1. Introduction

Measures of lexical frequency have played an important role in research on morphological processing. For example, word frequency and base frequency effects on acoustic duration have been used to draw inferences about how complex words are stored in the mental lexicon (e.g., N. K. Caselli, Caselli, M. K., & Cohen-Goldberg, 2016). These frequency measures seem to be accepted in the literature also as important predictors of acoustic duration, as a number of studies have demonstrated higher frequency to be associated with more phonetic reduction (see, e.g., A. Bell et al., 2003; J. L. Bybee, 2000; Gahl, 2008; Jurafsky, Bell, Gregory, & Raymond, 2001; Jurafsky, 2003; Losiewicz, 1995; Pluymaekers, Ernestus, & Baayen, 2005a, 2005b). In accordance with the idea that “[w]hat you do often, you do better and faster” (Divjak, 2019, p. 1), more frequent words are more quickly produced and thus more likely to be shortened.¹

However, a third possible frequency measure has been suggested which so far has produced rather mixed results: the relative frequency of a complex word compared to its base word (Hay, 2001, 2003). Relative frequency supposedly taps into morphological segmentability. If speakers encounter a base word often compared to its derivative, the derivative is more easily decomposed into its morphological constituents and is more likely to be processed compositionally. It is expected that words which are more easily segmentable, i.e., words with a stronger morphological boundary, are less likely to be phonetically reduced (Hay, 2001, 2003). However, relative frequency effects on acoustic duration have proven to be notoriously inconsistent. On the one hand, relative frequency effects on duration emerge in some studies under some conditions for some affixes (Hay, 2003, 2007; Plag & Ben Hedia, 2018); on the other, research has also yielded many null effects (Ben Hedia & Plag, 2017; Plag & Ben Hedia, 2018; Pluymaekers et al., 2005b; Schuppler, van Dommelen, Koreman, & Ernestus, 2012; Zimmerer, Scharinger, & Reetz, 2014; see also Hanique & Ernestus, 2012 for a critical review of the findings of earlier studies).

One potential reason for this seemingly inexplicable inconsistency is the prosodic structure of complex words. Plag and Ben Hedia (2018) speculate that it might be more difficult for a relative frequency effect to emerge in affixes that are phonologically integrated into the prosodic word of the derivative, compared to those that form independent prosodic words (Raffelsiefen, 1999, 2007). This is because pre-boundary lengthening caused by a stronger word-internal prosodic boundary might counteract potential reduction effects. While some previous evidence suggests that “morphological effects on fine phonetic detail cannot always be accounted for by prosodic structure” (Pluymaekers, Ernestus, Baayen, & Booij, 2010, p. 523; also see Plag, Homann, & Kunter, 2017, p. 210), there is also evidence in favor of an effect of prosodic word boundaries in complex words on duration. For example, Sproat and Fujimura (1993) show that English /l/ is longer and more likely to be realized as [ɫ] before compound-internal boundaries, which are comparatively strong, than before affix boundaries, which are comparatively weak, or than within simplex words. Auer (2002) shows that final devoicing of /b/ in German suffixed words is characterized by a plosive release which is longer in derivatives with a word-internal prosodic word boundary than in derivatives with no such boundary. Sugahara and Turk (2009) find that segments in base-final rhymes of English affixed words preceding a stronger prosodic boundary are lengthened. Bergmann (2018) demonstrates that segments straddling a boundary in infrequent German derivatives are lengthened when these derivatives feature prosodic word-forming suffixes, compared to when they feature integrating suffixes. These findings suggest that the prosodic word structure of complex words impacts on their durational patterning and needs to be considered when investigating segmentability effects.

In addition to the suspicion that reduction effects due to segmentability might be counteracted by effects of prosodic word structure, there are also two further problems of previous research which need to be addressed. One problem is that earlier studies often only looked at few affix categories individually. This makes it difficult to compare studies (with often different methodologies) across affixes. The second problem is that different studies investigated different domains of durational variation. For example, some studies investigated the duration of the affix, while others looked at the deletion of individual segments. This renders a comparison of studies even more difficult.

The present study addresses these issues. In a broad empirical study, we test how prosodic word structure and relative frequency influence duration, and how the two factors might interact. We do this by making use of three different speech corpora of English. We model the durations of words featuring eight different affixes each, looking at both affix durations and base durations. We show that, counter to what was hypothesized by Plag and Ben Hedia (2018), prosodic word structure is not a gatekeeper for relative frequency effects. Second, we demonstrate that across a large number of affixes, relative frequency effects still do not emerge consistently. Third, we show that in addition to the fact that prosodic word structure cannot explain the absence of relative frequency effects, prosodic structure as such also often fails to explain durational differences.

The paper is structured as follows. Section 2 discusses the role of morphological segmentability, relative frequency, and prosodic structure with regard to the duration of complex words, and develops the specific hypotheses tested in this study. This is followed by a description of our methodology. In Section 4 we present our results. We close with a discussion of the implications of our findings.

2. Segmentability and relative frequency

Morphological segmentability² refers to the degree to which speakers can decompose a complex word into its morphological constituents. Instead of categorizing words as being either simplex (monomorphemic) or complex (multimorphemic), it is widely assumed that there are different degrees of morphological complexity on a gradient scale: Words can be more complex or less complex; morphological boundaries may be stronger or weaker. The strength of a morphological boundary in a given word can be gauged, for example, on the basis of semantic transparency, type of base, various frequential measures, and the degree of phonetic-phonological integration across that boundary.

Consider the verbs dislike and discard. Both words are considered morphologically complex, as we can identify the bases like and card, which are prefixed with dis-. However, it seems that one of them is more complex than the other: Dislike appears to be more easily decomposable than discard. One reason for this is because dislike is semantically more transparent than discard. Its meaning ‘to not like’ is more straightforwardly compositional, while discard ‘to cast aside’ is semantically more opaque and idiosyncratic.

One way of operationalizing morphological segmentability is through lexical frequency (Hay, 2001, 2003). Derivatives which occur frequently compared to their base are assumed to be less segmentable than derivatives whose base is more frequent than the derived form. If the derivative is more frequent than its base, it is more difficult for speakers to decompose the word into its constituents because they encounter the derivative more often than its individual parts. The derivative will be perceived as a more simplex word. If, on the other hand, the base is more frequent than the derivative, speakers more likely or quickly recognize the base as a constituent and therefore more likely perceive the derivative to be complex. The examples dislike and discard above have shown how morphological segmentability is closely related to the idea of semantic transparency. Hay (2001) demonstrated that unlike the absolute frequency of the derivative, the relative frequency of base and derived form is a good predictor for semantic transparency. Relative frequency has therefore been considered an important operationalization of segmentability.

However, semantic and frequential properties are not the only correlates of morphological segmentability. It has been proposed that semantic opacity, and hence morphological segmentability, correlates with phonological opacity. Hay (2001, 2003), in what is now known as the segmentability hypothesis, suggests that morphological segmentability plays a crucial role in phonetic reduction: More segmentable words are less easily reduced (also see M. J. Bell, Ben Hedia, & Plag, 2020; Ben Hedia, 2019; Ben Hedia & Plag, 2017; Bergmann, 2018). This hypothesis relies on the idea that in derivatives which are infrequent compared to their base, phonetic segments must be more fully realized to facilitate morpheme recognition for lexical access, since the derivative’s meaning needs to be computed from its constituents. The rationale is that in words with strong boundaries, it might be important to fully produce individual segments to make it easier for the listener to recognize the constituents. In simplex words, in contrast, individual segments are less important for recognition. This idea relies on findings that non-morphemic phonemes are more likely to be deleted than morphemic ones (see Guy, 1980, 1991; Labov, 1989; MacKenzie & Tamminga, 2021). Thus, segments in words which are perceived as more simplex (and therefore likely accessed as wholes) should be more vulnerable to reduction than segments in words which are more complex or decomposable, and hence produced as multi-morphemic. In short, the more meaningful a unit, the less easily can it be reduced. Note, however, that this premise is not always supported by the data (see our discussion in Section 5).

The segmentability hypothesis thus relies on assumptions that belong to two classes of explanations for reduction. The first of these classes is what Jaeger and Buz (2017) call a communicative account, i.e., a listener-oriented explanation for reduction. Here we can fit the idea that speakers want to make constituent recognition easy for the listener. The second of these classes is the production ease account, which is speaker-oriented and relies on processing and memory demands (cf. Jaeger & Buz, 2017). It is this approach that fits best with the idea that words are accessed in different ways, or different stages of difficulty, and that this affects acoustic reduction. Both assumptions of the segmentability hypothesis are, however, dependent on online reduction effects. This makes the segmentability hypothesis contrast with the third class of explanations, the representational account, which argues that reduction is encoded offline in linguistic representations (Jaeger & Buz, 2017). It is at present unclear which one of these classes of explanations comes closest to the truth, but several discussions suggest a complex interaction of the three dynamics (Arnold & Watson, 2015; Clopper & Turnbull, 2018; Jaeger & Buz, 2017).

Based on the rationale outlined above, we can formulate the hypothesis that the higher the morphological segmentability (i.e., the higher the relative frequency as calculated by dividing base frequency by derivative frequency), the less reduction is to be expected, i.e., the longer will be the duration of the word. Crucially, such protection against reduction is expected to occur in all domains, i.e., both in the affix and in the base, since both constituents need to be recognized in more complex words. Both the affix and the base (and consequently the whole word) are expected to vary in duration due to relative frequency. The following hypothesis follows from these considerations:

2.2. The prosodic structure of complex words

As they found relative frequency effects for un- and dis-, but not for in- and -ly, Plag and Ben Hedia (2018, p. 112) hypothesize that these mixed results may arise because of prosodic integration. The affixes un- and dis- are considered to form prosodic words and thus to not integrate into the prosodic word of their hosts, while prosodic word status is less clear for in- and -ly. The question arises if their different prosodic word status might provide an explanation for why the affix categories differ with regard to where segmentability effects can emerge.

In the prosodic hierarchy (Figure 1), the prosodic word (represented by lowercase omega ω) is considered to be a constituent above the foot level and below the phonological phrase level (Hall, 1999; Hildebrandt, 2015; Nespor & Vogel, 2007). There are several diagnostics that can be used to justify postulating such a constituent, such as violations of syllabic constraints (onset or coda conditions, violation of the law of initials, ambisyllabicity), stress, vowel changes, or semantic criteria (Hildebrandt, 2015; Raffelsiefen, 1999, 2007). The prosodic word is assumed to be the lowest constituent in the hierarchy that reflects morphological information, making it a key player in the transfer of morphological structure to phonetic output.

Figure 1

The prosodic hierarchy, adapted from Hall (1999, p. 9) and Nespor and Vogel (2007, p. 11).

Within the hierarchy, researchers assume a number of constraints, one of which is especially important for the relationship between affix structure and prosodic word structure. Raffelsiefen (2007) suggests that the boundaries of grammatical categories must align with prosodic word boundaries, a constraint referred to as GP-ALIGNMENT. Crucially for our purposes, it follows from this constraint that whenever there are prosodic boundaries, they must coincide with morphological boundaries at the exact same place. This constraint, however, can be dominated by other constraints (such as, e.g., a constraint requiring syllables to have onsets). Because of this, if there are no prosodic boundaries, this does not necessarily mean that there are no morphological boundaries (Raffelsiefen, 2007, p. 212). In other words, a morpheme cannot include multiple prosodic words, but a prosodic word can include multiple morphemes. This means that in our study, there might be cases where an affix is a prosodic word on its own, as well as cases where the affix is just part of a larger prosodic word.

From these constraints, Raffelsiefen (1999) deduces three possible scenarios that describe how an affix can integrate into prosodic word structure. The three structure trees with example words are given in Figure 2. First, an affix can form a prosodic word on its own (the ProsodicWord case). This is, for example, the case with the affix pre-. In the word pre-war, both syllables are stressed and heavy, hence both form a foot as well as a prosodic word each. Second, an affix might form a clitic group with the prosodic word of the stem (the CliticGroup case). An example of a clitic group affix is -less. In the word sleepless, the suffix is unstressed, hence it cannot form a prosodic word. Yet, the suffix does not fully integrate into the host prosodic word either, as the base-final plosive is not resyllabified into the affix syllable, despite /pl/ being a possible onset in English. Third, there are affixes that fully integrate into the prosodic word of their host (the Integrating case). This is the case with -ize. In a word like patronize, the base-final coda nasal resyllabifies into the onset of the derivative-final syllable. The whole derivative is therefore considered to be one prosodic word. In sum, we can see that from left to right, there is an increasing degree of prosodic word integration. Standalone prosodic word affixes are least integrated, while integrating affixes are most integrated. The question remains which potential consequences these structural differences have for acoustic duration.

Figure 2

Three types of prosodic word integration for affixes (following Raffelsiefen, 1999), given as trees as well as in bracket notation. ProsodicWord: In this category, affixes form prosodic words on their own. CliticGroup: Here, affixes form a clitic group with their base. Integrating: In this case, affixes integrate into the prosodic word of their host base. Note that we use C to refer to the phonological domain of the clitic group, following the standard notation from the literature, whereas we use CliticGroup to refer to the category of derivatives in which such clitic group structure can be found.

One of the most important and well-known effects of (prosodic) constituent structure on acoustic duration is pre-boundary lengthening. Before a structural boundary, such as a phrase boundary or word boundary, phonetic material is lengthened, i.e., increases in duration. This phenomenon has long since been described in many different studies (see, e.g., Beckman & Pierrehumbert, 1986; Campbell, 1990; Edwards & Beckman, 1988; Klatt, 1975; Vaissière, 1983; Wightman, Shattuck-Hufnagel, Ostendorf, & Price, 1992) and is now considered to be a robust and reliable predictor of duration. Specifically, it has also been demonstrated to occur in complex words with different prosodic structure (Auer, 2002; Bergmann, 2018; Sproat & Fujimura, 1993; Sugahara & Turk, 2009). In the literature, the amount of lengthening is said to be dependent on two factors: the boundary strength and the position of the boundary type in the prosodic hierarchy.

First, how much a string of segments is lengthened depends on the amount, or strength, of the boundaries. The more constituents begin or end between two segments, the stronger the boundary, and the stronger the pre-boundary lengthening. This means that boundaries add up to form stronger boundaries. For example, the internal foot boundary in pre-war is stronger than the internal foot boundary in sleepless (Figure 2), because pre-war [[[ˌpriː]_Σ]_ω[[ˈwɔː]_Σ]_ω]_ω features a double foot boundary (one foot ends after the affix and provides a closing boundary, a second foot begins and provides an opening boundary), whereas sleepless [[[ˈsliːp]_Σ]_ωləs]_C just features a closing foot boundary after the base and no second foot. How strong a given boundary is, and consequently how much lengthening occurs before it, thus depends on the number of boundaries that co-occur together.

Second, the amount of lengthening depends on the position of the constituent providing the boundary in the prosodic hierarchy. Higher-level boundaries should be associated with stronger lengthening effects than lower-level boundaries. For example, segments before a prosodic word boundary are expected to be more lengthened than segments before a foot boundary, but less lengthened than segments before, e.g., a clitic group boundary. If the two boundaries in question belong to the same level in the prosodic hierarchy (like a prosodic word contained in another prosodic word), we would still expect the higher-level boundary in the tree to have the stronger lengthening effect than the lower-level boundary contained in the higher-level constituent. Based on these two factors governing prosodically induced lengthening, we can formulate predictions about how duration should vary between our affixes affiliated with different prosodic word categories, as well as predictions about how prosodic word structure could interact with segmentability.

Coming back to the question of how the prosodic structure outlined above might interfere with morphological segmentability, we can hypothesize that morphological segmentability effects on duration might be counteracted by a strong prosodic boundary: According to the segmentability hypothesis, barely segmentable words should be more reduced than highly segmentable words, but if a barely segmentable word has a stronger internal prosodic word boundary, the preceding domain might be protected against reduction. In other words, pre-boundary lengthening effects introduced by prosody might cancel out reduction effects which low segmentability would have allowed for. We can complement our segmentability hypothesis (repeated here for convenience) with this idea as follows:

1. H_seg1:

1. The higher the relative frequency of a derivative (i.e., the more segmentable a derivative is), the longer will be its affix duration and base duration.

1. H_seg2:

1. The more prosodically integrated an affix is (the weaker the prosodic boundary), the less likely can higher relative frequency protect the derivative against reduction.

Second, prosodic word structure should have an effect on duration in general, independent of segmentability. It is important to think carefully about which domains should be more lengthened or less lengthened in specific prosodic affix categories since these are nested with prefix or suffix status. For example, many English prefixes are considered to form prosodic words, whereas English suffixes never form prosodic words of their own (Raffelsiefen, 1999). Since the phenomenon of pre-boundary lengthening assumes lengthening only for the domain preceding the boundary in question, which prosodic category we look at will determine which domain (base or affix) we expect to be affected, depending on whether the affix is a prefix or a suffix.³ We can formulate the following predictions for the contrasts between the categories, depending on whether we compare the domains affix and base within a prosodic category, or the prosodic categories within a domain:

Comparing bases and affixes

1. H_PW:

1. ProsodicWord bases should be more lengthened than ProsodicWord affixes. This is because ProsodicWord affixes are prefixes and therefore the base will be subject to word-final lengthening, with the second base-final pword boundary in a word like [[[ˌpriː]_Σ]_ω[[ˈwɔː]_Σ]_ω]_ω ranking higher than the two internal pword boundaries.

1. H_INT:

1. Integrating affixes should be more lengthened than Integrating bases. Integrating affixes are mostly suffixes, so the suffix will be subject most strongly to word-final lengthening, with the final pword boundary outranking the internal foot boundaries, as illustrated in [[ˈpatrə]_Σ[ˌnʌɪz]_Σ]_ω.

1. H_CG:

1. CliticGroup affixes should be more lengthened than CliticGroup bases. CliticGroup affixes are generally suffixes and lack a foot boundary and prosodic word boundary compared to the bases, as seen in [[[ˈsliːp]_Σ]_ωləs]_C. However, the word-final C boundary ranks higher than the internal pword and foot boundaries, so word-final lengthening should be dominant.

Comparing prosodic categories

1. H_pros1:

1. ProsodicWord bases should be more lengthened than Integrating bases. This is because ProsodicWord bases end with one foot boundary and two pword boundaries and occur word-finally ([[[ˌpriː]_Σ]_ω[[ˈwɔː]_Σ]_ω]_ω), whereas Integrating bases end with just two foot boundaries and mostly occur word-internally ([[ˈpatrə]_Σ[ˌnʌɪz]_Σ]_ω).

1. H_pros2:

1. Integrating affixes (generally suffixes) should be more lengthened than ProsodicWord affixes (prefixes) due to word-final lengthening. The ProsodicWord prefix has two more boundaries provided by the derivative alone (compare [[[ˌpriː]_Σ]_ω[[ˈwɔː]_Σ]_ω]_ω and [[ˈpatrə]_Σ[ˌnʌɪz]_Σ]_ω), but since the Integrating affix occurs word-finally, it will be followed by at least the same amount of potentially stronger boundaries belonging to whatever word or phrase comes next.

1. H_pros3:

1. CliticGroup affixes should be more lengthened than Integrating affixes. This is because the word-final C boundary of CliticGroup affixes, as seen in [[[ˈsliːp]_Σ]_ωləs]_C, outranks the pword and foot boundaries of Integrating affixes, as seen in [[ˈpatrə]_Σ[ˌnʌɪz]_Σ]_ω.

1. H_pros4:

1. CliticGroup bases should be more lengthened than Integrating bases. The CliticGroup internal morphological boundary coincides with just one single foot boundary in words like [[[ˈsliːp]_Σ]_ωləs]_C instead of a double foot boundary like for the Integrating bases in words like [[ˈpatrə]_Σ[ˌnʌɪz]_Σ]_ω; however, the CliticGroup bases feature a higher-ranking internal pword boundary, which the Integrating bases do not.

1. H_pros5:

1. CliticGroup affixes (generally suffixes) should be more lengthened than ProsodicWord affixes (prefixes). CliticGroup affixes lack foot boundaries and pword boundaries compared to the ProsodicWord affixes (compare [[[ˈsliːp]_Σ]_ωləs]_C and [[[ˌpriː]_Σ]_ω[[ˈwɔː]_Σ]_ω]_ω), but CliticGroup affixes are mostly suffixes and are therefore subject to the higher-ranking word-final C boundary lengthening compared to the ProsodicWord prefixes.

1. H_pros6:

1. ProsodicWord bases should be more lengthened than CliticGroup bases due to word-final lengthening and because they feature an additional pword boundary compared to the CliticGroup bases (compare [[[ˌpriː]_Σ]_ω[[ˈwɔː]_Σ]_ω]_ω and [[[ˈsliːp]_Σ]_ωləs]_C).

We can summarize these predictions as follows (Table 1). We use the > sign to mean ‘should be more lengthened than’:

Table 1

Summary of predictions for prosodic category effects on duration. The right arrow sign between categories means that the left-hand element is expected to be more lengthened than the right-hand element.

Comparing bases and affixes
Integrating	CliticGroup	ProsodicWord
affix > base	affix > base	base > affix
Comparing prosodic categories
bases		affixes
ProsodicWord > CliticGroup > Integrating		CliticGroup > Integrating > ProsodicWord

It has become clear that an empirical investigation is called for that investigates segmentability and prosodic word effects on duration simultaneously. It is further necessary to conduct a study which examines more affixes at the same time, so we can better compare when effects do and do not emerge in the same conditions. We need to assess whether relative frequency is a useful predictor for duration, and under which prosodic circumstances it is not. The aim of the present study is to account for this gap by testing the hypotheses outlined above, as well as by aiming for a larger-scale investigation than previous studies.

4. Results

We report the p-values for the analysis of variance of the fixed effects in our three final models in Table 4. These p-values were calculated with the Anova() function (Type III) from the car package (Fox & Weisberg, 2011). We document the full models for one respective reference level each in Table 6. The interested reader can access the models in the scripts at https://osf.io/xuh42/.

Before we discuss the effects which turned out significant and remained in the models, let us first examine the null results. We can see from Table 4 that the interaction between relative frequency and prosodic category was not significant in any of the corpora and was therefore removed from the models. The lack of interaction between relative frequency and prosodic category means that we already must dismiss H_seg2 at this point. We do not find evidence that the effect of relative frequency depends on prosodic integration or vice versa.

One problem within the null hypothesis significance testing (NHST) framework is that it is strictly speaking not possible to interpret non-significance as the non-existence of an effect. While we do not find support for an interaction between relative frequency and prosodic category and thus no support for H_seg2, we cannot claim that the opposite is true, i.e., we cannot ‘confirm’ the null hypothesis. To be able to claim with more confidence that prosodic word integration does not affect whether relative frequency protects against reduction, it can be useful to quantify the evidence for the null. One way to do this is by using the BIC approximation to the Bayes Factor (Wagenmakers, 2007).⁸ With this method, we can approximate the Bayes Factor by using the difference between BIC values of a full model for H_seg2 (including the interaction between relative frequency and prosodic category) and a model for its null hypothesis (i.e., a model that does not include this interaction). If we assume that it is a priori equally plausible that relative frequency and prosodic category interact and that they do not interact, we can estimate the models’ posterior probabilities with the help of the Raftery (1995) classification scheme. Table 5 compares the BIC and Bayes Factor estimates for the three corpora.

We can see that in all three cases, the null hypothesis model (i.e., the one that assumes prosodic word integration to not have an influence on relative frequency effects) provides the better fit because of its lower BIC, and that it has the higher Bayes Factor value. The Bayes Factor, roughly speaking, tells us how many times ‘more’ we should believe in the respective hypothesis. According to Raftery (1995), if we start with the belief that the hypothesis and the null hypothesis are equally likely, a Bayes Factor of >150 constitutes ‘very strong’ evidence for the respective hypothesis (i.e., a posterior probability of >.99). We can thus say that for all three corpora, we find very strong evidence for the null. Prosodic word integration does not play any role in whether higher relative frequency can protect against reduction.

In addition, Table 4 shows that relative frequency was generally removed from all models both as interaction and as main effect due to non-significance, except from the Audio BNC. In the Audio BNC, we find one significant interaction between relative frequency and type of morpheme, where relative frequency is significant only if we look at the affix. In all three cases (despite the ‘significant’ effect in the Audio BNC), though, the BIC approximation to the Bayes Factor for the models with versus without relative frequency again tells us that these models constitute very strong evidence for the null (BF > 8000, posterior probability >.99 for all three corpora). H_seg1 is thus not well supported either: relative frequency generally does not affect duration in our data.

Before turning to the significant variables of interest, let us briefly look at the covariates. As seen in Table 6, the covariates generally behave as expected in the three models: speech RATE is always very highly significant and negatively correlated with duration. bigram frequency is significant in the Audio BNC and ONZE and negatively correlated with duration. biphone probability is significant in the Audio BNC and ONZE models and also negatively correlated with duration. Finally, number of syllables is positively correlated with duration in the three models.

Let us now examine the variables of interest that remained in the models, starting with relative frequency. relative frequency only showed one significant interaction with type of morpheme, namely in the Audio BNC. The interaction is illustrated in Figure 3. The x-axis represents the log of relative frequency; the y-axis represents the response variable duration difference. We use a blue, solid line to represent the slope of relative frequency when looking at the base, and an orange, dotted line to represent the slope of relative frequency when looking at the affix. Significance is indicated next to a given slope with asterisks, which means that only the slope of the dotted line is significantly different from zero.

Figure 3

Interaction of type of morpheme with relative frequency in the Audio BNC. Levels of slope significance within the conditions are marked by asterisks.

In general, and in accordance with hypothesis H_seg1, we expect higher relative frequency to lead to increased durations of both base and affix. In the AudioBNC, this is indeed the case for affixes, but not for bases: Affix durations in the Audio BNC increase with increasing relative frequency (i.e., increasing segmentability). In other words, in the one case where relative frequency interacts with type of morpheme, a relative frequency effect manifests itself only on the affix, not on the base. All the other cases yield a null result: Base durations in the Audio BNC, and affix and base durations in the two New Zealand corpora, do not increase with higher relative frequency. As mentioned above, thus, our data do not convincingly support the segmentability hypothesis H_seg1, even though we find one effect in the expected direction. In addition, as discussed above, there were no interactions of relative frequency with prosodic category.

Next, we turn to the effects of prosodic category on duration. Figure 4 shows the interaction effects between prosodic category and type of morpheme on duration difference in the three corpora (Audio BNC, QuakeBox, and ONZE). The x-axis represents the type of morpheme, i.e., the two domains of durational measurement, base or affix. The y-axis represents duration difference. We use purple dotted lines to represent the Integrating (INT) condition; green dashed lines to represent the CliticGroup (CG) condition; and blue solid lines to represent the ProsodicWord (PW) condition. Significance between the contrasts is indicated by asterisks on brackets connecting the respective conditions above and beside each plot. For the contrasts between prosodic categories (Integrating versus CliticGroup versus ProsodicWord) within a type of morpheme condition, significance brackets are given on the left-hand and right-hand side of each plot. For the contrasts between types of morpheme (base versus affix) within a prosodic condition, significance brackets are given above each plot with colored solid, dashed, or dotted lines, corresponding to the prosodic category within which base and affix durations are compared.

Figure 4

Interaction effects between prosodic category and type of morpheme in the three corpora. Significance levels of contrasts between conditions are indicated by asterisks on brackets. Abbreviations: PW for ProsodicWord, CG for CliticGroup, INT for Integrating.

First, let us look at the durations of affixes and bases in the different prosodic conditions. Figure 4 shows that seven of the 18 bars fall below the zero line: This means that in most cases, both affix durations and base durations are shorter than expected from their average segment duration.⁹ However, if we compare affixes and bases, we see that there are differences in the amount they deviate from their average segment duration (significance brackets above the plots).

Starting with the Integrating category (INT, purple dotted lines), we can see that integrating affixes behave as expected in all three corpora: They are consistently and significantly more lengthened than the bases to which they attach. In the ProsodicWord category (PW, blue solid lines), too, affixes behave as expected in all three corpora (they are less lengthened than their bases). In the CliticGroup category (CG, green dashed lines), affixes are less lengthened than their bases in all three corpora, while they would have been expected to be more lengthened.

Second, let us examine the contrasts between the prosodic categories within the respective domains of base and affix (significance brackets to the left and right of the plots, respectively). Let us look at the base condition first. We can see that in the Audio BNC, ProsodicWord bases are most lengthened. CliticGroup bases are less lengthened, and Integrating bases are least lengthened. Expressed in terms of the lengthening hierarchy formulated in Table 1 (Section 2.2.), the Audio BNC thus follows exactly the expected pattern ProsodicWord > CliticGroup > Integrating. However, two of the contrasts are not significant, so we could formulate the more accurate hierarchy ProsodicWord = CliticGroup = Integrating (with ProsodicWord > Integrating). The QuakeBox and ONZE corpora, too, are consistent with the expected lengthening hierarchy. However, the contrast between the clitic-group-forming category and the integrating category in the two New Zealand corpora does not reach significance. This results in the hierarchy ProsodicWord > CliticGroup = Integrating. Bases with prosodic-word-forming affixes are most lengthened, followed by bases with clitic-group-forming affixes and bases with integrating affixes.

Third, let us look at the affix condition. In the Audio BNC, integrating affixes are most lengthened, followed by prosodic-word-forming affixes and clitic-group-forming affixes. This is a different pattern from the expected one (which is CliticGroup > Integrating > ProsodicWord). However, since none of these contrasts are significant, the lengthening hierarchy is more accurately represented as Integrating = ProsodicWord = CliticGroup. In the QuakeBox corpus, Integrating affixes are most lengthened, followed by CliticGroup affixes and ProsodicWord affixes. The contrast between the integrating affixes and the other two affix types is significant, so that we are dealing with this hierarchy: Integrating > CliticGroup = ProsodicWord. Lastly, we also observe deviations from the expected lengthening hierarchy for the ONZE corpus. The ONZE affixes are most lengthened in the Integrating condition, followed by the ProsodicWord condition and the CliticGroup condition. This results in the pattern Integrating > ProsodicWord = CliticGroup.

We can now evaluate all of our contrasts in terms of how the observed lengthening hierarchies overall fit with the expected hierarchies. Table 7 summarizes the significance levels for all measured contrasts we have discussed in the three corpora, color-coded for the direction of a given effect. For convenience, the last column of this table displays the directional changes in duration we would have expected based on the hypotheses outlined in Section 2.2. We set up the contrasts for this table so that in every cell, we expect more lengthening from the first condition (for example base or CG) to the second condition (for example affix or PW). More lengthening is indicated by orange shading. In cases where we observe less lengthening, we use blue shading.

Table 7

Overview of prosodic category effects in the different conditions. Orange shading indicates a positive change in duration from the first to the second category, blue shading a negative change in duration. Abbreviations: PW for ProsodicWord, CG for CliticGroup, INT for Integrating.

Overall, we can observe that many, but not all of our expectations are confirmed by the data. Out of the 27 expectations (cells), 13 are in line with the predictions, five contradict the predictions, and nine do not reach significance. Prosodic contrasts within the base condition (Table 7, rows 4–6) are in line with the expectations, but two of the prosodic contrasts in the affix condition (row 7) go in the opposite direction from what was expected. A similar situation holds for the base-affix contrasts: The Integrating and ProsodicWord conditions (rows 2–3) behave as expected, while the CliticGroup condition (row 1) contradicts our expectations. The nine non-significant contrasts all pertain to the prosodic category contrasts (rows 4–9). Overall, only three out of nine rows are completely in line with the hypotheses.

Together with the findings for relative frequency, we can now relate all our findings to the hypotheses as follows. First, we saw earlier that H_seg1 is largely not supported, despite one effect in the expected direction in the Audio BNC: Higher relative frequency is not associated with longer durations. Second, H_seg2 is not supported either, as there was not a single significant interaction between relative frequency and prosodic category: How integrated an affix is into prosodic word structure does not modulate whether higher relative frequency can protect against reduction. In both cases, we have very strong evidence for the respective null hypothesis. Third, based on the findings summarized in Table 7, quite a few contrasts between bases and affixes within the prosodic categories (H_PW, H_INT, H_CG), as well as contrasts between the prosodic categories within the affix domain (H_pros1–6), do not behave as expected: Durations often do not pattern according to prosodic boundary strength. The prosodic category approach cannot explain the patterning of the durational differences satisfactorily. We will now proceed to discuss these findings in more detail, returning to the theoretical assumptions of segmentability and prosodic word structure.

5. Discussion

We discuss our findings in the light of the hypotheses given in Section 2, which we repeat here for convenience:

Three main findings emerge from our analysis: (1) H_seg1 is largely not supported by our data (with one exception), (2) H_seg2 is not supported by our data, and (3) H_PW, H_INT, H_CG as well as the hypotheses H_pros1-6 are sometimes contradicted by the data.

First, H_seg1 is not supported, with one exception: There is one expected, positive effect of relative frequency on duration in the Audio BNC. In this case, we observe longer durations the higher the relative frequency becomes (the more segmentable a derivative is). This speaks in favor of the idea that words are protected against reduction by morphological segmentability (Hay, 2001, 2003). This effect also supports the idea that the more meaningful a stretch of segments, the more important it is for speakers to fully realize these segments so as to facilitate recognition by their interlocutors (Guy, 1980, 1991; Labov, 1989; MacKenzie & Tamminga, 2021), resonating with listener-oriented or communicative accounts, as well as with the speaker-oriented accounts of production ease (Jaeger & Buz, 2017). If we took this one effect seriously (which we are not convinced we should), this finding would imply that morphological information is somehow still reflected at the subphonemic level. Models which assume an articulator module that has no access to morphological information, and that, therefore, always realizes phonemic representations with pre-programmed gesture templates independently of morphemic status, might not adequately capture the morphology-phonology-phonetics interaction (e.g., Kiparsky, 1982; Levelt, Roelofs, & Meyer, 1999). If a word’s morphological structure or semantics cause differences in articulatory gestures, pre-programmed templates are an unlikely architecture.

However, we observe mostly null effects. We are thus able to confirm with more affixes than previous studies that segmentability effects often do not emerge. In a way, our results are in line with previous studies inasmuch as they replicate the mixture of effects and null effects (Hay, 2003, 2007; Plag & Ben Hedia, 2018; Pluymaekers et al., 2005b; Schuppler et al., 2012; Zimmerer et al., 2014; Zuraw et al., 2020). They are also in line with Hanique and Ernestus (2012), one of the earlier attempts to consolidate work on the effects of morphological segmentability on acoustic duration. Reviewing several studies and re-analyzing data by Hay (2003) after identifying methodological issues, these authors conclude that the hypothesis that more easily decomposable words are longer in duration is not convincingly supported.

In addition, research has questioned the very premise on which the segmentability hypothesis is built, namely the rationale that segments which are important for morpheme recognition are enhanced. For instance, Poplack (1980) shows that Puerto Rican Spanish /s/ is frequently deleted even when it is a morphemic plural marker. J. Bybee (2002, 2017) suggests that morphemic strings may be durationally enhanced simply because they occur in contexts which disfavor reduction, compared to contexts of nonmorphemic strings. Finally, Hanique and Ernestus (2012) review several studies investigating the hypothesis that the morphemic status of segments is associated with longer durations and conclude that there is no convincing evidence for such an effect. Segments which are more relevant for the identification of a morpheme (e.g., word-initial segments or morphemic segments, i.e., single-segment morphemes) are not longer than less relevant segments (e.g., word-final segments). Previous studies either have failed to demonstrate an effect of a segment’s morphological status on reduction, suffer from methodological issues, or can be interpreted differently. Several studies, however, support the idea that segments which are more relevant for the identification of a complete word are enhanced. This indicates that rather than morphemic structure, it may be word-based information load that affects duration.

The emergence or non-emergence of relative frequency effects might, however, be related to the emergence of word frequency effects in general. We also investigated each of the individual affix categories as a separate dataset and found that we can only observe a relative frequency effect in datasets that also feature a word frequency effect (relative frequency and word frequency were tested in separate regression models due to collinearity). Whenever there is an expected (positive) effect of relative frequency on duration, there is an expected (negative) effect of word frequency in the same affix dataset. It seems that whether relative frequency affects duration is mainly dependent on whether word frequency affects duration. This is not surprising, since these two frequency measures must necessarily be correlated, as one is calculated on the basis of the other. If we assume that relative frequency effects mainly emerge together with word frequency effects, it is not unexpected that there will be some null results, since simple word frequency effects, too, sometimes fail to be observed (e.g., Bowden, Gelfand, Sanz, & Ullman, 2010; Pluymaekers et al., 2005b). The fact that relative frequency effects only emerge in the presence of word frequency effects may, however, also indicate that we should discard relative frequency as a predictor of duration.¹⁰

Second, H_seg2 is not supported by our data. Prosodic word structure does not interact with relative frequency in any of the corpora. This means that whether an affix is more or less prosodically integrated does not influence how relative frequency affects duration. A segmentability protection against reduction, then, is not diminished by the lack of a strong prosodic boundary. This conclusion is indirectly also supported by previous studies. Affixes for which effects of relative frequency on duration have been found before are sometimes non-integrating affixes (e.g., dis- and un- in Plag & Ben Hedia, 2018, un- in Hay, 2007) and sometimes integrating affixes (e.g., -ly in Hay, 2003). What is more, neither an integrating nor a non-integrating affix guarantees a relative frequency effect, as demonstrated by the null results for both integrating and non-integrating affixes (e.g., -ly and in- in Plag & Ben Hedia, 2018, un- and in- in Ben Hedia & Plag, 2017, ont-, ver-, and -lijk in Pluymaekers et al., 2005b). It thus seems that we need to look for further factors that might be responsible for the apparent arbitrariness of the emergence of relative frequency effects. Prosodic word structure is not the culprit.

Third, H_PW, H_INT, H_CG, and the hypotheses H_pros1-6 are often not supported. It seems that the prosodic structure of complex words can neither explain the capricious nature of relative frequency effects on duration, nor can it satisfactorily explain durational variation as such. For the base-affix contrasts, the contrasts for the Integrating category and the ProsodicWord category show a consistent and predicted pattern (see again Table 7, second and third row). In the CliticGroup category, however, not a single contrast behaves as expected (first row). For the contrasts between prosodic categories, the patterns are more difficult to interpret due to many non-significant effects. As summarized in rows 4 through 6 in Table 7 and in Figure 4, base durations mostly follow the predicted pattern ProsodicWord > CliticGroup > Integrating: Bases with prosodic-word-forming affixes are more lengthened than bases with clitic-group-forming affixes, which in turn are more lengthened than bases with integrating affixes (even though this often does not reach significance). In contrast, affix duration contrasts in two cases contradict the expected pattern CliticGroup > Integrating > ProsodicWord (row 7 in Table 7).¹¹

It is interesting that predictions for bases are never contradicted by the empirical data, whereas affixes sometimes produce the opposite behavior. The reasons for this difference between bases and affixes are not clear. Both the predictions for bases and the ones for affixes are based on the same underlying prosodic mechanisms assumed in the literature. Affixes are, of course, generally shorter in segments and consequently in duration than their bases, which an analysis of the affix-base ratio confirms for our data. With fewer segments and shorter durations, there might be less potential to reduce or enhance, and thus less potential for effects to play out significantly. While this could explain the fact that there are few significant effects for affixes, this cannot explain why there are effects going in unexpected directions.

One other possibility that has been suggested is that prosodic word effects may underlyingly be related to transitional probability effects (see Côté, 2013). A reviewer points us to the observation that patients who make few anticipatory speech errors often fail to apply cross-boundary phonology (Michel Lange, Cheneval, Python, & Laganaro, 2017), which would support this idea. While Côté (2013) makes this suggestion based on the transitional probability between words, not morphemes, it is conceivable that the transitional probability of an affix might also affect duration. We conducted a separate study with our data (for all three corpora) in which we tested the effects of what we called conditional affix probability. conditional affix probability is the probability of the affix given the preceding linguistic element, and thus captures the transitional probability between morphemes. It is calculated by dividing the preceding-element/affix bigram frequency by the frequency of the preceding element itself. Thus, for suffixes, it encodes the probability of the suffix given the probability of the base; for prefixes, it encodes the probability of the prefix given the probability of the preceding word. Unfortunately, this measure is very strongly correlated with relative frequency, which makes it impossible to include both measures in the same model. When tested separately from relative frequency, conditional affix probability very often did not affect duration significantly (similarly to relative frequency). Though an interesting option for further research, transitional probability so far does not provide a better account of our data than prosodic category. The interested reader can access this analysis in the scripts at https://osf.io/xuh42/.

Prosodic structure, if understood in terms of boundary strength, then, is not able to consistently account for the durational differences in English derivatives. This is interesting given the fact that some studies had previously suggested that the prosodic structure of complex words can explain some of their durational variation (Auer, 2002; Bergmann, 2018; Sproat & Fujimura, 1993; Sugahara & Turk, 2009). However, there are some important differences between these studies and the present one.

First, all of these studies investigated specific segments and did not consider other durational domains. Prosodic boundary effects might explain more of the variation in a very small domain, like a single base-final segment, than of the variation in a larger domain, like an affix. Second, some of the studies compared different prosodic categories than we did. For example, Sproat and Fujimura (1993) compared compound boundaries to affix boundaries and to simplex words. The durational difference between a prosodic boundary in an affixed word and a non-affixed word might be greater than the difference between prosodic boundaries in different types of affixed words. Third, some of the studies report that prosodic boundary effects only emerge in very specific conditions. For example, Sugahara and Turk (2009) find that stem-final rhymes in prosodic word-forming suffixes are only lengthened at a slow speech rate, and Bergmann’s (2018) segments in derivatives with prosodic word-forming suffixes are only lengthened if they are infrequent. Fourth, most of the studies investigated elicited data, while we investigated conversational data. Fifth, some of the studies suffer from methodological issues. For example, Sugahara and Turk (2009) only used data from five speakers and did not fit any statistical models that included potentially influential covariates. Their durational effects of prosodic structure might disappear if the data were analyzed with more controlled statistical modeling.

Taken together with these caveats, our results show that effects of the prosodic structure of complex words on duration are to be taken with much more caution than assumed. We thus join Pluymaekers et al. (2010, p. 523) in their conclusion that “contrary to received wisdom, morphological effects on fine phonetic detail cannot always be accounted for by prosodic structure.”

With regard to the previous work that found evidence for pre-boundary lengthening in general (e.g., Beckman & Pierrehumbert, 1986; Campbell, 1990; Edwards & Beckman, 1988; Klatt, 1975; Vaissière, 1983; Wightman et al., 1992), it must be noted that much of this evidence comes from boundaries that are higher in the prosodic hierarchy than the ones we investigated in this study. As explained in Section 2.2, prosodic boundaries, and thus lengthening, are expected to be stronger the higher these boundaries are ranked in the prosodic hierarchy. Hence, it is possible that lengthening effects before higher-level boundaries (for example phrase-final lengthening or utterance-final lengthening) show more consistent patterns than lengthening before low-level boundaries (like foot boundaries or pword boundaries). This means that our results do not necessarily have to be interpreted as refuting the prosodic account in general, but perhaps merely as demonstrating that effects become more unstable the lower we zoom in on the hierarchy. It may well be that in order to meaningfully observe prosodic lengthening effects, we need to look at higher-level constituents. To detect effects of very small magnitude, even though we would lose some advantages of spontaneous speech data, future studies could also use an experimental setup. This way, one could manipulate only relative frequency and prosodic category without the variance introduced by real conversations.

Overall, our results show that neither relative frequency nor prosodic word structure are able to explain our data perfectly for all corpora. At least for speech articulation, the predictions of a prosodic account thus are not satisfactory. Of course, the fault for the contradictory contrasts may not necessarily lie in the prosodic predictions themselves, but might also be caused by other, external factors. For example, potential prosodic differences between the varieties represented in the corpora, differences in the forced alignment, or differences in dataset size and statistical power might all be factors which introduce unwanted variation. It is interesting, for instance, that the Audio BNC seems to differ in its behavior somewhat from the two New Zealand corpora, while the results from the two New Zealand corpora are virtually the same (see again Table 7).¹² However, since not all affixes are present in all corpora (cf. again the affix distribution across the corpora in Table 2), we were not able to test whether an interaction of prosodic category with corpus in a single dataset would turn out significant or not. The differences between corpora might as well be a coincidence and should, in our opinion, be taken with a grain of salt.

One potentially important additional factor which needs to be discussed is syntactic position. In the present study, we did not control for part-of-speech factors. Which syntactic category a derivative belongs to, however, is related to prosodic structure. This is because derivatives of a certain affix category occur more often in certain positions in the sentence, and thus occur more often in certain prosodic positions. For example, the suffix -less derives adjectives and therefore often occurs in prenominal position within a noun phrase or after a copula in predicative position. The suffix -ness derives nouns and will therefore often be found in noun phrase-final position. This may affect how these suffixes are pronounced in these contexts and in other contexts (J. Bybee, 2002, 2017). In the present study, we investigated the effect of lower-level prosodic boundaries (foot boundaries, pword boundaries, and clitic group boundaries), but we would also expect duration to be affected by higher-level prosodic boundaries (such as phrase boundaries or utterance boundaries).

The present study did not control for effects of prosodic phrasing since the coding of prosodic phrasing with the natural conversation data as found in our corpora is extremely difficult and highly problematic in terms of rater reliability. We believe, however, that potential effects of prosodic phrasing are not overly influential in our study for several reasons.

First, we investigated a large number of different affixes which belong to different part-of-speech categories simultaneously. It is not the case that in our data, for instance, all prosodic word-forming affixes derive nouns, whereas all integrating affixes derive adjectives. If this were the case, syntactic position could be considered an important potential confound. Instead, our affixes come from different syntactic categories even within prosodic categories. Clitic group-forming affixes derive both nouns and adjectives; integrating affixes derive nouns, adjectives, and verbs; and prosodic word-forming affixes derive nouns, adjectives, verbs, and even adverbs.

Second, as mentioned above, we conducted additional analyses, investigating the tokens in one affix category at a time, for all eight affixes separately. These category-internal analyses again indicated that relative frequency effects frequently fail to emerge, without any clear pattern between categories and within categories (comparing base durations, affix durations, and word durations). The results indicate, then, that relative frequency is neither a reliable predictor within nor across affix categories, prosodic categories, or syntactic categories.

Finally, and crucially, phrase boundaries and utterance boundaries—just as other prosodic boundaries—cause the strongest lengthening of segments which are close to those boundaries, compared to those segments that are further away. In other words, lengthening effects weaken with increasing distance from the boundary. This has been shown in a number of acoustic and articulatory studies (e.g., Berkovits, 1993a, 1993b, 1994; Byrd, Krivokapić, & Lee, 2006; Cambier-Langeveld, 1997; Shattuck-Hufnagel & Turk, 1998). Higher-level boundaries, thus, will affect word-final segment lengthening more than word-internal segment lengthening. This in turn means that our predictions for base lengthening versus affix lengthening as well as the interpretation of the results would remain unchanged: We always expected a word-final element (bases in the case of prefixes, or affixes in the case of suffixes, respectively) to be lengthened more than the corresponding word-internal element. The presence of higher-level boundaries would only enhance that effect.

If relative frequency and prosodic categories cannot explain the durational variation we observe, the question remains whether there are alternative approaches that can. One recent approach that seems promising is to model speech production as the result of a dynamic discriminative learning process, where relations between form and meaning are constantly recalibrated based on the speaker’s experience (linear discriminative learning, Baayen, Chuang, & Blevins, 2018; Baayen, Chuang, Shafaei-Bajestan, & Blevins, 2019; Chuang et al., 2020). Such an approach does not rely on morphemic or prosodic boundaries, but estimates the strength of associations between sound and meaning based on their discriminative potential. Stein and Plag (2021) and Schmitz, Plag, Baer-Henney, and Stein (2021) demonstrate that it is possible to predict durations of words and affixes based on association measures derived from a linear discriminative learning network. These results indicate that we do not necessarily need boundary strength (morphological or prosodic) to model phonetic detail in speech production. We think it would be worthwhile for future studies to consider such alternative approaches in research on the morphology-phonology-phonetics interface.

6. Conclusion

This study set out to investigate the influence of prosodic structure and relative frequency on the durational properties of complex words. In particular, we wanted to test whether prosodic structure can explain the inconsistency in the emergence of relative frequency effects on duration in previous studies. We showed that for our data, we can rule out prosodic word structure as a gatekeeper for relative frequency effects. Second, we demonstrated that relative frequency effects can emerge, but mostly fail to emerge over a large set of affixes and a large number of tokens. Finally, we have presented evidence that word-internal prosodic boundaries fail to account consistently for durational differences. In many cases, with more strength and a higher position in the prosodic hierarchy, prosodic boundaries are indeed associated with more pre-boundary lengthening of morphological constituents. But in some other cases, this pattern does not hold—especially not for affixes.

What does that mean for the status of word-internal prosodic structure in phonological theory, or in models of speech production? Based on the findings of this study, as well as those of some other studies, we think the jury is still out on the question of how exactly the purported word-internal boundaries translate into articulatory gestures or acoustic properties. While there is good evidence for some phonetic correlates of word-internal prosodic structure (for example base-initial aspiration after certain prefixes, e.g., Zuraw et al., 2020), the durational evidence is much less convincing.

Funding information

This research was funded by the Deutsche Forschungsgemeinschaft (Research Unit FOR2373 ‘Spoken Morphology,’ project ‘Morpho-Phonetic Variation in English,’ PL 151/7-2 and PL 151/8-2), which we gratefully acknowledge.

Competing interests

The authors have no competing interests to declare.

Author contributions

Ingo Plag and Simon David Stein contributed to conception and design of the study. Simon David Stein retrieved and curated the data, performed the modeling and statistical analysis, and wrote the first draft of the manuscript. Funding acquisition and supervision: Ingo Plag. Both authors contributed to manuscript revision, read, and approved the submitted version.