1 Category mismatches in coordination

Traditionally it was assumed that coordinate structures can only conjoin elements of identical syntactic categories (Law of the Coordination of Likes, LCL, Chomsky 1957; Williams 1981). The debate on the validity of the LCL (recently Przepiórkowski 2022; Patejuk & Przepiórkowski 2023; Bruening 2025) seems to have come to the agreement that, when both conjuncts are independently selected, the LCL is too strict and mismatches in category are in fact allowed, (2). Instead, these structures have to obey Wasow’s generalization, (1) (see also Huddleston & Pullum 2002). Thus, while become in (2) selects both NP and AP, it does not select a PP, and does not allow PPs in coordinations.

But apparently Wasow’s generalization is still too strict for structures like (3). A CP that is not independently selected by the predicate, (3b), can appear in a coordination with a selected nominal, (3a). The order of the DP- and CP-conjuncts plays a role: reversal of the order leads to ungrammaticality, (3c).

These selection-violating coordinations have received analyses either as proper DP&CP coordinations violating (1) (e.g., Munn 1993; Peterson 2004; Zhang 2010), or as structures where a clause may be headed by nominal functional structure, [ DP & [ DP [ CP ]]], which technically obey Wasow’s generalization, (e.g., Sag et al. 1985; Neeleman et al. 2022). Recently, two new proposals take the analysis in different directions: Al Khalaf 2015; Bruening & Al Khalaf 2020; Bruening 2025 argue that linear adjacency to the selector is crucial in mismatching coordinations and propose a left-to-right derivation for linear order effects. Kim & Lu (2024) argue that selection-violating coordinations are not a real syntactic phenomenon at all, but instead an effect of processing: high processing costs make selection failures harder to detect, which gives rise to high acceptability ratings.

I present observations from German that argue against both the linear adjacency account and the processing account. German is an OV language, where a coordination of objects linearly precedes the selecting verb. Both of these accounts make the prediction that the rightmost conjunct should be the one selected by the verb, because it is linearly or temporally closer to it. Empirical evidence from a forced-choice experiment shows that this is not borne out. Speakers strongly prefer the order of conjuncts in which the selected DP is the leftmost conjunct, and the unselected CP is the rightmost one. The results are predicted in bottom-up derivations in which coordinations have an asymmetric structure, and raise questions about cross-linguistic variation.

This squib is structured as follows: section 2 gives an overview of the analyses of mismatching coordination. Section 3 presents some background on German and two experiments. Section 4 discusses theoretical implications of the results.

2 Previous analyses of mismatching coordinations and their predictions

Mismatching DP-CP coordinations still pose a theoretical puzzle. There are three groups of analyses for these coordinations, all of which face empirical challenges. In one group, sentences such as (3a) constitute real DP&CP coordinations, i.e., Wasow’s generalization can be violated. Grammaticality is attributed to the more prominent position of the initial conjunct: only the higher, c-commanding DP-conjunct is licensed in this position, while the other (CP-)conjunct is too deeply embedded to be accessible to the verb, and can thus be ‘smuggled’ into a complement position where it otherwise cannot surface. This approach is illustrated in (4). ‘Licensing’ here can be understood either in terms of c-selection (Peterson 2004; Zhang 2010) or in terms of case assignment (Munn 1993). These analyses cannot explain why these coordinations are as restricted as they are (CPs can occur in DP-positions, but almost no other violation of selection requirements seems to be possible, see Bruening & Al Khalaf 2020; Przepiórkowski & Patejuk 2025). A related approach posits a nominal shell on top of the CP-conjunct, such that we are actually dealing with a DP&DP structure, (5), e.g., Sag et al. (1985). The challenge for this type of account is to adequately restrict the availability of null DP shells such that they can derive the ungrammaticality of (3b). I will discuss both of these analyses under the label bottom-up group. They both assume some type of asymmetric structure for coordinations.¹ The possibility of a mismatch in these accounts comes from the structural asymmetry between the conjuncts. The first/left conjunct will always be more prominent for the selecting element than more deeply embedded ones. This group predicts that, all else being equal, mismatching coordinations in an OV-language like German should pattern exactly like in (3a), i.e., only a non-initial conjunct can be unselected.

In the second group of analyses, Bruening & Al Khalaf (2020); Bruening (2025) also postulate an empty noun on top of CPs, but they assume a left-to-right derivation. The motivation for this is their observation that it is not always the final, deeper embedded conjunct that can violate selectional requirements. In (6a), the linearly first conjunct is the non-selected one.

I call this type of approach the linear closeness group. Derivations in these analyses proceed not bottom-up but left-to-right (following e.g., Phillips 1996). In this analysis, selection has a syntactic and a semantic component. Only the conjunct that is linearly closest to the selector has to meet both syntactic and semantic selection requirements. Conjuncts further away only have to fit the syntactic requirement. If the noun phrase is closer to the selecting verb, i.e., the first conjunct in (3a) and the last conjunct in (6a), both the syntactic and semantic selection features can be checked, (7). If the closest conjunct is the that-clause, the semantic features will be unchecked, leading to a crash. This is derived in a left-to-right derivation by the order of Agree operations that dictate the accessibility of features in the highest projection of the coordination at the point when it merges with the selector. Space restrictions forbid going into further detail, but I refer the reader to Bruening (2025); Bruening & Al Khalaf (2020).

These analyses have similar problems as the bottom-up group in deriving the distribution of NP-shelled CP: they propose that CPs are disallowed in (3b) because they are semantically empty, i.e., not sentient or animate (Bruening 2025: 29, 31). However, this can certainly not be the whole story, since predicates like depend on can also combine with inanimate NPs and inanimate non-NPs, like small clauses, (8).

Crucially, in the linear closeness accounts the often observed selection of only the initial conjunct as in sentences like (3a) is an accident due to the verb-initial word order in English: the first conjunct in (3a) happens to be linearly closer to the verb than the second conjunct. In different contexts, English apparently also allows the reverse order, as in (6). The linear closeness accounts predict that OV languages should show the opposite pattern: the linearly final conjunct should generally be the selected one.

The last group of analyses is the temporal closeness one. Kim & Lu (2024) propose a processing-based account of mismatching coordinations in which they are a grammaticality illusion. They are actually ungrammatical, i.e., Wasow’s generalization is real and cannot be violated, but are rated as acceptable because the parser gradually ‘forgets’ the selectional requirements of the predicate as the sentence proceeds (Gibson & Thomas 1999; Futrell et al. 2020). Kim & Lu (2024) argue that the more time passes between parsing of the selector and parsing of the mismatching CP conjunct, the less likely the mismatch is to be detected. The verb is encountered first, and the parser registers its selectional features. When the first conjunct matches the features, parsing proceeds, and with passing time, the verb’s requirements fade in memory. When the parser encounters the second conjunct, a possible mismatch cannot be detected anymore.² Their evidence comes from an acceptability judgment experiment in English that found that the closer a CP-conjunct is to the selecting verb in a three-way coordination, the more acceptability decreases: (9b) is rated significantly worse than (9a).

In an OV language, the selectees are encountered before the selector, but the same logic should hold: increased dependency length (of feature checking) leads to decreased mismatch detection. The first conjunct prompts the parser to expect a selecting predicate. While waiting for the predicate, the representation and features of the conjuncts have to be held in working memory, incurring storage costs. The oldest information is the first conjunct. It will be forgotten first. Thus, when the predicate is encountered, the features of the second conjunct will still be in storage and can be checked against the selectional requirements. The expectation is that a mismatch here is more likely to be detected than mismatch with the first conjunct. This means that speakers should (erroneously) accept structures in which the mismatching conjunct is the leftmost one, i.e., they predict the same pattern as the linear closeness accounts: a non-selected CP should only be able to surface in the position that is further away from the selecting verb, (10a). This contrasts with the bottom-up group that predict (10b), where the unselected CP should be the more deeply embedded conjunct.

3 No linear or temporal order effect in German

3.1 Experiment 1: DP-CP coordinations in German

First, I tested whether mismatching DP-CP coordinations like (11a), are also possible in German. I tested four predicates that, according to informally collected judgments, select DPs but not CPs: beenden ‘end’, streichen ‘cancel’, (nicht) übereilen ‘(not) rush’, and entwickeln ‘develop’. In my native judgment, DP-CP coordinations with these predicates are grammatical, and contrast sharply with bare CP complements. This judgment is shared by five other speakers I consulted. In this acceptability study, the improvement of DP-CP coordinations over bare CPs was confirmed.

Method, material, participants

Experiment 1 investigates the acceptability of selected and non-selected bare CPs compared to a coordination context. The experiment, hosted on SoSciSurvey (Leiner 2025), had a Latin square design with the factors selection (yes/no) x complement (dass-clause/DP-CP-coordination). In addition to the four non-selecting predicates above I tested four CP- and DP-selecting counterparts: veranlassen ‘induce’, vergessen ‘forget’, erwarten ‘expect’, and beschließen ‘decide’, as well as the 10 items of the standard filler set (Featherston 2009) and three training items. A sample test item is given in (11)–(12). In the coordination condition, the DP is always the first conjunct. Each participant rated one lexicalization per condition and all fillers on a 1–5 Likert scale. 50 participants were recruited on Prolific and compensated for their participation. Six participants were excluded for deviating more than 2.5 standard deviations from the mean for more than two filler items. Data of 44 participants entered analysis. All participants stated that they grew up in a German-speaking region and that German is their native language. Four bilinguals were included in analysis.

1. (11)

1. Die
2. the
1. Stadt
2. city
1. beendet
2. ends
1. zum
2. at.the
1. Jahreswechsel…
2. year.turn

1.  
1. a.

1. …[_CP
2.  
1. dass
2. that
1. für
2. for
1. Neugeborene
2. newborns
1. ein
2. a
1. Baum
2. tree
1. gepflanzt
2. planted
1. wird].
2. aux.pass
1. ‘The city stops its scheme of planting trees for newborn children at the turn of the year.’ dass-clause

1.  
1. b.

1. …[[_DP
2.  
1. die
2. the
1. Überarbeitung
2. revision
1. des
2. of.the
1. Nahverkehrskonzepts]
2. public.transport.plan
1. und
2. and
1. [_CP
2.  
1. dass
2. that
1. für
2. for
1. Neugeborene
2. newborns
1. ein
2. a
1. Baum
2. tree
1. gepflanzt
2. planted
1. wird]].
2. aux.pass
1. ‘At the turn of the year, the city completes its revision of the local transport plan and stops the scheme of planting a tree for every newborn child.’coord.

1. (12)

1. Die
2. the
1. Stadt
2. city
1. veranlasst
2. starts
1. zum
2. at.the
1. Jahreswechsel…
2. year.turn

1.  
1. a.

1. …[_CP
2.  
1. dass
2. that
1. für
2. for
1. Neugeborene
2. newborns
1. ein
2. a
1. Baum
2. tree
1. gepflanzt
2. planted
1. wird].
2. aux.pass
1. ‘The city starts its scheme of planting trees for newborn children at the turn of the year.’ dass-clause

1.  
1. b.

1. …[[_DP
2.  
1. die
2. the
1. Überarbeitung
2. revision
1. des
2. of.the
1. Nahverkehrskonzepts]
2. public.transport.plan
1. und
2. and
1. [_CP
2.  
1. dass
2. that
1. für
2. for
1. Neugeborene
2. newborns
1. ein
2. a
1. Baum
2. tree
1. gepflanzt
2. planted
1. wird]].
2. aux.pass
1. ‘At the turn of the year, the city starts its revision of the local transport plan and the scheme of planting a tree for every newborn child.’coord.

Results

Figures 1, 3 and table (14) summarize the results. (Not) selected in Figure 1 refers to the context in which the two types of complements were presented: with a verb that usually selects CP-complements or not. Figure 2 shows how the fillers were rated. (Coordinate or dass-)complements in unselected positions are rated similarly to fillers of group C. The group C fillers are shown in (13).

1. (13)
1. a.

1. Was
2. what
1. ich
2. I
1. wissen
2. know
1. will
2. want
1. ist
2. ist
1. wen
2. who.acc
1. wer
2. who.nom
1. in
2. in
1. dieser
2. this
1. Affäre
2. affair
1. betrügt.
2. cheats
1. ‘What I want to know is who cheats on who in this affair.’

1.  
1. b.

1. Ich
2. I
1. habe
2. have
1. dem
2. the.dat
1. Kunden
2. customer.dat
1. sich
2. refl
1. selbst
2. self
1. im
2. in.the
1. Spiegel
2. mirror
1. gezeigt.
2. shown
1. ‘I have shown the customer to himself in the mirror.’ (Featherston 2009: 71)

1. (14)

1. Descriptive statistics experiment 1
2. 

Figure 1: Results of exp. 1.

Figure 2: Scores for standard fillers.

A linear mixed effects model was fit in R (R Core Team 2021) with the lme4 (Bates et al. 2015) and lmerTest packages (Kuznetsova et al. 2017) to investigate the influence of each factor. There was a simple effect of selection (β = 0.2, df = 11.86, t = 3.1, p < 0.001): Bare complement clauses are acceptable when paired with a selecting predicate and unacceptable when paired with a non-selecting one. This confirms the baseline assumption that verbs like beenden do not select a CP. DP-CP coordinations were also more acceptable with selecting verbs than non-selecting ones, as expected. However, there was also a significant interaction effect (β = 0.28, df = 11.86, t = 2.8, p < 0.01). The difference for coordination from selected to unselected contexts is smaller than the difference for dass-clauses, see Figure 3. This means that DP-CP-coordinations in unselected contexts are actually more acceptable than we would expect extrapolating from dass-clauses. If the 0.5 points difference between coordinations and bare dass-clause complements in a context where the CP is selected carried over the the unselected context, we would expect a median score for coordinations at around –1. But this is not what we find: coordinations are better than expected, with a median score of around –0.25. While it is possible that such a relative improvement in acceptability could in principle also hold between two ungrammatical structures,³ I take this improvement, combined with introspective judgments and the similarity to filler group C in the absolute z-scores, to suggest that the grammar of German allows DP-CP coordinations in environments where only DPs are selected, similar to English.

Figure 3: Interaction of complement type and selection.

The effect size (Cohen’s d) of unselected vs. selected DP-CP coordinations is d=0.85 (calculated with R’s lsr package, Navarro 2015). This is a large effect, for which 44 participants provide more than 80% statistical power for a Likert scale task (see Sprouse & Almeida 2017).

3.2 Experiment 2: Order of DP and CP

The linear and temporal closeness analyses predict that in OV word order, the DP should be the rightmost conjunct, as in (10a) above, since it would be closer to the selecting verb there. The bottom-up approaches expect a universal DP-first preference: The selected conjunct should be the one that is structurally closer to the selecting verb, even if it is linearly further away, i.e., (10b). An OV language like German thus makes the perfect test case since it allows linear adjacency to be teased apart from hierarchical relations.

To test the predictions of the temporal and linear closeness accounts, a complement clause must precede the verb, i.e., a CP must occur in the middle field as in (15).

1. (15)

1. ?Ich
2.   I
1. habe
2. have
1. [_CP
2.  
1. dass
2. that
1. man
2. one
1. Reis
2. rice
1. einfrieren
2. freeze
1. kann]
2. can
1. schon
2. already
1. gehört.
2. heard
1. ‘I have already heard that you can freeze rice.’

The status of middle field complement clauses in German is debated. It is clear that they are preferably extraposed. In the middle field, they are judged as acceptable (but marked) in e.g., von Stechow & Sternefeld (1988: 392), Bayer (1995: 53), Müller (1996: 231), Reis (1997: 129), and as unacceptable in e.g., Büring & Hartmann (1997: 29), Bader et al. (2013: 64). Since the preference for extraposition is quite strong, a Likert scale judgment task is unlikely to detect a difference between selected and unselected preverbal CPs, should there be any.^4,5 Instead, binary comparative judgments as in two-alternatives-forced-choice tasks (2AFC) are considered to be appropriate for finer grained differences between conditions (see e.g. Sprouse & Almeida 2017; Stadthagen-González et al. 2018). The idea is that the penalty for putting dass-CPs in preverbal position that would show up in Likert scale tasks disappears in 2AFC tasks because speakers don’t compare a test sentence to a hypothesized grammatical ideal, but to another sentence that also has a preverbal CP.

Method, material, participants

Thus, experiment 2 is designed as a 2AFC task. Participants were presented with two sentences that differed only in the order of the conjuncts, as in (16)-(17), and were asked to select the sentence that ‘sounded better to [them]’. The sentences were presented with preverbal (16) and postverbal order (17). The sentences within a pair (as well as test pairs overall) were presented in random order.

1. (16)

1. Die
2. the
1. Stadt
2. city
1. hat
2. has
1. zum
2. at.the
1. Jahreswechsel…                                                                                                                     OV
2. year.turn

1.  
1. a.

1. …[_DP
2.  
1. die
2. the
1. Überarbeitung
2. revision
1. des
2. of.the
1. Nahverkehrskonzepts]
2. public.transport.plan
1. und
2. and
1. [_CP
2.  
1. dass
2. that
1. für
2. for
1. Neugeborene
2. newborns
1. ein
2. a
1. Baum
2. tree
1. gepflanzt
2. planted
1. wird]
2. aux.pass
1. beendet.
2. ended

1.  
1. b.

1. …[_CP
2.  
1. dass
2. that
1. für
2. for
1. Neugeborene
2. newborns
1. ein
2. a
1. Baum
2. tree
1. gepflanzt
2. planted
1. wird]
2. aux.pass
1. und
2. and
1. [_DP
2.  
1. die
2. the
1. Überarbeitung
2. revision
1. des
2. of.the
1. Nahverkehrskonzepts]
2. public.transport.plan
1. beendet.
2. ended

1. (17)

1. Die
2. the
1. Stadt
2. city
1. beendet
2. ends
1. zum
2. at.the
1. Jahreswechsel…                                                                                                                VO
2. year.turn

1.  
1. a.

1. …[_DP
2.  
1. die
2. the
1. Überarbeitung
2. revision
1. des
2. of.the
1. Nahverkehrskonzepts]
2. public.transport.plan
1. und
2. and
1. [_CP
2.  
1. dass
2. that
1. für
2. for
1. Neugeborene
2. newborns
1. ein
2. a
1. Baum
2. tree
1. gepflanzt
2. planted
1. wird].
2. aux.pass

1.  
1. b.

1. …[_CP
2.  
1. dass
2. that
1. für
2. for
1. Neugeborene
2. newborns
1. ein
2. a
1. Baum
2. tree
1. gepflanzt
2. planted
1. wird]
2. aux.pass
1. und
2. and
1. [_DP
2.  
1. die
2. the
1. Überarbeitung
2. revision
1. des
2. of.the
1. Nahverkehrskonzepts].
2. public.transport.plan
1. all: ‘At the turn of the year, the city completes its revision of the local transport plan and stops the scheme of planting a tree for every newborn child.’

Experiment 2 used the same predicates as experiment 1. Since weight plays a role in the ordering of the conjuncts (e.g., Lohmann & Takada 2014), the conjuncts were designed to be equal in weight in terms of syllables (maximal difference: two syllables). Each participant saw four test sentence pairs and twenty control pairs. The control items also contained coordinations and were of similar lengths as the test items. The control items come in two groups: in control group 1 (10 pairs) both sentences were ungrammatical. They either contained an (ungrammatical) Left Branch extraction or a word order violation. This control group serves as a measure for the interpretation of the test items. Control group 2 (10 pairs) contained one clearly grammatical and one clearly ungrammatical choice. This control group helps us evaluate whether the task was performed correctly.

48 participants were recruited on Prolific. One participant from a non-German-speaking country was excluded. 17 participants were excluded for selecting the ungrammatical option over the grammatical one in control group 2 at least twice. Thus, 30 participants entered analysis, including five bilinguals.

Predictions

In control group 2, the grammatical sentence should be chosen more frequently than the ungrammatical one. Since participants were forced to make a choice, control group 1, where both choices are ungrammatical, should show a random distribution of answers. In the test condition, we expect a random distribution of responses only if preverbal CPs are outright ungrammatical. If preverbal CPs can be acceptable, we expect a non-random distribution. The three groups of accounts predict different patterns for the two contexts. The linear/temporal closeness accounts expect the CP-DP order to be more acceptable, therefore chosen more frequently, than the DP-CP order in preverbal position only. In postverbal position, DP-CP should be the preferred order. The bottom-up group predicts the DP-CP-order to be preferred in both contexts.

Results

In control group 2 there is a clear preference for the grammatical choice, indicating that the task was performed correctly. The responses for control group 1 had a near chance distribution, Figure 4. In the test condition, the preferences had the exact same distribution in preverbal and postverbal position: DP-first was chosen 23 times, CP-first was chosen seven times in both contexts. A logistic regression analysis confirms that the choice between DP-first and CP-first is not random; the probability of observing a DP-first answer (in both contexts) was 0.76 (logit difference to control group 1: +0.894, SE = 0.327, z = 2.74, p < 0.0001). Position had no effect on the choice of conjunct order. The participants strongly preferred DP-first order even in preverbal position, i.e., the order which is predicted to be worse than its alternative in linear/temporal closeness accounts, Figure 5.

Figure 4: Control groups.

Figure 5: Preference for DP-CP order.

Discussion

The results of this experiment align with the prediction of the bottom-up analyses and are exactly the opposite of those of the temporal/ linear closeness accounts. If licensing (e.g., via selection) is sensitive to structural, hierarchical closeness, as proposed in the bottom-up group, the uniform preference for the order in which the selected conjunct is closer to the selector is expected. This is because structural relations are identical in pre- and postverbal position. The temporal/ linear closeness accounts expect that order varies with position, which is not what we find in German. This is a serious problem for the left-to-right derivational model since it is designed to rule out the structure favored by German speakers. A processing account like Kim & Lu (2024) cannot explain the German pattern, either. The parser seems to be able to detect the selectional failure incurred by mismatching features on the conjunct that was encountered first, i.e., the features do not fade in memory. Otherwise, the dispreference of CP-first conjuncts cannot be explained. Thus, I conclude that DP-CP coordinations in German cannot be analyzed in a left-to-right derivation or as grammaticality illusions.

4 Theoretical implications & conclusion

This squib contributes to the theoretical debate of mismatching coordination structures by evaluating competing analyses. The group of approaches that makes use of structural asymmetries between conjuncts makes the right predictions for the acceptability of DP-CP-coordinations in German, whereas approaches that make use of linear or temporal asymmetries between conjuncts make exactly the wrong predictions. The effect of linear adjacency in (6), i.e., the motivation for the linear closeness accounts, cannot be observed in German. As far as I know, the order effect has never been demonstrated experimentally in English. (See also Patejuk & Przepiórkowski 2023; Przepiórkowski & Patejuk 2025 for criticism of the generality of data like (6)). Similarly, there was no effect of temporal adjacency such that greater temporal distance between mismatching conjunct and selector leads to greater acceptability.

The results suggest that adjacency, either in terms of linear order or temporal sequence, does not play a role for selection-violating coordinations in German. Instead, they are compatible with bottom-up analyses that exploit the asymmetry between conjuncts illustrated in (4) and (5) above. As an anonymous reviewer points out, the results presented here are not straightforwardly an argument for this approach, but only against the temporal/linear closeness approaches. There could be a general, independent preference for DP-first order, even with predicates that could select both the DP-conjunct and the CP-conjunct. But even if that were the case, the possibility of DP-CP orders in preverbal position is completely unexpected in linear/temporal closeness accounts. The bottom-up approach is therefore only supported indirectly, by weakening the motivation for linear/temporal approaches. As pointed out above, the bottom-up accounts also face problems. However, a full analysis of mismatching coordinations that overcomes the shortcomings of the bottom-up approaches is beyond the scope of this squib.

At the least, we can conclude that the data described for English mismatching coordinations do not constitute a general pattern. If there is a real difference between English and German, this raises the question of how a system looks like that is flexible enough to derive both types of patterns, or alternatively, whether the direction of derivation is something that could be parameterized. Symmetric coordination structures (Neeleman et al. 2022; Przepiórkowski 2024, see also fn. 1) could provide a direction for future research: it is possible that linear order effects are correlated with flat coordinate structures. There are arguments that English coordinate structures are symmetric, but these arguments don’t seem to carry over to German (Schwarzer & Weisser 2024). An exploration of this correlation could provide insights.

Abbreviations

acc = accusative, aux = auxiliary, dat = dative, nom = nominative, pass = passive, refl = reflexive

Data availability

Material, scripts, plots for experiments 1 and 2 are available at https://osf.io/kznyt/.

Acknowledgements

I would like to thank Nadine Bade, Andrew Weir, and Maud Westendorp for feedback and helpful comments. Parts of this research and data collection have been carried out at NTNU, Trondheim, and I gratefully acknowledge their support. The software and survey server for conducting the online survey were provided free of charge by the SoSci Survey GmbH. The SoSci Survey GmbH had no influence on the content of the study. I additionally thank Adam Przepiórkowski, two anonymous reviewers, and the editor Sol Lago for their detailed and very constructive comments and suggestions. All remaining errors are my own.

Competing interests

The author has no competing interests to declare.