2.1 Similar vowel co-occurrence effects

One of the most well-documented co-occurrence effects in vowels is harmony, a phonological process in which similar vowels in a particular domain (generally a word) are more likely to co-occur than dissimilar vowels. Vowel harmony processes have been documented in many languages, across many language families (Archangeli & Pulleyblank 2007; Rose & Walker 2011; Gordon 2016; Ritter & van der Hulst 2024).

While vowel harmony is typically described as applying categorically in the relevant contexts (with few exceptions), cases of gradient harmony, where the phonological process applies probabilistically, have been identified using statistical methods (Archangeli et al. 2012: for Bantu languages). By examining co-occurrence probability as a function of vowel similarity, gradient vowel harmony patterns can be identified in languages without documented vowel harmony processes. Walter (2010) identifies a gradient vowel harmony pattern in Croatian, and speculates that a tendency toward similar vowel co-occurrence may be universal – that similar vowels are more likely to co-occur than dissimilar vowels across all languages. Our paper explicitly tests this possibility by examining the effect of similarity on vowel co-occurrences across a large sample of languages.

While harmony appears to be the most widely studied vowel co-occurrence effect, cases of anti-harmony – where dissimilar vowels are more likely to co-occur – have also been documented, often as exceptions to otherwise regular harmony processes. For example, Russian loanwords in Tuvan appear to be exceptions to backness harmony ([ɨraketa] ‘rocket’, Harrison 1999). In other words, although similar vowel co-occurrences appear to be much more common across languages, similar vowel avoidance is also possible.

2.2 Similar consonant co-occurrence effects

In contrast to vowel co-occurrence effects, similar consonant co-occurrence appears to be avoided. Similar consonant co-occurrence restrictions have been documented in many languages. The Obligatory Contour Principle (OCP) is a widely discussed co-occurrence restriction that prohibits adjacent identical elements from co-occurring (Leben 1973; McCarthy 1986). While the OCP was originally formulated as a categorical restriction, gradient consonant co-occurrence restrictions have also been identified in several languages. Frisch et al. (2004) found that the more natural classes that are shared between a pair of consonants, the less likely that pair is to occur in an Arabic root. Pozdniakov & Segerer (2007), Coetzee & Pater (2008), Mayer et al. (2010), and Graff (2012) identified gradient co-occurrence restrictions in many languages (mainly on place of articulation features), suggesting that this may be a universal restriction against similar consonant co-occurrence. The models described in this paper will test for this, generalizing from similarity based only on place of articulation features to similarity across all features.

There are also languages where similar consonants are likely to co-occur. Consonant harmony has been identified in some languages (Rose & Walker 2004; Hansson 2010; Rose & Walker 2011), but it appears to be restricted to sets of segments defined by particular features (coronals, sibilants, etc.) or by intersections of features in most cases.

2.3 Identical segment co-occurrence effects

Further complicating this picture of co-occurrence effects, there is evidence that in some languages, completely identical pairs of segments can behave differently from merely similar segments.¹ We define identity as total identity: Agreement for all features. In contrast, we define similarity in terms of the shared features between a pair of non-identical segments. For example, [t] and [t] are considered identical because they share all features, while [t] and [d] are considered similar because they differ in the [voice] feature.

MacEachern (1999) found that in several languages with strong co-occurrence restrictions on similar consonants, identical consonants could still co-occur. In Peruvian Aymara, words with two ejective consonants are prohibited in general, but are allowed if they are identical.² Pozdniakov & Segerer (2007) and Coetzee & Pater (2008) found that identical consonant pairs occurred more frequently than expected in many languages. In Arabic roots, consonants with the same place of articulation cannot co-occur in general, but identical consonants can co-occur in specific circumstances (Greenberg 1950; McCarthy 1986).

There is less evidence for the effect of identity on vowel co-occurrence. In Croatian and Spanish, Walter (2010) found that identical vowel pairs are underattested. In Croatian, similar but not identical vowel pairs are overattested, but in Spanish they are underattested. There does not appear to be any evidence of vowel identity effects differing from similarity effects in other languages.

Finally, there is evidence that humans have a specialized cognitive mechanism for processing identical elements (Endress et al. 2009). This evidence, along with evidence of identical segments behaving unusually in several languages, suggests that identity does not function simply as a stronger form of similarity, and should be considered separately. For these reasons, identity and similarity were included as independent effects a priori in our models.

2.4 Relationships between vowel and consonant effects

Co-occurrence effects on vowels and consonants have previously only been investigated independently of each other, with analyses failing to include the possibility that they are related in some way. There are several ways in which vowel and consonant co-occurrence effects could be related. First, consonant or vowel effects could be systematically larger than the other. Differences in relative effect sizes could explain discrepancies between how often vowel and consonant co-occurrence patterns are identified in languages.

It could be possible that similar vowel co-occurrence restrictions are near-universal while similar consonant co-occurrence effects are fairly common but not universal, or that identical consonants co-occur freely while identical vowel co-occurrence is restricted. Another possibility is that both vowel and consonant co-occurrence effects are near-universal, but one is significantly smaller and harder to detect. We investigate these possibilities by comparing vowel and consonant effect sizes in our models.

Second, the size of consonant and vowel co-occurrence effects could be correlated across languages. The structure of the Bayesian regression models we use will allow us to estimate correlations between vowel and consonant effects across languages. We have no strong expectations about the existence or direction of a correlation. There could be no correlation, meaning that vowel and consonant effects are completely independent. Another possibility is that languages will have strong co-occurrence effects in both vowels and consonants, perhaps because learning “language x has harmony” is easier than “language x has harmony in vowels, but not in consonants.” Finally, languages could have strong co-occurrence effects in either consonants or vowels (but not both) due to information theoretic restrictions on the lexicon. If vowel co-occurrences are strongly restricted in a language, consonants would need to be relatively unrestricted to allow for sufficient coding space in the lexicon. As far as we know, no work has been done investigating these possibilities.

3.1 Data

We use data from NorthEuraLex (Dellert et al. 2020), a set of comparable lexicons for 107 Northern Eurasian languages, across 21 families. Language families included in NorthEuraLex are listed in Table 1, along with the languages and subfamilies included in them. For each language, there are IPA transcriptions of 1,016 basic concepts (where a “concept” is a whole word, including inflectional morphology). Because it is typically assumed that co-occurrence restrictions are influenced more by word types rather than tokens, we do not include any further information about concept frequency (Frisch et al. 2004; Wilson & Obdeyn 2009). Transcriptions for some languages were automatically generated, so some manual data cleaning was necessary to make transcriptions consistent across all languages. For example, different Unicode symbols are used to represent the same IPA symbols in some cases, and some transcriptions have erroneous IPA diacritics (e.g. occurring independently of a base segment).³

We chose NorthEuraLex over other parallel corpora because it contains a much larger set of languages than others. Although there are a relatively small number of words per language, we are interested in cross-linguistic generalizations about co-occurrences, rather than properties of individual languages. Although inflectional morphology is included in the data for some languages, the majority of concepts are lemmas without inflection (Pimentel et al. 2020). Thus, our results are unlikely to be affected by repeated instances of inflectional morphemes.

While NorthEuraLex represents 21 language families, two are particularly overrepresented – Indo-European with 37 languages, and Uralic with 26 languages. To account for this disparity in language family representation, we instead classify these languages by their subfamilies. This change allows for a more even distribution of language family sizes.⁴

Counting co-occurrences requires defining what counts as a co-occurrence in the lexicon. This has been done in various ways in previous work, e.g. just using parts of words (Frisch et al. 2004) or words of a certain shape (Graff 2012) to deal with statistical non-independence. We instead choose to maximize the amount of data per language, by making the following choices. Co-occurrences were counted as pairs of vowels separated by one consonant or consonant cluster, and pairs of consonants separated by one vowel. Because many languages in NorthEuraLex do not allow vowel or consonant clusters, only non-adjacent pairs were counted to ensure results are comparable across languages. For example, the word [kɑnsənənt] would result in the consonant pairs [kn], [sn], and [nn], and the vowel pairs [ɑə], and [əə].

3.2 Similarity metrics

To ensure that results are not dependent on a particular similarity metric, we fit models using two different feature-based similarity metrics – Feature Similarity, and Natural Class Similarity. Both of these similarity metrics are calculated using the phonological features of a pair of segments. Phonological features describe the articulatory and acoustic dimensions along which speech sounds vary, abstracting away from raw acoustic measurements. For all languages, we used the same set of binary features from PanPhon (Mortensen et al. 2016), which are listed in Appendix A.

Feature Similarity (Equation 1), first used by Pierrehumbert (1993), is the simplest possible measure: A normalized intersection size between the phonological features of two segments. Although the PanPhon feature set contains 24 features, not all of these are relevant in every language. For example, if a language has a consonant inventory of [p t k], the feature [strident] is not relevant because there are no [s] or [ʃ]-like consonants. The features [coronal], [labial], and [back] would be included in the feature set for this language, because they are contrastive for the set of three obstruents. In Equation 1, |Feats| refers to the number of relevant features in a given language.

$FeatSim(x,y)=\frac{|Feats(x)\cap Feats(y)|}{\left|Feats\right|}$           (1)

Although Feature Similarity has a range of [0, 1] (from sharing no features to being completely identical), in practice there is a minimum similarity value in real languages – no pair of consonants or vowels in an inventory share zero features. Features that are only relevant to consonants will be shared among all vowels, and features that are only relevant to vowels will be shared among all consonants. Because consonant inventories are generally larger than vowel inventories, thus requiring more distinctive features, this results in a skewed distribution – under the Feature Similarity metric, vowels are inherently more similar than consonants. This can be seen in Figure 1.

Figure 1: Density plot of similarity metrics across all consonant and vowel pairs.

The Natural Class Similarity metric, originally defined by Frisch (1996) and widely used in other studies of gradient phonotactics (Frisch et al. 1997; MacEachern 1999; Frisch et al. 2004; Wilson & Obdeyn 2009; Walter 2010), defines natural classes as sets of segments that share one or more features. In this similarity metric, features that are only partially contrastive in an inventory contribute less to the similarity score than fully contrastive features (in Feature Similarity, all features contribute equally).⁵ Natural Class Similarity is calculated according to Equation 2, where NC(x) gives the set of natural classes for segment x.

$NCSim(x,y)=\frac{|NC(x)\cap NC(y)|}{|NC(x)\cup NC(y)|}$           (2)

Natural Class Similarity also has a range of [0, 1], but is greater than zero in practice. Any consonant or vowel pair shares at least one natural class – the class including all consonants or vowels.⁶ However, unlike in Feature Similarity, vowels are not inherently more similar under the Natural Class Similarity metric, as shown in Figure 1. Features that are shared between all vowels are “ignored” in the Natural Class Similarity calculation, because they do not allow for the formation of a distinct natural class. Although these two metrics are clearly correlated, we fit models for both of them in part because of their different treatment of vowel similarity.

3.3 Models

Previous work has used observed/expected (O/E) ratios or logistic regression to model co-occurrences (Frisch et al. 2004; Graff 2012). An O/E ratio for a particular pair of segments x and y is calculated according to Equation 3, where N is the total number of observed pairs, O_x+ is the number of times x occurs as the first segment in a pair, and O_+y is the number of times y occurs as the second segment in a pair.

$\frac{O_{xy}}{E_{xy}}=\frac{O_{xy}}{N\cdot \frac{O_{x+}}{N}\cdot \frac{O_{+y}}{N}}$           (3)

While this ratio has the benefit of being easily interpretable (values greater than 1.0 correspond to over-attestation, while values under 1.0 correspond to under-attestation), it has several disadvantages. First, it assumes that the O/E ratio is directly correlated with the variables of interest (in our case, similarity and identity). As pointed out by Wilson & Obdeyn (2009), there is no theoretical justification for why we should choose O/E over a different value, like O – E. It is also not possible to account for control predictors in an O/E ratio: It simply accounts for the positional frequencies of individual segments. For example, we may want to account for varying inventory sizes across languages. Because similarity values depend on the number of distinctive features or natural classes in a language, they are expected to be somewhat dependent on inventory size: A larger inventory requires more distinctive features. This is shown in Figure 2. Thus, in order to compare results across languages, we need a method that allows for control predictors.

Figure 2: Consonant and vowel inventory size plotted against mean similarity per language, with linear smooths (lines) and 95% confidence intervals (shading).

To compensate for the shortcomings of O/E ratios, we use multivariate Bayesian regression to model the effects of similarity and identity on consonant and vowel co-occurrence. This type of model offers several advantages over previous models. This method follows Graff (2012) and Wilson & Obdeyn (2009) in using regression modeling, which allows for control predictors. We are able to directly model co-occurrence counts, rather than the probability of a co-occurrence being attested in a language. We are also able to estimate effects across a large set of languages, and include random effects for language and language family (as a basic control for typological relatedness). By using multivariate regression, we can simultaneously model consonant and vowel co-occurrence, and estimate correlations between random effects. Through Bayesian regression, we obtain posterior distributions for each parameter in the model, rather than point estimates and confidence intervals. From these posteriors, we can conduct Bayesian hypothesis tests, allowing us to reject or accept null hypotheses, as described in §4.

Although multivariate Bayesian regression allows for greater flexibility in modeling co-occurrence, the results obtained are not as directly interpretable as O/E ratios. Our model estimates the number of times a particular segment pair occurs – an estimate of the O_xy in Equation 3. $\frac{O_{+x}}{N}$ and $\frac{O_{+y}}{N}$ are the frequencies of x and y in a sample of N pairs, which can be obtained by counting segments in the NorthEuraLex data. These frequencies are included as offsets in the models, allowing us to interpret the model predictions as the degree of co-occurrence beyond what is expected from individual segment frequencies. Therefore, we can transform any model prediction into a predicted O/E ratio, accounting for the model’s control predictors and random effect estimates, according to Equation 3. This predicted O/E ratio can be calculated for every value of similarity and identity, for each language in our sample, and will be used to aid in interpretation of results in §4.

Observed pair counts for consonant (O_xy/C) and vowel (O_xy/V) co-occurrences are each modeled with a negative binomial distribution, as shown in Equations 4 and 5.⁷ Negative binomial regression is a generalization of Poisson regression (Winter & Bürkner 2021) used to model count data, which relaxes the latter’s assumption of equal mean and variance by including an additional shape parameter (ϕ_C and ϕ_V in Equations 4 and 5), allowing the data to be overdispersed.

$O_{xy/C}\sim \text{NegBinom}({\mu }_C,\hspace{0.17em}{\varphi }_C)$           (4)

$O_{xy/V}\sim \text{NegBinom}({\mu }_V,\hspace{0.17em}{\varphi }_V)$           (5)

The expected values of these distributions are the mean parameters μ_C and μ_V:

$\mathbb{E}[O_{xy/C}]={\mu }_C$           (6)

$\mathbb{E}[O_{xy/V}]={\mu }_V$           (7)

The variances of the distributions are functions of the means μ_C and μ_V and the shape parameters ϕ_C and ϕ_V:

$\text{Var}[O_{xy/C}]={\mu }_C+\frac{{\mu }_C^2}{{\varphi }_C}$           (8)

$\text{Var}[O_{xy/V}]={\mu }_V+\frac{{\mu }_V^2}{{\varphi }_V}$           (9)

The means of the distributions are modeled as linear functions of predictors. Main effect predictors, represented by β parameters in equations, include similarity (sim), identity (ident), log consonant inventory size (ln(|C_inv|)), log vowel inventory size (ln(|V_inv|)), and an intercept.⁸ For example, β_intercept|C is the intercept for the consonant co-occurrence model. Random effects for similarity and identity are included by language family (γ parameters, i.e. γ_sim|C: the by-family random effect of similarity in the consonant co-occurrence model), and by-language within family (α parameters, i.e. α_ident|V: the by-language random effect of identity in the vowel co-occurrence model). As an individual language only belongs to one family, these random effects are nested (see Sonderegger 2023: §10.2.2 for more details). The similarity effect parameters are multiplied by (1 – ident(x, y)), which has the effect of setting them to zero when x and y are identical. Thus, when x and y are identical the similarity effect parameters do not contribute to μ, and when x and y are not identical, the identity effect parameters do not contribute to μ. The log frequencies of each segment in the pair are included as offsets in the models (1 is added to observed counts to avoid ln(0) in the case where a segment does not occur in a position):

$\begin{array}{ll}\ln ({\mu }_C)=\hfill & {\beta }_{\text{intercept}|C}+{\gamma }_{\text{intercept}|C}+{\alpha }_{\text{intercept}|C}\hfill \\ \hfill & +\hspace{0.17em}(1–\text{ident}(x,y))\cdot \text{sim}(x,y)\cdot ({\beta }_{\text{sim}|C}+{\gamma }_{\text{sim}|C}+{\alpha }_{\text{sim}|C})\hfill \\ \hfill & +\hspace{0.17em}\text{ident}(x,y)\cdot ({\beta }_{\text{ident}|C}+{\gamma }_{\text{ident}|C}+{\alpha }_{\text{ident}|C})\hfill \\ \hfill & +\hspace{0.17em}{\beta }_{\text{C.inv}|C}\ln (|{\text{C}}_{\text{inv}}|)+{\beta }_{\text{V.inv}|C}\ln (|{\text{V}}_{\text{inv}}|)\hfill \\ \hfill & +\underset{\text{segment}\hspace{0.17em}\hspace{0.17em}\text{frequency}\hspace{0.17em}\hspace{0.17em}\text{offset}}{\underbrace{\ln \left(\frac{O_{x+}+1}{N}\cdot \frac{O_{+y}+1}{N}\right)}}\hfill \end{array}$           (10)

$\begin{array}{ll}\ln ({\mu }_V)=\hfill & {\beta }_{\text{intercept}|V}+{\gamma }_{\text{intercept}|V}+{\alpha }_{\text{intercept}|V}\hfill \\ \hfill & +\hspace{0.17em}(1–\text{ident}(x,y))\cdot \text{sim}(x,y)\cdot ({\beta }_{\text{sim}|V}+{\gamma }_{\text{sim}|V}+{\alpha }_{\text{sim}|V})\hfill \\ \hfill & +\hspace{0.17em}\text{ident}(x,y)\cdot ({\beta }_{\text{ident}|V}+{\gamma }_{\text{ident}|V}+{\alpha }_{\text{ident}|V})\hfill \\ \hfill & +\hspace{0.17em}{\beta }_{\text{C.inv}|V}\ln (|{\text{C}}_{\text{inv}}|)+{\beta }_{\text{V.inv}|V}\ln (|{\text{V}}_{\text{inv}}|)\hfill \\ \hfill & +\hspace{0.17em}\underset{\text{segment}\hspace{0.17em}\hspace{0.17em}\text{frequency}\hspace{0.17em}\hspace{0.17em}\text{offset}}{\underbrace{\ln \left(\frac{O_{x+}+1}{N}\cdot \frac{O_{+y}+1}{N}\right)}}\hfill \end{array}$           (11)

Exploratory data analysis showed that languages differ in the variance of pair counts. Therefore, the shape parameters ϕ_C and ϕ_V are allowed to vary by language family and by language within family:

$\ln ({\varphi }_C)={\gamma }_{\varphi |C}+{\alpha }_{\varphi |C}$           (12)

$\ln ({\varphi }_V)={\gamma }_{\varphi |V}+{\alpha }_{\varphi |V}$           (13)

In Bayesian regression, prior distributions need to be specified for each parameter in the model. Although priors can be informed by domain knowledge, any prior will be overwhelmed by a large quantity of data. We use weakly informative priors, meaning that they impose weak constraints on the likely values of parameters (Nicenboim & Vasishth 2016; Vasishth et al. 2018). For example, for all main effect parameters, the following prior is used:

$\beta \sim \mathcal{N}(\mathrm{0,}\hspace{0.17em}4)$           (14)

This distribution is plotted in Figure 3. Although all values are possible, it puts slightly more weight on values near zero with 95% falling between –7.84 and 7.84. A change of 7.84 in log space corresponds to a change of approximately 2540 in raw pair counts. All pair counts in NorthEuraLex are under 1000, making this a very conservative prior.

Figure 3: Prior distribution densities for standard deviation (σ), correlation (ρ), and fixed effect (β) model parameters.

The separate models for consonant and vowel co-occurrence are tied together through their random effect priors. Random effects by language have a multivariate normal prior:

$\left[\begin{array}{c}{\alpha }_{\text{intercept}|C}\\ {\alpha }_{\text{intercept}|V}\\ {\alpha }_{\text{sim}|C}\\ {\alpha }_{\text{sim}|V}\\ {\alpha }_{\text{ident}|C}\\ {\alpha }_{\text{ident}|V}\end{array}\right]\sim \text{MVNorm}(\mathrm{0,}\hspace{0.17em}{\Sigma }_{\alpha })$           (15)

The covariance matrix Σ_α is shared across the consonant and vowel models, and is parameterized in a standard way (Equation 16: See McElreath 2020 for more details). After fitting the model, correlations between consonant and vowel random effects can be extracted from this matrix. Σ_α is defined as:

${\Sigma }_{\alpha }=S_{\alpha }R{S}_{\alpha }$           (16)

Where S_α is a diagonal matrix:

$S_{\alpha }=\left[\begin{array}{ccccc}\sigma ({\alpha }_{\text{intercept}|C})& 0& & \cdots & 0\\ 0& \sigma ({\alpha }_{\text{intercept}|V})& & \cdots & 0\\ ⋮& & \ddots & & ⋮\\ 0& \cdots & & \sigma ({\alpha }_{\text{ident}|C})& 0\\ 0& \cdots & & 0& \sigma ({\alpha }_{\text{ident}|V})\end{array}\right]$           (17)

And R is a correlation matrix with an LKJ hyperprior (Lewandowski et al. 2009):

$R\hspace{0.17em}\sim \hspace{0.17em}\text{LKJcorr}(1.5)$           (18)

The LKJ prior penalizes strong (non-zero) correlations, and is plotted in Figure 3. We have no a priori evidence of any relationship between consonant and vowel effects, so we use a weakly informative prior that penalizes strong correlations. Language family random effects (γ parameters) are parameterized in exactly the same way as by-language random effects.

The prior for standard deviation parameters, plotted in Figure 3, is:

$\sigma \hspace{0.17em}\sim \hspace{0.17em}\text{HalfStudentT}(\mathrm{3,}\hspace{0.17em}\mathrm{0,}\hspace{0.17em}2.5)$           (19)

And finally, we specify a prior for the shape parameters ϕ_C and ϕ_V as the default weakly informative prior used by brms (Bürkner 2017):

${\varphi }_C,\hspace{0.17em}{\varphi }_V\hspace{0.17em}\sim \hspace{0.17em}\Gamma (\mathrm{0.01,}\hspace{0.17em}0.01)$           (20)

Two models, one using Natural Class Similarity (referred to as the NC model) to define sim(x, y) in Equations 10 and 11, and one using Feature Similarity (the Feat model) to define sim(x, y) in Equations 10 and 11, were implemented in brms (Bürkner 2017), an R (R Core Team 2020) interface to the Stan probabilistic programming language (Stan Development Team 2019; Gabry et al. 2023). Models were fit using four Markov chains with 5000 warmup samples and 20000 post-warmup samples each. R̂ and ESS values suggested model convergence.

4.1 Vowel effects

4.2 Consonant effects

4.3 Relationships between vowel and consonant effects

Although vowel and consonant co-occurrence effects are in different directions, we can compare the absolute value of the effect sizes because both are measured on the same similarity scale. Consonant identity effects are on average larger than vowel identity effects in both models (NC: |β_ident|C| – |β_ident|V| = 0.31, 95% CredI = [0.13, 0.48], BF = 2.92 × 10²; Feat: |β_ident|C| – |β_ident|V| = 0.84, 95% CredI = [0.60, 1.07], BF = ∞). Identical consonant co-occurrence is disfavored to a greater degree than identical vowel co-occurrence is preferred. The same is true for similarity effects. In both models, consonant similarity effects are larger than vowel similarity effects (NC: |β_sim|C| – |β_sim|V| = 0.74, 95% CredI = [0.65, 0.83], BF = ∞; Feat: |β_sim|C| – |β_sim|V| = 0.96, 95% CredI = [0.80, 1.09], BF = ∞). This suggests that across languages, consonant co-occurrence is more strongly constrained than vowel co-occurrence.

We also see no evidence of correlations between vowel and consonant effects, as shown in Tables 6 and 7 and Figure 6: All credible intervals include zero, and all Bayes factors are between 1/3 and 3. There is no evidence of a correlation between consonant and vowel similarity effects across language families or across languages within families. There is also no evidence of a correlation between consonant and vowel identity effects across families or languages. As with previous results for correlations, we cannot conclude anything about correlations between consonant and vowel effects without more data.

5.2 Identity effects

The same universals do not appear to apply to identical consonants and vowels. In both consonants and vowels, we see significantly more variation in identity effects than in similarity effects across languages. Identical consonant co-occurrence is dispreferred, but varies greatly across languages. The effect is strongly negative enough that in the O/E plots in Figures 7 and 8, identical consonants occur less often than expected in nearly all languages, but a small number have a zero or positive effect. While languages like Peruvian Aymara (MacEachern 1999) and Arabic (McCarthy 1986) allow identical consonant co-occurrence but prohibit similar consonant co-occurrence, they are fairly uncommon and perhaps have been noted in the literature because of their surprising nature. The majority of languages do not follow this pattern.

The effect of identity on vowel co-occurrence also differs from the effect of similarity. We find a positive vowel identity effect, suggesting that languages tend to repeat identical vowels within words while having no preferences for the co-occurrence of similar vowels. Like consonant identity effects, vowel identity effects vary enough to allow for languages with a zero or negative effect, like in Spanish and Croatian (Walter 2010). This can be seen in Figures 7 and 8, where most languages have pairs of identical vowels occurring more often than expected, and some less often than expected. In particular, we see languages with vowel harmony processes, like Turkish, with an O/E ratio greater than one for identical vowels even though the O/E ratio is near one for similar vowels.¹³ While vowel harmony is typically thought to arise from phonologized coarticulation (Ohala 1994), this suggests that it may have a source in the lexicon as well. Perhaps identical vowel pairs in the lexicon are more salient to language users, and this is phonologized as a more general rule that identical features must co-occur, resulting in vowel harmony.

5.3 Relationships between vowel and consonant effects

We find that consonant co-occurrence is more strongly restricted than vowel co-occurrence across languages. While vowels can co-occur relatively freely, there are much stronger constraints on similar and identical consonant co-occurrence. Nespor et al. (2003) hypothesize that there is a division of labor between vowels and consonants: Consonants are responsible for making distinctions between lexical items, while vowels signal rhythmic class and syntactic structure.

Our results appear to go against this hypothesis. While restricting similar and identical consonant co-occurrence promotes distinctness in consonants within a word, the total coding space available for the lexicon is reduced. Any phonotactic constraint reduces the number of possible words available to a language, and thus the number of possible lexical items that can be distinguished. Vowel co-occurrence, on the other hand, is relatively unrestricted. While Nespor et al. (2003) claim that vowels tend to neutralize (i.e. become more similar) within words, we find little evidence of this. In our analysis, most languages have a tendency towards identical vowel co-occurrence, but there are plenty that have the opposite tendency. Nespor et al.’s (2003) claim that consonants are crosslinguistically more numerous than vowels which makes them more informative is still consistent with our results. However, their claim that the specialized role of consonants goes beyond their numerical superiority is not.

Our finding that consonant identity effects are larger than vowel identity effects may also help explain why identical consonant effects have been found more frequently than identical vowel effects. Consonant identity effects have been found in many languages through examination of OCP effects (McCarthy 1986; Pozdniakov & Segerer 2007; Coetzee & Pater 2008). Vowel identity effects are rarely mentioned (Walter 2010). This may not be because vowel identity effects are uncommon, but rather because they are smaller and more difficult to detect.

Beyond differences in effect size, we found no further relationships between vowel and consonant effects. All correlations estimated by the Bayesian models were near zero, but with large credible intervals. Bayes factors for these parameters were all approximately 1.0, suggesting that we don’t have enough evidence to determine if there is or is not a correlation. If we found Bayes factors significantly smaller than 1.0, we would be able to conclude that there is no correlation, but this is not the case. Instead, we have found that either more data or a different statistical model is needed to make conclusions about the existence of a correlation between vowel and consonant co-occurrence effects.

5.4 Natural class similarity and feature similarity

To determine the robustness of our results, models were fit using two different similarity metrics, each with slightly different properties. The choice of similarity metric appears to have only minor effects on qualitative results. For all main effects, the conclusions drawn from both models are the same. The only difference between the two is found in Bayes factors for language-level random effects in three model parameters. For consonant similarity (α_sim|C) and vowel identity (α_ident|V), both models estimate a positive standard deviation across languages within families, but this result is only confirmed by large Bayes factors in the NC model. In the Feat model, the Bayes factors suggest that there is no variance in these effects. Similarly, for consonant identity (α_ident|C), a small Bayes factor in the NC model suggests no variation across languages within families, but the Bayes factor in the Feat model shows uncertainty about the existence of this variance.

Many language families in NorthEuraLex contain a very small number of languages: One or two in many cases. Because of this, our results for these parameters may be due to the size of our dataset, rather than any real difference between the two similarity metrics. The consistency in parameter estimates using both metrics suggests that perhaps one is not “better” than the other when investigating co-occurrence across a large number of languages: Both feature similarity and natural class similarity appear to be equally valid.

5.5 Future work

While these results present a clear picture of general trends in co-occurrence effects, they have several limitations which could be addressed in future work. First, the two similarity metrics used treat all phonological features equally. It is likely that certain features contribute more to similarity than others (such as place of articulation features), or that individual features have different effects on co-occurrence restrictions. Modeling the co-occurrence of individual features would allow us to examine whether or not the co-occurrence effects identified are a result of specific feature co-occurrences, or an aggregate measure of similarity.

Furthermore, we only examine co-occurrence in pairs of segments. Harmony and OCP processes are known to operate in the domain of an entire word or root. While co-occurrence restrictions that affect an entire word can be identified by examining local co-occurrences, our results are not informative about any long-distance patterns. Modeling pairs across longer distances, or modeling longer sequences of segments, could help account for this possibility.

We also acknowledge that while NorthEuraLex contains a fairly large set of languages, it is a sample of languages from specific geographic areas, and does not represent a truly random sample of the world’s languages. In future work, gathering a similar dataset of a larger variety of languages would allow for more reliable results. A larger set of languages could also allow us to estimate the correlation parameters in our model. Unfortunately, this dataset does not currently exist, although recent work on grapheme-to-phoneme transcription suggests that it may be within reach (McCarthy et al. 2023).

Finally, we note that individual languages or families are not statistically independent. There are further dependencies between languages that are not captured by these controls, such as geographic and historical relationships. While controlling for language family provides a simple baseline, some language families are obviously more related than others. Including some measure of geographic or typological distance in the models would better account for dependencies between languages, but we leave this for future work.

5.6 Conclusion

In summary, we have shown that there is something fundamentally different about the way consonants and vowels interact within words. Across languages and families, similar and identical consonant co-occurrence is restricted. In vowels, similarity does not appear to constrain co-occurrence, but there is a preference for identical vowels to co-occur in most languages. These co-occurrence effects are consistent across a large sample of languages and language families, showing the benefit of a large-scale cross-linguistic study to shed new light on the longstanding question of what forces shape the structure of lexicons.