2.1. Quantitative approaches to modelling reanalysis

Existing quantitative models of reanalysis (or more generally of morphophonological paradigm learning) are inductive, and therefore predict change to be driven purely by statistical distributions. One representative model of this variety is the Minimal Generalisation Learner (MGL; Albright Reference Albright2002; Albright & Hayes Reference Albright and Hayes2002; Albright & Hayes Reference Albright and Hayes2003 et seq.).

The MGL first compares different members of the paradigm, and learns word-specific rules mapping from one form to another. For the MHG pattern introduced above, the MGL would generate rules like those in (2). When forms share the same change, the model finds what features they share in common, and generalises rules based on these shared features. For example, a rule $\varnothing \rightarrow $ ə / [ $-$ voice, $-$ continuant] _ _# may be generated from a comparison of (2a) and (2b). The result is a system of stochastic rules which predict the inflected form of a paradigm given an input base.

In the MGL, reanalysis occurs when the grammar derives the incorrect output for certain derived forms, and these errors come to replace the older, exceptional forms. This model has been shown to explain the direction of historical restructuring in various languages, including Lakhota (Albright Reference Albright2008b), Yiddish (Albright Reference Albright2010) and Korean (Kang Reference Kang2006). Details of model implementation can be found in Albright & Hayes (Reference Albright and Hayes2003). What is important to note is that this model learns rules inductively, and predicts reanalysis to be in the direction of the statistically most probable outcome, given the distribution of sounds in a paradigm.

The MGL is rule-based, and generates sets of rules that predict the outcome of paradigm reanalysis. An alternative analogical approach is exemplified by the Generalised Context Model (GCM; Nosofsky Reference Nosofsky, Pothos and Wills2011). This approach is ‘similarity-based’, meaning that in principle, any words that are similar enough to each other can serve as the basis for reanalysis. Broadly speaking, similarity-based models are less restrictive than rule-based models, and are potentially able to capture a wider range of effects (Albright & Hayes Reference Albright and Hayes2003). However, both approaches predict that reanalysis will match the distributions of the input data.

Inductive learning is also possible in stochastic constraint-based models such as Maximum Entropy Harmonic Grammar (MaxEnt; Smolensky Reference Smolensky, Rumelhart and McClelland1986; Goldwater & Johnson Reference Goldwater, Johnson, Spenader, Eriksson and Dahl2003). As a preview, in §4, an inductive constraint-based model will be used as a baseline, and compared to models which incorporate learning biases.

2.2. Malagasy phonology and weak stem alternations

Malagasy, the national language of Madagascar, is an Austronesian language belonging to the Malayo-Polynesian subgroup (Rasoloson & Rubino Reference Rasoloson, Rubino, Adelaar and Himmelmann2005). The term Malagasy really refers to a macro-language that covers many dialects distributed throughout Madagascar (Lewis et al. Reference Lewis, Simons and Fennig2014). The following study uses data from Official Malagasy (OM), which is the standardised, institutional dialect that is based on the Merina dialect spoken in the capital city Antananarivo. All subsequent descriptions and analysis will assume data from OM.

Malagasy has inflectional and derivational morphology, much of which involves morphophonological alternations. In a subset of so-called ‘weak-stem’ consonant alternations, the expected alternant (based on historical evidence) often does not match the observed alternant, suggesting that substantial reanalysis has occurred.

Malagasy has been studied extensively. The phonetic system is described by Howe (Reference Howe2021), and basic facts on the morphology and phonology are documented in work such as Keenan & Polinsky (Reference Keenan, Polinsky, Spencer and Zwicky2017) for OM, and O’Neill (Reference O’Neill2015) for the closely related Betsimisaraka dialect. Formal analyses of Malagasy phonology, including of weak stem alternations, have been done in both generative rule-based frameworks (Dziwirek Reference Dziwirek1989) and OT (Albro Reference Albro2005). Moreover, the history of Malagasy can be traced in some detail through the work of Austronesianists (e.g., Dahl Reference Dahl1951; Mahdi Reference Mahdi1988; Adelaar Reference Adelaar2013). Additionally, dictionary data are digitised in the Malagasy Dictionary and Encyclopedia of Madagascar (MDEM; de La Beaujardière Reference de La Beaujardière2004), which compiles data from multiple Malagasy dictionaries. Historical comparative data are also available in the Austronesian Comparative Dictionary (ACD; Blust et al. Reference Blust, Trussel and Smith2023).

In this section, I provide a descriptive account of Malagasy phonology and weak stem alternations, based on work by Keenan & Polinsky (Reference Keenan, Polinsky, Spencer and Zwicky2017) and Howe (Reference Howe2021).

2.2.1. Malagasy phonology

Malagasy words have a strict (C)V syllable structure, where codas are not allowed. Word stress is phonemic but generally penultimate, though there are exceptions to be discussed in the following section.

Malagasy has five phonemic monophthongs /i e a o u/. /o/ is considered to be non-phonemic (or marginally phonemic) in many descriptions of Malagasy (e.g., Rasoloson & Rubino Reference Rasoloson, Rubino, Adelaar and Himmelmann2005; O’Neill Reference O’Neill2015). However, it has become much more common because /ua/ and /au/ sequences have merged to /o/ in many dialects, including OM (Howe Reference Howe2021). The consonants of Malagasy are given in Table 1. /ŋ/ is included in parentheses because although it is non-phonemic in OM, it is phonemic in many dialects of Malagasy.

Table 1

Malagasy consonants.

All subsequent examples are presented in IPA, with the following caveats. Prenasalised obstruents are written as nasal–obstruent sequences (e.g., mb corresponds to [ᵐb]). [ʈʂ] and [ɖʐ] are generally retroflexed, but can vary in production between speakers (Howe Reference Howe2021), and have been described in prior work as postalveolar (e.g., Keenan & Polinsky Reference Keenan, Polinsky, Spencer and Zwicky2017). In addition, [r] is a short alveolar trill in most dialects, including OM, but is often realised as a tap [ɾ] in casual speech (Howe Reference Howe2021).Footnote ¹

2.2.2. Weak stems

Malagasy has a class of forms that Keenan & Polinsky (Reference Keenan, Polinsky, Spencer and Zwicky2017) refer to as weak stems. These roots have antepenultimate stress (if long enough), and always end in one of the three ‘weak’ syllables [ʈʂa], [ka] or [na].Footnote ²

When weak stems are suffixed, the consonant of the weak syllable ([ʈʂ], [k] or [n]) may alternate with another consonant. Patterns of alternation are summarised in Table 2, using the active and passive forms of verbs. In addition to these alternants, the lexicon also contains four words that exhibit minority patterns, including stems where final ʈʂa alternates with [s]. I exclude these here because they are so low in frequency that they do not affect my analysis, but they are given in the Appendix (Table A1) for reference. In the suffixed forms, the final vowel of the weak stem is not present, leaving the alternating consonant at a morpheme boundary. As demonstrated in these examples, suffixation also shifts stress one syllable to the right.

Table 2

Patterns of consonant alternation in Malagasy weak stems.

Note that even though the weak stem alternants are neutralised in stem-final prevocalic position, the same phonemes are fully contrastive in other positions (i.e., in initial and medial position). Table 3 provides minimal pairs that demonstrate this. For example, /t/ and /r/ are neutralised to [ʈʂa] in unsuffixed weak stems, but are contrastive as demonstrated by minimal pairs like [atu] ‘close at hand’ and [aru] ‘barrier, rampart’.

Table 3

Minimal pairs showing that weak stem alternants are contrastive.

The standard formal analysis for weak stems is that they are underlyingly consonant-final (Albro Reference Albro2005). For example, the surface forms [m-iˈanaʈʂa] $\sim $ [iaˈnar-ana] would have the stem UR /ianar/, with surface forms derived as in (3). First, all words are assigned penultimate stress, and the stem-final consonant is neutralised to [ʈʂ], [k] or [n] (here, /r/ neutralises to [ʈʂ]). In the suffixed form, /r/ is medial and therefore protected from neutralisation. Finally, an epenthetic /a/ is added to resolve the violation against codas (counterbleeding the final-C neutralisation). Antepenultimate stress falls out naturally from this rule ordering, because stress assignment precedes vowel epenthesis. As I discuss below, the analysis in (3) is in fact a recapitulation of the historical development of weak stem alternations.

• 

2.2.3. Historical development of weak stem alternations

The linguistic history of Malagasy has been studied in detail. The following description summarises findings from a large body of scholarship, including Dahl (Reference Dahl1951), Hudson (Reference Hudson1967), Mahdi (Reference Mahdi1988) and Adelaar (Reference Adelaar2012, Reference Adelaar2013).

Malagasy weak stem alternations started as a series of relatively common final consonant neutralisations, which were subsequently obscured by a process of final vowel epenthesis. Vowel epenthesis was motivated by a phonotactic restriction against codas which developed around 600 C.E., when speakers of Proto-Malagasy migrated from Kalimantan into the Comoro Islands. Contact with Bantu during this migration significantly influenced Malagasy grammar, and is largely thought to have caused the development of final open syllables in Malagasy. For most final consonants, epenthesis of a final vowel removed final codas, resulting in the weak stems of current Malagasy.

The development of Malagasy from Proto-Austronesian (PAn) can be broadly be split into three stages: Proto-Malayo-Polynesian (PMP), Proto-Southeast Barito (PSEB) and Proto-Malagasy (PMlg). The examples in (4) trace a subset of weak stems through these stages, to illustrate the historical development of some weak stem alternations.Footnote ³

(4a) illustrates the development of ʈʂa $\sim $ t alternating weak stems, which historically end in voiceless coronal stops, in this case *t. Final *-t neutralised to *-ʈʂ in PMlg; this affected the non-suffixed forms, while stem-final [t] was preserved in suffixed forms. Following this, epenthesis of a final vowel resulted in the current ʈʂa $\sim $ t alternation.

In (4b), on the other hand, the PMP stem ends in *D [ɖ]. In the non-suffixed form, this final consonant devoiced to *-t and then neutralised to [ʈʂ]. In the suffixed form, *D lenited to [r] due to regular sound change (*D > r; Adelaar Reference Adelaar2012). This was followed by final vowel epenthesis, resulting in the observed ʈʂa $\sim $ r alternation. Note that while final devoicing (*-D > -t) and lenition (*D > r) are both thought to have taken place in PSEB, devoicing must have preceded lenition for the observed alternations to be possible.

Examples (4c) and (4d) provide similar illustrative cases for ka-final alternations. First, in PMlg, historical *k spirantised to [h] intervocalically (before the epenthesis of final vowels). This affected the stem-final *-k of suffixed forms, but not the unsuffixed forms, resulting in ka $\sim $ h alternations, as shown in (4c). The development of ka $\sim $ f alternation follows from a similar process, given in (4d). First, *-p and *-k neutralised to [-k] word-finally. This affected the unsuffixed form, but not the suffixed forms, where stem-final *p is intervocalic. This was followed by spirantisation in the suffixed forms from *p $>$ [f].

• 

Table 4 summarises all the expected weak stem alternants in Malagasy, given the historical final consonants in PMP. In general, the historical origin of weak stems are well-understood, and the observed alternants in modern Malagasy are expected to correspond to specific historical final consonants.

As a caveat, most consonant-final PMP forms reflect as weak stems in Malagasy, but there are three exceptions. First, PMP *s, *q, *h were deleted in all environments in PSEB, so do not result in consonant alternations. Additionally, PMP glides *w,*y [j] deleted or coalesced with the preceding vowel in final position, and hardened to *v and *z elsewhere. Stems with a historic final glide therefore have $\varnothing {\sim} $ C alternations in modern Malagasy (e.g., [ˈlalu $\sim $ laˈluv-ana] <*lalaw, ‘pass without stopping’). Finally, *s in early Malay loanwords was deleted word-finally, but retained in other positions. These forms have $\varnothing {\sim} $ s alternation in modern Malagasy (e.g., [miˈlefa $\sim $ leˈfas-ana] <*ləpas (Malay) ‘gone, escaped’). The reflexes of different PMP final consonants are summarised in Table 5.

Table 4

Weak stem alternants and corresponding historical consonants.

Table 5

Malagasy reflexes of stem-final PMP consonants.

Where there is a lot of mismatch between the expected alternant (given the PMP final consonant) and the actual alternants observed in Malagasy, this suggests that reanalysis has occurred. Examples of mismatches are given in (5). In (5a), for example, [ˈlumuʈʂa] is expected to have [t] as the alternant because the stem historically ended in *t. Instead, the alternant that surfaces is [r], indicating reanalysis in the direction of t $\rightarrow $ r. As will be seen in §3, the ʈʂa-final weak stems, in particular, seem to have undergone extensive reanalysis, and often do not surface with the expected alternant given the PMP final consonant.

• 

In fact, in modern-day Malagasy, weak stem alternations appear to be partially conditioned by phonological factors, and partially dependent on the historical final consonant. Mahdi (Reference Mahdi1988), in one of the most comprehensive studies of Malagasy weak stems, notes the following generalisations. First, na-final weak stems usually alternates with [n], but may alternate with [m] if the stem-final consonant was historically *m. Final ka usually alternates with [h], but may alternate with [f] if the historical stem-final consonant was labial, or if the nearest consonant in the stem is [h]. In other words, alternation in ka-final weak stems is partially driven by a dissimilative pattern.

For final [ʈʂa], Mahdi again finds a dissimilative effect. Specifically, in present-day Malagasy, [ʈʂa] alternates with [r] in general, but will alternate with [t] if the stem already contains an [r]. Where there are exceptions to this pattern (i.e., where the alternant is [t] or [f] in a non-dissimilatory environment), it is because the historical final consonant was historically *t, *p or *b.

Mahdi’s findings (and existing work on Malagasy weak stems) have noted the connection between Malagasy alternants and their historical consonant. However, they have not focused on exactly what direction reanalysis happened in, or why there is so much mismatch between the historical consonant and observed alternant in modern-day Malagasy.

3.1. Predicted reanalyses under an inductive approach

In a purely inductive model of morphophonological learning, reanalysis would always be in the direction of the more frequent alternant (subject to phonological conditioning). The alternants predicted under this approach can be approximated by looking at the distribution of final consonants in PMP, before extensive reanalysis had taken place. Table 7 shows the distribution of all PMP protoforms with final consonants which would be reflected as weak syllables in Malagasy ( $n=805$ ). Results are organised by the alternant each PMP final consonant would correspond to.

Table 7

Expected distribution of Malagasy weak stem alternants, based on the distribution of PMP final consonants.

There is one complication when [f] is the alternant. Historically, final *-p and *-b neutralised to either *-k or *-t, with a slight bias towards *k (Dahl Reference Dahl1951; Adelaar Reference Adelaar2012). Consequently, PMP forms ending in a labial stop tend to reflect as ka-final weak stems, but also often reflect as ʈʂa-final weak stems. In Table 7, all PMP forms ending in labial stops are assumed to correspond to ka-final weak stems in Malagasy. This simplification should not impact the analysis, since ʈʂa $\sim $ f alternating forms make up a very small proportion of ʈʂa-final weak stems ( $n=7$ , $\approx $ 2.4%).

From this data, we see that ka-final weak stems have more h-alternating forms, na-final weak stems have more non-alternating forms, and ʈʂa-final weak stems have more t-alternating forms. An inductive approach predicts that reanalysis should generally be in the direction of these more frequent alternants. For example, reanalyses of ʈʂa-final stems should be in the direction of r $\rightarrow $ t, rather than t $\rightarrow $ r. Predictions are summarised in the rightmost column of Table 7.

Mahdi’s (Reference Mahdi1988) findings on dissimilatory effects in weak stems are also partially replicated in the PMP data. Consider (7), which summarises the protoforms corresponding to ʈʂa-final stems by whether or not there is a preceding (non-final) [r]. PMP *r,*d and *j (in non-final position) are coded as corresponding to Malagasy [r], but excluded if they occurred as the first consonant in a CC cluster. This is because consonant clusters were historically simplified in PMP by deleting the first consonant (e.g., vavaʈʂa < *bajbaj).

From this data, there appears to be evidence for r-dissimilation. Out of the 28 protoforms coded as containing a preceding [r], only one would reflect as [t]-alternating in Malagasy. Put another way, when the expected alternant is [r], only one form was coded as containing a preceding [r] ( $n=1/52$ , 2%). In contrast, when the expected alternant is [t], 27 forms have a preceding [r] ( $n=27/163$ , 17%).

For ka-final weak stems, the evidence for a dissimilatory pattern in PMP is weaker. If dissimilation were present, we would expect the proportion of stems with an immediately preceding *k (corresponding to [h] in modern Malagasy) to be smaller when the expected alternant is [h]. When the expected alternant is [h], around 7% ( $n=13/183$ ) of protoforms have a preceding *k. When the expected alternant is [f], 22% of forms ( $n=9/42$ , 21%) have a preceding *k. In other words, there is a dissimilatory pattern, but it is weaker than the r-dissimilation pattern observed in (7).

3.2. Observed directions of reanalysis

In this section, I discuss form-by-form comparisons of PMP stems to their weak stem reflexes. Where there is a mismatch between PMP and Malagasy, the direction of reanalyses can be inferred. The ACD contains 143 protoforms that reflect as productive suffixed forms in Malagasy. Fifty-six protoforms were removed following the exclusionary criteria discussed above, leaving 87 forms to be analysed. The data are also supplemented with 49 Malay and Javanese loanwords from the World Loanword Database (WOLD; Adelaar Reference Adelaar, Haspelmath and Tadmor2009) and Adelaar (Reference Adelaar1994). These are all early loans, introduced to Malagasy before the development of weak stems (Adelaar Reference Adelaar1989). Tables 8–10 summarise whether the alternant observed in Malagasy matches the expected one given the historical consonant (or in the case of loanwords, the final consonant of the source word).

Table 8

Expected (PMP) vs. observed (Malagasy) alternant of na-final stems, based on known protoforms and loanwords.

Table 9

Expected vs. observed alternant of ka-final stems, based on known protoforms and loanwords.

Table 10

Expected vs. observed alternant of ʈʂa-final stems, based on known protoforms and loanwords.

Table 8 shows the results for na-final weak stems. The column named ‘PMP’ shows the expected alternant given the PMP protoform, while the column named ‘Mlg’ shows the actually observed alternant in Malagasy. Mismatches between PMP and Mlg indicate that a reanalysis has occurred. Overall, there are relatively few reanalyses ( $n=3$ ), but most are in the direction of m $\rightarrow $ n (e.g., [ˈlalina $\sim $ lalˈin-ina] $<$ *dalem ‘inside, deep’). This is in line with the predictions of an inductive approach.

Of the stems expected to be n-alternating, only one has been reanalysed in the direction of n $\rightarrow $ m ( $n=1/39$ , 3%); the reanalysed stem is [ˈtenona $\sim $ teˈnom-ina] (<*tenun) ‘to weave/be woven’. Given the lack of data, it is hard to tell what the cause is.Footnote ⁵ Overall, comparisons for the na-final weak stems are tentatively in line with a statistical learning approach.

Table 9 shows the reanalyses for ka-final weak stems. Once again, there are relatively few cases of reanalyses ( $n=2$ ). However, both case are in the direction of f $\rightarrow $ h (e.g., [ˈaʈʂika $\sim $ fiaˈʈʂeh-ana] $<$ *qadep ‘face, facade’), in line with the predictions of an inductive approach. In contrast, there are no reanalyses in the direction of f $\rightarrow $ h.

Note that the data did not contain any stems where the immediately preceding consonant is [h]. As such, it is unclear whether a dissimilatory effect was active in the reanalysis of ka-final weak stems. However, one item, which was excluded because it was only reconstructed to PWMP (Proto-Western Malayo-Polynesian), shows reanalysis in the direction of h $\rightarrow $ f that could potentially be attributed to h-dissimilation. This word, [ˈlauka $\sim $ laˈufana] (<PWMP *lahuk) ‘meat/relish eaten with rice’, historically had a preceding [h] which was subsequently elided in PSEB.

Table 10 shows results for ʈʂa-final weak stems. The rightmost column, ‘Has r?’, indicates, for each row, the number of forms which had an [r] in the stem. For ʈʂa-final stems, extensive reanalysis has occurred towards [r]. Of the stems that were historically expected to have [t] as the alternant, over half ( $23/40$ , 57%) have been reanalysed in the direction of t $\rightarrow $ r (e.g., [ˈhudiʈʂa $\sim $ huˈdir-ina] $<$ *kulit, ‘skin, hide’). In contrast, when the expected alternant is [r], there is only one case of reanalysis ( $n=1$ ). Moreover, the one case of reanalysis in the ʈʂa $\sim $ f alternating forms is in the direction of f $\rightarrow $ r ([ˈhalaʈʂa $\sim $ aŋaˈlar-ina] < *alap, ‘theft, robbery’).

Additionally, r-dissimilation appears to be active in the reanalysis of ʈʂa-final weak stems, in that reanalysis to [r] is blocked if the stem has a preceding [r]. As seen in Table 10, when the alternant was reanalysed to be [r], the stem never contained a preceding [r]. In addition, out of the t-alternating stems that were not reanalysed, a relatively larger proportion ( $n=7/17$ , 41%) had a preceding [r] (e.g., [ˈuriʈʂa $\sim $ uˈritana] $<$ *qurit, ‘stroke, line’).

The only example of reanalysis in the direction of r $\rightarrow $ t is likely also motivated by r-dissimilation. The reanalysed form [ˈsanɖʐaʈʂa $\sim $ anaˈnɖʐat-ana] ( $<$ sandar, Malay loan) does not have a preceding [r] in modern Malagasy, but [nɖʐ] sequences are historically [nr], and only affricated to [nɖʐ] in a later stage of PSEB (Proto Southeast-Barito).

Overall, the direction of reanalysis in ʈʂa-final weak stems goes against predictions of an inductive approach. Based on the PMP distribution, there should more [t]-alternating forms than [r]-alternating forms. However, reanalyses are overwhelmingly towards the less frequent alternant, in the direction of t $\rightarrow $ r.

3.3. The result of reanalysis: weak stem alternations in modern Malagasy

This section describes the distribution of weak stem alternants in modern Malagasy, using 1,628 stems taken from the MDEM. This data supplement the above results, by providing indirect evidence for the direction of reanalysis that has taken place.

Table 11 summarises the distribution of weak stem alternants in modern Malagasy; the rightmost column shows the expected directions of reanalysis for each weak stem type, given the historical distributions discussed so far. The na-final weak stems are overwhelmingly non-alternating, where 97.7% of the sampled forms are non-alternating. This distribution is consistent with the finding that reanalyses have been in the direction of m $\rightarrow $ n, increasing the relative frequency of non-alternating na-final weak stems.

Table 11

Proportion of alternants for modern Malagasy weak stems.

For ka-final weak stems, [h] is overwhelmingly the preferred alternant, accounting for 94.8% of the sampled forms. Again, this distribution is consistent with the finding that reanalyses have been in the direction of f $\rightarrow $ h.

In addition, recall that Mahdi (Reference Mahdi1988) finds evidence for h-dissimilation in ka-final weak stems. Although no such effect was found in PMP (or in the attested reanalyses), h-dissimilation does seem to be present in modern Malagasy. This is illustrated in Figure 1, which shows the distribution of alternants for ka-final stems, by whether or not the consonant nearest to the alternant is [h]. When there is an immediately preceding [h], the observed alternant is always [f]. In contrast, when the stem does not have a preceding [h], only 3% ( $n=21/689$ ) stems have [f] as the alternant. Based on these results, dissimilation could have affected reanalyses of ka-final stems.

Figure 1

Distribution of alternants in ka-final weak stems.

The data in Table 11 show that for ʈʂa-final stems, there is a general preference for alternation with [r] (relative to [t] or [f]), such that around 70.2% ( $231/329$ ) of relevant stems are r-alternating. Figure 2 shows the proportion of alternants, organised by whether or not there is a preceding [r] somewhere in the stem. From here, it is evident that in modern Malagasy, there is a strong dissimilatory pattern. Specifically, final ʈʂa never alternates with [r] if there is already an [r] in the stem. In contrast, when there is no preceding [r], there is a strong preference for alternation with [r]. Overall, the distribution of alternants in modern Malagasy supports the finding that reanalysis in ʈʂa-final weak stems is in the direction of t $\rightarrow $ r, except when blocked by r-dissimilation.

Figure 2

Distribution of alternants in ʈʂa-final weak stems.

3.4. Markedness effects in the reanalysis of ʈʂa stems

For the ʈʂa-final weak stems, reanalysis in the direction of t $\rightarrow $ r cannot be explained by an inductive approach. Additional factors are needed to explain this direction of reanalysis.

I propose that reanalysis towards [r] is the result of a markedness bias in Malagasy against intervocalic oral stops. There is support for the presence of this constraint internal to the Malagasy lexicon. Historically, Malagasy underwent intervocalic lenition which affected all oral stops except for *t (*b>v, *p>f, *d,*ɖ>r, *k,*g>h; Adelaar Reference Adelaar1989, Reference Adelaar2012). It’s therefore likely that there were very few intervocalic stops at some point in historical Malagasy.

A constraint against intervocalic stops is also independently motivated cross-linguistically. Studies have found phonetic support for intervocalic lenition, from both an articulatory (Kirchner Reference Kirchner1998) and perceptual (Kaplan Reference Kaplan2010; Katz Reference Katz2016) point of view. There is also sizeable typological support for intervocalic lenition at morpheme boundaries, including (among many other examples) Sanskrit stop voicing (Selkirk Reference Selkirk, Arnoff and Kean1980), English phrasal tapping (Hayes Reference Hayes2011: 143–144), Korean lenis stop voicing (Jun Reference Jun and Kim-Renaud1994) and Catalan fricative weakening (Wheeler Reference Wheeler2005: 163). Malagasy ʈʂa $\sim $ r alternation fits into this typology, and can be explained as the result of stop lenition at morpheme boundaries.

The fact that only ʈʂa-final stems, and not other weak stems, have undergone reanalysis in a direction not predicted by distributional information, follows naturally from this markedness-based account. For ka-final stems, the possible alternants are [f] and [h]; both are fricatives and would not violate a constraint against medial stops. For na-final stems, the attested alternants are [m] and [n]. Again, neither violate a constraint against medial oral stops, so are equally unmarked if all else is held equal.

One alternative possibility is that speakers are driven by a perceptual bias, rather than a markedness bias (Wilson Reference Wilson2006; Steriade [2001] Reference Steriade, Hanson and Inkelas2009; White Reference White2013). That is, if the retroflex affricate [ʈʂ] has a smaller perceptual distance to [r] than to [t], reanalysis towards [r] could be explained as the result of a bias towards perceptually similar alternations.

Although there have been no studies on perceptual distance of Malagasy phonemes, there is indirect evidence from English that [ʈʂ] is perceptually closer to [t] than to [r]. If this is true, than a perceptual distance account predicts that [ʈʂ] $\sim $ [t] alternation is preferred over [ʈʂ] $\sim $ [r] alternation. English does not phonemically have [ʈʂ] and [r], but Warner et al. (Reference Warner, McQueen and Cutler2014) have found that for English, [tʃ] is perceptually closer to [t] than to [ɾ]. If we use [tʃ] and [ɾ] respectively as proxies for Malagasy [ʈʂ] and [r], this would suggest that [ʈʂ] is perceptually more similar to [t] than to [r]. This assumption is not unreasonable because Malagasy [ʈʂ] is variably realised as postalveolar, and [r] is realised as a tap in fast speech (Howe Reference Howe2021).Footnote ⁶

Finally, it is worth noting that the pattern of r-dissimilation, though already present in the distributional information, also has typological support. Suzuki (Reference Suzuki1998), in a typological study of dissimilation, finds multiple examples of tap dissimilation. More generally, liquid dissimilation is also crosslinguistically attested, both as a phonotactic tendency and in active phonological processes (e.g., French and Spanish; Colantoni & Steele Reference Colantoni and Steele2005).

3.5. Interim summary

Comparison of PMP protoforms with Malagasy suggests that reanalysis of weak stems is driven not just by distributional probabilities of the lexicon, but also by additional markedness effects. Findings of this section are summarised in (9). On one hand, reanalysis of na- and ka-final weak stems is largely predictable from distributional probabilities.

However, the ʈʂa-final stems underwent reanalysis towards r-alternation, which is the opposite of what is predicted by lexical statistics. In other words, a purely inductive model of reanalysis would fail to predict the direction of reanalysis found in Malagasy.

Instead, reanalysis of ʈʂa-final stems is argued to be driven by a markedness constraint against intervocalic stops. In the following section, I propose a model of reanalysis that incorporates a markedness bias, and show that it better captures the Malagasy data than an unbiased model.

Note that for the ka-final weak stems, there is some evidence for h-dissimilation both in the historical distribution and in Malagasy. However, the pattern is hard to confirm due to a lack of evidence; as such, the rest of this article will not consider effects of h-dissimilation. Additionally, the rest of the article will focus on the ʈʂa-final weak stems, where the effects of markedness are most pronounced.

4.1. Components of a MaxEnt model of reanalysis

Because rates of Malagasy weak stem alternation are probabilistic (as opposed to categorical), I adopt MaxEnt, which uses weighted (instead of ranked) constraints and generates a probability distribution over the set of candidate outputs. In principle, other stochastic inductive models of morphophonological learning, such as the MGL (§2.1), would work equally well in matching the Malagasy input data. MaxEnt is adopted because there is existing work on incorporating learning biases in MaxEnt (Wilson Reference Wilson2006; White Reference White2013).

Note that unlike classic OT, where strict ranking ensures that losing candidates never surface, all candidates in MaxEnt grammars receive some probability. However, if constraint weights are sufficiently different, MaxEnt produces results that are functionally very similar to classic OT, where the winning candidate gets near-perfect probability.

In all subsequent models, constraint weights were learned in R (R Core Team 2021), using the maxent.ot package (Mayer et al. Reference Mayer, Tan and Zuraw2022). Constraint optimisation is done using the optim function from the R-core statistics library. Constraint weights are restricted to finite, non-negative values.Footnote ⁷

For explanatory ease, tableaux used to demonstrate the effect of different constraints will be shown in classic strictly ranked OT. However, for the actual model, the output is a set of candidates, each with a predicted probability.

4.1.1. Inputs

The input to the model is a set of 1,616 nonce weak stem, designed to represent historical Malagasy, presumably before extensive reanalysis had occurred. The value 1,616 was chosen to match the number of weak stems found in the MDEM (i.e., modern Malagasy) corpus (after removing irregularly alternating forms). Relative frequencies of ka, ʈʂa and na stems match that of the MDEM corpus. The relative frequency of each alternant was based on the distribution of final consonants in the historical PMP data. Nonce stems are used in place of actual PMP stems because of number PMP forms available is too few.

For simplicity, only candidates with observed alternants are included in the model. A potential alternate like [p], which is in the Malagasy inventory, but not observed as a weak stem alternant, is assumed to be ruled out by highly weighted faithfulness constraints. In addition, ʈʂa $\sim $ f alternating forms and irregular alternants (e.g., na $\sim $ f alternating forms) are excluded, because they are extremely low-frequency and do not influence model outcomes. The input data are summarised in Table 12.

Table 12

Sample inputs to the Malagasy model of reanalysis.

The input matches the surface stem allomorphs, and the output candidates are suffixed allomorphs. This is because all reanalyses in Malagasy weak stems are from the non-suffixed to suffixed allomorphs. Reanalysis happens in this direction if speakers have access to the surface stem (or another non-suffixed allomorph), but not the suffixed allomorph. The inputs therefore match the conditions under which speakers would reanalyse weak stems.

This choice of inputs relies on the assumption that the base of reanalysis is always a non-suffixed allomorph. A similar approach is taken by Albright (Reference Albright2008b, Reference Albright2010), who argues that the base of reanalysis is fixed, and is always a single slot of a morphological paradigm.

Albright also argues that the base should be the most informative allomorph, which has the most contrastive information. The Malagasy base appears to contradict this hypothesis, since it is the suffixed forms that are more informative, and retain contrastive information about weak stem consonant alternations. The Malagasy data may lead us to slightly rethink Albright’s hypothesis that informativeness always determines the base of reanalysis. It may be that the base of reanalysis is generally the most informative one (per Albright’s hypothesis). However, if learners only have access to limited paradigm slots, reanalyses may still occur from these paradigm slots even if they are not the most informative.

Other factors such as token frequency may also affect how learners select the base of reanalysis. Albright (Reference Albright and Good2008a) suggests that when one slot of the paradigm is used with much higher frequency than others, it may be preferred as the base of reanalysis. However, Keenan & Manorohanta (Reference Keenan and Manorohanta2001) find, based on written corpora, that actives (unsuffixed) and passives (mostly suffixed) occur at roughly equal rates, making this explanation less likely. Another possible factor is the tendency for bases to be isolation stems or other shorter, ‘unmarked’ forms (Kuryłowicz Reference Kuryłowicz1945; Vennemann Reference Vennemann1972).

4.2. Learning additional markedness constraints

The central argument of the current study is that reanalysis in Malagasy is partially driven by markedness effects that cannot be learned inductively. In this section and the subsequent section, I outline a process for incorporating this markedness component to the model.

First, when we consider markedness bias in reanalysis, it is also important to consider how such effects are constrained – in other words, what is the range of markedness effects that are able to influence reanalysis? I propose that markedness constraints can only affect reanalysis if they are already active in the lexicon, in the form of stem phonotactics.

This ‘active markedness’ proposal is attractive because it ties into existing theories of acquisition and empirical findings about the relationship between phonotactics and morphophonology. First, this approach predicts a strong relationship between phonotactics and alternations. Crosslinguistically, similar phonological generalisations tend to hold within morphemes and across morpheme boundaries; in other words, alternations are consistent with stem phonotactics (Chomsky & Halle Reference Chomsky and Halle1968; Kenstowicz Reference Kenstowicz, Durand and Laks1996). This is especially true once we consider gradient effects; Chong (Reference Chong2019) shows that even in cases of apparent mismatch between phonotactics and alternations, there is often some gradient phonotactic support for an alternation pattern. Additionally, alternations that are not supported by phonotactics tend to be under-attested.

In work on compound formation, Martin (Reference Martin2011) also finds similar effects of active markedness. In particular, Martin presents evidence from Navajo and English that the same phonotactic constraints present within morphemes are also active in compound formation, albeit as a weaker, gradient effect. In other words, there is evidence that speakers generalise phonotactic constraints across morpheme boundaries. Given Martin’s findings, it is conceivable that stem-internal phonotactics could also constrain cross-morpheme alternation patterns.

An active markedness restriction is also consistent with the view that phonotactics guide alternation learning (Tesar & Prince Reference Tesar and Prince2003; Hayes Reference Hayes, Kager, Pater and Zonneveld2004; Jarosz Reference Jarosz2006), which is supported by experimental evidence (see, for example, Pater & Tessier Reference Pater and Tessier2005; Chong Reference Chong2021). This restriction also makes empirically testable, language-specific predictions that should be tested in follow-up work, about which markedness effects can affect reanalysis.

For these reasons, I propose that markedness bias is restricted to active markedness effects. As a preview, the Malagasy results are consistent with this active markedness principle. In §5.1, other alternatives are discussed.

To test whether a constraint against intervocalic stops is present in Malagasy phonotactics, I constructed a phonotactic model of Malagasy stems using the UCLA Phonotactic Learner (Hayes & Wilson Reference Hayes and Wilson2008), which learns a grammar of n-gram constraints that fits the distribution of natural classes in a set of learning data. The grammar was restricted to learning maximally trigram-length constraints. The UCLA Phonotactic Learner also allows the user to specify different projections, in order to test for long-distance dependencies. The Malagasy phonotactic grammar included two projections, a vowel tier ([+syllabic]) and a consonant tier ([−syllabic]). The consonant tier is included to test whether r-dissimilation (and potentially other dissimilative effects) are present in Malagasy stem phonotactics. The vowel tier is included because, although it is not directly relevant to the current study, there is evidence for vowel dissimilation in Malagasy (Zymet Reference Zymet2020).

The input to the grammar was 3,800 Malagasy stems sampled from the MDEM. Completely reduplicated forms (e.g., pakapaka) were automatically removed, but partially reduplicated forms still remain. Only non-suffixed stems were used; suffixed allomorphs were not included because the alternants of weak stems reflect the distribution of the lexicon after reanalysis, while the phonotactic grammar is supposed to approximate patterns already present in Malagasy pre-reanalysis.

The resulting grammar learned four constraints, given in (13), that penalise intervocalic stops and specifically favour [r] over [t] as the alternant for ʈʂa-final weak stems. The constraints listed here all motivate reanalysis of t $\rightarrow $ r. Crucially, they also do not affect the relative preference for different alternants in ka- or na-final weak stems.

In general, the phonotactic grammar also learned constraint weights in a way that favoured r-alternating candidates over t-alternating candidates. This is demonstrated in (14), which shows the Harmony scores assigned by the phonotactic grammar to suffixed forms of hypothetical weak stems. The higher the Harmony, the more a form is penalised by the grammar and phonotactically dispreferred.

For the ʈʂa-final weak stems, the grammar assigns the lowest harmony to the r-alternating candidate ([vukir-ana]). Notably, for the na- and ka- final weak stems, the phonotactic grammar also assigns harmony scores that are either neutral or favour the statistically preferred alternant. Specifically, for ka-final weak stems, the grammar assigns very similar Harmony scores to all three candidates. For the na-final weak stems, the grammar assigns a higher Harmony to the m-alternating candidate, which is statistically dispreferred.

For simplicity, I added only the constraint *V[−cont,−voice]V to the model of reanalysis. Although the phonotactic grammar found multiple constraints which penalise intervocalic stops, I included only one because all four constraints have the same violation profile with respect to the candidates in weak stem reanalysis.

Alternation in ʈʂa-final weak stems is also driven by a strong r-dissimilation constraint. The phonotactic grammar did not learn this constraint in the consonant tier; other projections that were tested, such a Coronal tier, also did not learn a constraint for r-dissimilation. Constraints on dissimilation of larger classes of segments (e.g., approximants) were also found to be non-significant. Thus, r-dissimilation differs from lenition in that it is a markedness constraint learned from the local distribution of weak stem alternants, and does not receive additional phonotactic support.

In other words, although *r…r] and *V[−cont,−voice]V look similar on the surface, they have different underlying mechanisms. Reanalysis driven by *V[−cont,−voice]V is supported by stem phonotactics. In contrast, reanalysis driven by *r…r] is better characterised as frequency-matching of patterns within the weak stem paradigm.

4.3. Incorporating a soft markedness bias

The constraint *V[−cont,−voice]V is added to the model and assigned a bias towards higher weight. Following Wilson (Reference Wilson2006) and White (Reference White2017), a bias term, or ‘prior’, is implemented as a Gaussian distribution over each constraint weight. The bias term, calculated as in (15), is defined in terms of a mean ( $\unicode{x3bc} $ ) and standard deviation ( $\unicode{x3c3} $ ). In unbiased models, the goal of learning is to maximise log probability. With the inclusion of the prior, the goal becomes to maximise a different objective function, which is the prior term subtracted from the log probability of the observed data.

For each constraint, w is its learned weight, and $\unicode{x3bc} $ can be thought of as the ‘preferred’ weight. As such, the numerator of the bias term reflects how much the actual weight deviates from the preferred weight of each constraint, and the penalty resulting from the bias term increases as constraint weights diverge from $\unicode{x3bc} $ . The value of $\unicode{x3c3} ^2$ determines how much effect the preferred weight ( $\unicode{x3bc} $ ) has; lower values of $\unicode{x3c3} ^2$ result in a smaller denominator, and therefore greater penalty for weights that deviate from their $\unicode{x3bc} $ .

In principle, both $\unicode{x3bc} $ and $\unicode{x3c3} ^2$ can be varied to give constraints a preference towards a certain weight. In the current models, $\unicode{x3c3} ^2$ is set to fixed values. The markedness constraints *ʈʂ]V, *k]V, *n]V and *r…r] have no phonotactic support from the lexicon, but are supported by distributional information within the paradigm. For these constraints, I assume that the weight is learned from the input data, and that the effect of a bias is negligible. This is done by setting $\unicode{x3c3} ^2$ to an arbitrarily high value (1000).

For the rest of the constraints, $\unicode{x3c3} ^2$ is set to 0.5, and $\unicode{x3bc} $ is varied to implement different learning biases. For example, a markedness bias is implemented by assigning *V[−cont,−voice]V a higher $\unicode{x3bc} $ than competing faithfulness constraint(s). As a result, *V[−cont,−voice]V will be biased to have a higher weight than the relevant faithfulness constraints. In §4.5, I provide the specific $\unicode{x3bc} $ values used for the markedness-biased model, as well as the $\unicode{x3bc} $ values of baseline control models.

4.4. Iterated modelling

To simulate reanalysis over time, I use a generational model where the output of one iteration of the model becomes the input to the next iteration. Similar models of language change are by no means new, and there are various approaches to doing so. For example, Weinreich et al. (Reference Weinreich, Labov, Herzog, Lehmann and Malkiel1968) use phonological rules that apply variably to predict change in progress. Other approaches that have been explored include modelling change in dynamical systems (Niyogi Reference Niyogi2006), connectionist frameworks (Tabor Reference Tabor1994), as the result of competing grammars (Yang Reference Yang1976), in exemplar-based frameworks (Pierrehumbert Reference Pierrehumbert, Gussenhoven and Warner2002), and more recently in variants of OT (e.g., Boersma Reference Boersma1998; Zuraw Reference Zuraw2000, Reference Zuraw, Bod, Hay and Jannedy2003; Staubs Reference Staubs2014).

To simulate the cumulative effects of reanalysis over time, I assume an agent-based iterated learning model. Under this approach, small changes to an alternation pattern can accumulate over iterations (each corresponding roughly to a generation of speakers), resulting in large-scale reanalyses of a pattern.

In an agent-based iterated model, the output of one model iteration becomes the input to the next iteration. The current study adopts a simplified model in which each generation (or iteration) has just one agent and one learner, as illustrated in Figure 3. In the first generation, the agent A1 produces the output language based on their grammatical knowledge (i.e., Hypothesis 1; H $_1$ ). More concretely, a hypothesis is the speaker’s grammar, represented in this case using MaxEnt, as the probabilistic weighting of Optimality-Theoretic constraints. The learner observes these data, induces the relevant generalisations, and forms another hypothesis (H $_2$ ), which then becomes the basis of the output data presented to the next generation. This process is repeated for many iterations.

Figure 3

Structure of an iterated learning model, adapted from Ito & Feldman (Reference Ito and Feldman2022: 3). H $_i$ indicates hypotheses of each generation.

When providing input for a learner in the next generation, not all of the information of the language is presented, resulting in a learning ‘bottleneck’ (Kirby Reference Kirby2001; Brighton Reference Brighton2002; Griffiths & Kalish Reference Griffiths and Kalish2007). As a result of this bottleneck, input patterns that are easier to learn should be more likely to pass through this bottleneck, and become more prominent over generations of learning. In the current study, the bottleneck is implemented by having the Agent ‘forget’ some proportion of forms at each iteration. The remembered forms are retained to the next generation, while the forgotten forms are generated from the Agent’s grammar (Hypotheses 1, 2, 3, etc.). A similar approach is taken up by Ito & Feldman (Reference Ito and Feldman2022), who use iterated learning to model accent change in Sino-Korean.

Note that the iterated learning paradigm I adopt makes several simplifying assumptions. In particular, I assume just one agent and one learner, when in fact language change takes place at the level of the population. Future work should therefore consider more complex models which incorporate multiple interacting Agents in a way that models the speech community. Baker (Reference Baker2008) finds that such multi-agent models produce more empirically accurate results.

The iterated learning model has two parameters: forgetting rate and number of iterations. The forgetting rate is the proportion of forms forgotten and relearned in each iteration. I test five forgetting rates (0.05, 0.1, 0.15, 0.2, 0.25). In the interest of clarity, and because the model trended in the same direction across all five forgetting rates, the rest of this article will only present models with a forgetting rate of 0.2.

The number of iterations is set to 50 to reflect the time span in which reanalysis of weak stems should have occurred. First, I follow Ito & Feldman (Reference Ito and Feldman2022) in equating each iteration to roughly one generation of speakers, where a generation lasts 25 years. The number of iterations was then chosen to reflect the maximal span of time in which reanalyses of weak stems could have occurred. The sound changes that resulted in weak stem alternations took place around 600 C.E., while the modern Malagasy data start around the 1800s. Therefore, reanalysis must have occurred within the span of around 1,200 years. This corresponds to roughly 50 generations, assuming that each generation is 25 years. Fifty generations are meant as a conservative estimate, since in reality, reanalysis of the ʈʂa-final weak stems may have happened in a much shorter span of time.

Forgetting rate and the number of iterations are closely related; in general, when the forgetting rate is low, rate of change over time is slower, but this can be offset by increasing the number of iterations. However, increasing the forgetting rate has the additional effect of increasing variation between different runs of the model. This is because as forgetting rate increases, the input data for each model iteration become more variable.

Because random sampling causes each iteration of the model to vary slightly, all subsequent models were run 30 times, and predicted probability values are the mean of these 30 trials.

4.5. Model comparison

This section compares markedness biased models against controls to evaluate the effect of markedness in improving model predictions. Although it is not the focus of the current article, models with a p-map bias are also tested. These models are included to confirm that markedness effects improve model predictions after controlling for perceptual similarity effects, which have been substantiated by prior research (White Reference White2013, Reference White2017).

A total of four models are compared: the first two conditions, flat-prior and p-map, are controls. They are compared to two conditions with a markedness bias, labelled markedness and full (which includes both a markedness and p-map bias). The priors assigned to each condition are explained below and summarised in Table 13.

Table 13

Constraints and bias terms by condition (P = p-map condition, M = markedness condition).

If reanalysis is in fact driven by a markedness bias in Malagasy, then the Markedness and Full models should outperform their respective control conditions, flat-prior and p-map. If, instead, reanalysis is rooted in a p-map bias, adding a markedness bias should not improve model fit. Instead, the P-map condition (and potentially the Full condition) should perform better than the flat-prior model, and the Full condition should not perform better than the P-map condition.

• Flat-prior condition (control): The flat-prior model (labelled flat in Table 13) is a control condition. In this condition, every constraint with a bias term has the same $\unicode{x3bc} $ of 3.3, which is the mean of all $\unicode{x3bc} $ values assigned to the *Map constraints in the P-map condition below. This condition will be compared against the markedness condition. It is included because as discussed in White (Reference White2013), a model with uniform (but non-zero) $\unicode{x3bc} $ values is a better control than a model with no bias terms at all.Footnote ¹⁰

• P-map condition (control): The p-map condition (labelled P in Table 13) has a bias towards higher-weighted faithfulness constraints, scaled by perceptual similarity. The $\unicode{x3bc} $ of *Map constraints is higher for mappings between perceptually dissimilar sounds, and lower for mappings between perceptually similar sounds. In addition, all markedness constraints are assigned $\unicode{x3bc} $ =0.

  To approximate perceptual similarity, I adopt White’s (Reference White2013, Reference White2017) method of using confusability as a measure of perceptual similarity, where the confusability of two speech sounds is determined according to the results of standard identification experiments.Footnote ¹¹ As there are no confusability experiments for Malagasy, I use results from Warner et al. (Reference Warner, McQueen and Cutler2014), a study of consonant confusability in English, as a proxy.Footnote ¹² English [ɾ] is used in place of Malagasy $\langle r \rangle $ [r $\sim $ ɾ]. Additionally, English does not have a retroflex affricate (except allophonically when [t] precedes [ɹ]), so [tʃ] is used as a substitute for [ʈʂ].

• Markedness condition: The Markedness condition (labelled M in Table 13) assigns a uniform prior, $\unicode{x3bc} =3.3$ , to all faithfulness constraints. The markedness constraint *V[−cont,−voice]V is assigned a high prior ( $\unicode{x3bc} =7$ ). This value is higher than the $\unicode{x3bc} $ assigned to the competing faithfulness constrain *Map(ʈʂ,r), but is otherwise arbitrary. This condition differs from the flat-prior condition only in the $\unicode{x3bc} $ value assigned to *V[−cont,−voice]V; the two models are otherwise identical.

• Full condition: The Full condition has both a markedness bias and a p-map bias. Like the markedness condition, *V[−cont,−voice]V is assigned a $\unicode{x3bc} $ value of 7. The P-map and Full conditions are identical except for the $\unicode{x3bc} $ values assigned to *V[−cont,−voice]V.

Note that the Flat-prior condition does bias learners slightly in favour of ʈʂa $\sim $ r alternation.Footnote ¹³ To see why, we can consider the constraints that, respectively, enforce ʈʂa $\sim $ t and ʈʂa $\sim $ r alternation. *Map(ʈʂ,r) enforces ʈʂa $\sim $ t alternation, while both *V[−cont,−voice]V and *Map(ʈʂ,t) enforce ʈʂa $\sim $ r alternation. The Flat-prior condition gives all three constraints the same prior weight, and will therefore prefer an outcome where the two constraints that enforce ʈʂa $\sim $ r alternation have a higher combined weight than *Map(ʈʂ,r). As will be seen in the rest of the section, however, the magnitude of t $\rightarrow $ r reanalysis predicted by the Flat-prior condition is too small to match the amount of reanalysis that has occurred between PMP and Malagasy.

4.5.1. Model results after one iteration

Table 14 shows results after one model iteration. The column titled ‘Obs (PMP)’ shows the observed probability of the input candidates, and reflects the distribution of alternants before reanalysis. The column ‘Obs (Mal)’ reflects the distribution of alternants in modern Malagasy, after reanalysis. Due to reanalysis of ʈʂa-final forms in the direction of t $\rightarrow $ r (see §3), modern Malagasy shows a much higher rate of ʈʂa $\sim $ r alternation than PMP.

Table 14

Predicted probability of models after one iteration (mean of 30 trials).

Results in the control conditions (flat-prior and p-map) are comparable, as both match the frequencies of the input data closely. The two conditions with a markedness bias, whose predictions are indicated in bold in Table 14, perform essentially the same. Both predict an increase in the probability of [vuˈkirana] (by 4%), and therefore, reanalysis to be in the direction of t $\rightarrow $ r. In other words, adding a markedness bias does appear to improve model predictions. The magnitude of change is relatively small after one iteration of the model. However, as seen in the following section, the model will approach the distribution seen in modern Malagasy after multiple iterations.

4.5.2. Model results after 50 iterations

Table 15 shows the constraint weights learned by each model after 50 iterations. Because each model was run 30 times, these weights are averaged over 30 runs. Additionally, Table 16 shows the proportion of variance explained (adjusted $R^2$ ) and log likelihood ( $\hat {L}$ ) for each model after 50 iterations, fit to the modern Malagasy distribution. Log likelihood was calculated by fitting model predictions to the frequency counts of weak stem alternants in Malagasy (given in §3.3).

Table 15

Model predicted weights after 50 iterations (mean of 30 trials).

Table 16

Results after 50 iterations: Proportion of variance explained (adjusted $R^2$ ) and log likelihood ( $\hat {L}$ ), of model predictions fit to modern Malagasy.

Based on Table 16, the models with a markedness bias clearly outperform corresponding control conditions. The models differ primarily in the weights they learn for *V[−cont,−voice]V. In particular, the markedness-biased models (Markedness and Full) both learn a higher weight for *V[−cont,−voice]V than for *Map(ʈʂ,r), and will therefore prefer ʈʂa $\sim $ r alternation over ʈʂa $\sim $ t alternation. Between the two control models, the Flat-prior does slightly better than the P-map model. Interestingly, when comparing between the two markedness-biased models, the Full model does slightly better than the Markedness model (in terms of both $R^2$ and log-likelihood). Figure 4 compares the proportion of variance explained (adjusted $R^2$ ) in the four conditions over 50 iterations. As seen in this figure, the model fit of the flat-prior control model improves only slightly over the 50 iterations ( $R^2=0.70$ ). In the p-map control model, model fit does not really improve over iterations ( $R^2\approx 0.6$ ). In contrast, both the markedness and full are able to account for over 97% of the variation in the observed Malagasy data, and achieve this high model fit by around 30 iterations.

Figure 4

Model fit (adjusted $R^2$ ) by condition over 50 iterations (mean of 30 trials).

Overall, adding a p-map bias does not strongly affect model fit, as the P-map condition actually performs worse than the Flat-prior condition. However, the full model ( $\hat {L}=-303.9$ ) actually performs slightly better than the markedness model ( $\hat {L}=-261.1$ ). In other words, adding a p-map bias on top of a markedness bias does slightly improve model fit. This is because, as will be discussed below, adding a p-map bias improves predictions for the ka-final weak stems.

A more detailed examination of model predictions shows that the bulk of improvement in model fit is driven by changes to ʈʂa-final weak stems. Consider Figure 5, which plots the change in predicted probabilities over 50 iterations for ʈʂa-final weak stems. Rates of alternation in the input data (PMP) and modern Malagasy (Mlg) are given at the endpoints of the x-axis for reference. The candidates labelled with ‘(r…)’ have a preceding [r] in the stem; for example, ‘(r…)ʈʂ $\sim $ t’ refers to input-output pairs like [ˈvuriʈʂa] $\sim $ [vuˈritana]. Non-alternating candidates (e.g., [ˈvukiʈʂa] $\sim $ [vuˈkiʈʂana]) are not shown, since they are never observed in either PMP or Malagasy, and are consistently assigned zero or near-zero probabilities by all models.

Figure 5

Predicted probabilities of candidates over 50 iterations for ʈʂa-final weak stems (mean of 30 trials). Grey intervals indicate standard error, and observed rates of alternation in PMP and Malagasy are given for reference.

In the two conditions with a markedness bias, the model successfully predicts an increase in the ʈʂ $\sim $ r alternating candidate, and therefore closely matches the Malagasy data. At the same time, for inputs with a preceding [r], where r-dissimilation should block the r-alternating candidate, all four models do similarly well and predict the t-alternating candidate at near-exceptionless rates.

The Flat-prior model also predicts some reanalysis in the direction of t $\rightarrow $ r. This is because, as discussed above, this model assigned the same $\unicode{x3bc} $ to *Map(ʈʂ,r), *Map(ʈʂ,t), and *V[−cont,−voice]V. This means that the combined $\unicode{x3bc} $ values of *Map(ʈʂ,t), and *V[-cont,-vc]V, which both enforce r-alternation, will be greater than the $\unicode{x3bc} $ of *Map(ʈʂ,r) (which enforces t-alternation). However, the magnitude of reanalysis predicted by the Flat-prior model is too small; after 50 iterations, it still predicts a higher rate of ʈʂa $\sim $ t alternating forms than ʈʂa $\sim $ r alternating forms.

For the na-final weak stems, all four models perform similarly well. This is demonstrated in Figure 6, which plots the change in predicted probabilities over 50 iterations for na-final weak stems. In both the historical and modern distributions, there is a strong preference for n-alternation; all four models can capture this pattern. These results show that the markedness-biased models are able to predict frequency-matching in environments where markedness is neutral (i.e., where all alternants are equally marked).

Figure 6

Predicted probabilities of candidates over 50 iterations for ka-final weak stems.

Figure 7 shows results for ka-final weak stems. Between PMP and Malagasy, there is a slight increase in the rate of k $\sim $ h alternation (from P = 0.81 in PMP to P = 0.95 in Malagasy). Notably, the models with a p-map bias (P-map and Full) are able to match this pattern, while the other two models predict roughly stable rates of alternation that match the PMP distribution. The Full model, in particular, predicts the most increase in k $\sim $ h alternation. The p-map and Full models do well because the p-map bias assigns a higher $\unicode{x3bc} $ to *Map(k,f) than *Map(k,h), motivating higher rates of ka $\sim $ h alternation.

Figure 7

Predicted probabilities of candidates over 50 iterations for ka-final weak stems.

Table 17 shows the detailed predictions of each condition on the 50th iteration. The two control models (flat-prior and p-map) generally match the historical PMP distribution, and therefore under-predict rates of ʈʂa $\sim $ r alternation. Although the Flat-prior model does predict a slight increase in ʈʂa $\sim $ r, it still does not come close to matching the Malagasy pattern. In contrast, as shown in the bolded cells, both the markedness and Full conditions predict a large magnitude of reanalysis in the direction of t $\rightarrow $ r, and assign the r-alternating candidate (vukirana) a high probability ( $P=0.94$ in both models).

Table 17

Predicted probability of models after 50 iterations (mean of 30 trials).

As shown in the boldface cells of Table 17, the Full model actually does better than the Markedness model for ka-final weak stems. In particular, it predicts higher rates of k $\sim $ h alternation ( vs. ). This explains why the Full model does slightly better than the Markedness model in terms of overall model fit (as measured by $R^2$ and log-likelihood).

Overall, model results support the hypothesis that reanalysis in Malagasy weak stems is largely driven by a markedness bias which penalises intervocalic stops. Additionally, comparison of the markedness and full models shows that a perceptual bias (when combined with a markedness bias) improves model fit. Where alternants are equally marked, such as with the na-final weak stems, both of the markedness-biased models are also able to match the frequencies of the input data.

4.6. Iterated learning and the choice of $\sigma ^2$

In the current model, $\unicode{x3c3} ^2$ is set to 0.5, which allows for the bias to have a small magnitude of effect that adds up over multiple iterations. By the 10th iteration, the model closely matches the rates of alternation observed in modern Malagasy.

A superficially similar outcome can be achieved by removing the generational component of the model, and simply setting $\unicode{x3c3} ^2$ to a lower value. A lower $\unicode{x3c3} ^2$ allows the bias to have a stronger effect, so that the model predicts a greater magnitude of change in just one iteration. Figure 8 shows the model fit over 50 iterations for the Full model when $\unicode{x3c3} ^2$ is varied and $\unicode{x3bc} $ values are held constant. Both the high-sigma model ( $\unicode{x3c3} ^2=0.5$ ) and low-sigma model ( $\unicode{x3c3} ^2=0.1$ ) converge on the same outcome, but the low-sigma model does so much faster, after just 1-2 iterations.

Figure 8

$R^2$ over 50 iterations of the Full model, when $\sigma ^2$ is varied.

Although a low-sigma model achieves the same outcome as an iterative high-sigma model, I argue that the multi-generational model is preferable for the following reasons. First, it is conceptually more plausible that reanalysis happens gradually. This is especially true for a case like Malagasy, where the reanalysis of t $\rightarrow $ r cannot be attributed to sound change, and both alternants are phonemic.

A generational model also predicts randomness and variation; in the current article, this comes from randomly sampling the winning candidate that becomes the input to the next model iteration. This matches how language change happens in reality, where markedness bias may affect different languages to a different degree, and the same language will undergo dialect divergence.

5.1. Sources of markedness effects in reanalysis

Throughout this study, I have proposed that active markedness effects in reanalysis are restricted to so-called ‘active markedness’ effects already present in the stem phonotactics. In other words, learners notice a phonotactic tendency and use it to guide reanalysis. This approach is attractive for the reasons discussed in §4.2; namely, it ties into work showing that people tend to acquire phonotactics before alternations, and use phonotactics to aid in the learning of alternations.

Within work on language change, findings from Garrett (Reference Garrett and Garrett2008) also support the idea that markedness-motivated paradigm reanalyses are a product of language-specific factors rather than a direct manifestation of UG. While Garrett’s focus is on semantic (rather than phonological) markedness patterns, his findings still provide support for the idea that reanalysis is driven by markedness effects already present in the language.

Notably, the Malagasy results are consistent with the active markedness principle, but also amenable to other analyses. One alternative is that phonotactics do not constrain reanalysis, and only external factors are responsible for the bias against intervocalic stops. For example, this bias could be rooted in principles of phonetic naturalness; that is, speakers are biased against intervocalic [t] because it is harder to produce or perceive. Alternatively, sound changes specific to Malagasy made have made intervocalic [t] harder to produce or perceive at some point in the history of the language. This is likely because (as discussed in §3.4), Malagasy underwent multiple intervocalic lenition processes, which affected all oral stops except for [t]. Future work should expand on the typology of markedness effects in reanalysis, to confirm whether the active markedness principle holds true crosslinguistically.

5.2. When can markedness-driven reanalysis occur?

My proposal, broadly speaking, is that reanalysis should be phonologically optimising. This ties into other findings, such as The Emergence of the Unmarked effects (TETU; McCarthy Reference McCarthy and McCarthy2004), where markedness-reducing behaviour surface across morpheme boundaries. The active markedness principle (the idea that speakers draw on stem phonotactics when reanalysing paradigms), in particular, predicts that reanalysis will result in a close correspondence between stem-internal phonotactics and cross-morpheme alternations. Importantly, this type of markedness-driven reanalysis only comes into play when there is uncertainty in an alternation pattern. In other words, markedness effects in reanalysis are only observed when there is conflicting evidence for which alternant should surface, and one alternant is less marked than the competing alternants.

This distinction is important because it allows mismatches between phonotactics and alternations to persist if an alternation pattern is predictable. In Malagasy, given a ʈʂa-final weak stem, there is generally ambiguity in whether the alternant will be [t] or [r]. This uncertainty allowed a constraint against intervocalic stops (specifically intervocalic [t]) to affect reanalysis. In contrast, for the subset of ʈʂa-final weak stems with a preceding [r], there was near-exceptionless distributional evidence that the alternant should be [t]. In this case, where the alternation pattern had less uncertainty, the r-dissimilation pattern was able to persist even in the absence of phonotactic support.

More generally, there is crosslinguistic evidence that phonotactics-alternation mismatches can persist in a language. For example, Turkish vowel harmony operates within stems but not across compounds or phonological words (Kabak & Vogel Reference Kabak and Vogel2001); see also Gouskova (Reference Gouskova and Aronoff2018) for an overview of similar mismatches. Experimental evidence from Gallagher et al. (Reference Gallagher, Gouskova and Rios2019) also supports the idea that speakers are able to learn different cross-morpheme and morpheme-internal phonotactic generalisations.

Relatedly, morphophonological patterns which are not phonologically optimising can also persist if the relevant pattern is predictable. In particular, there is crosslinguistic evidence for phonologically conditioned suppletive allomorphy, or cases where allomorphy has clear phonological conditioning but is not output-optimising (Paster Reference Paster2005, Reference Paster2009). For example, in Tzeltal, the perfective allomorph that surfaces (-eh vs. -oh) depends on how many syllables the stem has, in a way that is not output-optimising.

In summary, although my proposal of markedness-driven reanalysis predicts a strong connection between within-morpheme and cross-morpheme phonotactics, it is also consistent with cases of mismatch because reanalysis occurs only when there is uncertainty in the morphophonology.