According to the literature, Spanish as spoken on Gran Canaria is well-known for multiple weakening processes and frequent consonant elisions (Alvar 1972; Oftedal 1985; Almeida & Díaz Alayón 1988). While syllable- and word-final consonant deletions are well-extended in rural areas, in urban communities and certain geographical areas of the island weakening without deletion, especially s aspiration, is the dominant output. Our data are in line with these general observations as they show syllable-final and word-final consonant weakening in spontaneous speech. One of the outcomes of this weakening is full elision, examples of which are presented in words taken directly from the collected corpus in (1).

Our data show that consonant deletion is prevalent in most speakers. More specifically, the representatives of the (sub)dialect tend to delete most word-final consonants unless they can resyllabify them into the onset of the following syllable (e.g. por aquí /poɾ#aki/ [po.ɾa.ˈki] ‘(around) here’), although in many cases these segments are deleted anyway and the following onsets remain unrepaired (e.g. montamos un panel /montamos#un#panel/ [mon.ˈta.mo.um.pa.ˈne(l)] ‘we assembled a panel’). As for the scope of application, consonant deletion is well advanced and has narrowed down to the word domain. It applies (variably) whenever there is a word-final consonant, independently of bigger constituents such as phrases or sentences. However, it is much more frequent phrase-finally. To provide some numbers, while the rate of consonant deletion in word-final position in general is slightly higher than 50% (55% in our young speakers), it rises to over 90% phrase-finally, which is the position we will focus on in this paper. Furthermore, it must be noted that the process applies regardless of age or gender, the only difference lying in the relative rates of application vis à vis other forms of weakening, e.g. debuccalisation of /s/ to [h] or [ɦ].4

The second process of concern in this paper is vowel apocope, i.e. the deletion of word-final unstressed vowels. Some examples from our corpus are provided in (2).

It must be stressed that vowel apocope has not been reported in the literature on the dialect to date. Thus, this paper presents novel data. To provide full information on the contexts of occurrence of apocope and generalisations, we had to take a closer look at the corpus, both quantitatively and qualitatively. We list the results of this inquiry below.

First, as shown by the examples in (2), word-final vowels undergo deletion, which results in word-final codas, regardless of the number of consonants (cf. perfecto). Crucially, stressed vowels are not affected by the process. It does not apply in words such as papá ‘daddy’. Additionally, it is worth noting that vowel apocope applies only to final unstressed vowels. For instance, in the word ofertas ‘offers’ the initial unstressed vowel is retained as it occupies a strong (initial) position. Similarly, unstressed vowels in words with antepenultimate stress, such as pájaro /paxaɾo/ ‘bird’ are retained beyond the final syllable ([ˈpa.ɦaɾ] and not *[ˈpaɦɾ] or *[ˈpaɦ.ɾo]). Furthermore, we determined that there is usually no apocope in monosyllables, even if they are function words, and that apocope seems to be less often applied in verb forms (e.g. se negaba /se#negaba/ [se.ne.ˈɣa.(β)a] ‘(s)he was denying’, te enteras /te#enteras/ [ten.ˈte.ɾa] ‘you find out’, estuve /estube/ [eh.ˈtu.βe] ‘I was’). It is also often blocked or hidden by other processes, e.g. intervocalic stop deletion and the resultant vowel merger/simplification: nada /nada/ [ˈna] ‘nothing’, lesionado /lesionado/ [le.sjo.ˈna] ‘injured’, relajado /relaxado/ [re.la.ˈɦa] ‘relaxed’.5

The above description provides a general picture of vowel apocope in the dialect. The process has further restrictions, however. Importantly, it is not word- but phrase-final, and dependent on information load and intonation.6 For instance, when information is incomplete and an explanation or a second part of the message follows, there is no apocope. The same applies to hesitations and incomplete sentences. Such phrases are characterised by rising intonation and often final vowel or syllable lengthening (possibly an intonational boundary process). When information is completed, the phrase or sentence is finished and the intonation is level or falling, vowel apocope occurs. Some examples of phrases containing the context necessary for apocope to occur, as well as examples of phrases excluded from the count are provided in Appendix 1.

Two more observations should be mentioned. First, vowel apocope may be incomplete – whereas numerous cases of full elision can be found in the data, in some cases the vowel is fully devoiced and some remnant of it is still present in the signal (see Figure 1).

Second, as for the final consonants left after apocope applies, there seems to be some sort of emphatic strengthening. For instance, the word curioso /kuɾioso/ ‘curious’ is reduced to [gu.ˈɾjos] with a lengthened [s], while in the words ofertas /ofeɾtas/ ‘offers’ > [o.ˈfeɾt] or gente /xente/ ‘people’ > [ˈhent] there is a strong plosion with aspiration on the [t] despite the fact that stops are usually produced with a weak plosion or no plosion at all in this dialect (Broś & Lipowska 2019) and Spanish in general has no stop aspiration (see the spectrograms in Figure 2).

Given the above we can conclude that the process of vowel apocope is only incipient as it applies optionally and only in the outer domains of prosodic structure. In our data, vowels tend to be dropped at the end of an intonational phrase. In some cases, vowel deletion is incomplete, which means that some parts of the signal are still present and visible on a spectrogram, as shown in Figure 1. In most cases, however, we have full deletion (as in Figure 2), i.e. unstressed post-tonic vowels are removed, and the loss of the whole final rhyme tends to be accompanied by some degree of strengthening of the resultant final segment.7 All in all, the observed changes seem to be driven by ongoing generalised lenition typical of the Gran Canarian dialect.8

Another important aspect of vowel apocope in the dialect is that it is socially restricted. As already mentioned at the beginning of §2, it seems to be produced almost exclusively by young male speakers. It can be found to some extent in the speech of middle-aged inhabitants of the island but it does not occur in older speakers, and it can occasionally take the form of vowel devoicing and shortening in some females. The latter, however, is not as yet systematic.9

In order to provide the most reliable quantitative data possible, we should pursue the age-related differences in the application of vowel apocope further. Besides, the age factor provides additional evidence that apocope is an incipient process. More specifically, when comparing young speakers (10 speakers aged 18–25) with the older generation (8 speakers aged 37–59), one can observe a substantial difference in the frequency of apocope but not C deletion. Out of a total of 199 contexts across the middle-aged speakers, 81 show either full or incomplete vowel apocope, while 58 show consonant deletion. In the case of the younger speakers, we counted 192 contexts, with 142 cases of full and incomplete apocope and 56 cases of C deletion. The overall percentage of lenitions in the investigated contexts is 58% in middle-aged speakers, which is substantially less than in the younger age group in which 86% of all final sounds are weakened. At the same time, however, C deletion in C-final words happens 95% of the time in middle-aged speakers, and 92% of the time in the younger population, which means that this process does not differ depending on the age. The difference between the groups lies in the application of vowel apocope. Here, we divided the words into V-final and C-final since both can have apocope but only the latter ones can undergo C deletion and apocope depends on whether C deletion applied. As a result, only 30% in V-final words and a mere 13% in C-final words undergo apocope in the middle-aged group, compared to 61% and 36%, respectively in the younger age-group.10 These differences have been tested statistically and are illustrated in Figure 3. Two sample t-tests run in R (R Core Team 2017) showed a significant difference between the two age groups both in overall apocope application (t(16) = –4.297, p < 0.001) and in V-final and C-final words separately (t(16) = –3.738, p = 0.002 and t(16) = –4.057, p = 0.001, respectively). No statistical difference was found for C deletion (t(16) = 0.238, p = 0.81).

All in all, given our empirical results, since the occurrence of apocope is much less frequent in older speakers compared to the young ones, we can conclude that vowel apocope is an incipient change, especially given that no instances whatsoever have been detected in the speech of a yet older generation (males or females over 60 years old) in the initial corpus of Gran Canarian speech. The quantitative comparison between the middle-aged and the young speakers suggests that vowel apocope is an ongoing change that seems to be spreading among the young speakers of the dialect. It is therefore this community that we will focus on in the rest of the paper. Most importantly, we will provide data on the rates of consonant and vowel deletion that will be used in the subsequent formal analysis based on the representatives of the young generation.

Perhaps the most interesting aspect of the processes described in this paper is that they interact in phrase-final position, i.e. where apocope optionally applies. This is illustrated in (3).

The data in (3) show that with the two processes operating side by side there are some interesting results. Most often, plural nouns and adjectives will lose the final segment and may additionally lose the resultant word-final vowel under certain circumstances. Naturally, however, not all phrase-final words have a word-final consonant and/or unstressed vowel. If the word is consonant-final but with a stressed syllable, the consonant usually deletes but the vowel is retained. If the word is vowel-final, the stressed vowel is retained as well.

Since neither of the described processes applies 100% of the time, their interaction may lead to a wide range of outcomes. If we look only at the words in which these processes have a chance to apply, i.e. vowel- and consonant-final words with final unstressed vowels, the possibilities are as follows. In vowel-final words there may be no change, incomplete vowel apocope or full vowel apocope. In consonant-final words, there may be no change, consonant deletion only or consonant deletion accompanied by incomplete or full vowel apocope. To illustrate these outcomes with an example, the word plaza /plasa/ ‘square’, an example of a V-final context, and its plural form plazas /plasas/ ‘squares’, an example of a C-final context, are presented in (4) together with a list of possible outcomes.

Thus, we have several output options among the V-final and C-final words, some of which overlap. For instance, the output [ˈplas] can be a result of full apocope in the word plaza, and of C deletion + full apocope in the word plazas, etc. Additionally, it is worth underlining that C deletion applies only once, i.e. only to the underlyingly final segment. Whenever vowel apocope ‘uncovers’ a final consonant, that consonant is not weakened any further. In the word plaza, an output form *[ˈpla] is impossible. This is an opaque interaction of the fed counterfeeding type. As the combination of feeding and counterfeeding has proved problematic in formal analyses to date (Kavitskaya & Staroverov 2010), it is important to investigate this complex pattern in formal terms.

As we have seen, the interaction of C deletion and apocope leads to a variety of surface forms, but it is also crucial to look into how often a given form occurs in the dialect. To obtain quantitative data, we turned to the surface sounds used in the speech of the young males (see §2.2 above), as they are the ones who use both processes systematically. The results are presented in Table 1, which shows the number of contexts fulfilling the criteria described in §2.2 per speaker, together with the number of vowel apocope instances in each context, including incomplete apocope, and the number of C deletions (when applicable). Thus, phrases containing the context for apocope (both vowel-final and consonant-final words) were selected based on the criteria of information load, intonation and stress, after which we counted instances of deletion that actually occurred. The table shows quantitative results, including percentages.12

As can be observed in Table 1, the data included a total of 192 contexts of apocope, 131 in vowel-final words (68%) and 61 in consonant-final words. All speakers have both vowel and consonant deletions in most cases. However, the probability of occurrence of vowel apocope changes depending on the word type. In vowel-final words, speakers delete final unstressed vowels 61% of the time. An additional 24% of the words has incomplete apocope, which means that an overwhelming majority of unstressed vowels is weakened in absolute phrase-final position. In consonant-final words, however, only 36% of the tokens exhibit vowel apocope (plus 15% incomplete deletions), and the conditional probability of vowel apocope given that consonant deletion has applied is 22/56 = 39%. Under either calculation, full apocope applies in a minority of cases, and even the rate including incomplete apocope is lower than for vowel-final words (probability of full or incomplete apocope given consonant deletion: 31/56 = 55%). At the same time, the consonant deletion rate is very high – as many as 92% of final consonants are deleted in these words. This makes consonant deletion without apocope the preferred lenition strategy in consonant-final words.

All in all, it can be concluded that although apocope is still not fully established in the language and seems to be restricted mostly to (young) males, it is nevertheless very frequent in phrase-final contexts corresponding to falling intonation (completing information), especially in vowel-final words. At the same time, the very high final consonant deletion rate is important as it suggests a phonological effect, since the mean consonant deletion rate for the same speakers, calculated based on all consonant-final words, regardless of the position in the sentence or phrase, is only 55%.13 Compared to this much lower rate, consonant deletion is (near-)categorical rather than merely optional in the phrase-final context.14 Finally, perhaps the most important observation about the data is the difference in the proportion of tokens of apocope between V-final and C-final words. As already mentioned, the numbers are 61% and 36% (39% if conditioned on the occurrence of consonant deletion), respectively. This marked difference in apocope rates between underlyingly V- and C-final words, even when no final consonant is observed, should be accounted for in any formal model of this phenomenon. It will be referred to as a latent opacity effect (i.e. dispreference for apocope when followed by a deleted consonant) that is not motivated by any specific surface form, but instead by the frequency distribution between surface forms. We discuss it in detail in §3.2.

An important observation concerning the data from this dialect is that the interaction between apocope and consonant deletion, and the resultant ban on multiple deletions are due to opacity. If we look at surface forms like [ˈpas] (Table 2), we can immediately notice the underapplication of an otherwise prevalent process of consonantal lenition. We are dealing with a counterfeeding rule order (Kiparsky 1971). If we were to establish rules for the discussed processes, we would note that apocope counterfeeds consonant deletion as the output of apocope meets the context of application of consonant deletion, but deletion does not apply. This counterfeeding relationship between the two rules is not so straightforward, however, given that in a subset of cases, i.e. in consonant-final words, consonant deletion provides the context for, and thus feeds, apocope. As a result, we have an instance of fed counterfeeding (Kavitskaya & Staroverov 2010; see also Baković 2011).

In Table 2, the transparent case shows the application of consonant deletion at the end of a word. Apocope does not apply because the word-final vowel is stressed. There are two types of opaque outputs that can be produced, assuming that the two rules apply whenever their structural descriptions are met. In the case of a vowel-final form (e.g. paso ‘step’), we can see the counterfeeding relationship between apocope and consonant deletion. The latter cannot apply since it is ordered before apocope. In the case of a consonant-final form (e.g. pasos ‘steps’), we see that consonant deletion first feeds apocope and is then counterfed by it. This can be referred to as fed counterfeeding on environment, since the processes potentially feed each other but each process applies at most once. This is especially problematic for parallel OT, in which no rule ordering can be imposed. Also, we can imagine that the situation will get even more complicated with words such as pájaros ‘birds’, in which transparent feeding would lead to the deletion of most parts of the word (e.g. /paxaɾos/ → [ˈpa] mapping reflecting the following changes: /paxaɾos/ → [ˈpaɦaɾo] → [ˈpaɦaɾ] → [ˈpaɦa] → [ˈpaɦ] → [ˈpa]).

As pointed out by an anonymous reviewer, our case is similar to a fed counterfeeding interaction in Lardil (Kavitskaya & Staroverov 2010; Baković 2011; see also references therein). In Lardil words longer than 2 syllables, final vowels and non-coronal consonants are deleted. Final vowel deletion feeds final consonant deletion, but not vice versa: mungkumungku → mungkumu, *mungkum ‘wooden axe’ (Kavitskaya & Staroverov 2010: 2). Both the Gran Canarian Spanish and the Lardil interaction involve word-final consonant and vowel deletion. However, in Lardil, the processes apply in the opposite order (vowel deletion before consonant deletion). In addition, Gran Canarian Spanish conditions vowel deletion through stress (stressed vowels remain), whereas Lardil does so through word length. Finally, no variation is reported for the Lardil case, which makes that case simpler in some aspects. As will be shown in the next subsection, variation is crucial in understanding surface options and all process interactions involved in our data, and later modelling them in a successful manner.

As indicated in §2, our data crucially involve variation so all surface variants must be generated (/pasos/ → [ˈpasos ~ ˈpaso ~ ˈpas], /ˈpaso/ → [ˈpaso ~ ˈpas]). However, underlyingly V-final words tend to surface without their unstressed final vowel (61% /paso/ → [ˈpas] vs. 39% /paso/ → [ˈpa.so]), while underlyingly C-final words, when their final C is deleted, tend to surface with an unstressed final vowel (36% /pasos/ → [ˈpas] vs. 56% /pasos/ → [ˈpa.so]; 39% vs. 61% when only tokens with consonant deletion are considered). We will now argue why this is a latent opacity effect.

Since V- and C-final words have to be modelled with the same grammar, the difference in vowel deletion rates between them must be captured. In a variable ranking grammar (such as the one we will be working with, see §4.1–2), this means we must have rankings that generate various combinations of surface patterns, as indicated in Table 3.16 Logically speaking, apart from the ranking under which both processes apply in all word types, which we can refer to as A – full lenition, there can be a ranking under which neither process applies (B – no lenition); a ranking under which final vowels are retained, but final consonants are deleted (C – consonant deletion only), and a ranking under which final vowels are deleted, but final consonants are retained (D – apocope only). However, as we argue below, to obtain a higher rate of apocope in V-final words compared to C-final words, we also need an additional ranking (E – mixed pattern) where final consonants and final underlying vowels are deleted, but underlying vowels which become final after consonant deletion are retained. The surface pattern derived by each ranking will henceforth be called a (surface) variant.

The need for variant (and ranking) E can be shown as follows. If there are rankings that generate only variants A, B, C, and D, and speakers pick a different ranking at each instance of grammar use (cf. Boersma 1998), the following conundrum ensues. We know that faithful realization of /pasos/ occurs 8% of the time (in the remaining 92% of the cases, C deletion applies), meaning that rankings B and D together should be picked in no more than 8% of language use. Furthermore, /pasos/ → [ˈpaso] occurs 56% of the time, meaning that ranking C is picked 56% of the time, and /pasos/ → [ˈpas] occurs 36% of the time, meaning that ranking A is picked 36% of the time. This is shown in Table 4.

A model without a mechanism to generate Variant E cannot match the correct rates for vowel deletion for C-final and V-final words. This is because the model generates /pasos/ → [ˈpaso] at the same rate as /paso/ → [ˈpaso], which grossly overestimates how often the latter occurs: 56% of the time instead of the attested 39%. At the same time, if /paso/ → [ˈpas] is only generated by rankings A and D, its rate of occurrence will be grossly underestimated. Ranking D cannot be chosen more than 8% of the time (because of /pasos/ → [ˈpasos]), while ranking A must be chosen 36% of the time (/pasos/ → [ˈpas]), meaning that /paso/ → [ˈpas] could occur at most 8% + 36% = 44% of the time instead of the attested 61%. To correctly predict the rate of /paso/ → [ˈpas], we must assume that there is also a different ranking that generates /paso/ → [ˈpas] but not /pasos/ → [ˈpasos] or [ˈpas]: the mixed E pattern.

Note that this mixed pattern is, in itself, opaque. C-final words like /pasos/ undergo consonant deletion, but fail to undergo vowel apocope afterwards: /pasos/ → [ˈpaso] *→ ˈpas. V-final words like /ˈpaso/ undergo vowel apocope, but fail to undergo consonant deletion afterwards: /paso/ → [ˈpas] *→ ˈpa. This constitutes a chain shift (VC# → C#, C# → ∅#; Baković 2011), but it is also a case of mutual counterfeeding (Wolf 2011): consonant deletion counterfeeds vowel deletion and vice versa. Since this opaque mapping is not necessary to derive any of the individual surface forms observed in the language, but only to model the quantitative pattern of variation, we refer to this as a case of latent opacity.

In the remainder of this section, we present an analysis of the Gran Canarian data in the framework of Serial Markedness Reduction (SMR, Jarosz 2014), which offers constraints on ordering in derivations that help model opacity of various types. Thus, it is appropriate for generating vowel apocope and consonant deletion in interaction. While other frameworks exist that could in principle model the opaque data,17 SMR has one major advantage – there is an existing probabilistic learner for it (Jarosz et al. 2018), which allows us to test numerically how well a probabilistic ranking version of SMR can capture the variation in our data (see §4).

Jarosz’s (2015) framework operates on strictly ranked constraints, as opposed to weighted-constraint alternatives such as Harmonic Grammar (Legendre et al. 1990) and related approaches like Maximum Entropy Grammar (Goldwater & Johnson 2003). Like Stochastic OT (Boersma 1998), Jarosz’s framework defines probabilities over rankings. Differently from Stochastic OT, Jarosz (2015) represents these probabilities directly: for every pair of constraints, the grammar represents what the probability is that one of these constraints is ranked over the other. Accordingly, Jarosz names these grammars Pairwise Ranking Grammars. Assigning probabilities to rankings allows the expression of variation: multiple rankings are possible given the grammar, with potentially different outcomes for the same input (an example will be given below). The reason for representing these probabilities directly rather than through weights as in Stochastic OT comes from learning efficiency (Jarosz 2015): they allow for Expectation-Driven Learning.

An example of a Pairwise Ranking Grammar is given in Table 5, where ranking probabilities over three constraints – *UnstrV, *Final-C, Max(seg) – are represented. This grammar represents a fixed ranking *Final-C >> Max(seg), as can be seen in the top right cell of the tableau with 100% probability for *Final-C >> Max(seg) and in the bottom left cell with 0% probability for Max(seg) >> *Final-C. *UnstrV has a variable ranking with a tendency to rank in between the former two constraints. This can be seen in the middle row and the centre column of the table. The top centre cell indicates 70% probability for *Final-C >> *UnstrV (the mid left cell correspondingly indicates 30% probability for *UnstrV >> *Final-C), so *UnstrV is most likely below *Final-C. The mid right cell indicates an 80% probability for *UnstrV >> Max(seg), while the bottom centre cell correspondingly indicates a 20% probability for Max(seg) >> *UnstrV. This tells us that there is a tendency for *UnstrV to rank above Max(seg).

Like in Stochastic OT, every time the grammar is used, a specific ranking of these constraints is sampled from the grammar (see Jarosz 2015 for the sampling procedure).27 For the grammar in Table 5, the most likely ranking is *Final-C >> *UnstrV >> Max(seg), which yields final C and V deletion: /pasos/ → [ˈpas] (Variant A, presuming high ranking of SM(*Final-C,*UnstrV)). However, there is a chance of sampling *Final-C >> Max(seg) >> *UnstrV (since there is a 20% probability that Max(seg) >> *UnstrV), which would lead to the deletion of final consonants only: /pasos/ → [ˈpaso] (Variant C). Crucially, there is no chance in this grammar that Max(seg) >> *Final-C >> *UnstrV, which would lead to /pasos/ → [ˈpasos] (Variant B), since the probability of Max(seg) >> *Final-C is 0. The relative likelihood of each of these rankings means that /pasos/ → [ˈpas] will occur most often, /pasos/ → [ˈpaso] less often, and /pasos/ → [ˈpasos] will never occur. The precise probability of a mapping given the grammar can be estimated by taking many samples from the grammar (in our case, 1000) and counting how often a ranking is chosen under which this mapping wins; for instance, if 832 of 1000 sampled rankings yield /pasos/ → [ˈpaso], the probability of /pasos/ → [ˈpaso] will be estimated as 83.2% (the same procedure is used in Stochastic OT, Boersma 1998, and Noisy Harmonic Grammar, Coetzee and Pater 2011).

Since this framework is based on ranked constraints, and the properties of gen and eval remain unaltered, it can be straightforwardly applied to HS: every time the grammar is used, a ranking is picked, and this ranking fully determines the HS derivation. For instance, if from the grammar in Table 4 the learner samples *Final-C >> *UnstrV >> Max(seg), the HS derivation will be /pasos/ → /ˈpaso/ → /ˈpas/ → [ˈpas] (corresponding to Variant A); if a different ranking is sampled from the Pairwise Ranking Grammar, this ranking may determine another HS derivation. Such a setup is different from the MaxEnt implementation of probabilistic HS (Staubs & Pater 2016) in which each step of the HS derivation is made probabilistic (changing eval). The probabilistic nature of the latter setup alters some of the properties of HS and requires some ad-hoc adjustments (see Staubs & Pater 2016).

To simulate the learning of the Canary Islands Spanish patterns, we use the batch version of Jarosz’s (2015) Expectation-Driven Learning (EDL) mechanism, which learns Pairwise Ranking Grammars from data using the general principles of Expectation Maximization (EM; Dempster et al. 1977), a method of machine learning that is guaranteed to maximize a model’s fit to the training data even when the learning problem has great complexity. When using a serial framework like HS, this is especially relevant, since the outcome of the model is mediated by potentially many derivational steps, each of which reflects on the overall ranking that must be learned. Our choice for EDL is also motivated by the fact that the only existing implementation of learning SMR grammars is in EDL (Jarosz 2016; Jarosz et al. 2018).

The learner starts with an initial grammar hypothesis (we used a uniform distribution over all pairwise rankings) and then iterates a cycle consisting of the E(xpectation)-step (compute the expected ranking probabilities given the current grammar hypothesis and the data set) and the M(aximization)-step (replace the current grammar hypothesis by the expected ranking probabilities just found at the E-step) until convergence (the M-step does not significantly change the grammar hypothesis) or until timeout. The details of how this learner updates the grammar hypothesis are given in Appendix 4.

The application of this method to HS is straightforward: it only requires an implementation of standard HS and a way of checking whether the output of the HS derivation given a particular ranking and input matches the intended mapping. We use a slightly updated version of Jarosz et al.’s (2018) code, which integrates Expectation-Driven Learning and SMR (as well as other variants of HS); our updates to their code allow for the definition of faithfulness constraints that use context (Max(V)/Initial and Contiguity) and for a more general application of Serial Markedness constraints.

Table 8 shows the numerical results of the simulations. These results demonstrate that having SM constraints improves the fit of the model to the frequency distribution: no SM constraints yields a data log-likelihood of –∞ (because some attested forms have a predicted probability of 0) and a high MAE (about 19), while models with SM constraints do have nonzero probability for all attested forms leading to finite negative log-likelihood and a markedly lower MAE (with non-overlapping confidence intervals (CIs)). Furthermore, the 2SM model does better than the 1SM model: it has a higher data log-likelihood and a lower MAE (both with non-overlapping confidence intervals). In fact, the 2SM model is only an average of 3 percentage points off on the relative frequency of each form.

Qualitatively, as predicted, the model with no SM cannot handle the opaque interaction in /paso(s)/ and /paxaɾo(s)/: it is unable to produce final VC deletion, deleting all segments up until the stressed vowel instead: /paxaɾos/→[ˈpa], since SM(*Final-C,*UnstrV) is not available (cf. ranking A, Appendix 3). /metɾo(s)/ and /ofeɾta(s)/ are mapped to attested candidates, but the frequency distribution is not captured adequately (Appendix 5, Table 11).

The 1SM model, as predicted, can generate all mappings in the data. However, since it does not allow ranking E, in which final unstressed vowels delete in underlyingly V-final words but not underlyingly C-final words, it cannot match the relative frequencies of vowel deletion in V-final and C-final words well: it predicts that it will happen equally often in both (Appendix 5, Table 13).

This is solved in the 2SM model. This model is able to generate the difference between underlyingly V-final and underlyingly C-final words ranking by not fixing the ranking between SM(*UnstrV,*Final-C) and *UnstrV, but representing a tendency for SM(*UnstrV,*Final-C) to rank above Max(seg) (see Table 9), so that the crucial subranking SM(*UnstrV,*Final-C) >> *UnstrV >> Max(seg) from ranking E (Appendix 3), which blocks vowel deletion specifically in underlyingly C-final words, appears often enough to ensure that C-final and V-final words receive the correct percentages of vowel apocope. In fact, this model very closely tracks the frequency distribution in the data file (Appendix 5, Table 15).

Table 9 shows the resulting ranking probabilities for the noSM, 1SM and 2SM models. The Hasse diagrams are to be read as follows. A solid line indicates that the relevant ranking has a probability of at least 90% for all 20 runs for that model. A dashed line indicates that the relevant ranking has a probability of at least 70% for all 20 runs for that model, but it has a probability below 90% for at least 1 run.

In Table 9, it can be observed that, as more SM constraints are added, the ranking probabilities among the indicated constraint pairs increase or remain the same (no line < dashed line < solid line), meaning that the ranking of these constraint pairs gradually becomes more predictable.30 For instance, *Final-C >> Max(seg) has a probability of 65% for noSM (no line) and a probability of 89-90% for the 1SM and 2SM models (dashed line). The latter corresponds more closely to the desired 8% occurrence of final consonant retention, as it predicts Max(seg) >> *Final-C about 10% of the time. This increase in constraint ranking predictability corresponds to an increase in accuracy in the models’ predictions. In noSM, ranking A is unavailable because of the crucial role of SM(*Final-C,*UnstrV), leading the learner to overestimate the chance of full faithfulness to prevent mappings like /pasos/ → [ˈpa] from occurring too often (see Appendix 5, Table 11). In noSM and 1SM, Variant E is unavailable (since it crucially involves both SM constraints), leading the learner to settle on overestimating the rate of vowel deletion in vowel-final words and underestimating it in consonant-final words (see Appendix 5, Table 13). It is only the 2SM model that steers clear of this over- and underestimation and closely matches the attested distribution.

As mentioned in the previous sections, a crucial point of our analysis is that it accounts for variable surface distributions. Our SMR analysis, in which ranking probabilities are optimised by machine, offers a comprehensive treatment of opacity-ridden variation. In §4 we showed that the variable surface distributions can be successfully mapped with the use of two serial markedness constraints mandating precedence relations between the two analysed processes. To the best of our knowledge, this is the first attempt to address opacity with variation using a learning algorithm and the first application of the SMR framework (and the EDL learner) to opacity patterns with variation.32

Importantly, the simulations in §4 show that the Canary Islands Spanish pattern of variation can be learned as long as the learner has access to the necessary Serial Markedness constraints. Alternatives to such constraints exist, including Prec constraints in Optimality Theory with Candidate Chains (OT-CC, McCarthy 2007), and contextual faithfulness constraints in parallel OT or HS (Hauser & Hughto 2020). Both approaches have been claimed to need additional mechanisms to deal with fed counterfeeding (Kavitskaya & Staroverov 2010; Hauser & Hughto 2020). Below (§5.1.1), we show an alternative analysis in OT-CC in which we model fed counterfeeding without additional mechanisms. We then show that mutual counterfeeding poses a greater challenge, however. This is followed by an alternative analysis using contextual faithfulness (§5.1.2), which shows, contra Hauser & Hughto (2020), that fed counterfeeding is possible in this framework, and that there is potential to analyse the current data in parallel OT.

Apart from showing unusual complexity in terms of opaque process interactions, our study also raises another important question: morphophonological restrictions. In OT, opacity is most often tied directly to cyclicity (Kiparsky 1971; 2000; Bermúdez-Otero 1999). Kiparsky (2015: 21) states explicitly that opacity is “a side effect of domain stratification” and that there are at most two levels of opacity corresponding to the changes in rankings between the three strata in Stratal OT opacity (Bermúdez-Otero forthcoming). Instead, we contend that the two processes involved necessarily act on the same stratum and morphological structure is not responsible for the opacity effect. Without any doubt, apocope should be assigned to the phrase-level stratum given its restricted application. However, positing C deletion at the word level is problematic because this process is in competition with other repair strategies: the final consonant can be devoiced or aspirated (if it is an s). Resyllabification is another complicating factor: word-final consonants tend to form an onset of the following word whenever the latter begins with a vowel. In the case of the s, a weakened variant is preserved in the newly formed onset (weak glottal [h], and in the Spanish from the Canary Islands, its voiced version, [ɦ], e.g. los ejemplos ‘the examples’ /los#exemplos/ [lo.ɦe.ˈɦem.plo]). Since deletion is avoided in resyllabification contexts, positing that deletion occurs at the word level, where no information concerning the following word is available to prevent unnecessary elision, is problematic. Thus, as far as Stratal OT is concerned, we are forced to assume that both deletion processes presented in §2 belong to the domain of the phrase (third stratum), and hence the problem of opacity cannot be solved.

Furthermore, Kiparsky (2015) argues that opacity should be investigated in obligatory processes only because with optional processes we cannot reliably establish whether the observed opacity effect is genuine or simply a result of not applying an optional process. However, our data show clearly that the opacity effect is caused by the non-application of consonant deletion after vowel apocope has taken place. Since vowel apocope is the undoubtedly optional process and consonant deletion practically always applies phrase-finally, we must conclude that the observed pattern is a genuinely opaque interaction. Taking the surface distributions into account, we can calculate the probability of each option. In words such as pasos the probability of [ˈpasos] is 8% while the probability of (transparent) [ˈpa] is 0% and the conditional probability of (opaque) [ˈpas] is 39%. In vowel-final words, the probability of (opaque) [ˈpas] is 61% while (transparent) [ˈpa] surfaces 0% of the time. Thus, mathematically speaking, the zero probability of transparent final C deletion cannot be derived from merely assuming that vowel apocope and final consonant deletion apply optionally at every derivational step: if the latter were the case, we would see at least some occurrences of forms like [ˈpa]. Consequently, we argue that opaque interactions within a stratum are not only possible but also quite productive across languages. Arguments against morphophonological explanations of opacity have been set forth based on examples from Catalan and Bedouin Arabic by McCarthy (2007: 40–41, 196–197). Similarly, Broś (2016) reports a different case of post-lexical opacity in Spanish, and a recent contribution to the topic by Milenković (2022) shows an interaction of two non-optional lexical processes in a stratum-internal opaque interaction in Gallipoli Serbian. Moreover, the seminal case of fed counterfeeding in Tundra Nenets mentioned in this paper is also argued to be a within-stratum interaction (Kavitskaya & Staroverov 2010: 283). These pieces of evidence taken together make it necessary to adjust the formal mechanisms used to address the opacity problem in phonology and add weight to the discussion of the structural restrictions governing opaque vs transparent process interactions.

The opacity case presented in this paper also adds evidence to the fact that opaque interactions can be very diverse and have different implications depending on the type of processes involved, as well as the type of rules or constraints that can be used as a solution. More specifically, in §3.3 and §5.1 we demonstrated that our case of fed counterfeeding is less problematic in terms of formal analysis compared to previous accounts of similar interactions (e.g. Tundra Nenets).

In addition to the above, it must be stressed that analysing variation, apart from staying true to the actual productions of native speakers, has an additional advantage. As we have shown, certain ordering restrictions and rankings can only be found once variation is taken into account, which is an important contribution to the study of phonological interactions. §3 shows the roles both SM constraints play in our derivations. While SM(*Final-C,*UnstrV) appears to be the only serial markedness constraint necessary to derive each of the individual surface forms, including the fed counterfeeding pattern (Variant A), another high-ranked constraint SM(*UnstrV,*Final-C) is necessary when the quantitative aspect of variation is taken into account (Variant E). Such latent opacity effects need to be investigated further. Moreover, the effect of opacity versus different types of rankings necessary to derive surface forms should be mentioned in this context. Note that the different percentages of process application are independent from the attested counterfeeding interaction.37 The fed counterfeeding opacity, for instance, concerns both C-final and V-final words regardless of the differing rates of process application. Nonetheless, the latter lead to the discovery of the need to construct an additional ranking for the probabilistic grammar. Thus, the existence of a possibility that the two interacting processes apply differentially, i.e. that not only both apply, both fail to apply or one of them fails to apply, but that one of them may apply only if a preceding process did not apply, is a potential challenge for the formal representation of the dialect. The option in which pasos is pronounced [ˈpaso] but paso is pronounced [ˈpas] requires a framework that goes beyond mimicking extrinsic rule ordering and derivational steps, with or without reranking. Note that even if we assumed that apocope and consonant deletion apply at different strata, a Stratal OT approach and the like would fail to predict such outputs. Reranking constraints responsible for the occurrence of either of the processes is not enough without a probabilistic component in the grammar. Consequently, our data show that optionality leads to variation that obscures possible analyses, which is of consequence for phonological theory and should be considered in future research linking language variation and change with phonological computation.

Finally, we have seen that a single variety of a language can show not one but two complex opacity cases that are presumably typologically rare. Especially, mutual counterfeeding has been questioned as a linguistic reality. Wolf (2011) discusses one possible case of /ə/-syncope and VN coalescence in Hindi-Urdu, which has been contested in the literature. Exchange rules can be listed as another possible mutual counterfeeding pattern (see Wolf 2011: 103–106 for a review). The present study adds yet another example which, in our opinion, is difficult to dismiss. Thus, the Gran Canarian data contribute to discussion on the typology of opacity and raise the question of whether more mutual opacity cases might be encountered cross-linguistically as more research is done into optional processes and the resultant variation.