Abstract
Adult learners acquire second language (L2) allophones with experience. We examine two mechanisms which may support the acquisition of allophonic variants in second language acquisition. One of the mechanisms is based on the distribution of phones with respect to their phonological context (i.e. phonological distribution). The other is based on the role the phones play in contrasting words (i.e. lexical contrast). Experiment 1 established adult native English speakers’ baseline sensitivity to the novel [b]–[β] auditory contrast. In Experiment 2 we examined whether adult native English speakers infer the phonological status of [b] and [β] in an artificial language based only on their distributions to phonological contexts. We observed no evidence that these participants were able to do so. In Experiment 3 we investigated whether learners infer the phonological status of [b] and [β] from the role they play in lexical contrast and observed both perceptual and lexical processing evidence to suggest that adults may use meaning-based cues to the lack of contrast to learn that two phones are allophones of the same phoneme. Together our findings suggest that adult L2 learners may prioritize information about function (in this case, lexical contrast) over the phonological distribution of phones as they determine the phonological status of L2 sounds.
I Introduction
The spoken language input available to language learners is highly variable due to factors such as speech rate, dialect, individual talker differences, speaker’s emotions, phonological context, gender, and age. In the face of this variability both first (L1) and second language (L2) learners must interpret patterns of acoustic variability together with other available cues to infer which sound categories exist in the target language and how those categories pattern and function in the phonology of the language. This entails determining whether the speech sounds are target language phonemes or are allophones of the same phoneme. Phonemes are language-specific abstract categories which occur in the same phonological environments as other phonemes (overlapping distribution) and are used to cue meaning distinctions between words (e.g. the phonemes /ð/ and /d/ distinguish meaning between the minimal pairs [ðeɪ] ‘they’ and [deɪ] ‘day’ in English). Allophones, by contrast, are a set of phonetically distinct realizations of phonemes. Phonologically conditioned allophones of the same phoneme occur in mutually exclusive contexts (complementary distribution) and are thus predictable from their phonetic or phonological context (e.g. the phones [t] and [th] are phonologically conditioned variants of the same phoneme category /t/ in English). Not all classes of allophones are predictable from their phonological environment, however. Allophones which are in free variation, may occur in overlapping distribution like phonemes. Yet, free allophonic variants do not serve to distinguish word meanings (e.g. [t] and [t̚] occur in free variation in words like ‘pit’ in English). Despite being non-contrastive, knowledge of the allophones associated with particular phoneme categories, and the context in which each occurs, is essential for speech production and is implicated in efficient speech perception and lexical access (Beddor et al., 2013).
While research has addressed the mechanisms used by infants to discover native language phonemes and allophones (Feldman et al., 2013; Maye et al., 2002; Noguchi and Hudson Kam, 2018; Seidl and Cristià, 2012; Thiessen, 2007; White et al., 2008; Yeung and Werker, 2009), much less research has addressed the mechanisms available to and used by adult second language learners (e.g. Hayes-Harb, 2007; Noguchi and Hudson Kam, 2018). We contribute to this literature by examining two mechanisms which may support the acquisition of L2 allophonic variants – phonological distribution and lexical cues – in adult second language acquisition.
II Background
It is well established that infants begin to attune to the phonology of their native language during the first year of life (Kuhl et al., 1992; Polka and Werker, 1994; Seidl et al., 2009; Werker and Tees, 1984). Research on infant phonological development has provided support for two plausible mechanisms to account for this early learning: statistical (also referred to as distributional) and lexical (also referred to as functional) mechanisms. Statistical learning approaches emphasize the ways in which infants leverage their propensity to track bottom-up, statistical regularities in their input (Gomez, 2002; Maye et al., 2002; Saffran et al., 1996), whereas lexical approaches emphasize the importance of contrastive information present in word–object pairings (Yeung and Werker, 2009). In a seminal study, Maye et al. (2002) demonstrated that infants can track the frequency with which specific acoustic values are observed along a stop consonant voicing dimension to infer whether that dimension contains one or more speech sound categories. Two groups of 6- to 8-month-old English-learning infants were exposed to sounds from a continuum between the pre-voiced stop [d] and the voiceless unaspirated stop [t] in either a bimodal distribution (with values falling into one of two clusters) or a unimodal distribution (with all values falling into a single cluster). At test, only the infants in the bimodal group discriminated stimulus tokens from the endpoints of the continuum, suggesting that they learned to classify sounds along the continuum into two categories following exposure (for a meta-analysis, see Cristià, 2018).
Infants’ interpretation of phonetic variation is also influenced by another distributional property of speech input, namely the word-form context in which sounds occur. Feldman et al. (2013) exposed 40 8-month-old infants to vowel sounds ranging from [ɑ] to [ɔ] along a continuum. One group of infants heard stimuli from the [ɑ] and [ɔ] ends of the continuum in distinct lexical contexts ([gutʰɑ], [litʰɔ] or [gutʰɔ], [litʰɑ]), whereas [ɑ] and [ɔ] occurred interchangeably in the same word-form contexts for another group of infants ([gutʰɑ], [gutʰɔ], [litʰɑ], [litʰɔ]). At test, the infants who heard [ɑ] and [ɔ] in distinct lexical contexts distinguished the vowels, whereas infants who heard [ɑ] and [ɔ] interchangeably in the same word contexts did not, suggesting that 8-month-old infants can use information from word forms to constrain their interpretations of phonetic variability. Interestingly, adults also exhibited this pattern, suggesting they are likewise influenced by word-level information in a non-referential context.
In contrast with this approach, Yeung and Werker (2009) demonstrated that young infants can use contrastive pairings between objects and sounds to learn language-specific phonetic categories. The first experiment established that by 9 months of age English infants fail to discriminate syllables which differed only in the Hindi dental-retroflex contrast (e.g.[d̪a]–[ɖa]). In the second experiment, syllables differing in two non-native phones were consistently paired with two distinct novel objects ([d̪a] auditory tokens always co-occurred with object 1 and [ɖa] auditory tokens always occurred with object 2) during exposure, providing lexical evidence that [d̪] and [ɖ] are allophones of separate phonemes. The third group of infants heard the same auditory forms, but these were inconsistently paired with the two novel objects (both [d̪a] and [ɖa] auditory tokens occurred half the time with object 1 and half of the time with object 2), providing evidence that [d̪] and [ɖ] are allophonic variants of a single phoneme. At test, infants exposed to consistent pairings of auditory forms with distinct visual referents discriminated the contrast, while those who were exposed to inconsistent pairings did not, suggesting that 9-month-old infants may use information present in word–object pairings to inform their interpretation of phonetic variability.
Infants can also use information from the phonological distribution of phones relative to their phonological context (phonological distribution) to group allophonic variants. Across a series of experiments White et al. (2008) familiarized 8.5-month-old and 12-month-old infants with artificial languages whose distributional properties exhibited one of two phonological patterns of alternation. In one condition, voiced and voiceless fricatives occurred in the same phonological context (e.g. na
Research with adults supports the idea that adults also leverage statistical and lexical evidence in the acquisition of L2 phonemes (Chládková and Šimáčková, 2020; Escudero et al., 2011; Feldman et al., 2013; Maye, 2000). For example, Hayes-Harb (2007) compared adult second language learners’ use of statistical and lexical evidence to learn a novel contrast between the voiceless unaspirated and voiced unaspirated velar stops (i.e. [k] and [g]). Native English-speaking participants assigned to the bimodal and unimodal groups received only statistical evidence for the presence or absence of a contrast, respectively. The contrastive and non-contrastive groups were exposed to lexical evidence (contrastive vs. non-contrastive images, respectively), while statistical distribution was held constant. Following exposure, participants were tested on their perceptual sensitivity to the phonetic distinction in an AX discrimination task. A comparison of the statistical learning conditions found that the bimodal group demonstrated greater sensitivity to the novel contrast than did the unimodal group. More accurate discrimination performance was also observed for the contrastive group relative to the non-contrastive group. Interestingly, the contrastive group also outperformed the bimodal group. In a second experiment, Hayes-Harb (2007) examined whether learners’ perceptual sensitivities translated into differential encoding of the contrast in the lexicon. Participants were taught 12 ‘words’ involving the novel contrast together with pictures indicating their meanings and were later tested on their phonolexical knowledge using an auditory word–picture matching task. At test, none of the groups showed evidence of having established lexical representations that encoded the [g]–[k] contrast. Together, these findings suggest that both statistical and lexical learning mechanisms continue to be available in second language learning of L2 phonemes, though lexical evidence may play a more important role in adult acquisition of novel contrasts.
Despite evidence that adult learners acquire knowledge of L2 allophones with experience (Barrios et al., 2016; Shea and Curtin, 2010, 2011), few studies to date have directly examined the mechanisms responsible for the acquisition of allophonic variants (Moeng, 2018; Noguchi and Hudson-Kam, 2018). Noguchi and Hudson Kam (2018) investigated whether phonological distribution affects listeners’ perception of an unfamiliar phonetic distinction. A group of 62 native English speakers were exposed to a bimodal distribution of speech sounds drawn from a continuum between the Mandarin retroflex and alveolopalatal fricatives, [ʂ] and [ɕ], and the phonological distribution of the phones was manipulated. For participants in the overlapping condition, [ʂ] and [ɕ] were followed by both [u] and [i]. In the complementary condition, fricative tokens from the [ʂ] end of the continuum were always followed by [u], and tokens from the [ɕ] end of the continuum with [i]. The authors predicted that participants would show differential sensitivity to the [ʂa]–[ɕa] pairs at test depending on whether they were exposed to [ʂ] and [ɕ] in overlapping or complementary distribution. As adult listeners are generally less sensitive to allophonic than phonemic contrasts in their native language (Boomershine et al., 2008; Harnsberger, 2001; Johnson and Babel, 2010; Kazanina et al., 2006; Pegg and Werker, 1997; Whalen et al., 1997), participants in the complementary condition were expected to be less sensitive to the [ʂ]–[ɕ] contrast than participants in the overlapping group, as well as a control group with no training. This is indeed what they found, suggesting that adults may use information available from the context in which speech sounds occur to infer their phonological status. A second experiment demonstrated that the changes in perceptual sensitivity reported in the first experiment were contingent on phonetic naturalness. That is, they were observed only when the allophones and their respective contexts were phonetically similar to one another (see also Peperkamp et al., 2006a, 2006b). The results of the first experiment have since been replicated using new materials modeled after those originally used by Noguchi and Hudson Kam (2018) and collected via the online platform, Mechanical Turk (Moeng, 2018), suggesting that the effect of phonological distributional evidence on the perception of [ʂ]–[ɕ] reported in Noguchi and Hudson Kam (2018) is robust to these methodological changes.
In sum, the literature that has investigated learners’ use of phonological distribution in the adult second language acquisition of allophonic alternants is sparse, and support for the hypothesis to date comes from a single phonetic distinction. Additional research is needed to examine whether adult learners use evidence from phonological distribution to determine phonological status. In Experiment 1, we establish native English speakers’ perceptual baseline for our experimental contrast [b]–[β] and control contrast [m]–[l]. [b]–[β] is a suitable phonetic distinction since it is used phonemically in languages such as Ewe and allophonically in languages such as Spanish and Portuguese, suggesting that the sounds involved are neither too phonetically similar to be used contrastively or too distinct to be assigned to the same category. In Experiment 2, we ask whether adult L2 learners use phonological distributional cues – whether phones occur in overlapping distribution or complementary distribution – to learn whether two phones are allophones of the same or two different phonemes. Two groups of native English-speaking participants were exposed to word forms involving the experimental contrast, [b]–[β], in either overlapping or complementary distribution. Following exposure, their discrimination of the experimental and control contrasts was assessed with an ABX task. If naïve adult learners can use phonological distribution to determine whether [b] and [β] are allophones of the same phoneme or allophones of separate phonemes, the participants exposed to [b] and [β] in complementary distribution should be less sensitive to the contrast following exposure than participants who were exposed to the sounds in overlapping distribution.
Alternations between phonologically conditioned allophones are not the only kind that occur in languages. Allophones of the same phoneme may also occur in free variation. To the best of our knowledge no study has explored the role of lexical (meaning-based) cues in the adult acquisition of free allophonic variants. In Experiment 3, we use an artificial lexicon study paradigm, in which participants learn novel word forms and meanings, to examine whether adult L2 learners use lexical evidence to infer whether [b] and [β] are allophones of the same phoneme or two different phonemes. To do so, we held statistical and phonological distribution constant ([b] and [β] were bimodally distributed and occurred in overlapping distribution) and we manipulated the lexical evidence available in the input between participants. One group was exposed to acoustically similar auditory word forms paired with the same image, while a second group heard the same auditory forms but saw them paired with two different images. Following a brief exposure, we examined learners’ perception of the phonetic distinction. If learners use the lexical information associated with the [b] and [β] words to infer their phonological status, then participants who are exposed to [b] and [β] words paired with different images should demonstrate greater perceptual sensitivity to the [b]–[β] contrast at test than those who are exposed to [b] and [β] words paired with the same (non-contrastive) images.
To further determine whether participants established phonolexical representations of new words that encode the [b]–[β] distinction we conducted two additional lexical tasks. In the first (Lexical Test), we ask whether our lexical cue manipulation results in differential encoding of the experimental contrast for the two exposure conditions for trained items. In the second (New Word Test), we explore whether participants from the two exposure conditions extend their knowledge of the phonetic distinction to new (untrained) words. In both tasks we expected that participants exposed to acoustically similar auditory word forms paired with two distinct images, but not those exposed to non-contrastive images, would encode the distinction lexically.
III Experiment 1: Baseline
1 Participants
Twenty-four native English speakers (12 male, 12 female; mean age = 22.83 (95% CI: 20.18, 25.49) years; median (Q1, Q3) = 22 (19, 22.25); range = 18–49 years) were recruited from undergraduate linguistics courses at the University of Utah and received course credit for their participation. Participants reported no history of speech, hearing, developmental, or neurological disorders, and no formal or informal experience learning Spanish. Thirteen participants reported knowledge of one or more second languages. These included Afrikaans (1), Chinese (1), French (5), German (4), Gujarati (1), Hindi (1), Japanese (2), Korean (1), Latin (1), Persian (1), Russian (1).
2 Stimuli
The stimuli for Experiment 1 consisted of 16 unique auditory forms (8 involving the experimental contrast, [b]–[β], 8 involving the control contrast, [m]–[l]), summarized in Table 1. Each auditory stimulus contained one of four target phones ([b], [β], [m], [l]) followed by the vowel [a]. The syllable containing the target phone was either preceded or followed by a context syllable [ti] or [ku].
Auditory stimuli used in Experiment 1.
Note. Shaded auditory forms were not heard by the Complementary group during the exposure phase.
Each auditory form was produced several times by a female Spanish–English bilingual with phonetic training in the carrier phrase Diga la/una _______, por favor (‘Say the/a____, please’) with stress on the penultimate syllable. Care was taken to ensure that the quality of the vowel in the final syllable was not altered or reduced to schwa. Four tokens of each stimulus type were selected for use in the study. The same four tokens of each word were used during exposure and for the perceptual test in Experiment 2, and for the exposure phase 1, perceptual test, and lexical test in Experiment 3. To ensure that there was indeed a distinction between [b] and [β] tokens, an acoustic analysis of the intensity ratios, a measure of degree of consonant constriction, was made for each production following Carrasco et al. (2012). The mean intensity ratio for [β] tokens = .82 (SD = .04; min = .77, max = .93), whereas the mean intensity ratio for [b] tokens = .60 (SD = .05; min = .46, max = .65), consistent with there being greater constriction for [b] than [β] stimulus tokens. The auditory and visual stimuli for experiments 1, 2, and 3 can be found at: https://osf.io/eaf5u.
3 Procedure
The experimental procedure consisted of a perceptual test followed by a language background questionnaire. The experiment was implemented online via PsychoPy/Pavlovia (Peirce et al., 2019). Participants were asked to complete the study at a computer in a quiet space with headphones on and volume adjusted to a comfortable level. First, participants were presented a consent document in accordance with the protocol approved by the University of Utah Institutional Review Board. Four practice ABX trials with no feedback using English words were presented prior to beginning the test. A keyboard was used to record participant responses. Following the experimental task, participants completed a language background questionnaire hosted on Qualtrics (www.Qualtrics.com).
4 Perceptual test
The perceptual test consisted of an ABX discrimination task in which the participant indicated whether the third auditory stimulus they heard was the same as the first stimulus or the second. Each triad consisted of three unique auditory tokens, such that the task could not be completed on a purely acoustic basis. There was a total of 64 trials, with each unique auditory token (16 auditory forms × 4 tokens) appearing once as X. Half of the trials (32) involved the [b]–[β] contrast (16 word-initial, e.g. [βaku]–[baku]–[βaku] and 16 word-medial, e.g. [tiba]–[tiβa]–[tiβa]). The other half (32 trials) involved the [m]–[l] contrast word-initially or word-finally (e.g. [lati]–[mati]–[mati], [kuma]–[kula]–[kuma]). For each contrast there were 16 ABA trials and 16 ABB trials. The test was divided into two blocks of 32 trials, which were presented in a random order for each participant. The three tokens in each trial were separated by an ISI (interstimulus interval) of 500 ms and trials timed out after 2,500 ms.
5 Data analysis
A dʹ score, a measure of sensitivity which factors out participants’ response bias, was computed for each participant for each contrast. The ‘hit rate’ was computed as the proportion of trials in which the participant responded A when X was indeed the same as A, divided by the total number of trials in which X was the same as A. The ‘false alarm rate’ was the proportion of trials in which the participant responded A when X was the same as B, divided by the total number of trials in which X was the same as B. To correct for extreme proportions (i.e. hit rates and false alarm rates of 0 or 1), we applied a log-linear correction by which .5 is added to all cells of the contingency table irrespective of the contents of the cell (Hautus, 1995). Given that there were 32 ABX trials (16 ABA and 16 ABB) for the experimental contrast and the control contrast, respectively, the maximum hit rate and false alarm rate was .97 (16.5 /(16.5 + .5)) and a the minimum was .03 (.5/(16.5 + .5)) and the highest possible dʹ score 3.78.
6 Results
Figure 1 shows the mean proportion correct (left) and the mean dʹ score (right) by contrast for Experiment 1. As expected, native English speakers experienced little difficulty perceiving the [m]–[l] control contrast (mean proportion correct = .9; mean dʹ = 2.58). Relative to the [m]–[l] contrast, the [b]–[β] contrast was perceived less accurately (mean proportion correct = .82; mean dʹ = 1.93).

Mean proportion correct (left) and mean dʹ score (right) on the perceptual test in Experiment 1 by contrast. Superimposed text represents group means by condition. Error bars represent one standard error of the mean.
Statistical analyses of the dʹ data throughout were conducted using a linear mixed-effects model using the lme4 package (version 1.1-15; Bates et al., 2015) in R (version 4.0.3; R Core Team, 2020) and were fit using a maximum likelihood technique. The analyses included sum-to-zero coded fixed effects and random effects included random intercepts for participants. As our data consisted of one dʹ score per participant per contrast, it was not possible to estimate by-participant random slopes for contrast. A fixed effect was considered significant if the absolute value of the t statistic was greater than or equal to 2.0 (Gelman and Hill, 2007). Our analysis of the dʹ data from Experiment 1 included the fixed effect for contrast (−.5 = [b]–[β], .5 = [m]–[l]). There was a significant main effect of contrast (estimate = .65, SE = .15, t = 4.321), with more accurate performance observed for the [m]–[l] than the [b]–[β] contrast. The model output is summarized in Table 2.
Mixed effects model analysis examining the effects of contrast on dʹ score in Experiment 1.
Notes. Factors were coded as follows: Contrast (–.5 = [b]–[β], .5 = [m]–[l]). Model Formula: dprime ~ Contrast + (1|Part_ID). *|t| > 2.0, indicating a significant effect (Gelman and Hill, 2007).
7 Discussion
In Experiment 1 we examined native English speakers’ baseline perceptual sensitivity to the experimental and control contrast using an ABX task. As expected, native English-speaking listeners were found to be less sensitive to the phonetic distinction between [b]–[β] which is not found in their native language relative to the native [m]–[l] contrast. Nevertheless, perception of the [b]–[β] contrast was well above chance (the lowest participant mean proportion correct = .63; dʹ score = .61). Importantly, perception of the experimental contrast by native English-speaking participants is neither at ceiling or floor, such that perception of this phonetic distinction might show sensitivity to the experimental manipulations in Experiments 2 and 3.
IV Experiment 2: Phonological distribution
1 Participants
An additional 30 native English speakers (10 male, 19 female, 1 non-binary; mean age = 22.67 (95% CI: 20.36, 24.97) years; median (Q1, Q3) = 21 (19, 23); range = 18–50 years) who had not participated in Experiment 1 were recruited from undergraduate linguistics courses at the University of Utah and either received course credit or were compensated $10 for their hour-long participation. Participants reported no history of speech, hearing, developmental, or neurological disorders, and no formal or informal experience learning Spanish. Twenty-four participants reported knowledge of one or more second languages. These included ASL (American Sign Language) (4), Dutch (1), French (10), German (9), Italian (3), Japanese (5), Korean (3), Laotian (1), Latin (1), Mandarin (2), Russian (3), Thai (1). Participants were randomly assigned to one of two exposure conditions: the Complementary group (7 male, 7 female, 1 non-binary; mean age = 24.4 (95% CI: 19.98, 28.82) years; median (Q1, Q3) = 22 (18, 25); range = 18–50 years) or the Overlapping group (3 male, 12 female; mean age = 20.93 (95% CI: 20.05, 21.82) years; median (Q1, Q3) = 21 (19, 22); range = 18–24 years).
2 Stimuli
The stimuli for Experiment 2 consisted of 16 unique auditory forms from Experiment 1.
3 Procedure
The experimental procedure consisted of two phases: an exposure phase followed by a perceptual test. During the experimental procedure the participant was seated in a sound-attenuated booth in front of a computer screen. Auditory stimuli were presented using DMDX experiment presentation software (Forster and Forster, 2003) and were played at a comfortable listening level over headphones. At test, a keyboard was used to record participant responses. Following the experimental task, participants completed a language background questionnaire. The entire visit lasted 40–50 minutes.
a Exposure phase
During the exposure phase participants heard 768 auditory tokens (16 auditory forms × 4 tokens × 12 randomized blocks) separated by an ISI of 500 ms. Participants in the overlapping exposure condition were exposed to [b] and [β] in both word-initial and word-medial position, whereas participants in the complementary exposure condition heard [b] and [β] in mutually exclusive contexts (i.e. [b] occurred in word-initial position, and [β] word-medially between vowels). Because the complementary exposure condition was exposed to half of these [b]–[β] auditory forms, the four [b]–[β] forms were presented twice as often to ensure that the exposure phase was equal in length for the two exposure conditions. The distribution of [m] and [l] was identical for the two exposure conditions; [m] and [l] occurred in both word-initial and word-medial position. To ensure that participants attended to the auditory stimuli being presented during the exposure phase, they were instructed to ‘check a box on a sheet provided each time they heard a word’. The exposure phase lasted approximately 16 minutes.
b Perceptual test
Participants completed the perceptual test described in Experiment 1 to examine their perception of the test and control contrasts following exposure.
4 Results
Figure 2 shows the mean proportion correct (left) and the mean dʹ score (right) by exposure condition and contrast for Experiment 2. As expected, all participants generally performed well on the [m]–[l] contrast which was discriminated with relatively high accuracy. Performance on the experimental contrast (i.e. [b]–[β]) was also quite accurate and varied little as a function of exposure condition.

Mean proportion correct (left) and mean dʹ score (right) on the perceptual test in Experiment 2 by exposure condition and contrast. Superimposed text represents group means by condition. Error bars represent one standard error of the mean.
Statistical analyses of the dʹ data included fixed effects for exposure condition (−.5 = Complementary, .5 = Overlapping), and contrast (−.5 = [b]–[β], .5 = [m]–[l]) in a 2 × 2 factorial design with random intercepts for participants. Data and analysis code can be found at: https://osf.io/eaf5u/. There was a significant main effect of contrast (estimate = .36, SE = .13, t = 2.73), with more accurate performance observed for the [m]–[l] than the [b]–[β] contrast. No other main effects or interactions were significant. The model output is summarized in Table 3.
Mixed effects model analysis examining the effects of exposure condition and contrast on dʹ score in Experiment 2.
Notes. Factors were coded as follows: Exposure Condition (–.5 = Complementary, .5 = Overlapping), Contrast (–.5 = [b]–[β], .5 = [m]–[l]). Model Formula: dprime ~ Condition * Contrast + (1|Part_ID). *|t| > 2.0, indicating a significant effect (Gelman and Hill, 2007).
5 Discussion
Experiment 2 investigated the role of phonological distributional information in the adult acquisition of L2 allophonic variants. If participants can infer the status of [b] and [β] based on their phonological distribution, then participants in the Complementary group should show less sensitivity to the phonetic distinction than participants in the Overlapping group following exposure. However, we failed to observe a difference between the two groups’ performance on the [b]–[β] contrast. These results suggest that, at least under these constrained laboratory conditions, participants were not able to use evidence from phonological distribution alone to infer the phonological status of the phones. In Experiment 3, we examine whether adult learners can learn to relate the phones in question as allophones of the same phoneme (free variants), when lexical evidence suggests a lack of contrast.
V Experiment 3: Lexical cues
1 Participants
Twenty-nine speakers of English (14 male, 15 female; mean age = 24.5 (95% CI: 22.26, 26.64) years; median (Q1, Q3) = 23 (21, 26); range = 18–43 years) who had not already participated in Experiment 1 or 2 were recruited from undergraduate linguistics courses at the University of Utah and earned course credit for their participation. None of the participants reported having a hearing, speech, language processing, or neurological disorder, nor did they report experience with Spanish as a native or subsequently learned language. Twenty-two of these participants reported knowledge of one or more second languages, including Akeanon (1), Albanian (1), ASL (1), Cambodian (1), Cantonese (1), Dutch (1), Finnish (1), French (9), German (8), Hiligaynon (1), Japanese (3), Korean (2), Latin (2), Lithuanian (1), Navajo (1), Russian (3), Sarantongo (1), Swedish (1), and Tagalog (1). Participants were randomly assigned to either the Different Image group (9 male, 7 female; mean age = 23.56 (95% CI: 21.70, 25.42) years; median (Q1, Q3) = 23 (20.75, 25); range = 18–33 years) or the Same Image group (5 male, 8 female; mean age = 25.5 (95% CI: 21.19, 29.89) years; median (Q1, Q3) = 22 (21, 27); range = 19–43 years).
2 Stimuli
Our stimuli consisted of the 16 auditory forms from Experiment 1 plus an additional 16 auditory forms which were recorded by the same speaker. The new auditory forms also contained the target phones in the onset of a C[a] syllable, either preceded or followed by one of four syllables (i.e. [xi], [so], [fa], [nu]). Eight were used for Exposure Phase 2 and the other 8 were untrained and were used for the New Word Test. Each of 24 auditory word forms used during Exposure Phase 1 or 2 were paired with a visual referent portraying the word’s meaning (line drawing of vehicles, animals, clothing, etc. from Snodgrass and Vanderwart, 1980). The full set of auditory and visual stimuli used for Experiment 3 are shown in Tables 4 and 5.
Auditory and visual stimuli used for Exposure Phase 1 and Lexical Test.
Note. Shaded ‘meanings’ were not part of the exposure of the Same Image group, as both [b] and [β] words were paired with the same image.
Auditory and visual stimuli used for Exposure Phase 2 and New Word Test.
Note. Shaded auditory forms were not heard by either group during the exposure phase but were used in minimal mismatch trials at test.
3 Procedure
Experiment 3 consisted of five phases (described in detail below). Like Experiment 2, the experimental procedure took place in a sound-attenuated booth and DMDX software was used to present auditory and visual stimuli and record responses. Following the experimental task, participants completed a language background questionnaire. The entire visit lasted between 50–60 minutes.
a Exposure phase 1
During the first exposure phase, participants heard the auditory form of a word and saw a corresponding image depicting the word’s meaning displayed in the center of the computer screen in front of them. Participants in both the Different Image and Same Image groups heard the same auditory forms. However, their exposure differed in whether similar sounding word pairs (differing only in [b] and [β]) were paired with distinct objects (Different Image group) or the same object (Same Image group). Participants heard a total of 768 auditory tokens (16 words × 4 tokens × 12 randomized blocks) separated by an ISI of 500 ms and were instructed to ‘learn the words’. Exposure Phase 1 lasted approximately 16 minutes.
b Perceptual test
Following exposure, participants completed a perceptual test (identical to the one used in Experiment 1 and 2) to examine their perception of the [b]–[β] and [m]–[l] contrast.
c Lexical test
Following the perceptual test, participants completed a two-way forced-choice auditory word–picture matching task. The test was used to assess whether participants learned the word–object pairings and whether the groups differed in their lexical encoding of the [b]–[β] contrast following exposure. In the test, 8 images (4 [m]–[l] and 4 [b]–[β]) were presented three times: once with the auditory form it was paired with during the exposure phase (‘match’ trial), and twice with a different auditory form (‘mismatch’ trial), for a total of 24 trials. Mismatched trials were of two types: ‘global mismatch’ or a ‘minimal mismatch’. On ‘global mismatch’ trials familiar images were paired with an auditory form that had been paired with a different image during the exposure phase (e.g. the picture of a ‘penguin’, which had been paired with [βati] during exposure, was presented with the auditory form [tima] ‘squirrel’). On ‘minimal mismatch’ trials, familiar images were paired with an auditory form that differed from the auditory forms heard during the exposure phase in only the [b]–[β] or the [m]–[l] contrast (e.g. the picture of a ‘penguin’, which had been paired with [βati] during exposure, was presented with the auditory form [bati] ‘apple’). Since success on match and global mismatch trials did not require that participants encode the [b]–[β] contrast, we expected that both groups of participants would perform well on these trial types if they learned the words. Both groups of participants were also expected to perform well on minimal mismatch trials involving [m]–[l] since this contrast is a native one. Of interest was the groups’ performance on the [b]–[β] minimal mismatch trials. If following exposure, the two groups differ in whether they lexically encode the [b]–[β] distinction, with the Different Image group encoding the contrast and the Same Image group not, we should observe better detection of minimal mismatch trials involving [b]–[β] words for the Different Image than the Same Image group (for a similar paradigm with young children, see, for example, Ramon-Casas et al., 2009). On a given test trial, the presentation of auditory forms and images were simultaneous. The picture remained on the screen for 500 ms, and 6 seconds were provided to give a response. The next trial began 500 ms following a participant’s button press response or timeout. All test trials involved novel acoustic tokens which were not heard during the exposure phase. The entire task lasted approximately 2 minutes.
d Exposure phase 2
During the second exposure phase participants learned 8 new words (4 involving [b] and 4 involving [β]). Importantly, there was no difference in the word–object pairings for the two exposure conditions. Neither group was exposed to [b]–[β] minimal pairs. Participants heard a total of 384 auditory tokens (8 words × 4 tokens × 12 randomized blocks), which lasted approximately 8 minutes.
e New word test
Following Exposure Phase 2, participants performed a second two-way forced-choice auditory word–picture matching task to learn whether any knowledge of [b] and [β] acquired during Exposure Phase 1 extended to items that were not used to demonstrate the contrastiveness or non-contrastiveness of phonetic distinction. Again, test trials used novel acoustic tokens which were not heard during the exposure phase. The New Word Test included 24 test trials (8 match, 8 global mismatch, and 8 minimal mismatch). Of interest was the participants' performance on ‘minimal mismatch’ trials (e.g. participants saw the image of a ‘toaster’, which had been paired with [faβa] during exposure and heard [faba]). If participants, based on the lexical cues available during Exposure Phase 1, determined that the difference between [b] and [β] was important for distinguishing word meanings, then they should reject [faba] as a possible production of ‘toaster.’ However, if participants learned that the phones [b] and [β] can occur in the same phonological environment and can vary freely, then they should accept [faba] as a possible pronunciation of ‘toaster.’
4 Data analysis
For the Perceptual Test, a dʹ score was computed for each participant and each contrast, following the procedure described for Experiment 1 and 2. A dʹ score was also computed for each condition for the Lexical and New Word Test. On these tasks, the ‘hit rate’ was computed as the proportion of trials in which the participant responded ‘mismatch’ when the auditory form indeed mismatched the image it was presented with, divided by the total number of mismatch trials. The ‘false alarm rate’ was the proportion of trials in which the participant responded ‘mismatch’ when the auditory form matched the image it was presented with, divided by the total number of match trials. A log-linear correction was again applied to correct for extreme proportions (Hautus, 1995). Given that there were 4 match and 4 mismatch trials per condition, the maximum dʹ score on the Lexical Test was 2.56. The maximum dʹ score was 3.19 for the New Words Test since there were 8 match and 8 mismatch trials per condition. Data from two participants (ALC014 and ALC024) who had a dʹ of 0 for the [m]–[l] global trial types were excluded from analysis, since failure on this condition suggested that they had not learned the words presented during Exposure Phase 1.
5 Results
a Perceptual test
Figure 3 shows the mean proportion correct (left) and the mean dʹ scores (right) by exposure condition and contrast.

Mean proportion correct (left) and mean dʹ score (right) on the perceptual test in Experiment 3 by exposure condition and contrast. Superimposed text represents group means by condition. Error bars represent one standard error of the mean.
Statistical analyses of the dʹ data included fixed effects for exposure condition (−.5 = Same Image, .5 = Different Image), and contrast (−.5 = [b]–[β], .5 = [m]–[l]). Random effects included random intercepts for participants. Planned comparisons were conducted using simultaneous tests for general linear hypotheses with the multcomp() package (Hothorn et al., 2008). P-values were adjusted using the single-step method and a family-wise error rate protection via Bonferroni correction. The model output is summarized in Table 6.
Mixed effects model analysis examining the effects of exposure condition and contrast on dʹ score on the Perceptual Test in Experiment 3.
Notes. Factors were coded as follows: Exposure Condition (–.5 = Same Image, .5 = Different Image), Contrast (–.5 = [b]–[β], .5 = [m]–[l]). Model Formula: dprime ~ Condition * Contrast + (1|Part_ID). *|t| > 2.0, indicating a significant effect (Gelman and Hill, 2007).
A significant main effect of contrast was observed (estimate = .61, SE = .11, t = 5.30), with more accurate performance on the [m]–[l] than the [b]–[β] contrast, but no main effect of exposure condition (estimate = 0.20, SE = 0.21, t = .97). However, the main effect of contrast was qualified by a two-way interaction of exposure condition and contrast (estimate = −0.66, SE = 0.23, t = −2.89), suggesting that sensitivity to the two contrasts differed as a function of exposure condition. Planned pairwise comparisons of the two exposure conditions revealed no difference in perceptual sensitivity for the [m]–[l] contrast (estimate = −.13, SE = 0.23, z = −.56, p = .79). However, a significant difference was observed for the [b]–[β] contrast (estimate = 0.53, SE = 0.23, z = 2.25, p = .04).
b Lexical test
Figure 4 shows the mean proportion correct (top) and mean dʹ scores (bottom) by exposure condition, trial type, and contrast. Participants performed accurately on the global mismatch trials regardless of exposure condition or the contrast involved. For the minimal mismatch trials, participants were again accurate on the [m]–[l] control contrast. However, their performance differs on the minimal mismatch trials containing the [b]–[β] target contrast, with the Different Image group more readily detecting mismatches between images and auditory forms.

Mean proportion correct (top) and mean dʹ score (bottom) on the lexical test in Experiment 3 by exposure condition, trial type, and contrast. Superimposed text represents group means by condition. Error bars represent one standard error of the mean.
Statistical analyses of the dʹ data included fixed effects for exposure condition (−.5 = Same Image, .5 = Different Image), contrast (−.5 = [b]–[β], .5 = [m]–[l]) and trial type (−.5 = global, .5 = minimal) and random intercepts for participants. The full model is summarized in Table 7.
Mixed effects model analysis examining the effects of exposure condition, contrast, and trial type on dʹ score on the Lexical Test in Experiment 3.
Note. Factors were coded as follows: Exposure Condition (–.5 = Same Image, .5 = Different Image), Contrast (–.5 = [b]–[β], .5 = [m]–[l]), Trial Type (–.5 = global, .5 = minimal). Model Formula: dprime ~ Condition * Contrast * Trial Type + (1|Part_ID).
|t| > 2.0, indicating a significant effect (Gelman and Hill, 2007).
There was a significant main effect of contrast (estimate = .68, SE = .10, t = 6.73), with more accurate performance observed for the [m]–[l] than the [b]–[β] contrast. There was also a significant main effect of trial type (estimate = −0.84, SE = 0.10, t = −8.29). No main effect of exposure condition (estimate = 0.00, SE = 0.16, t = 0) was observed. The main effects of contrast and trial type were qualified by a two-way interaction of exposure condition and trial type (estimate = .71, SE = 0.20, t = 3.50), contrast and trial type (estimate = 1.56, SE = 0.20, t = 7.72), and a three-way interaction of exposure condition, contrast, and trial type (estimate = −1.49, SE = 0.41, t = −3.67), suggesting that sensitivity to the two contrasts differed as a function of exposure condition and trial type.
Pairwise comparisons of the two exposure conditions revealed no differences between their performance on global mismatch trials containing the [b]–[β] (estimate = −.54, SE = 0.24, z = −2.28, p = .08) or the [m]–[l] contrast (estimate = −.16, SE = 0.24, z = −.68, p = .92). On minimal mismatch trials involving [b]–[β], a significant difference was observed between groups with the Same Image group having significantly lower dʹ scores than the Different Image group (estimate = 0.90, SE = 0.24, z = 3.79, p < .001). No difference in dʹ score was observed between groups for trials containing [m]–[l] minimal mismatches (estimate = −0.19, SE = 0.24, z = −0.83, p = .86).
c New Word Test
Figure 5 presents the mean proportion correct (top) and mean dʹ scores (bottom) by exposure condition and trial type. As before, all participants performed well on the global mismatch trials, suggesting they had learned the new words. For the minimal mismatch trials, mismatch detection was less reliable and varied between the two exposure conditions.

Mean proportion correct (top) and mean dʹ score (bottom) on the new word test in Experiment 3 by exposure condition, and trial type. Superimposed text represents group means by condition. Error bars represent one standard error of the mean.
Statistical analyses of dʹ scores for the New Word Test included fixed effects of exposure condition (–.5 = Same Image, .5 = Different Image) and trial type (–.5 = global, .5 = minimal), as well as their interactions, and random by-participant intercepts. The model results are summarized in Table 8.
Mixed effects model analysis examining the effects of exposure condition, and trial type on dʹ score on the New Word Test in Experiment 3.
Notes. Factors were coded as follows: Exposure Condition (–.5 = Same Image, .5 = Different Image), Trial Type (–.5 = global, .5 = minimal). Model Formula: dprime ~ Condition * Trial Type + (1|Part_ID). *|t| > 2.0, indicating a significant effect (Gelman and Hill, 2007).
We observed a significant main effect of trial type (estimate = −2.03, SE = 0.13, t = −15.68) and the interaction between exposure condition and trial type was also significant (estimate = 0.54, SE = 0.26, t = 2.09), suggesting that the differential encoding of the [b]–[β] contrast reported in the Lexical Test was extended to untrained items. No main effect of exposure condition was observed (estimate = .23, SE = .17, t = 1.36). Pairwise comparisons of the two exposure conditions revealed no differences between their performance on global mismatch trials (estimate = −.04, SE = 0.21, z = −.20, p = .98). However, a significant difference was observed between groups for the minimal mismatch trials (estimate = 0.50, SE = 0.21, z = 2.35, p = .04).
6 Discussion
Experiment 3 was designed to investigate whether adult L2 learners can use lexical cues to infer whether [b] and [β] are allophones of the same or different phonemes. We observed that exposure to acoustically similar word forms paired with either the same or different images altered participants’ perception of the experimental contrast, suggesting that exposure to lexical cues indeed shaped the inferences that participants made and in turn their perceptual sensitivity to the [b] and [β] distinction.
We also examined whether participants in the two exposure conditions differed in their lexical encoding of [b]–[β], and if so, whether this differential encoding extended to untrained items. On the Lexical Test, we observed that the participants indeed demonstrated differential encoding of the [b]–[β] contrast for trained items. In particular, the Different Image group detected minimal mismatches involving [b]–[β], suggesting that they distinguish [b] and [β] in their lexical representations of the trained words, whereas the Same Image group did not. On the New Word Test, the Different Image group demonstrated greater sensitivity to minimal mismatch trials involving the [b]–[β] contrast than the Same Image group, suggesting that they extended their knowledge of the [b]–[β] contrast to untrained items. By contrast, the Same Image group learned that the acoustic difference between [b]–[β] is not used to distinguish word meanings (but instead is free to vary in the target language) and have extended this knowledge to their phonolexical representation of new words.
VI General discussion
In the present set of experiments, we examined two mechanisms which may support the acquisition of allophonic alternants by adult second language learners. Experiment 1 established that perception of the [b]–[β] contrast differed from the [m]–[l] contrast, and importantly was neither at floor nor at ceiling. In Experiment 2 we examined whether adult L2 learners use phonological distribution – whether phones occur in overlapping distribution or complementary distribution – to learn whether two phones, [b] and [β], are allophones of the same or different phonemes. We failed to observe a difference between the two exposure conditions. In Experiment 3 we held phonological distribution constant and examined whether adult L2 learners can use lexical evidence – whether acoustically similar auditory word forms are paired with the same or different referents – to infer phonological status. We found that exposure to meaning-based cues indeed alters perception and leads to differential lexical encoding of the [b]–[β] contrast which extends beyond trained to untrained items.
Together the findings from Experiment 2 and 3 suggest that lexical cues play a powerful role in adult acquisition of L2 allophonic alternants. Despite equivalent exposure, the findings of the present study establish that adult learners acquire L2 allophones (free variants) when cued by non-contrastive visual information, but not when cued by phonologically natural and predictable conditioning contexts (phonologically conditioned allophones). Adult learners’ sensitivity to lexical cues has precedent in the literature on the acquisition of novel phonemic contrasts. Indeed Hayes-Harb (2007) reported that while adult learners could make use of information available from the frequency distribution of sounds in acoustic space to acquire a novel contrast, lexical evidence outweighed statistical evidence when the two were in conflict. In Experiment 3, statistical and phonological distributional evidence was held constant (i.e. [b] and [β] were bimodally distributed and presented in an overlapping distribution), and lexical evidence was manipulated between participants. When lexical cues to the lack of contrast were present (i.e. phonetically distinct auditory word forms were paired with the same image), adult learners demonstrated less sensitivity to the phonetic distinction on both a perceptual and a lexical test, relative to participants who were exposed to lexical evidence for the presence of a contrast. As such, our study provides the first evidence that we are aware of for the emergence of allophonic perception and lexical representation following learners’ exposure to lexical cues to a lack of contrast.
As others have reported evidence that adults indeed demonstrate sensitivity to the manipulation of phonological distribution (Noguchi and Hudson Kam, 2018), it remains an open question why we failed to find support for this hypothesis in Experiment 2. One possibility is that participants’ baseline perceptual sensitivity to the [b]–[β] distinction was too great for perceptual changes to be observed following a 16-minute exposure phase. According to the Perceptual Assimilation Model (PAM; Best, 1995; Best and Tyler, 2007), nonnative contrasts are perceived quite well when the sounds in question are assimilated to two distinct native language categories, whereas poorer perception is expected when the nonnative sounds are assimilated to the same native language category (either as a ‘same category’ assimilation or a ‘category goodness’ assimilation). While it was expected that both [b] and [β] would be perceived by native English listeners as instances of English /b/, it is possible that native English-speaking participants assimilated our [b] and [β] stimuli to English /b/ and /v/, respectively, resulting in accurate performance on the perceptual task. Importantly, participants’ relatively high baseline sensitivity to the experimental contrast alone would not explain why differences in perception were observed between exposure conditions for the test contrast in Experiment 3, but not Experiment 2. Nevertheless, given that different target language categories can be assimilated to native categories in different ways by language learners, future research should directly explore the effectiveness of various learning mechanisms for the typology of assimilation patterns described in Best’s Perceptual Assimilation Model to gain a more complete understanding of the effects of prior linguistic experience in adult phonological development (for a similar suggestion, see Moeng, 2018).
Another possible explanation for the lack of interaction between exposure condition and contrast in Experiment 2 has to do with the nature of the phonological distributional evidence provided to the participants. Noguchi and Hudson Kam (2018) hypothesize that the type of inferences that learners make based on phonological distribution is related to the amount of variability in phonological context available in the input. Accordingly, learners may interpret context as phonological when the dependency between the sounds and their conditioning contexts comes from a generalization over multiple stimulus items, and as lexical when the alternation is limited to a small number of lexical items. Indeed, Feldman et al., (2013) reported that infants and adults assigned acoustically similar vowels (e.g. [ɑ] and [ɔ]) to different categories more often when those vowels occurred consistently in different words (e.g. [ɑ] appears in [gu.tʰɑ] and [ɔ] in [li.tʰɔ]), than when those vowels occur interchangeably in the same relatively limited number of word-forms (e.g. [gu.tʰɑ], [gu.tʰɔ], [li.tʰɑ], [li.tʰɔ]). In the complementary distribution exposure condition in Experiment 2, [b] occurred word-initially (e.g. [bati] and [baku]) and [β] occurred after a vowel or between vowels (e.g.[tiβa] or [kuβa]). It is possible that the lexicon learners were exposed to was insufficient for them to determine the conditioning context and infer that [b] and [β] are allophones of the same phoneme. Future research should further examine learners’ interpretation of context and the factors that are believed to shape their inferences, such as phonetic naturalness and number of lexical items exhibiting the alternation.
Finally, it is possible that distributional learning in adults is simply not as effective as it is in young infants (Wanrooij et al., 2014) and requires substantially more exposure (Pierrehumbert, 2003) which includes more acoustic variability in both relevant and non-relevant dimensions (Rost and McMurray, 2009, 2010) or exposure separated by a period of sleep (Gaskell and Dumay, 2003). Indeed, given that both statistical and lexical mechanisms are likely available to adult language learners, a more systematic examination of these factors will be helpful for establishing which learning mechanisms are used by adults to determine phonological status and under which conditions.
VII Limitations and future directions
This study is not without limitations. We chose not to employ a pre-test post-test design as a perceptual pre-test would require participants in the Complementary group to experience [b] and [β] tokens in positions where they are not found during their exposure phase. As a result, use of a pre-test could have limited or interfered with any effects of the experimental manipulation. Instead, evidence of native English speakers’ baseline sensitivity to the [b]–[β] and [m]–[l] distinction was based on the performance of a separate group of participants from the same population who were tested online due to lab closures during the ongoing Covid-19 pandemic. Using a separate control group leaves open the possibility that the perceptual sensitivity of the control participants is not representative of the participants in Experiment 2 or Experiment 3 either due to individual differences and/or due to differences between on-line and in-lab data collection. Moreover, while the findings reported here do not rely on a direct comparison of the control and test contrasts, but on the comparison of the two exposure conditions in Experiment 2 and 3 for each contrast, the test and control contrasts were not equivalent in terms of feature differences. Future research will need to explore other solutions to these challenges presented by the study of the acquisition of phonologically conditioned allophonic variants using perceptual tasks, such as our ABX task.
An additional methodological consideration is whether the presence of minimal pairs in the stimulus set may have exaggerated the effect of lexical cues in Experiment 3. Indeed, minimal pairs are known to draw participants’ explicit attention to the fact that a contrast is phonemic (Llompart and Reinisch, 2020). It remains an open question whether effects of lexical cues such as those reported in Experiment 3 here depend on the presence of minimal pairs in the input.
Finally, it is worth noting that, here we explored the role of phonological distribution and lexical cues in the acquisition of L2 allophones. However, there are other sources of information, such as written input, which may also provide literate adult second language learners with information about the function of speech sounds in the target language (for discussion of the orthography–phonology interaction with respect to L2 allophones, see Shea, 2014, 2017). Indeed, a growing body of research has demonstrated that adult learners' reliance on the mappings between graphemes and phonemes in their L1 can interfere with target-like representation and processing of L2 allophonic alternants (Barrios and Hayes-Harb, 2020; Hayes-Harb et al., 2018; Özçelik and Sprouse, 2016; Shea, 2017; Young-Scholten, 2002). There is also some evidence that orthographic input which cues learners into differences among allophonic variants can be helpful to adult learners (Han and Kim, 2017). More research along these lines is needed to better our understanding of when and how orthographic input is used by adult learners in L2 phonological development.
VIII Conclusions
In the present study we demonstrated that adult learners’ perception and lexical encoding of a nonnative phonetic distinction was affected by the lexical cues present in their input whereas cues available from the phonological context were not found to have such an effect. Together the experiments reported here suggest that adults exhibit greater sensitivity to lexical cues, relative to evidence from phonological distribution present in their input. Future research should further explore how these learning mechanisms interact with learners’ pre-existing sensitivity to a phonetic distinction, the amount and type of variability present in the input, and other input variables such as exposure to minimal pairs or orthographic input.
Supplemental Material
sj-docx-1-slr-10.1177_02676583221099237 – Supplemental material for The acquisition of L2 allophonic variants: The role of phonological distribution and lexical cues
Supplemental material, sj-docx-1-slr-10.1177_02676583221099237 for The acquisition of L2 allophonic variants: The role of phonological distribution and lexical cues by Shannon L Barrios, Joselyn M Rodriguez and Taylor Anne Barriuso in Second Language Research
Footnotes
Acknowledgements
We are grateful to the members of the Speech Acquisition Lab and our study participants for their contributions to this research. We are also grateful to Rachel Hayes-Harb, as well as the Associate Editor and three anonymous reviewers for their insightful comments and suggestions.
Declaration of Conflicting Interests
The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
Funding
The author(s) received no financial support for the research, authorship, and/or publication of this article.
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References
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