Researchers have argued that languages’ lexicons over-represent phonologically licit sound sequences that are consistent with cognitive, phonological and phonetic constraints and under-represent sequences that violate these constraints (e.g., Frisch et al. 2004; Wilson 2006; Walter 2010). This paper investigates the extent to which vowel co-occurrence patterns universally reflect such pressures. Recent corpus research has found evidence for an identity bias1 in vowel co-occurrence patterns, but also that gradient vowel similarity does not have a strong or cross-linguistically consistent effect on lexical attestation (Doucette et al. 2024). The current corpus analysis thus tests whether the frequency of vowel sequences is universally sensitive to featural dimensions.

The existence of vowel harmony, a phonological constraint requiring vowels within a word to share certain features, suggests that vowels may be subject to universal pressures toward featural alignment (e.g. Rose & Walker 2011; van der Hulst 2016). A diverse range of explanations for the emergence of productive vowel harmony rules posit the existence of universal and phonetically-motivated pressures that favor harmony. These include accounts proposing that assimilatory processes like vowel-to-vowel coarticulation are a universal precursor to productive vowel harmony (e.g. Ohala 1994; Cole 2009), as well as formal grammatical accounts which posit the existence of universal harmony-inducing and featurally-specific constraints on segmental co-occurrence (e.g. Prince & Smolensky 1997; Wilson 2006; Goldsmith 1985). However, the phonemic organization of lexicons has also been argued to be subject to lexical pressures, including communicatively-motivated pressures to avoid ambiguity in the lexicon (e.g. Flemming 2004; Blevins & Wedel 2009; Mahowald et al. 2018), that may prevent the phonological organization of lexicons from being influenced by assimilatory pressures like those argued to underlie vowel harmony.

In concurrent analyses of two large-scale corpora, 92 lexicons in the XPF corpus (Cohen Priva et al. 2021) and 107 Northern Eurasian languages in the NorthEuraLex Corpus (Dellert & Jäger 2020), the current paper investigates whether the featural dimensions of height or backness constrain vowel-co-occurrence in cross-linguistically systematic ways. We find evidence that vowel identity is over-represented in the world’s languages but no evidence for a backness- or height-harmony bias. We also find some evidence that the extent of vowel identity varies across vowel categories in a cross-linguistically systematic way. The findings call into question the notion that assimilatory pressures like coarticulation or feature-specific alignment constraints can alone account for the phonological organization of lexicons.

The term ‘vowel harmony’ refers to a phonological constraint in some languages whereby all vowels within a word must align with respect to some phonological feature or property (e.g., Aoki 1968; Goldsmith 1985; Ringen & Vago 1998; Hayes & Londe 2006; Rose & Walker 2011; van der Hulst 2016). Hungarian, for example, exhibits productive backness harmony: roots are highly unlikely to have vowels with opposite places of articulation along the dimension of backness (e.g. Hayes & Londe 2006). While there are lexicalized exceptions, the productivity of Hungarian backness harmony is evident in its morpho-phonological alternations: when a suffix is appended to a stem, the vowel of the suffix adopts the backness feature of that stem; the dative morpheme /-nɛk/, for example, surfaces as [-nɛk] after stems with front vowels, and as [-nak] after stems with back vowels (Hayes & Londe 2006). Another frequently attested form of vowel harmony is Advanced Tongue Root harmony (ATR), common in African languages, whereby vowels within a word must agree in the position of the tongue root—either advanced ([+ATR]) or retracted ([-ATR])—typically affecting vowel height and contributing to systematic alternations across morphological paradigms (e.g. Casali 2008). Other forms of productive vowel harmony include height harmony, found in some Bantu languages (e.g. Hyman 2003), and a combination of rounding harmony and backness harmony, found in Turkish (e.g. Ohala 1994), among others (see Aoki 1968 and Rose & Walker 2011 for comprehensive typological overviews of harmony systems). While phonological harmony systems are typically not exceptionless, with some languages having lexicalized violations (Finley 2010; Archangeli & Pulleyblank 2007) or loanwords that deviate from the harmony pattern (Harrison et al. 2002), they are generally synchronically productive (e.g. Aoki 1968; Hayes & Londe 2006), and all have in common some non-adjacent dependency between a surface property of one vowel and that of another vowel within a particular domain like a word (Aoki 1968; Rose & Walker 2011).

While languages with productive vowel harmony comprise a minority of the world’s languages, they are nevertheless frequent and typologically diverse (e.g. Rose & Walker 2011). Productive vowel disharmony, in contrast, is rare (e.g. Martin & White 2021). The fact that languages frequently exhibit vowel harmony rules suggests that the existence of these rules is not an accident of historical change but rather that there exist at least some universal pressures or constraints that underlie harmony.

The claim that vowel harmony is a manifestation of universal pressures is consistent with research that describes harmony as phonetically grounded (e.g. Ohala 1994; Fagyal et al. 2003; Linebaugh 2007; Cole 2009). Specifically, vowel harmony has been argued to have a phonetic underpinning in the form of vowel-to-vowel coarticulation, an inevitable (and thus universal) result of articulatory overlap between adjacent or nearly adjacent sounds that renders those sounds more acoustically similar than they would be if they occurred separately (e.g. Ohala 1994; Magen 1997; Flego & Forrest 2021; Cohen Priva & Strand 2023). To account for the phonologization and spread of vowel harmony across the lexicon, some researchers have proposed that, given some degree of phonetic overlap between a pair of vowels, a listener may reinterpret an ambiguous vowel token as belonging to a different vowel category, one that is in harmony with the other vowel (e.g. Ohala 1994; Beddor 2009; Blevins & Wedel 2009). Such word-specific reanalysis is argued to spread to other words or phonological contexts incrementally (e.g. Ohala 1994) or rapidly via analogy (e.g. Hyman 2003).

Some studies have also posited inductive learning biases in favor of harmony relative to disharmony (e.g. Martin & Peperkamp 2020; Finley & Badecker 2008). Martin & Peperkamp (2020), for example, found that when exposed to an ambiguous artificial grammar input, speakers of English are more likely to infer a harmony rule than a disharmony rule. The putative asymmetry in learning between harmony and disharmony has been attributed both to the fact that learners’ knowledge of harmony’s phonetic naturalness constitutes a substantive bias (e.g. Martin & Peperkamp 2020), and that, as an abstract rule, harmony is formally more concise than disharmony (e.g. Finley & Badecker 2008). Moreover, infants have been shown to exhibit biases in favor of detecting vowel harmony patterns in acoustic inputs (e.g. Omane et al. 2024; Solá-Llonch & Sundara 2025). Solá-Llonch & Sundara (2025) in fact show that even 4-month old infants can detect vowel harmony in acoustic inputs, meaning that harmony patterns are perceptually accessible even to naive learners. However, the ostensible learning advantage bestowed by harmony does not manifest in all learning conditions. For example, Huang & Do (2023) find only a bias in favor of harmony under conditions of high variability in the training input, which suggests that disharmony is not intrinsically difficult to learn.

There is also evidence that the within-word, inter-segmental redundancy that results from harmony is beneficial for segmenting speech for learners of an unfamiliar language (e.g. Suomi 1983; Vroomen et al. 1998; Suomi et al. 1997; Mintz et al. 2018; Mersad & Nazzi 2011; Vroomen et al. 1998). Specifically, the fact that vowel transitions within words are more predictable than those between words serves as a robust cue for word boundaries. Beyond harmony, there is evidence that sounds are distributed in words in a way that facilitates spoken word recognition and lexical disambiguation in perception (e.g. Dautriche et al. 2017; King & Wedel 2020). The mutually informative word-internal cues between vowels bestowed by vowel harmony systems or harmony biases might make online lexical access easier since it reduces the listener’s reliance on any particular sound in the word to retrieve the word form from the speech signal. In short, as a form of inter-segmental redundancy, harmony may facilitate robust lexical retrieval in a noisy channel.

Given the evidence that harmonious vowel sequences are both phonetically and perceptually motivated at the word level, it appears plausible that vowel harmony is a universal “soft constraint”- a constraint that manifests not merely as a near-exceptionless or productive rule but as a statistical over-representation in the lexicon (e.g. Frisch et al. 2004) or as a graded bias in speakers’ acceptability judgments of phonological patterns in perceived speech (e.g. Coleman & Pierrehumbert 1997; Hay et al. 2004; Breiss & Albright 2022). An extensive body of work has argued that phonological grammars should shape gradient statistical patterns in the lexicon (e.g. Boersma & Hayes 2001; Frisch et al. 2004; Wilson 2006; Albright 2009), or that the same universal constraints that produce near-exceptionless segmental dependencies in some languages are likely to appear as exceptions or statistical trends in others (e.g. Zuraw 2000; Hayes & Wilson 2008).

In the current study, we test whether vowel co-occurrence patterns in the world’s lexicons universally reflect featural vowel harmony. This study fits within an extensive body of work that uses frequency distributions of sound sequences in languages’ lexicons to infer languages’ phonological biases or constraints (e.g. Frisch et al. 2004; Pozdniakov & Segerer 2007; Walter 2010; Stanton 2021). Broadly, the logic of this approach is that if a sound or sequence relevant to a particular property occurs more often than would be expected relative to some baseline (in which the effect of a potential bias is absent by design while other aspects of the language are preserved or controlled for), this over-representation can be taken as evidence that the language in question has a soft constraint or latent statistical bias in favor of that property. Frisch et al. 2004, for example, found that, compared to a baseline where sounds can combine freely, Arabic roots over-represent dissimilar non-adjacent consonant pairs. They also find that the degree of pairs’ over- or under-representation is a function of consonants’ gradient similarity. Subsequent studies have also found evidence that languages’ lexicons exhibit statistical avoidance of similar consonants (e.g. Walter 2010; Frisch et al. 2004; Pozdniakov & Segerer 2007; Doucette et al. 2024).

Research on vowel co-occurrence patterns, however, has not reported clear cross-linguistic evidence of featurally-constrained co-occurrence biases. In fact, evidence from recent studies suggests that pressures that restrict vowel co-occurrence are qualitatively distinct from those that restrict consonant co-occurrence, and that vowels do not appear to be driven by OCP-like similarity avoidance (e.g. Walter 2010; Doucette et al. 2024). Walter 2010, for example, compared vowels’ and consonants’ co-occurrence biases in Spanish and Croatian lexicons and found no evidence of a harmony bias among either for consonants or vowels, but did find that consonants were uniquely subject to a similarity avoidance constraint. Among studies focusing exclusively on vowel co-occurrence patterns, Alderete & Finley (2016) found that sequences of identical vowels were over-represented while sequences of similar but non-identical vowels were under-represented in four Polynesian languages. Stanton (2021) similarly found that for Ngbaka, sequences of identical vowels were over-represented, but also that backness and height harmony were significant predictors of pair counts, independent of identity. The most cross-linguistically comprehensive analysis of vowel co-occurrence patterns and their difference from consonants, to the authors’ knowledge, is an analysis of 107 Northern Eurasian languages by Doucette et al. (2024) that compares vowel and consonant co-occurrence restrictions. Consistent with prior work on fewer languages like Walter (2010), these authors find evidence for a cross-linguistically consistent anti-similarity bias for consonants, while they find no effect of vowel similarity on vowel co-occurrence. They do, however, also report some evidence for a universal bias in favor of vowel identity.

The finding that vowel identity is cross-linguistically over-represented while similarity has no effect on vowel co-occurrence is consistent with work suggesting that copying operations are distinct from the kinds of partial assimilatory processes that produce featural harmony (e.g. Gallagher & Coon 2009; Kawahara 2007). In some analyses, identical segments arise primarily through morphological processes such as reduplication (McCarthy 1995), rather than through gradient assimilation of features like [back] or [high]. Other work argues for a phonological preference for identity itself (Gallagher & Coon 2009; Stanton 2021), or proposes copying mechanisms that do not require reference to fine-grained featural structure (Kawahara 2007). That is, copying-based identity creates an exact repetition of a vowel (e.g., /i/ → [i…i]) without requiring that the repeated vowel share just one feature such as [+high] or [+front], whereas assimilatory harmony operates by aligning individual features (e.g., a suffix vowel becoming [+back] to match the stem). Thus, if copying processes contribute to lexical structure, identity may surface independently of any pressure for featural similarity. A separate possibility is that assimilatory influences are themselves nonlinear, such that identical vowels surpass a similarity threshold that triggers stronger alignment than partially similar vowels (e.g. Gallagher & Coon 2009; Wayment 2009). In any case, the widespread over-representation of identical vowel pairs suggests that identity may constitute a distinct organizing principle in phonological systems, rather than simply being the endpoint of featural harmony processes.

Results like those reported in Doucette et al. (2024) and Walter (2010) might indicate that substantive properties of vowels do not measurably restrict vowel co-occurrence in a cross-linguistically consistent way. However, in Doucette et al. (2024), vowel similarity was operationalized as a continuous value aggregating featural similarity across a variety of featural dimensions or natural classes. Under this approach, a pair of vowels is considered to be more similar if they have more matching specifications or features or natural classes. It is possible that such measures of similarity that aggregate over many featural dimensions obscure featurally-constrained variability in vowel co-occurrence patterns, that might be consistent across languages. Unlike Doucette et al, the current study tests whether there are systematic biases constraining vowel-co-occurrence along featural dimensions of backness or height. In addition, we explore whether identity biases vary by vowel category in a cross-linguistically consistent manner, in order to examine whether there is any evidence substantive properties of vowels might mediate their co-occurrence patterns in universal ways. In a supplementary analysis, we also test whether any detected co-occurrence constraints apply to local vowel pairs or more generally to vowel pairs separated by one or more syllables. Across all analyses we examine two large-scale cross-linguistic datasets: the NorthEuraLex corpus previously used by Doucette et al. (2024) as well as 92 languages’ lexicons from the XPF corpus.

The frequency distribution of sound sequences in a lexicon not only provides evidence for latent phonetic pressures or phonological constraints, but it can itself reflect global pressures on the lexicon to preserve its communicative efficacy (e.g. Piantadosi et al. 2012; King & Wedel 2020; Trott & Bergen 2020). Some researchers have argued that lexicons and sound inventories contain measurable evidence of ambiguity reduction. Trott & Bergen (2020), for example, argue that languages exhibit fewer homophones than would be predicted by a phonotactic baseline alone. Flemming (2004) further suggests that vowel inventories are themselves organized to preserve distinctiveness between vowel categories. There is also evidence that natural phonological changes are sensitive to the structure of the lexicon. For example, several accounts argue that homophony avoidance is a factor in language change (e.g. De Smet & Rosseel 2023) and that languages are more likely to undergo the loss of phonological contrasts between sounds whose merger would collapse fewer lexical distinctions (e.g. Blevins & Wedel 2009; Wedel et al. 2013; Gurevich 2013; Yin & White 2018). Some work has also found that (language-specific) informativity of particular sound classes itself predicts which of these sounds will undergo natural sound changes like lenition (e.g. Cohen Priva 2017). Because vowel assimilation is an information reducing process (Goldsmith & Riggle 2012), it could be at odds with supposed pressures to preserve distinctiveness among lexical items.

The claim that lexicons are shaped by factors beyond local phonetic and phonotactic pressures is not new. Zipf’s Law of Abbreviation, for example, famously states that frequent word forms are likely to be shorter in length (Zipf 1945), and this generalization appears to be universal (e.g. Bentz & i Cancho 2016; Linders & Louwerse 2023). While it is contested to what extent this property of lexicons actually constitutes communicative optimization, or can emerge at random (e.g. see Caplan et al. 2020), it is nevertheless apparent that factors beyond local phonological interactions of sounds can influence the attestation of forms in lexicons, and in cross-linguistically consistent ways. Importantly, such pressures on lexicons need not be understood as teleological. The attestation of forms in lexicons can be shaped by historical change, wherein the retention of certain forms in the lexicon over time is constrained by a range of factors beyond local segmental interactions, like the cognitive biases of its users, learnability, communicative efficiency, or perceptual salience, among others (e.g. Blevins 2004; Blevins & Wedel 2009). To the extent that these broader pressures are themselves universal or prevalent, they could complicate the prediction that lexicons should universally reflect phenomena like vowel harmony that may be desirable phonotactically.

This study investigates whether vowel co-occurrence is universally structured along featural dimensions. Specifically, we use Bayesian negative binomial regression to test whether languages’ frequency distributions of vowel pairs are biased in favor of height and backness harmony, as well as segmental identity. Each analysis is replicated on two distinct corpora, 92 languages in the XPF corpus (Cohen Priva et al. 2021), as well as 107 Northern Eurasian languages in the NorthEuraLex corpus (Dellert & Jäger 2020), both of which are described in greater detail in the Materials section.

There is an abundant variety of dimensions along which a pair of vowels could, in principle, exhibit harmony or featural alignment. We choose to focus on the dimensions of height and backness, because speakers of many languages use at least the first and second formants (the acoustic correlates of front-ness and backness) to distinguish vowels (e.g. Oganian et al. 2023). It is of course possible that other phonological dimensions (e.g. ATR, vowel roundness) may influence vowel-co-occurrence patterns across languages. Given that height harmony and backness harmony are both well attested, and constitute at least loosely orthogonal articulatory and perceptual dimensions, they are a useful starting point for testing in a coarse-grained manner whether co-occurrence patterns might be featurally constrained in a language-general manner. To make our modeling approach sufficiently flexible to control for dependencies along a variety of dimensions, we include vowel-specific random effects (described in more detail in the Model section), but we ultimately leave more fine-grained and explicit testing of biases along other vowel dimensions to future work.

To evaluate the universality of potential vowel-to-vowel dependencies consistent with harmony and identity, the current study analyzes phonologically-transcribed word lists for many languages from a diverse range of language families. We look for converging evidence from two resources with separate G2P pipelines, the XPF corpus (Cohen Priva et al. 2021), and NorthEuraLex (Dellert & Jäger 2020), the latter of which was the source of data for Doucette et al. (2024)’s recent investigation of consonant and vowel co-occurrence in 107 Northern Eurasian languages.

The 92 languages from XPF corpus were selected out of a total of 201 languages. Given that grapheme-to-phoneme transcription can be noisy, we aimed to maximize the reliability of our data by filtering out languages whose phonologically transcribed word lists are likely to be unreliable. For every language in the XPF corpus (Cohen Priva et al. 2021), we applied the following exclusion procedure:

An exhaustive breakdown of the 92 languages that met which exclusion criterion is also shown in Supplementary Appendix, Table 1.

For NorthEuraLex, we do not filter languages based on the number word types in the original dataset, because all languages have fewer than 2,500 total words. The fact that the data consist of shared concepts independently helps guarantee that these corpora, while small, are representative of language use and are comparable across languages.

For the remaining phonemically transcribed words across the XPF languages and NorthEuraLex languages, we employ the following modifications to transcriptions:

Across both datasets, filtering removed roughly one quarter of lexical items on average (25.8% in XPF; 29.0% in NorthEuraLex), with mean post-filter lexicon sizes remaining substantial (4632 and 763 types per language, respectively). No language was excluded based on these criteria, and even the smallest post-filter lexicons (1181 types in XPF; 200 in NorthEuraLex) were sufficiently large for the vowel co-occurrence analyses because observations are vowel bi-grams extracted from all multi-vowel lexical items, and not the lexical items themselves (see Supplementary Appendix, Tables 2 and 3 for a breakdown of word counts and vowel pair counts by language). Because not all symbols across the two datasets are compatible with PHOIBLE, we conduct corpus-specific manual data cleaning for both XPF and NorthEuraLex corpora to ensure that the transcription conventions are compatible with symbols used in the PHOIBLE dataset. We note that nasal contrasts between vowels were collapsed in the NorthEuraLex pipeline but not in our XPF pipeline. For our purposes, this, amounts to a difference in whether oral vowels and their nasal counterparts are treated as identical or not. More generally, “identity” in the current study should be understood simply as two vowels having identical labels given the granularity of labels available in the datasets and normalization across transcriptions used; we do not make a theoretical commitment to a phonetic or phonological threshold based on which a pair of vowels should be judged as being identical or not.

In NorthEuraLex, there are 26 Uralic languages and 8 Turkic languages, all of which are reported to have backness harmony. Our sample of XPF languages includes 3 Uralic languages, and 7 Turkic languages. We show which languages we were able to confirm have some sort of vowel harmony based on academic sources in Supplementary Appendix, Tables 2 and 3. We ultimately control for any harmony biases based on genetic affiliation by including language and language family as random effects (discussed in more detail below).

18 languages appear in both XPF and NorthEuraLex: Armenian, Bashkir, Basque, Bulgarian, Czech, Erzya, Georgian, Hungarian, Kannada, Korean, Malayalam, Romanian, Slovak, Spanish, Tatar, Telugu, Turkish, and Ukrainian. Concurrent analyses across multiple corpora thus allows for judging whether different datasets of the same languages yields similar co-occurrence estimates.

The analytical framework used in this paper is to measure the over-representation of segmental sequences relative to some baseline or expected probability to get observed over expected (O/E) values (e.g. Stanton 2021; Alderete & Finley 2016). We implement this approach using a Bayesian negative binomial model (see Table 1), which predicts the counts of vowel sequences with the binary predictors corresponding to constraints like height or backness harmony. More specifically, the model predicts how often each vowel pair occurs in a corpus relative to how often it would be expected to occur purely on the basis of the individual frequencies of the two vowels. The log link function means that predictors are interpreted as multiplicative effects on counts (e.g., a coefficient of 0.7 corresponds to roughly twice the expected count). The model’s estimates for binary phonological predictors fulfill a similar purpose as the aforementioned observed/expected (O/E) used in studies like Frisch et al. (2004). Using a log-linear model instead provides an estimate of a given bias for one pattern while controlling for the effect of other patterns or constraints (e.g. Wilson & Obdeyn 2009; Albright & Breiss 2024; Doucette et al. 2024).

Following prior work (e.g. Stanton 2021; Doucette et al. 2024), we consider as observations type frequencies of local vowel pairs extracted from a word separated by at least one consonant. A word like [animo], for example, would result in pairs [a, i] and [i, o] (see Supplementary Materials for analysis that treats non-local pairs as observations as well, and includes locality as a covariate.). Our model thus uses properties like identity and featural harmony to predict the counts of these pairs. Tables 1 and 2 summarize the model parameters, and Table 3 illustrates the input into our negative binomial model on a toy dataset.

As mentioned, we test for harmony biases along the dimensions of backness and height. We code each in our model using two distinct predictors for a given dimension, labeled as dimension.harmony and dimension.violation.avoid. For example, we define a backness.viol_avoid as any pair of vowels that is on opposite ends of the backness dimension where one vowel is marked as [+back] and the other as [+front], and accordingly height.violation.avoid as any non-identical pair of vowels where one vowel is marked as [+high] and the other [+low]. We define the variable backness.harmony.nonident as any non-identical pair of vowels that are both [+front] or both [+back].

One motivation for this coding scheme is that along a given featural dimension like height, the separate predictors can account for distinct ways in which vowels marked as doubly negative (e.g. /a/, which is marked as -front -back, for backness in PHOIBLE) might participate in harmony. The binary violation.avoid predictor includes pairs of such vowels intended to detect a preference against extreme differences along a given dimension, which may include a preference for vowels marked as [-front, -back] for a particular dimension. The harmony.nonident predictor, in contrast, captures harmony biases that manifest as alignment of vowels with positive values, and it is restricted to non-identical pairs to avoid collinearity with identity.

This operationalization of predictors yields an orthogonal coding scheme that allows the posterior distributions for two sets of predictors to be added to produce a joint distribution that shows the overall strength of the underlying construct. For example, a combination of posteriors for predictors like backness_viol_avoid + backness_harmony_nonident can thus be interpreted as reflecting the overall effect of alignment along the dimension of backness.

The model includes random intercepts and random slopes, which allow it to capture variation across languages rather than assuming that all languages behave the same way. A random intercept means that each language is allowed its own baseline rate of vowel co-occurrence; some languages may show higher or lower overall counts than others, independent of any specific effect we test. A random slope, which is more critical for our purposes, means that the size or even direction of a particular effect (for example, a tendency for identical vowels to co-occur) can differ from one language to another. In other words, the model estimates both the overall trend (the main effect) across all languages and how individual languages deviate from that trend (the random slope). This approach allows the analysis to generalize to the population of languages while allowing the model to measure between language variability in particular biases, and estimate biases for specific languages.

We control for positional frequencies of each vowel in each language by using position-specific probabilities of vowels to compute an expected proportion, which is treated in the model as an offset term, following Doucette et al. (2024). In short, the offset term normalizes its estimates based on the expected counts of vowel pairs. This ensures that the model asks not simply which pairs occur frequently, but which occur more (or less) often than would be predicted from the marginal frequencies of the vowels involved.

To control for the effect of a language’s vowel inventory size on co-occurrence biases, we include a predictor inventory.size and its interaction with the binary main effects. Along with the position-specific baseline, and between-language random slopes, having inventory.size as a covariate should keep effects from being skewed by the trivial fact that languages with smaller inventories are likely to have a greater raw proportion of any configuration like identity just by virtue of having fewer possible vowel combinations.

For all binary fixed effects, we also include random slopes for each vowel category in each language in the first position of a vowel pair v1.in.language. This grouping variable provides additional control for the independent probabilities of vowel categories, and also allows the model to robustly model idiosyncrasies of particular vowels and particular languages. Allowing the model to account for phoneme-specific variability across languages helps make the model sufficiently flexible to control for co-occurrence biases along a variety of dimensions.

To aid in interpreting this model given collinearity between predictors, we fit an auxiliary model identical to the model in Table 1, except that the identity predictor is omitted. This allows us to carry out model comparison to assess the unique contribution of identity to the predictive capacity of the model. It also allows us to separately quantify the extent of featural biases when identity is assumed to play no role in restricting vowel co-occurrence. By removing the identity predictor from the model structure, we can ask whether it is even possible for the model to account for co-occurrence counts with the given featural predictors alone.

Across all analyses and plots, positive values of coefficients for a particular pattern like identity indicate that the model over-represents that pattern relative to what would be expected at chance, and negative values (below or to the left of zero) indicate that the model measures that pattern as being under-represented relative to what would be expected at chance and relative to the effect of other predictors. The plotted posterior distributions represent the model’s uncertainty for each coefficient. Each distribution shows the full range of parameter values that are plausible given the data, with wider distributions indicating greater uncertainty and narrower ones indicating more precise estimates.

All r-hat values across the XPF-trained and NorthEuraLex-trained models were between 1.0 and 1.01, suggesting that the chains adequately mixed and that the models converged. Figure 1 shows the posterior distributions for the binary model estimates. Tables 4 and 5 show the raw estimates and credible intervals for every fixed effect coefficient for the NorthEuraLex and XPF data respectively. Given the presence of inventory.size as an interaction term, the coefficients reflect the expected effect of each variable at the average inventory size across all languages, which is 5.82 in our sample of XPF languages, and 8.21 in the 107 NorthEuraLex languages.

Identity is a reliable positive predictor of adjacent vowel pair counts in both the XPF and NorthEuraLex datasets. In XPF, the identity effect is estimated at β = 0.50 (95% CI: [0.26, 0.72]), corresponding to a mean 65% increase over expected frequency (exp(0.50)=1.65; 95% CI: [exp(0.26)=1.30, exp(0.72)=2.05]). In NorthEuraLex, the effect is even stronger at β = 0.55 (95% CI: [0.29, 0.82]; exp(0.55)=1.73; 95% CI: [1.34, 2.27]), suggesting that adjacent identical vowels are reliably over-represented cross-linguistically.

In XPF, vowel pairs that avoid violations of backness harmony are modestly over-represented (β = 0.06, 95% CI: [–0.14, 0.25]; exp(0.06)=1.06; 95% CI: [0.87, 1.28]), though the effect is not reliable. NorthEuraLex shows a similarly small, uncertain effect (β = 0.07, 95% CI: [–0.16, 0.30]; exp(0.07)=1.07; 95% CI: [0.85, 1.35]). Vowel pairs that conform to non-identical backness harmony (e.g. two +front or two +back vowels) are also underrepresented or only weakly favored (XPF: β = 0.03, 95% CI: [–0.15, 0.20]; exp(0.03)=1.03; 95% CI: [0.86, 1.22]; NorthEuraLex: β = 0.22, 95% CI: [–0.02, 0.43]; exp(0.22)=1.25; 95% CI: [0.98, 1.54]). This pattern suggests that vowel pairs involving unmarked values for backness (e.g, two mid vowels that are neither back nor front) may be preferred.

There are no reliable positive effects of height harmony in either corpus. In fact, violations of height harmony appear to be favored: in XPF, height-violation-avoiding pairs are underrepresented (β = –0.10, 95% CI: [–0.19, –0.00]; exp(–0.10)=0.90; 95% CI: [0.83, 1.00]), while in NorthEuraLex the direction is similar (β = –0.08, 95% CI: [–0.25, 0.10]; exp(–0.08)=0.92; 95% CI: [0.78, 1.11]), but not reliable based on credible intervals. Meanwhile, vowel pairs that share non-identical height features show no meaningful bias (XPF: β = –0.10, 95% CI: [–0.37, 0.16]; exp(–0.10)=0.90; 95% CI: [0.69, 1.17]; NorthEuraLex: β = 0.01, 95% CI: [–0.09, 0.11]; exp(0.01)=1.01; 95% CI: [0.91, 1.12]).

Interactions with inventory size are generally small and weak, suggesting that vowel inventory size does not exhibit a consistent effect on the extent of identity or harmony biases. The identity–inventory.size interaction is positive in XPF (β = 0.07, 95% CI: [–0.00, 0.14]; exp(0.07)=1.07; 95% CI: [1.00, 1.15]) but negative in NorthEuraLex (β = –0.05, 95% CI: [–0.08, –0.02]; exp(–0.05)=0.95; 95% CI: [0.92, 0.98]), indicating opposing trends of small magnitude: the identity bias is slightly stronger in larger-inventory languages in XPF, and slightly weaker in larger-inventory languages in NorthEuraLex. A small but reliable interaction between non-identical backness harmony and inventory size appears in XPF (β = 0.04, 95% CI: [–0.02, 0.11]; exp(0.04)=1.04; 95% CI: [0.98, 1.12]), consistent with the idea that languages with larger vowel inventories are somewhat less likely to under-represent harmonious backness pairs. For height violations, NorthEuraLex shows a modest positive interaction (β = 0.03, 95% CI: [0.01, 0.05]; exp(0.03)=1.03; 95% CI: [1.01, 1.05]), suggesting that the attestation of height violations relative to baseline decrease slightly with a higher inventory size. Generally, the small magnitude of these interactions with inventory size likely reflects the fact that inventory size partially overlaps with language-level variation, which is already captured through random intercepts. In addition, trivial effects of inventory size on the prevalence of identity (e.g. higher identity proportions in systems with fewer vowels) are likely to be accounted for by the model’s position-specific expected values, so the inventory size interaction estimates reflect effects beyond what would be expected given the more trivial effects.

We also show distributions of raw O/E values for each binary main effect predictor. Values for each language are derived by comparing the overall expected count of a particular configuration like identity or backness harmony to the observed count of that configuration in Figure 2. Qualitatively, the distributions of languages’ O/E values for each binary predictor are broadly compatible with the effects reported in the model. They align with the notion that observed counts of vowel pairs do not strongly deviate from those predicted by a random baseline, and thus that a harmony bias along featural dimensions is not likely to be reflected in vowel co-occurrence patterns. There is also no language that strongly under-represents identity in either corpus.

Next we explore whether there is any difference between the extent of backness harmony and the extent of height harmony. To get an overall estimate of a given language’s harmony bias, we add posterior samples for violation avoidance, and non-identical harmony (Figure 3). In both corpora, there appears to be a slight positive bias for backness relative to height.

It is possible, given collinearity between predictors, that a model without an identity predictor would sufficiently account for the count data, suggesting that a bias in favor of identity could still be reducible directly to the aggregate of the featural predictors. Specifically, because a given vowel pair with harmony might also be identical, there might be no optimal way to allocate credit for a high count of pairs that have both harmony and may thus inflate the estimate of one predictor, like identity, at the expense of the harmony predictors. To verify whether identity in fact robustly contributes to the predictive capacity of the model, we conduct a model comparison with the same model as in Table 1, but in which there is no identity predictor. The main effects of this “null” model are shown in Figure 4, and the full data are shown in Supplementary Materials.

The model comparison between the null model and the model with identity is carried out using approximate leave-one-out cross-validation (LOO; Vehtari et al. 2017), which estimates the out-of-sample predictive performance of each model. LOO evaluates how well a model predicts data it has not seen. If a model with an identity predictor has better LOO performance than a model without identity, this indicates that identity meaningfully improves predictions of vowel co-occurrence patterns. For the North Euralex data, the identity model was strongly favored over the null model (ELPD difference = –233.5, SE = 33.2), indicating that the identity effect captures meaningful structure in the data beyond what can be explained by a simpler model. For XPF data, the identity model was also favored over the null model (ELPD difference = –150.5, SE = 32.3). Because LOO accounts for model complexity by evaluating predictive performance on held-out data, these differences cannot be attributed solely to the identity model’s increased flexibility when the identity predictor is included.

To assess whether a preference against alignment for height relative to backness in Figure 3 might arise solely as an artifact of collinearity with identity, we examine these biases in the null model where identity is excluded as a predictor, and thus where the feature-based predictors can assume “credit” for all cases of identity. Figure 4 shows the posterior distributions for all binary effects in the model. Figure 5 shows a weaker asymmetry between height and backness. This suggests that identical pairs may account for some of the positive effects of height harmony (the credit for which the full model assigns to identity rather than to height harmony).

To further qualify the relationship between featural alignment along the dimensions of backness and height absent the effect of identity, we fit a model identical to the null model except that identical vowel pairs are omitted from the data entirely. In this model, featural predictors are left to account for just variability among non-identical pairs, which distills the relative influence of backness and height on vowel co-occurrence absent any possible effect of identity. The binary fixed effects are shown in Figure 6. While evidence for a robust cross-linguistic harmony bias is still weak, there is evidence that co-occurrence patterns favor alignment along the dimension of backness more strongly than along the dimension of height. The qualitative similarities in the correspondence between backness predictors in this and the original model (e.g. see Figure 3) suggest that backness and height predictors in the full model are adequate for capturing featural harmony as an over- or under-representation of vowel pairs with height or backness harmony.

To summarize, the current study of vowel co-occurrence patterns across two large cross-linguistic datasets shows that languages over-represent identity, while there is a lack of strong evidence for universal harmony along featural dimensions, as most languages individually do not represent any form of harmony. A model comparison further confirms that identity meaningfully contributes to the predictive capacity of the model, beyond what would be expected from the added model complexity of including an extra predictor and its random effects. Lastly, a post-hoc exploration of between-vowel variability for identity reveals some systematic tendencies for identity to be over-represented in certain vowels more than others, suggesting that vowel co-occurrence is nevertheless likely to be sensitive to phonetic and phonological properties of vowel categories.

The findings for featural harmony are consistent with the notion that vowel co-occurrence is not driven by either a preference for or avoidance of similarity which aligns with work by Walter (2010) and Doucette et al. (2024). Interestingly, the aggregate vowel similarity measures used by Doucette et al. (2024) did not detect identity-independent similarity biases even for Turkic languages, so the current results nevertheless underscore that aggregate similarity measures like those used in that study can obscure real featurally structured dependencies in vowel co-occurrence. Still, given evidence for identity biases but no evidence for universal partial similarity biases (outside of languages with productive harmony), one might conclude that the articulatory properties of vowels or the effects of vowel-to-vowel coarticulation are generally too weak to be reflected in the co-occurrence patterns of non-adjacent vowels. Our exploration of vowel-specific effects on vowel identity biases, however, shows that some vowels exhibit a greater over-representation of identity than others. In particular, across both the XPF and NorthEuraLex corpora, identity for /i/ and /a/ is underrepresented relative to other vowel categories like /y/, /e/ and /o/. Thus, there are likely to be language-general tendencies for certain identical vowel sequences to be more over-represented than others, and the current results suggest more broadly that universal properties of vowels can affect their co-occurrence patterns in measurable ways.

The statistical bias toward vowel identity was the most reliable cross-linguistic effect observed in this study and is in line with prior findings (Alderete & Finley 2016; Stanton 2021; Doucette et al. 2024). While languages varied in the extent to which they over-represented identity, this pattern persisted across modeling approaches and corpora, and no language showed reliable evidence of a robust statistical bias against vowel identity. The findings align with earlier corpus studies that have reported positive vowel identity effects, and support the view that segmental identity is distinct from alignment along featural dimensions, or more generally that the relationship between vowel pairs’ similarity and their attestation is nonlinear.

One possible explanation for the presence of an identity bias and absence of harmony biases is that identity emerges as a result of vowel assimilation but that assimilation is itself nonlinear. This view is compatible with some accounts of phonology proposing that assimilation is subject to similarity thresholds (Wayment 2009; Cole & Trigo 1988; Gallagher & Coon 2009). For example, parasitic vowel harmony is a well-documented nonlinearity in vowel co-occurrence whereby agreement along one featural dimension A is contingent on agreement along another featural dimension B (e.g. Alderete & Finley 2016; Cole & Trigo 1988). For example, Wayment (2009) argues that examples of nonlinear assimilation like parasitic harmony follow from a general attractor principle, wherein assimilation is driven by forces that strengthen representational connections between sufficiently similar segments. It is thus possible that there are universal interaction effects between particular featural dimensions that account for the excess of identity. That the strength of identity varies by vowel category is at least broadly consistent with this notion, as interactive thresholding might result in asymmetries in which vowel in a pair is a target of a change that results in identity. We ultimately leave investigation of such interactions, and the extent to which they are typologically widespread or language-specific, to future work.

An alternative account is that identity effects in the lexicon arise not from assimilation but from distinct copying mechanisms such as reduplication or epenthesis. Some work has suggested that identity is uniquely privileged in phenomena like reduplication (e.g. McCarthy 1995) as well as in echo epenthesis, where for some languages, the epenthetic vowel is a copy of another vowel in the stem rather than a single default vowel (e.g. Kitto & de Lacy 1999; Kawahara 2007). While the precise computational mechanism of these processes is contested, a generalization is that vowel identity can in principle emerge independently of processes for enforcing sub-phonemic featural similarity, via mechanisms that simply add information to an unfilled slot. Additionally, because they add to an unfilled slot, such mechanisms can also preserve lexical contrast and are thus less likely than assimilation to be disruptive to the phonological organization of the lexicon. Consider a toy case of reduplication:

These changes increase identity while maintaining the distinctiveness of the original stems. Identity in this case is no different than adding an affix. In contrast, partial assimilation in (d): /o/ → [e] conditioned by a following /i/ to resolve a lack of agreement for backness:

If synchronic processes or diachronic changes akin to morphological or epenthetic copying are in fact distinct from local assimilation as some work suggests (e.g. Kitto & de Lacy 1999; McCarthy 1995), this could provide one account for why identity is systematically preserved in the lexicon, while featural assimilation is not. It is not clear, however, that such mechanisms alone could account for vowel-specific (and language-general) tendencies for exhibiting identity, meaning that a preference for identity must at least to some extent be sensitive to the phonological properties of particular sounds and cannot “bypass” such properties entirely. While the current results suffice to show that identity is unlikely to emerge solely from linear assimilation, more work is necessary to empirically substantiate the possibility that distinct non-assimilatory mechanisms account for an identity over-representation in any meaningful way.

It is also possible that surface-level factors like the relative perceptual salience of identical vowel pairs may contribute to their over-representation compared to featurally aligned pairs. For example, Mintz et al. (2018), found that identity, but not featural harmony, facilitated lexical segmentation in infants. They argue that featural harmony does not offer a sufficiently robust cue for segmentation. Because identity is directly perceptible on the surface, possibly at the level of conscious awareness, and does not require listeners to group vowels by sub-phonemic features, it may be easier to encode and recall, leading to its persistence in the lexicon over time. To the extent that some vowels are more perceptually salient than others, such a proposal is consistent with the finding that identity biases vary systematically by vowel category.

More generally, there is evidence that the constraints learners infer from linguistic data do not follow linearly from the data; for example, Breiss & Albright (2022) find that learners make super-additive inferences from exposure to vowel co-occurrence data in an artificial language, and their grammaticality judgments do not match the frequency distributions of the input. In short, language users may themselves exhibit nonlinearities in terms of the inferences they draw from phonetic input, and to the extent that such inferences underlie grammars, they could result in nonlinearity in lexical data. Whether nonlinearities in learners’ inferences can actually account for the empirical results presented here remains to be determined.

To better adjudicate the role that communicative or information-theoretic factors like preservation of lexical contrasts play in determining attestation of assimilation-driven phonological patterns, it would be necessary to quantify the actual effect such statistical biases have on the lexicon. An inviolable constraint for complete identity within words is intuitively untenable, so there is likely an upper limit at which point a language cannot sustain an over-representation of identity. What constitutes such an upper-limit, however, is ill-defined. The current O/E-based linear modeling approach is well-equipped to detect deviations from a baseline where sounds are allowed to combine freely, but is limited in its ability to show what the proximity of any effects is to such an upper limit. It is thus also necessary to describe the nature and extent of redundancy already present in a language’s baseline model of free combination that is attributable only to the relative frequency of sounds themselves. If a substantial degree of structure emerges even in the absence of explicit co-occurrence restrictions, then the overattestation of phenomena like identity could be lower than in a language whose baseline exhibits a high degree of lexical distinctiveness.

While this study shows that there is no universal alignment of vowel pairs along the dimensions of backness or height, the effect of other featural dimensions cannot be ruled out. It is also possible that all languages exhibit harmony-like biases in at least one dimension but that the dimensions of these biases are language-specific. This proposal is consistent with the notion that productive harmony systems more generally vary by the features they use to enforce agreement like ATR and roundness. These are not included because they are not contrastive in many languages, and roundness is redundant with back in many languages. The hierarchical modeling structure partially mitigates this limitation. Because the model includes random slopes by language and family, languages are not forced to conform to the patterns predicted by these two features alone; languages exhibiting harmony or co-occurrence patterns based on other dimensions (e.g. ATR, rounding, nasality) will show this through systematic deviations in their language-specific random effects. But more work is necessary to explicitly rule out the possibility that these or other featural dimensions consistently mediate co-occurrence patterns.

Relatedly, the current corpora do not make use of fully narrow transcriptions, and thus the analyses may ignore pressures in favor of similarity that occur along more granular dimensions that could be captured with narrower transcriptions. Future work should extend the current approach to more featural dimensions and to data with narrower transcriptions. Analyses of individual languages should also be carried out to uncover sources of variability that are potentially obscured in the large-scale approach taken here.