chadic family more transparently, as it is reasonable to suppose that the /-a-/ infix and the /-ə-/ infix ultimately have the same origin. One possibility is that synchronic /ə/ in the Ɓata subgroup derives historically from short */a/ in Proto-Ɓata, and syn-  15 The languages of the Ɓata subgroup are much less well documented than those of the Mandara subgroup, but hopefully this section provides enough evidence to present a basis for the case that an /-ə-/ infix strategy is actually fairly common.

Sharwa
Sharwa, like Ɓacama and Nzanyi in the Ɓata subgroup can be analysed with two phonemic vowels /a/ and /ə/, as well as an epenthetic /ɨ/. The pronunciation of /ə/ and /ɨ/ is affected by neighbouring palatalised and labialised segments, as summarised in Table 22. Limited data is available on Sharwa, but what exists shows some evidence that an /-ə-/ infix is used for some nominal and verbal plurals, as shown in Table 23 and Table 24. Many nominal plurals also take a suffix /-j/, which is a common plural suffix on nouns in the Ɓata subgroup. The data is taken from Gravina (2009), who analyses the /ɨ/ as phonemic, even though he reports that it is often unrealised between consonants (and thus has zero as an allophone), and could be considered epenthetic. /kʷakʷr-ə/ [kʷakori] /kʷakʷ-ə-r-j/ 'bank' [dɨglə] /dgl-ə/ [dʲegəli] /dʲ-ə-g-ə-l-j/ Note that in the words for 'hoe' and 'bank', one of the root consonants is palatalised in the plural, which is a common feature of plural nouns in some languages of the Ɓata subgroup. Synchronically, it is analysed as a word-level prosody which affects certain root consonants (with laminals and alveolar consonants preferred over labials), but historically, it was likely caused by a *-j suffix, which is still common on many nouns (Gravina 2014: 318).  (Gravina 2009: 14). Thus in Jimi, verbal plurals are formed by the insertion of the vowel /i/, pronounced as a long vowel [ii], as in Table 25: No data is currently available on Jimi nominal plurals, although Jimi is closely related to Guɗe, which is discussed later in this paper.

Ɓacama
Ɓacama has the same two phonemic vowels as Sharwa (/a/ and /ə/) and the same rules for pronunciation (Table 22), with the exception that /ə/ is pronounced as [e] word-finally before a pause or a major syntactic boundary. Noun roots either end in /a/ or a consonant, in which case /ə/ is affixed to the end of the root. This final /-ə/ is usually still present in the singular mid-phrase, but it is sometimes deleted in the plural, although it is currently not clear what determines this deletion since it doesn't appear to be optional. The general plural marker is the suffix /-j/, which attaches to the end of the root, but roots that don't contain a vowel also have /ə/ inserted between the consonants in the plural, as shown in Table 26. Some roots also have a /-g/ suffix added in the plural between the root and the general plural suffix /-j/. /-j/ also functions as a prenominal quantifier meaning 'some, other' (e.g. [i mandi] /j maⁿd-j/ 'some, other women', [i dʷe] /j dʷa-j/ 'some, other pots').
Identifying an /-ə-/ infix in the plural, along with understanding the regular phonological rules affecting the pronunciation of vowels, provides a relatively straightforward analysis which fits in nicely with comparative data. Adjectival modifiers also take an /-ə-/ infix in the plural, although those that are derived from verbs (e.g. /kltə/ 'swell, inflate') do not also take the /-j/ plural suffix, as shown in Table 27: Verbal plurals are particularly interesting, since they use either an /-a-/ infix or an /-ə-/ infix depending on whether the root ends in /a/, as shown in Table 28. A similar situation also holds in Guɗe. This suggests that /-a-/ infix and /-ə-/ infix are underlyingly the same morphological process, with /a/ and /ə/ being phonologically   Note from the verb /zaᵐbɹ-ə/ 'hit' that if a root contains an /a/, but doesn't end in /a/, the /a/ in the root is replaced by /ə/ in the plural. This would constitute one of the few cases of vowel replacement.

Nzanyi
Nzanyi as the same vowel phonemes (/a/ and /ə/) and phonological conditioning as Sharwa, and like Sharwa and Ɓacama, a /-j/ suffix is used in nominal plurals, along with an /-ə-/ infix if the root contains adjacent consonants, as shown in Table 29. As in Ɓacama, some nouns also take a /-g/ suffix in the plural, and it is possible that this segment was originally part of the root but has been lost in the sin-gular, since included in such nouns are all nouns that end in [o] in the singular. However, it also possible that the /-gi/ suffix is a remnant of the Proto-Chadic nominal plural suffix *-aki. Some nouns whose polyconsonantal roots end in /a/ take an /-a-/ infix in the plural, whilst for others, the only change is a replacement of the final /a/ with the /-j/ suffix, as shown in Table 30. Plural verbs in Nzanyi are yet to be fully investigated, but preliminary findings suggest that Nzanyi uses the same strategy as Ɓacama does, except that monoconsonantal roots are reduplicated, as shown in Table 31:

Guɗe
Guɗe has been left to last because it has the most complicated phonology which is far from transparent. Hoskison (1975Hoskison ( , 1983 analyses Guɗe with four vowel phonemes /a/, /ɨ/, /aa/ and /ɨɨ/. However, it is possible to consider [ɨ] as an epenthetic vowel, and [ɨɨ] as the realisation of the phoneme /ə/. Such an analysis makes both the underlying vowel system and the morphology of nominal and verbal plurality more typologically consistent, since it has the same system as Sharwa, Ɓacama and Nzanyi, and the nominal plural suffix /-j/ is clearer to see. In many cases, it also helps to show more consistency among lexical roots across the group. Singular nouns in Guɗe fall into two basic lexical categories: those which take a petrified /-n/ suffix, and those which do not. Those which do not can be split into two further groups: those whose final /a/ disappears before another word, and those whose final /a/ remains. Most plural nouns also take the /-n/ suffix. The main synchronic plural features are the suffixes /-nʲ/ or /-j/, or palatalisation of the final root consonant and sometimes other root consonants as well. A small subset of nouns take the irregular plural suffixes /-gʲ/ or /-sʲʔʲ/ instead. Generally, singular noun stems which end in a consonant (plus all loanwords) take the /-nʲ/ suffix, and stems which end in /a/ replace the /a/ with the /-j/ suffix, as shown in Table 32. A few /a/-final stems can optionally take the /-nʲ/ suffix instead. Plural nouns which don't take either of the plural suffixes /-j/ or /-nʲ/ palatalise the final consonant of the root instead, and sometimes other consonants as well, with a preference for coronal consonants over non-coronal consonants, and labials over velars, as shown in Table 33.

Conclusion
It is often the case that looking at the morphological patterns of a group of closely related languages yields insights into the analysis of individual languages within the group, and this has certainly been the case in this paper, where new morphological analyses of plural marking in individual languages has yielded a remarkable degree of internal consistency within the groups. A number of general observations can be made regarding nominal and verbal plurality within each group as summarised here. The Mandara subgroup typically uses an /-ax/ suffix for nominal plurals, sometimes in conjunction with an /-a-/ infix. It is certainly possible that this suffix is a reflex of the best attested and most widespread Proto-Chadic nominal plural suffix *-aki. Indeed, Newman (1990: 19) suggests that /-ak/ could be a reflex of *-aki in Musgu, another Central Chadic language, and so it would be easy to see how /-ax/ (or /-ah/ or /-aw/) could also be reflexes of this, especially given that the suffix has the form /-ak/ in Podoko. If the /-a-/ infix does go back to Proto-Chadic, as tentatively suggested by Newman (2006: 195), the vestigial traces of an /-a-/ infix in a basic subset of kinship terms in several languages of the Mandara group is certainly compatible with such an idea. Podoko is interesting in that both the /-ak/ suffix and /-a-/ infix strategies have become rather mixed, with nouns taking one or the other (or both) on a seemingly random basis. Another feature of plural marking in the Mandara group is that the singular form is actually unmarked for number, or to be more precise, the unmarked number form can be used with both singular and plural reference. The marked plural form is used only when specific plural reference is deemed pragmatically necessary.
For verbal plurality, it is clear (in all cases except Podoko) that different strategies are employed depending on how many consonants the root contains, and whether the root contains a vowel. Such strict conditioning of verbal plurality strategies was first pointed out for Lamang by Wolff (1983: 107). An /-a-/ infix is the preferred strategy for vowel-less polyconsonantal roots, with the /-ax/ suffix generally used elsewhere. Less common strategies include partial reduplication, and an /-aɗ/ suffix in the case of Dghweɗe. Podoko is the exception in that both an /-aw/ suffix and the /-a-/ infix are used in a seemingly haphazard manner, regardless of root structure, but given the similar situation for nouns, this is hardly surprising.
It therefore seems likely that the /-ak/, /-ax/, /-ah/ and /-aw/ suffixes found in the Mandara subgroup are reflexes of the same PC plural marker *-aki. Newman (1990) presents *-aki as a PC nominal suffix and *-aw as a tentative PC verbal suffix, but it is perhaps possible that both have the same origin, especially as he also posits *-ɗ(i) as a possible PC nominal suffix and *-ɗ as a possible PC verbal suffix. Frajzyngier (1977: 37) suggests that such extensive similarities between nominal and verbal plurality can hardly be accidental, although Newman (1990: 86) essentially claims that they are, with Wolff (2009) also suggesting an alternative explanation for nominals. Given that an /-a-/ infix is much more widespread in Chadic as a marker of verbal plurality than nominal plurality, Frajzyngier (1977: 51-52) suggests that it originally started out as a marker of verbal plurality and then some languages transferred it into the nominal system. As borrowing often goes in both directions, given that the suffix *-aki is much more widespread as marker of nominal plurality, it is at least possible that this suffix was borrowed in the opposite direction, particularly for verb roots whose structure made the /-a-/ infix strategy difficult (e.g. monoconsonantal verbs, and verbs which already contained an /a/ vowel). The Podoko data raises a further interesting question, namely whether that the PC *-aki suffix could actually comprise two separate PC suffixes *-ak and *-i, as *-i is also generally accepted as a PC nominal plural suffix (Newman 1990: 48). The Ɓata group most widely uses a /-j/ suffix to mark nominal plurality, presumably originating from the PC nominal plural suffix *-i. In some languages, this suffix has become incorporated into the root, surfacing as palatalisation of the final consonant and often other consonants as well. Infixed vowel plurals are also common, and it is interesting to note that, just as in the verbal plurals of the Mandara group, the internal vowel strategy for nominal plurals of the Ɓata group is somewhat dependent upon root structure. An /-ə-/ infix is the default strategy, but for roots which end in /a/, an /-a-/ infix is preferred. If the /-ə-/ infix is an historically reduced form of /a/, then one could say that a final /a/ blocked the weakening of an original medial */a/ to /ə/. Roots which already contain a vowel, for which an infix vowel strategy wouldn't be appropriate, the usual /-j/ suffix normally suffices. Less common plural suffixes include /-gi/ and /-n/, which are presumably vestigial traces of the PC nominal plural suffixes *-aki and *-n.
For verbal plurals, vowel infix plurals are almost exclusively used, with both /-ə-/ and /-a-/ being used according to whether the root ends in /a/, again compatible with the idea that a final /a/ blocked the weakening of medial /-a-/ to /-ə-/. In Jimi, the reflex of pan-Ɓata /ə/ is [i], whilst in Guɗe, it is [ɨɨ]. For monoconsonantal roots, reduplication is also sometimes used, as an infix vowel strategy alone would not be feasible.
Looking at both groups, is it possible to draw any possible conclusions about pluralisation strategies in Central Chadic as a whole? Such an undertaking would certainly need to look at other subgroups as well in at least as much detail as this paper has done for the Mandara and Ɓata groups. Given that infixed vowel nominal plurals are still relatively common in the Ɓata group, with remnants of it in the Mandara group, an initial hypothesis could be that infixed vowels were originally used for marking verbal plurality (a generally undisputed claim) and at some point early in the history of Central Chadic were adapted by the nominal system for marking plurality on certain nouns, or for certain semantic distinctions or pragmatically marked situations. Then, as the use of existing nominal plural suffixes inherited from Proto-Chadic became more systematic, the use of infixes gradually became more restricted and largely disappeared, with vestigial traces of them now discernable only among certain kinship terms, which is precisely where one might expect to find remnants of archaic systems (cf. the -en plural suffix in English (e.g. 'children', 'brethren')). In the case of the Mandara group, the dominant nominal suffix was */-ak/, and in the case of the Ɓata group, the nominal suffix was mostly /-j/, with /-n/ also found either as a petrified trace of the PC plural demonstrative determiner */-n/ or as the distinct PC nominal plural suffix */-n(a)/. As noted above, there may also have been borrowing going on in the opposite direction, particularly among verbs whose roots made the use of infixes problematic. This would explain the various overlaps between nominal and verbal plurality in both groups beyond the use of vowel infixes. Hopefully, as