Auditory pseudoword rhyming effects in bilingual children reflect second language proficiency: An ERP study

This study investigated second language (L2-English) phonological processing in 31 Spanish-English bilingual, 6- to 8-year-old schoolchildren in an event-related potential (ERP) auditory pseudoword rhyming paradigm. In addition, associations between ERP effects and L2 proficiency as measured by standardized tests of receptive language and receptive vocabulary were explored. We found a classic posterior ERP rhyming effect that was more widely distributed in children with higher L2 proficiency in group analyses and was larger for children with better L2 proficiency in correlation analyses. In contrast, the amplitude of an early (75-125 ms) auditory positivity was larger in children with lower L2 proficiency. This pattern suggests differential use of early and late auditory/phonological processing resources in the pseudoword rhyme task associated with L2 proficiency, which is consistent with the predictions of the lexical restructuring model in a bilingual context.


Introduction
Monolingual English-speaking and bilingual Spanish-speaking children appear to acquire phonological awareness in both their first (L1) and second (L2) languages in a similar sequence, beginning with basic awareness of syllables, followed by rhyme awareness (first nucleus and coda, then onset and rime), and then phonemic awareness (initial and final phoneme) (Cisero & Royer, 1995;Denton et al., 2000;Leafstedt & Gerber, 2005). Thus, rhyming ability, as an aspect of phonological awareness, is typically acquired relatively early (e.g., Carrillo, 1994;López & Greenfield, 2004;Tabors et al., 2003). Spanish-English bilingual children represent more than one quarter of the school-aged population in the United States (Census, 2018). However, to our knowledge, there have been no published studies of on-line phonological processing in terms of rhyme in bilingual, school-aged children in America. Here, we used an auditory rhyming paradigm and the recording of eventrelated potentials (ERPs) to investigate real-time L2 phonological processing in 6-to 8-year-old, Spanish-English bilingual children in relation to second language proficiency. Standardized tests of receptive language and receptive vocabulary served as measures of L2 proficiency and allowed for investigation of brain-behavior relations in L2 development.
There is some controversy in the bilingual literature regarding whether (or how much) L2 language proficiency (i.e., vocabulary), among other factors such as L1 phonological awareness and L1-L2 similarity, influences L2 phonological awareness (e.g., Saiegh-Haddad, 2019). Here, if experience with L1-Spanish, a phonologically similar language, is sufficient to support the kind of L2 phonological awareness and processing used in a pseudoword rhyming task, there may be no relationship between L2 proficiency and L2 ERP rhyming effects in Spanish-English bilingual children. However, if L2 proficiency modulates L2 ERP rhyming effects, it would suggest that language-specific lexical acquisition plays a role in shaping phonological processing in bilingual children (e.g., Saiegh-Haddad, 2019).
Indeed, some previous behavioral research has shown that phonological processing abilities in both L1 and L2 in bilingual children are associated with language proficiency, suggesting that proficiency within a specific language is associated with the development of phonological awareness in that language (e.g., Atwill et al., 2007;Gathercole et al., 1999;Gathercole et al., 1991;Goodrich & Lonigan, 2016;Gottardo et al., 2008;López & Greenfield, 2004). For example, in one study of Spanish-English bilingual kindergarteners, phonological awareness (measured by rhyming, alliteration, and sentence segmentation tasks), on the one hand, and receptive and expressive language skills, on the other, were weakly (L1: r = 0.33) and moderately (L2: r = 0.52) related within each language (López & Greenfield, 2004). In another study, L2 rhyming ability and L2 receptive vocabulary knowledge were moderately correlated (r = 0.47) for Spanish-English bilingual preschoolers (Lund et al., 2014). Other studies have reported similar findings (e.g., Dixon et al., 2012;Krenca et al., 2022;Smith et al., 2022) consistent with a close association between phonological and lexical development within-language (e.g., Fowler, 1991;Goswami, 2000;Metsala & Walley, 1998;Walley et al., 2003). But there is also evidence for cross-language effects; for example, in a study with low-income, Spanish-English bilingual kindergarteners, performance on initial sound fluency and phoneme segmentation phonological awareness tasks in both L1 and L2 was moderately, positively correlated with receptive vocabulary scores withinbut also betweenlanguages (Atwill et al., 2007).
Beyond language proficiency effects, other behavioral findings suggest that L2 phonological awareness is primarily related to L1 phonological awareness (e.g., Branum-Martin et al., 2006;Cisero & Royer, 2005;Dickinson et al., 2004;Durgunoglu et al., 1993). For example, performance in Spanish and English on deletion detection and rhyming tasks in low-income, Spanish-English preschoolers was related in one study; the strongest correlations in this study were between Spanish and English phonological awareness measured both in the fall (r = 0.60) and the spring (r = 0.78) of a school year (Dickinson et al., 2004). In contrast, L2 phonological awareness and L2 receptive vocabulary were less strongly, but still significantly, associated (r = 0.29 in the fall, r = 0.48 in the spring) (Dickinson et al., 2004). And in another study, performance on blending, segmenting, and elision phonological awareness tasks was strongly positively correlated between languages in Spanish-English kindergartners in bilingual education programs, again suggesting cross-language overlap in phonological awareness abilities (Branum-Martin et al., 2006).
Still other behavioral findings suggest that, in some cases, being bilingual itself may boost phonological awareness (e.g., Bialystok et al., 2005); in these cases, as well, L2 proficiency may not be strongly associated with L2 phonological processing abilities, with other factors (such as L1-L2 linguistic similarity) playing more significant roles. Indeed, bilingual children acquiring more phonemically similar languages (e.g., Spanish and English) tend to show stronger phonological awareness than bilingual children acquiring less phonemically similar languages (e.g., Chinese and English), and, in some cases, may show stronger phonological awareness than monolingual children (Bialystok et al., 2005;Genesee & Geva, 2006;Geva & Wang, 2001). For example, Bialystok et al. (2005) compared phonological awareness skills (phoneme counting and nonword decoding) across three groups of bilingual children and a group of monolingual English-speaking children in first grade. They found that the two groups of bilingual children with an L1 that was more phonologically like English (i.e., Hebrew and Spanish) showed stronger phonological awareness in comparison to the monolingual group. In contrast, the Cantonese-English bilingual group (with an L1 that was more phonologically unlike English) performed similarly to the monolingual group.
But contrary to these findings based on phoneme-level phonological awareness tasks (Bialystok et al., 2005), studies using tasks at the onsetrime level (i.e., specifically investigating rhyme processing) suggest little advantage for bilingual children, regardless of the relationship between L1 and L2 phonology. For example, a recent cross-sectional study of three groups of children ages 4 to 7 (monolingual Dutch students, Dutch students enrolled in early-English schools, and simultaneous Dutch-English bilinguals) in the first three grades of primary school found only "small and unstable" (p. 437) differences between the groups with respect to phonological awareness (measured with rhyming, phoneme blending and deletion, and onset phoneme identification tasks), even though Dutch and English are phonologically similar (Goriot et al., 2021). In another study, there were no significant differences in performance on a rhyme production task in 6-to 9-year-old monolingual and bilingual children in German primary schools (Hein & Kauschke, 2022). The performance of Turkish-Persian and Kurdish-Persian bilingual preschoolers on a picture rhyme recognition task also did not differ, as compared to Persian monolingual preschoolers (Ahmadian et al., 2016;Soleimani & Arabloo, 2018). And in a study in Britain, monolingual English-speaking children outperformed British Asian children learning English as an L2 on a rhyme detection task in primary school years 2, 3, and 4 (Hutchinson et al., 2004).
Overall, behavioral research with children is not conclusive regarding a role for L2 proficiency in the development of phonological processes involved in L2 rhyme recognition. However, electrophysiological studies with monolingual infants and children do suggest a relationship between language proficiency and auditory phonological processing. For example, ERP studies using oddball paradigms with monolingual infants (Rivera-Gaxiola, Klarman, et al., 2005;Rivera-Gaxiola, Silva-Pereyra, et al., 2005) have confirmed the behavioral finding that categorical processing of native phonemes and lack of discrimination between non-native phonemes predicts later vocabulary size (e.g., Kuhl et al., 2005). Other studies have found later onset of the early ERP mismatch response in infants at risk for language impairment (Riva et al., 2018) as well as differences in the polarity of the effect (Maurer et al., 2003). While Cheour et al. (1998) reported a negativegoing mismatch response to infrequent vowel phonemes (measured as the mean amplitude of the 80-ms period centered on the largest peak between 250 and 450 ms, p. 352) already in 6-month-old infants, Maurer et al. (2003) reported a more positive frontal response (accompanied by a posterior negativity, measured in a 179-207 ms window) in monolingual 6-and 7-year-old children for infrequent naturally spoken syllables, especially when the difference between the standard and deviant was small (i.e., /ba/ and /da/ compared to /ba/ and /ta/). Taken together, these findings suggest that participant maturity, stimulus complexity, and language proficiency are associated with phonemic processing as reflected in the ERP mismatch response in oddball tasks in L1 in children.
There is also a substantial ERP literature on phonological processing in terms of rhyme in monolingual populations, with the consistent finding that target words that do not rhyme with immediately preceding prime words elicit a larger negativity (N450) than target words that do rhyme with preceding prime words (Rugg, 1984a(Rugg, , 1984b. With visual or auditory words or letters presented in pairs, the ERP rhyming effect is larger over posterior regions and peaks about 450 ms after target onset (Bann & Herdman, 2016;Coch et al., 2002Coch et al., , 2005Coch et al., , 2011Dumay et al., 2001;McPherson et al., 1996McPherson et al., , 1998Praamstra & Stegeman, 1993;Praamstra et al., 1994). In addition to this posterior effect, some studies have reported a larger negativity in response to rhyming targets over anterior regions (e.g., Gerwin & Weber, 2020;Grossi et al., 2001;Rugg, 1984aRugg, , 1984bWeber-Fox et al., 2003) whereas others have not (e.g., Andersson et al., 2018;Coch et al., 2008;Perrin & García-Larrea, 2003). This anterior effect may require the active processing involved in making overt rhyming judgments (Davids et al., 2011;Perrin & García-Larrea, 2003).
In studies to date, the posterior ERP rhyming effect appears relatively consistent over developmental time, with a similar onset latency and topographical distribution in monolingual adults and children as young as 3 years of age (Andersson et al., 2018;Coch et al., 2002Coch et al., , 2005Grossi et al., 2001). Further, the latency and amplitude of this effect have been related to phonological awareness and overall language proficiency in monolinguals: Higher levels of phonological awareness and proficiency are associated with an earlier onset of a larger posterior rhyming effect (e.g., Andersson et al., 2018;Coch et al., 2005).
Whereas no previous studies have considered auditory ERP rhyming effects in bilingual children, a handful of ERP studies have considered rhyming effects for written words in bilingual adults (e.g., Botezatu et al., 2015;Chen et al., 2010). For example, Botezatu and colleagues (2015) asked adult bilinguals and native speakers to read English word pairs that were either orthographically similar (right/fight, dough/cough) or dissimilar (white/fight, church/cough) and make rhyme judgments. A posterior rhyming effect was evident in all three participant groups: proficient bilinguals sharing orthography (Spanish-English) or not (Chinese-English) and native English speakers. The difference between bilinguals and monolinguals was restricted to a lower amplitude effect in proficient adult Chinese-English bilinguals in comparison to native English speakers for the dissimilar orthographical condition only. For both groups of bilinguals, the amplitude of the N450 correlated with L2 proficiency measures: self-rating (r = 0.30), word reading (r = 0.30), and phonemic decoding (r = 0.31), suggesting that the amplitude of the ERP rhyming effect may be "a phonological index of proficiency" under conditions of orthographical dissimilarity (Botezatu et al., 2015, p. 122).
In ERP studies of rhyming effects like this, using real word stimuli, it is important to consider the possibility that vocabulary is a potential confound; particularly developmentally, some child participants may already know the stimulus words while others may not. To disentangle the effects of phonological awareness and item-specific vocabulary knowledge in the rhyming task, some studies have employed nonwords as stimuli (by definition, nonwords or pseudowords follow the phonological and phonotactic rules of the language but are equally unfamiliar to all participants). Such studies have reported a smaller and later posterior ERP rhyming effect, as well as longer response times to make the rhyme decisions, suggesting the use of similar neural networks for processing but a more difficult or effortful task in comparison to word rhyming (Coch et al., 2005;Dumay et al., 2001;Praamstra & Stegeman, 1993;Rugg, 1984a).
As no previous ERP studies have addressed whether L2 proficiency is related to the auditory and phonological processes involved in L2 rhyming in bilingual children, the current study was designed to investigate phonological (rhyme) processing in 6-to 8-year-old, Spanish-English bilingual children with higher and lower L2 (English) proficiency. We used the same auditory pseudoword stimuli previously employed in studies with monolingual children of similar and younger ages (Andersson et al., 2018;Coch et al., 2005) and expected the same robust posterior rhyming effect in our bilingual children as previously observed in monolingual children of similar ages (Coch et al., 2005); this would also conceptually replicate, in a younger population and with spoken stimuli, the previous finding of a posterior ERP rhyming effect for written word stimuli in Spanish-English bilingual adults similar to monolingual adults' (Botezatu et al., 2015). Further, the amplitude of the posterior rhyming effect was expected to reflect L2 proficiency in much the same way that it reflects proficiency in monolingual children (e.g., Andersson et al., 2018) and bilingual adults (Botezatu et al., 2015); that is, we predicted that children with stronger L2 proficiency would show larger rhyming effects. Without a rhyme judgment required on every trial, we did not anticipate an anterior ERP rhyming effect (Andersson et al., 2018;Davids et al., 2011;Perrin & García-Larrea, 2003). In addition, to further explore the relationship between early perceptual processing of speech sounds and language proficiency in a bilingual child sample, we included a measure of rhyme match and mismatch in an earlier (75-125 ms) time window; we predicted that the amplitude of the early anterior positivity would vary with rhyme condition and language proficiency (e.g., Maurer et al., 2003). Our goals were to investigate ERP rhyming effects in bilingual children and to explore relations between these neurophysiological measures of L2 phonological processing and behavioral measures of L2 proficiency.

Participants
This study was conducted in accordance with the Declaration of Helsinki. Participants were recruited by native Spanish speakers who acted as liaisons to Latino communities proximal to the University. A parent or legal guardian gave informed consent (approved by the Institutional Review Board of the University) prior to each child's participation. The final sample of bilingual children with L1-Spanish and L2-English consisted of 31 6-to 8-year-olds. ERPs were recorded from four additional children, but data from these children were excluded because there were fewer than 10 usable trials in at least one condition. All participants were right-handed (Oldfield, 1971), had normal or corrected-to-normal vision, normal hearing, and were not known to have behavioral or neurological problems, by report of their caregivers. Participants were paid for their participation. This study was part of a larger investigation in which children participated in multiple ERP recording paradigms in a single session and other behavioral measures, not reported here, were taken.

Behavioral testing
Language proficiency tests in English included a receptive vocabulary measure (the Peabody Picture Vocabulary Test: PPVT; Dunn & Dunn, 1997) and the receptive language subtest of the Clinical Evaluation of Language Fundamentals: CELF (Semel, Wiig, & Secord, 1995) 1 . As previous studies have shown a strong relationship between language proficiency and socioeconomic status (SES) (e.g., Bornstein et al., 2003;Hoff, 2003), we collected maternal education levels as a proxy for SES (Hollingshead, 1975) and for use as a control for SES when comparing the higher and lower L2-proficiency groups (parents of one child in the higher proficiency group did not provide maternal education information). The children were divided into two L2-proficiency groups by a median split of standard scores on the CELF receptive language subtest (cut-off score: 95) while controlling for age, SES, and age of L2 acquisition (AoA; Table 1). The higher L2-proficiency (HP) group included 15  (Hollingshead, 1975) included (1) less than 7 years of education, (2) between 7 and 9 years of education, (3) 10 to 11 years of education (part of high school), (4) high school graduate, (5) 1 to 3 years at college (also business school), (6) four-year college graduate (BA, BS, BM), and (7) a professional degree (e.g., MA, MS, ME, MD, PhD). *** p <.001.
children and the lower L2-proficiency (LP) group included 16 children. The groups also differed in terms of receptive vocabulary (Table 1); however, unlike their scores on the receptive language subtest, the groups' scores on this measure were overlapping ( Fig. 1).

ERP recording paradigm
The auditory pseudoword stimuli and basic ERP rhyming paradigm have been used previously with monolingual 3-to 5-year-old children (Andersson et al., 2018) and monolingual 6-to 8-year-old children and adults (Coch et al., 2005). (Please refer to Coch et al., 2005, for more details regarding the paradigm and list of stimuli.) The pseudoword stimuli were derived from English word structures. There are numerous differences between the English and Spanish languages; for example, Spanish is syllable-timed whereas English is stress-timed, most content words in Spanish are polysyllabic whereas many content words in English are monosyllabic, few consonants can occur in word final position in Spanish but most consonants can close English words, Spanish has less frequent and simpler consonant clusters than English (e.g., there are only two complex word-final clusters, /ns/ and /ld/, in Spanish), and Spanish has a smaller phoneme inventory than English (e.g., Spanish has only five tense vowels and diphthongs whereas English has numerous tense and lax vowels as well as diphthongs) but more articulatorily complex phonemes (e.g., trills and lateral liquids) (Gildersleeve- Neumann et al., 2009;Gorman & Gillam, 2003;Schnitzer & Krasinski, 1994). Such differences (e.g., vowels and word-final letters/sounds) are reflected in differences in rime units between the languages, although the two languages are considered relatively similar phonologically.
Replicating previous studies with children (Andersson et al., 2018;Coch et al., 2005), the pseudowords (e.g., gite [ɡa͜ ɪt], and trum [tɹʌm], derived from the words white and some) were presented in 88 primetarget pairs such that half of the targets rhymed with the primes and half of the targets did not rhyme with the primes. Each pseudoword was stored in a separate file with 10 ms of silence before sound onset; the average length of the pseudowords was 516 ms (SD = 93.5). Primes and targets were presented with a stimulus onset asynchrony of 1167 ms (i. e., the shortest interstimulus interval was 250 ms). Two lists were created such that primes were identical for each list and targets were also identical for each list; however, a nonrhyming target in one list appeared as a rhyming target in the other list to control for any possible effect of a specific pseudoword target. Primes were never identical to targets. Both lists were presented to each participant, in counterbalanced order across participants. The stimulus pairs were presented at a comfortable listening level (65 dB SPL, A-weighted) from a single freefield speaker located 57 in. directly in front of the participant.
As previously described (Andersson et al., 2018), pairs of novel cartoon creatures that seemed to speak the pseudowords were presented as movies on a monitor 57 in. in front of the participant during auditory stimulus presentation. To ensure that the movies would not affect the ERP rhyming effects, the creatures entered the screen and remained in position for 1000 ms prior to and 1500 ms after the onset of the auditory stimuli. In addition, 16 probe movies in which a creature asked "did they sound alike?" or "what did they say?" were included to maintain children's attention. These 16 probes appeared randomly across participants and well after (2,500 ms after) presentation of the pseudoword targets. All stimulus trials were conflated in analyses (i.e., whether or not a given trial was followed by a delayed probe question) as there were no differences in the actual prime-target stimulus pair trials related to the delayed probe movies. Participant responses to the delayed probe questions were not measured for accuracy.

Procedure
Procedures were explained to participants and accompanying parents or guardians by both an English-speaking experimenter and a native Spanish-speaking liaison. Then the electrode cap was applied and the child was seated in an electrically shielded and sound attenuating booth with an experimenter. In the booth, the experimenter provided examples of pseudowords that did and did not rhyme and asked the children if they knew about rhyming. Subsequently, the experimenter provided instructions to listen carefully and answer the probe movie questions as well as possible. The movies were then presented in a randomized order along with the 44 rhyming and 44 nonrhyming pairs that were independently randomized. The overall recording session, which also  Table 1). a) Shows the CELF receptive language scores used to divide children into lower proficiency (LP) and higher proficiency (HP) L2 groups by median split; all individuals in the HP group had higher scores than individuals in the LP group. b) Shows that the two groups also differed in performance on PPVT receptive vocabulary; however, individuals in the HP and LP groups had overlapping scores on this measure. included other ERP paradigms not considered here, lasted approximately one hour; the duration of the rhyming portion was about 20 min.

ERP recording
During presentation of the auditory pseudoword pairs, the continuous electroencephalogram (EEG) was recorded from 29 tin electrodes mounted in an elastic cap (Electro-Cap International, Eaton, Ohio). Data from 6 pairs (left and right hemisphere) of lateral sites (F7/8, FT7/8, T3/ 4, CT5/6, T5/6, and TO1/2) and 6 pairs of medial sites (F3/4, FC5/6, C3/4, C5/6, P3/4, O1/2) were included in analyses, replicating a previous study with monolingual children with similar length of exposure to English (Andersson et al., 2018). Data from midline (Fz, Cz, and Pz) and frontopolar (FP1/2) sites were used only for artifact rejection analyses and creation of voltage maps. In addition, electrodes placed at the outer canthi of the eyes and below the right eye were used to detect eye movements and blinks for artifact rejection. Each scalp electrode was referenced to the right mastoid during recording but re-referenced to the averaged mastoids in offline processing. Mastoid and scalp electrode impedances were maintained below 5 kΩ and impedances for the electrodes near the eyes were maintained below 10 kΩ. The EEG was amplified with Grass 7P511 amplifiers (bandpass 0.01-100 Hz) and digitized at a sampling rate of 250 Hz. ERPs for each participant were time-locked to the presentation of the rhyming and nonrhyming targets and were plotted at each electrode site from 100 ms pre-stimulus to 1000 ms post-stimulus onset.

Artifact rejection
Processing of ERPs was conducted using EEGLAB software (Delorme & Makeig, 2004). Two steps were applied prior to the independent component analysis (ICA) routine 'runica'. First, all trials containing large artifacts such as those induced by movement or amplifier saturation were identified visually and removed from further analysis. Second, a digital low-pass 40 Hz filter was applied to reduce high-frequency noise and a digital high-pass filter of 0.1 Hz was applied to reduce drift. Ocular artifacts were identified and removed by visual inspection of the scalp topographies and the component time series of the ICA. A final manual artifact rejection step detected any residual ocular artifacts not completely removed with ICA. The average number of trials remaining in individual averages did not differ by rhyming status or language proficiency group (all Fs less than 1; rhyme: M = 27.1, SD = 6.0, nonrhyme: M = 27.5, SD = 6.3; rhyme HP: M = 27.7, SD = 5.1, nonrhyme HP: M = 27.8, SD = 5.8; rhyme LP: M = 26.5, SD = 6.9, nonrhyme LP: M = 27.3, SD = 6.9).

Statistical analyses
Based on a previous study (Andersson et al., 2018), the ERP rhyming effects were measured as the mean amplitudes in three time windows: 300-500, 500-700, and 700-1000 ms; beyond methodological replication, this allowed for consideration of earlier, central, and later aspects of the rhyming effect, separately, as related to L2 proficiency. Also consistent with previous studies (e.g., Coch et al., 2005), the anterior rhyming effect was measured across frontal, fronto-temporal, and temporal sites whereas the posterior rhyming effect was measured across central, parietal, and occipital sites. These mean amplitude measurements were subjected to omnibus repeated-measures ANOVAs with four within-subjects factors: rhyme condition (rhyme/nonrhyme), hemisphere (right/left), lateral/medial position, and anterior/posterior position (anterior effects: F/FT/T; posterior effects: C/P/O) and one between-subjects factor: proficiency group (LP/HP). A similar ANOVA was used with the mean amplitude data for the early auditory mismatch effect (75-125 ms time window), measured across all six levels of anterior/posterior. Subsequent step-down analyses performed to isolate the effects of proficiency group and rhyme condition evident in significant interactions used Bonferroni-corrected p-values based on the number of comparisons conducted. The Greenhouse-Geisser correction was applied to within-subjects measures with more than one degree of freedom. Corrected p-values are reported along with uncorrected degrees of freedom. Partial eta squared (η p 2 ) values are reported for effect sizes of the ERP rhyming effects.
To further examine associations between the language proficiency measures (CELF receptive language and PPVT receptive vocabulary scores) and the amplitude of the rhyming effects as well as early perceptual processing of speech sounds, Pearson's correlations were calculated. For these analyses, the rhyming effects were calculated for each participant over anterior and posterior sites separately as the difference amplitudes (nonrhymerhyme condition) and the early auditory processing mismatch effect was calculated as the mean amplitude difference (nonrhymerhyme condition) within the 75-125 ms epoch over all sites. Correlation analyses were included in addition to the ANOVAs because "group comparisons run the risk of masking real effects" (Grundy et al., 2020, p. 9); the inclusion of a continuous measure of proficiency with a measure of the size of the ERP rhyming effect was used to confirm a relationship between proficiency and sensitivity to rhyming and better determine the strength of that relationship across individuals.

Behavioral tests
Every Spanish-English bilingual child categorized into the HP group scored within the normal limits (standard scores 85-115) for monolingual English speakers on the CELF receptive language measure, with standard scores ranging from 96 to 108 (refer to Table 1, Fig. 1). With the exception of one child (with a score of 80), standard scores ranging from 88 to 108 on the PPVT receptive vocabulary measure also placed bilingual children in the HP group within normal limits for same-age monolingual children. In contrast, about half (9 of 16) of the children categorized into the LP group scored below 85 (below normal limits, with scores between 65 and 84) on the CELF, but about half (7 of 16) scored within normal limits (scores from 86 to 94) (refer to Table 1, Fig. 1). Similarly, standard scores ranging from 68 to 97 on the PPVT placed about half of the children in the LP group below normal limits (9 with scores between 68 and 80) and about half within normal limits (7 with scores between 86 and 97). As noted, scores for the two groups differed significantly on both proficiency measures (refer to Table 1).

Early auditory mismatch effect
Consistent with the mismatch response to syllables reported by Maurer et al. (2003) in an auditory oddball paradigm, the early auditory component observed here (mean amplitude 75-125 ms) to pseudowords was a positive deflection with a frontal distribution, anterior/posterior, F(5,145) = 16.47, p <.001, η p 2 = 0.36 (Fig. 2). The response tended to be stronger medially, especially over left hemisphere and frontal sites, Correlational analyses confirmed that the mean amplitude of the early Fig. 2. Grand average ERPs (N = 31) at all analyzed sites. The response to rhyming targets is shown in the blue lines and the response to nonrhyming targets is shown in the red lines. A classic ERP rhyming effect was evident (and statistically significant) in the 300-500, 500-700, and 700-1000 ms time windows, particularly at posterior, left hemisphere, lateral sites (identified at site P3). Effects were measured in four time windows (gray shading): 75-100, 300-500, 500-700, and 700-1000 ms. Negative is plotted up, tick marks on the x-axis indicate 100 ms, the height of the t-bar on the y-axis indicates − 10 µV, and onset of the pseudoword targets was at time 0 ms. auditory component calculated across all sites and conditions was associated with both proficiency measures: CELF receptive language, r = -0.36, p <.05, 95% CI [-0.64, -0.01] and PPVT receptive vocabulary, r = -0.39, p <.05, 95% CI [-0.66, -0.04].

ERP posterior rhyming effect
As predicted, 6-to 8-year-old Spanish-English bilingual children listening to English pseudoword pairs evidenced a posterior rhyming effect (a larger negativity in response to nonrhyming targets compared to rhyming targets), as previously observed in monolingual English speakers of the same age listening to English word pairs (Coch et al., 2002). An omnibus ANOVA with mean amplitude measured in the 300-500 ms epoch showed a rhyming effect that appeared most pronounced at left, lateral sites (Table 2, Fig. 2). Follow-up at left posterior sites confirmed the more lateral distribution of the effect at the Bonferroni-corrected p level (Table 2).
In the omnibus ANOVA with mean amplitude measured in the 500-700 ms time window at posterior sites, there was a main effect of rhyme condition: the classic ERP rhyming effect (Table 2, Fig. 2). The earlier distributional pattern of the effect appeared to continue into this epoch; follow-up at left hemisphere sites confirmed a significant rhyming effect, particularly at lateral sites (Table 2, Fig. 2). Follow-up at right hemisphere sites revealed an interaction between rhyme condition and proficiency group (Table 2, p =.029). In exploratory follow-ups by group (Fig. 3), there were no significant effects involving rhyme condition for the LP group (all ps > 0.149), but a main effect of rhyme condition for the HP group survived Bonferroni correction, F(1,14) = 7.78, p =.014, η p 2 = 0.36.
In the omnibus ANOVA with mean amplitude measured in the 700-1000 ms epoch at posterior sites, the rhyming effect appeared to continue to vary by hemisphere (Table 2, Fig. 2); however, follow-ups by hemisphere were unable to confirm hemispheric differences at the Bonferroni-corrected p value (left hemisphere, p =.044; right hemisphere, all ps > 0.219).

ERP anterior rhyming effect
An omnibus ANOVA with mean amplitude measured in the 300-500 ms epoch at anterior sites yielded no significant results (refer to Table 2, Fig. 2).
The omnibus ANOVA with mean amplitude measured in the 500-700 ms epoch yielded a significant four-way interaction (refer to Table 2). Follow-up analyses by group indicated no significant effects involving rhyme condition in this epoch for the LP group (all ps > 0.228). However, the rhyming effect appeared to vary by site for the HP group (refer to Table 2). Follow-ups by anterior/posterior tentatively showed an extension of the posterior rhyming effect over lateral, temporal sites, T: Rhyme × Lateral, F(1,14) = 7.19, p =.018, η p 2 = 0.34, but this effect did not survive Bonferroni-correction at p =.0125; F: all ps > 0.196, FT: all ps > 0.074 (see Fig. 4).
The omnibus ANOVA in the following (700-1000 ms) epoch also yielded a significant four-way interaction (refer to Table 2). Follow-up analyses by group showed a similar pattern as in the previous time window, with no significant effects involving rhyme condition for the LP group (all ps > 0.109) and a significant three-way interaction for the HP group such that the posterior rhyming effect appeared to extend to temporal and fronto-temporal sites, especially medially; however, in follow-up analyses by anterior/posterior, no effects involving rhyme condition for the HP group in this time window survived Bonferroni correction, F: all ps > 0.153, FT: all ps > 0.089, T: all ps > 0.035.

Correlations between ERP effects and proficiency
As expected, there were relationships between the ERP rhyming effects and the behavioral measures of proficiency; these correlations were restricted to the posterior rhyming effect (all ps > 0.174 for the anterior rhyming effects). More specifically, the rhyming effect measured as the difference amplitude (nonrhymerhyme condition) across posterior sites showed a moderate relationship with CELF receptive language scores in both the 300-500 ms, r = -0.37, p =.039, CI [-0.64, -0.02], and 500-700 ms, r = -0.38, p =.035, CI [-0.65, -0.03], epochs, indicating a tendency for a larger rhyming effect to be associated with higher CELF receptive language standard scores. The amplitude of the posterior rhyming effect in the 500-700 ms epoch was also moderately correlated with PPVT receptive vocabulary standard scores, in a similar way, r = -0.43, p =.016, CI [-0.68, -0.09]. There were no significant correlations between the amplitude of the posterior rhyming effect in the 700-1000 ms time window and the proficiency measures.

Discussion
We investigated the neurophysiological processing of L2 phonology in Spanish-English bilingual, 6-to 8-year-old schoolchildren in a pseudoword auditory rhyming paradigm. Although Spanish-English bilingual children represent more than one quarter of school-aged children in the U.S. (Census, 2018), no previous ERP studies have addressed L2 phonological (rhyme) processing or explored associations between this and receptive L2 proficiency in this population. Consistent with our predictions, we found a classic posterior ERP rhyming effect that varied with L2 proficiency in our bilingual children, which may suggest a role for language-specific lexical acquisition in L2 phonological processing. These findings that ERP effects in an auditory pseudoword rhyming paradigm reflect second language proficiency as measured by receptive language and receptive vocabulary tests are consistent with findings from behavioral studies with monolingual children indicating that "phonological development may be intimately connected to lexical development" (Goswami, 2000, p. 251) and the claim that L2 vocabulary plays a role in L2 phonological awareness development in bilingual Table 2 Analyses of L2 rhyming effects over anterior (F FT T) and posterior (C P O) electrode sites. In the 500-700 ms epoch (darker gray shading), both groups showed a rhyming effect over left hemisphere, lateral sites; in the same time window, the HP group also showed a rhyming effect over right hemisphere sites, but the LP group did not (identified at sites P3 and P4). The early (75-100 ms time window) positivity, significantly larger in the LP group than in the HP group, is identified at site P3. Negative is plotted up, tick marks on the x-axis indicate 100 ms, the height of the t-bar on the y-axis indicates − 10 µV, and onset of the pseudoword targets was at time 0 ms. Each panel also includes topographic voltage maps for each of the three time windows used to analyze the rhyming effect (300-500 ms, 500-700 ms, and 700-1000 ms), created based on difference waves (the subtraction of ERPs to rhyming targets from ERPs to nonrhyming targets).

Fig. 4.
Comparison of the anterior ERP rhyming effect [the response to rhyming targets (blue lines) in contrast to the response to nonrhyming targets (red lines)] in bilingual children with higher (HP, upper panel) and lower (LP, lower panel) L2 proficiency. In the 500-700 and 700-1000 ms epochs (darker gray shading), there were no significant effects of rhyming condition in the LP group, but the rhyming effect varied by site in the HP group; the posterior rhyming effect appeared to extend to temporal sites for the HP group (identified at site C3), but this effect did not survive Bonferroni correction in either epoch. The early (75-100 ms time window) positivity (thin box, light gray shading), which was significantly larger in the LP group than in the HP group, is identified at site F3. Negative is plotted up, tick marks on the x-axis indicate 100 ms, the height of the t-bar on the y-axis indicates − 10 µV, and onset of the pseudoword targets was at time 0 ms. children (Saiegh-Hadded, 2019). Inconsistent with our predictions, the amplitude of an early (75-125 ms) auditory component was not sensitive to rhyme condition but was reflective of proficiency. Overall, we found a posterior auditory ERP rhyming effect in 6-to-8year-old bilingual children, such that nonrhyming L2 pseudowords elicited a more negative N450 than rhyming L2 pseudowords. The rhyming effect extended across the analysis epochs from 300 to 1000 ms and was largest over left hemisphere, lateral sites. This timing is similar to longlasting effects reported in previous studies of rhyming with children (Andersson et al., 2019;Coch et al., 2002;Coch et al., 2005). Likewise, the distribution with a stronger effect over left hemisphere sites is consistent with previous studies of auditory processing (e.g., see Holcomb & Neville, 1990, for a comparison of visual and auditory effects), although a hemispheric difference has not always been reported in studies of auditory rhyming (e.g., Coch et al., 2005;Davids et al., 2011). Prior studies with auditory targets have described the posterior rhyming effect as medial (e.g., Mitra & Coch, 2019) and a medial distribution of the posterior rhyming effect has been reported previously for the same auditory pseudoword stimuli used here (Andersson et al., 2018;Coch et al., 2005). Speculatively, this distributional inconsistency between studies may suggest a slightly differently oriented neural generator for auditory rhyme processing in L2 in bilingual children as compared to in L1 in monolingual children and adults; future research could be designed to address this unsubstantiated conjecture and consider possible associations with a larger, growing phonemic inventory in bilingual children.
Holding aside the distributional differences, the posterior ERP rhyming effect resembled the effect reported in a study of same-age monolingual children and adults using the same auditory pseudoword stimuli in a different paradigm (Coch et al., 2005) and the effect found in 3-to 5-year-old monolingual children with the same stimuli in the same paradigm (Andersson et al., 2018). Thus, although direct statistical comparison across studies was not possible, electrophysiological phonological (rime) processing without semantic support (in pseudowords rather than real words) appears similar in L2 in bilingual children and L1 in monolingual children. This is consistent with behavioral studies that have reported similar performance on rhyming tasks in monolingual and bilingual preschool and school-age children (e.g., Ahmadian et al., 2016;Goriot et al., 2021;Hein & Kauschke, 2022;Soleimani & Arabloo, 2018) and relatively strong phonological awareness skills, on average, in young bilingual children acquiring phonemically similar languages such as Spanish and English (e.g., Bialystok et al., 2005;Genesee & Geva, 2006;Geva & Wang, 2001). Further, this finding replicates and extends (to children and auditory pseudoword stimuli) the pattern in a previous ERP study with written stimuli in which Spanish-English bilingual adults showed a rhyming effect similar to monolingual adults' (Botezatu et al., 2015).
To investigate a possible role for language-specific lexical acquisition on auditory and phonological processing as indexed by L2 proficiency effects, we considered how this electrophysiological measure of phonological processing might be related to behavioral L2 proficiency in two ways. First, categorically, by dividing the 31 children into higherproficiency (HP) and lower-proficiency (LP) groups by a median split of standardized scores on the receptive language subtest of the CELF (Semel, Wiig, & Secord, 1995). This yielded non-overlapping groups for which scores were significantly different on both the receptive language (Semel, Wiig, & Secord, 1995) and the PPVT receptive vocabulary (Dunn & Dunn, 1997) measures while being balanced on age, SES, and age of L2 acquisition. Second, we considered brain-behavior relations continuously, by correlating the electrophysiological measures with the CELF receptive language and PPVT receptive vocabulary standard scores.
Before addressing the neural-behavioral proficiency findings, it is important to evaluate the findings related to the behavioral proficiency measures themselves. Remarkably, receptive language (Semel, Wiig, & Secord, 1995) standard scores for all the children in the HP group were within normal limits, meaning that their L2 receptive language skills were essentially the same as what would be expected for L1 receptive language skills for same-age, monolingual peers. This was also true for the HP group for the receptive vocabulary measure (Dunn & Dunn, 1997), except for one child who performed just below the monolingual norm. In contrast, only about half of the children in the LP group scored within normal limits, with the other half below. It is not known whether the bilingual children who scored below normal limits for monolinguals in their L2 would meet the criteria for language disorder. It is possible that children with low scores on the L2 proficiency measures would also have low scores in L1, indicating low overall language proficiency; previous studies have shown that language disorder affects all languages of a bilingual or multilingual child (Nayeb et al., 2021;Salameh et al., 2004). However unlikely it seems that about one-quarter of our volunteer sample of children would have language disorder, we cannot rule this out with the available data. Overall, though, whereas there has been some concern in the literature regarding adequate development of L2 spoken language proficiency in bilingual children (e.g., Spencer & Wagner, 2018), this pattern of findingsthat about three-quarters of our bilingual sample (with AoA about 4½ years old and, on average, 2.5 years of L2 experience) did not score at risk, but rather within normal limits for monolingual peerssuggests that it is unwarranted to assume that all bilingual children are at risk for lower L2 proficiency (as measured by standardized tests of receptive language and vocabulary).
Previous studies with bilingual children have shown that performance on behavioral measures of L2 phonological awareness are predictive of performance on behavioral measures of L2 proficiency (e.g., Atwill et al., 2007;Gottardo et al., 2008). However, to our knowledge, there have not been previous investigations of whether neurophysiological measures of L2 phonological awareness are associated with performance on behavioral measures of L2 proficiency in school-aged bilingual children. In our categorical analysis, we found that the distribution of the posterior ERP rhyming effect varied with L2 proficiency: The effect extended to right hemisphere sites for the HP, but not the LP, group. This is not the simpler pattern of a larger amplitude posterior rhyming effect with better phonological awareness skills observed in group analyses with younger monolingual children in this paradigm (Andersson et al., 2018); the amplitude of the rhyming effect over the left hemisphere was similar between the L2 proficiency groups here, but there was a significant rhyming effect over the right hemisphere (500-700 ms) only for the HP group. This broader distribution in the HP group could be interpreted as more neural processing resources (perhaps an extended neural network) used for phonological processing of L2 pseudowords in bilingual children with higher L2 proficiency.
In our continuous analysis approach to brain-behavior relations, we found that the amplitude of the posterior rhyming effect (measured as the difference between rhyming and nonrhyming conditions) was moderately associated with CELF receptive language (Semel, Wiig, & Secord, 1995) scores in both the 300-500 ms (r = -0.37) and 500-700 ms (r = -0.38) epochs and with PPVT receptive vocabulary (Dunn & Dunn, 1997) scores in the 500-700 ms window (r = -0.43). Overall, better receptive language skills (i.e., higher L2 proficiency) were related to a larger ERP rhyming effect (i.e., more differentiation between rhyming and nonrhyming targets) from 300 to 700 ms. These associations in the 500-700 ms window are relatively consistent with the results of the categorical analysis: The higher-proficiency group showed a more extensive rhyming effect. However, there were no significant effects involving proficiency group in categorical analyses of the posterior rhyming effect in the 300-500 ms window; evidently, the correlational analysis allowing for greater consideration of variability was able to reveal earlier effects of proficiency than the categorical approach. These findings in bilingual children are similar to our previous findings of moderate, negative correlations between receptive vocabulary standard scores and the amplitude of the posterior ERP rhyming effect in younger, monolingual children in this paradigm (Andersson et al., 2018).
Taken together, our two approaches to exploring brain-behavior relations extend findings of associations between behavioral measures of phonological skill and language proficiency in bilingual children (e.g., Atwill et al., 2007;Gottardo et al., 2008) and findings of relations between behavioral measures of rhyme judgement performance and language proficiency in bilingual adults (e.g., Oz-Vecht & Degani, 2022;Saiegh-Haddad, 2019) to include associations between real-time neural measures of auditory phonological processing and behavioral measures of spoken language proficiency in bilingual children. This is consistent with the claim that the ERP rhyming effect may be "a phonological index of proficiency" (Botezatu et al., 2015, p. 122) -not only in adult bilingual reading under specific orthographic circumstances, but also in child bilingual listening.
Without an overt response required in the task, as predicted (refer to Andersson et al., 2018), there was little evidence of an anterior ERP rhyming effect. However, the posterior rhyming effect tended to extend anteriorly to temporal sites (sites included in the anterior analyses) only in the HP group. Although not statistically reliable with conservative correction, this trend toward more widespread distribution of the posterior rhyming effect in this group is consistent with our finding of extension of the posterior effect to right hemisphere sites only in the HP group: In both cases, better L2 receptive language proficiency tends to be associated with more extensive electrophysiological processing of L2 auditory rhyme information. Not surprisingly, given the lack of evidence for a reliable rhyming effect at anterior sites, there were no significant correlations between ERP measures of L2 phonological processing at anterior sites and scores on the behavioral measures of L2 proficiency.
Finally, in addition to the late rhyming effects, we explored an early (75 to 125 ms window), basic auditory response and its relation with L2 proficiency. We identified an early left frontal positivity similar to that reported by Maurer et al. (2003) as sensitive to acoustic-phonetic mismatch in the processing of spoken syllables in children. The similarity was in terms of the timing and distribution of the positivity elicited by spoken language stimuli, although the type of stimuli, paradigm, and task were quite different between studies. Moreover, the amplitude of our early positivity was not sensitive to rhyme mismatch. In oddball paradigms as used by Maurer et al. (2003), a mismatch effect is reported for rare stimuli that are inconsistent with multiple previous presentations of a standard stimulus; that is, the oddballs are inconsistent with an expectancy template set by the preceding context (e.g., Donchin & Coles, 1988). In rhyming paradigms, only one prime is presented prior to each target; this may not be adequate context to create the sort of memory template that a series of standard stimuli does, necessitating update by a rare oddball stimulus and elicitation of a mismatch effect. Moreover, the rhyme and nonrhyme probabilities in our paradigm were each 50%, such that the incidence of mismatch was not rare in the way that it is in an oddball paradigm. Thus, the mismatch effect for this early positivity may be related more to auditory "oddballness" than to auditory mismatch between subsequent stimuli per se.
Despite the apparent lack of sensitivity to rhyme status, the overall amplitude of this early auditory positivity was sensitive to L2 proficiency: The positivity was comparatively smaller in the HP group than in the LP group. This association with proficiency was corroborated by moderate negative correlations between the amplitude of the early positivity and standard scores on both the receptive language (r = -0.36) and receptive vocabulary (r = -0.39) tests (Dunn & Dunn, 1997;Semel, Wiig, & Secord, 1995). This pattern suggests that Spanish-English bilingual children with lower, as compared to higher, English proficiency tend to use more early auditory (acoustic-phonetic) processing resources when listening to English pseudoword targets. This is intriguing in combination with the proficiency findings regarding the later posterior rhyming effect. In the context of this paradigm, higher L2 proficiency may be associated with fewer resources expended on early, basic (acoustic-phonetic) auditory processing and more resources allocated to later phonological processing of rhyme (rime), whereas lower proficiency may be associated with more resources used on early, basic auditory processing and fewer resources marshalled for later rhyme processing.
In the wider context of spoken language development, it is interesting to consider this pattern through the lens of the lexical restructuring model (e.g., Fowler, 1991;Metsala & Walley, 1998;Walley et al., 2003). According to this model, in typical monolingual development, the growth of spoken vocabulary prompts "the implemetation of more fine-grained, segmental respresentations for lexical items" (first onsetrime and then phoneme level) across early to middle childhood as lexical items in increasingly dense neighborhoods must be differentiated from one another (e.g., buy from pie in onset and rime ;Fowler, 1991;Walley et al., 2003, p. 5). This relation between vocabulary knowledge and phonological awareness, as predicted by the model, holds with tasks indexing both implicit and explicit phonological segmental analysis (Ainsworth et al., 2019) and has been found in bilingual children for L2 (e.g., Dixon et al., 2012;Krenca et al., 2022;Lund et al., 2014;Smith et al., 2022). Here, we defined L2 proficiency in terms of performance on the PPVT, which measures receptive vocabulary, and the CELF, which measures not only receptive vocabulary and semantic knowledge but also syntactic and morphosyntactic skill; thus, an imprecise measure of language-specific lexical acquisition. Our ERP rhyming task required implicit (and explicit, in delayed probe movie trials) phonological segmental analysis (by rime). Thus, speculatively, our findings may reflect a similar pattern, in a different way: In terms of the relative allocation of attention and resources to different aspects of L2 (pseudo) word processing with proficiency. Bilingual children with lower L2 proficiency (i.e., receptive language and vocabulary) may have devoted comparatively more resources to processing L2 word-like speech as holistic, undifferentiated sound (as indexed by the greater amplitude early auditory positivity), whereas bilingual children with higher L2 language proficiency may have used comparatively more extensive resources processing the rime segment (derived from real English words) of the pseudowords (as indexed by the more widespread L2 posterior rhyming effect in our categorical analyses and the correlations between the size of the ERP rhyming effects and L2 proficiency in our continuous analyses). That is, if the growth of spoken vocabulary (i.e., increasing proficiency) prompts more fine-grained, segmental processing of spoken language (e.g., Walley et al., 2003), the children with lower L2 proficiency may have spent limited attention and resources on acoustic-phonetic processing of the pseudowords as unsegmented wholes in comparison to the children with higher L2 proficiency spending their resources on segmenting/recognizing the rimes. While the pattern of our findings aligns well with the lexical restructuring model and the behavioral data that support it (e.g., Fowler, 1991;Metsala & Walley, 1998;Walley et al., 2003), further investigation is necessary to replicate and follow up on this speculation.
As with every study, this study has some limitations. For example, although the overall sample size of 31 bilingual children is more than sufficient, dividing the participants into two proficiency groups resulted in relatively small ns; this may have contributed to a lack of power in the group analyses that led to our missing small proficiency effects. However, we did have adequate power to identify some proficiency effects and we also conducted correlation analyses across all participants to address effects of proficiency. In addition, this study was limited by a lack of L1 measures; this could have been particularly useful for providing more insight into the children with L2 CELF and PPVT scores below normal (monolingual) limits and thus the potential confound of overall low proficiency. Moreover, this would have been useful for differentiating whether the associations between L2 proficiency and the ERP effects were just specific to L2 or also related to L1, suggesting a relation with more general language learning ability. Ideally, we would have had comparable data from a rhyming task with pseudowords derived from Spanish words and proficiency measures from Spanish versions of the behavioral tests for all participants. In reality, 6-to 8year-olds have limited attention and patience, parents and guardians have limited time, and this was simply too much to ask of our participants in the context of the study. Finally, a direct comparison group of age-and SES-matched monolingual students would have afforded a different perspective on bilingual effects; however, as a first foray into developmental bilingual ERP rhyming work, we leave that to future replications and extensions. Our primary aimsto investigate ERP rhyming effects in bilingual children and to explore relations between neurophysiological measures of L2 phonological processing and behavioral measures of L2 proficiencywere met.
In summary, this study provided new insight into the on-line processing of L2 phonological (rhyme) information in school-aged Spanish-English bilingual children. For the first time, we report an L2 posterior ERP rhyming effect in bilingual children. This effect resembles the auditory pseudoword rhyming effect in monolingual children (Andersson et al., 2018;Coch et al., 2005), but a seemingly more lateral distribution suggests the possibility of a differently oriented neural generator in bilingual children. Moreover, this ERP rhyming effect was related to L2 proficiency: It was more widely distributed in children with higher L2 proficiency in group analyses and its amplitude tended to be larger for children with better L2 proficiency in correlation analyses. In contrast, the amplitude of an early auditory positivity tended to be larger in children with lower L2 proficiency, suggesting differential use of early and late auditory processing resources in 6-to 8-year-old Spanish-English bilingual children in our pseudoword rhyme task. Taken together, these findings suggest that language-specific lexical acquisition plays a role in auditory and phonological L2 processing even in bilingual children with phonologically relatively similar first and second languages. In turn, this pattern of findings is consistent with the lexical restructuring model (Metsala & Walley, 1998;Walley et al., 2003) in a bilingual, developmental context.

Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.