Methodological frameworks influence the classification and interpretation of temporal coordination in African savanna elephant vocalizations

Acoustic communication plays a fundamental role in coordinating social behaviors. From primates to elephants, social species use vocalizations to maintain contact, coordinate movement, and regulate social interactions. While the acoustic structure and contextual use of vocal signals have been widely studied, the temporal organization of vocal exchanges remains comparatively underexplored, despite increasing evidence that call timing carries meaningful social information and plays a central role in collective behavior. Here, we analyzed a dataset of semi-free African savanna elephants (Loxodonta africana) recorded in a standardized subgroup-separation context to elicit frequent contact rumbles. We applied three previously published methodological frameworks to the same dataset, each characterizing a different aspect of temporal coordination: quartile-based categories, bout criterion interval, and antiphonal probability analysis. We found that these statistical frameworks resulted in substantial variation in temporal boundaries and the classification of antiphonal signals, both within our dataset and relative to previous work. Quartile-based methods yielded shorter inter-call intervals, likely reflecting the high proportion of overlapping calls. Antiphonal probability analyses provided limited evidence for turn-taking across individuals. In contrast, bout criterion interval analysis revealed a comparatively longer temporal threshold, indicating that most vocalizations occurred within extended calling bouts. Overall, these findings demonstrate that methodological decisions strongly influence the identification and interpretation of temporal coordination, particularly antiphony, and can lead to differing conclusions about the presence and extent of coordinated vocal behavior. Consequently, given the limited number of existing studies on elephant vocal timing, early methodological choices may have a disproportionate impact on how temporal coordination is defined and detected, potentially shaping our understanding of coordinated vocal behavior in elephants.

Temporal coordination of vocalizations plays a crucial role in regulating social interactions across a wide range of group-living species (Pika et al., 2018; Ravignani, 2019). Such coordination, including turn-taking, chorusing, and clustered vocal sequences or bouts, may facilitate social cohesion, signal intent, and support the organization of collective behavior. For example, antiphonal exchanges (i.e., call-and-response interactions between individuals) have been documented across taxa, from insects to birds and mammals; in the latter two groups they serve multiple functions, including individual recognition and group cohesion (Miller et al., 2005; Pika et al., 2018). In duetting species such as stripe-backed wrens (Campylorhynchus nuchalis), precisely timed vocal exchanges help to strengthen pair bonds, guard mates, or defend territories (Soma and Brumm, 2020), thereby reducing conflict with neighbors (Wiley and Wiley, 1977). In meerkats (Suricata suricatta), group members engage in vocal turn-taking to minimize overlap and maintain coordination during vocal interaction (Demartsev et al., 2018).

Chorusing, in contrast, involves simultaneous or overlapping vocalizations and typically requires less precise coordination (Pika et al., 2018). Despite structural variation, chorusing may serve key functions, such as predator deterrence through signal amplification, encoding group size in female lion prides (Panthera leo; McComb et al., 1994), mate attraction in frogs and cicadas (Gerhardt and Huber, 2002), and heightened social arousal in African savanna elephants (Loxodonta africana; Poole, 2011). These examples underscore that vocal timing, whether alternating or overlapping, contains rich social information and facilitates collective activity, suggesting that the temporal structure of vocal exchanges may be a key mechanism underlying coordinated behavior in socially complex species such as elephants.

African elephants possess a rich vocal repertoire and exhibit complex social dynamics (Berg, 1983; Poole, 2011; Soltis, 2010; Stoeger-Horwath et al., 2007). Decades of research have focused on the acoustic structure and functional context of their calls, with a strong emphasis on low-frequency rumbles (see Baotic and Stoeger, 2017a; Poole et al., 1988; Poole, 2011; Soltis, 2010; Soltis et al., 2005b), greatly advancing our understanding of their communicative complexity. However, the temporal patterns of their vocal behavior, that is, how calls are sequenced, timed, and coordinated across individuals in interaction, remain comparatively underexplored (but see Leighty et al., 2008; Leong et al., 2003; O’Connell-Rodwell et al., 2012, 2024; Soltis et al., 2005a).

Elephant vocal behavior is strikingly diverse, including solitary rumbles, combinatorial calls, overlapping calls, choruses, and temporally structured sequences, highlighting a complex and flexible vocal system shaped by social context and arousal state (Leighty et al., 2008; Moss et al., 2011; Pardo et al., 2019; Soltis et al., 2005a). Particularly during reunions, arrivals of musth males, or coordinated departures, elephants often produce collective, overlapping vocalizations known as choruses, which can include low-frequency rumbles, trumpets, and roars (Moss et al., 2011). Overlapping sequences account for the majority of calls during these events, suggesting a group-level communicative function (O’Connell-Rodwell et al., 2024).

Particularly, the latency between calls from different group members is often used as a proxy for socially responsive behavior in elephants, where shorter intervals may indicate turn-taking or antiphonal calling (Leighty et al., 2008; Leong et al., 2003; Soltis et al., 2005a). In contrast, overlapping vocalizations may reflect collective arousal or a shared motivational state (Leighty et al., 2008; Moss et al., 2011; O’Connell-Rodwell et al., 2012, 2024). Such temporal patterns are likely to be crucial in African elephants, especially in contexts involving group movement, social reunions, or coordination of collective actions. Although specific examples like the “let’s go rumble” suggest that elephants use temporally coordinated vocalizations to facilitate group decisions, systematic analysis of these dynamics remains limited and is further hindered by inconsistent terminology in existing literature (Leong et al., 2003; O’Connell-Rodwell et al., 2012, 2024). However, how such temporal relationships are quantified varies substantially across studies, raising the possibility that different analytical approaches may lead to different interpretations of the same vocal behavior.

Importantly, terms such as “chorusing”, “turn-taking”, “duetting”, “bouts”, and “antiphonal calling” are often used interchangeably in elephants and other taxa (Leong et al., 2003; O’Connell-Rodwell et al., 2012, 2024; Pika et al., 2018), even though these interaction types are not mutually exclusive and may capture partially overlapping aspects of vocal coordination. This inconsistent use of terminology raises the question of whether these labels reflect distinct communicative strategies or instead arise from differences in analytical approaches and research traditions across taxa and studies (Ravignani, 2019). Consequently, such inconsistencies in terminology may obscure meaningful biological patterns and hinder comparisons across studies and species.

In elephant vocal timing research, three distinct methodological frameworks have emerged (Table 1), each producing potentially divergent classifications and interpretations of similar behavioral phenomena. (1) The quartile-based approach categorizes calls as “overlapping”, “adjacent”, “intermittent”, or “single” based on median latency values between vocalizations, using these temporal boundaries to distinguish responsive from non-responsive calls (Leighty et al., 2008; Leong et al., 2003; Soltis et al., 2005a). (2) Bout criterion interval (BCI) analysis applies statistical models to identify natural breakpoints in vocal sequences, defining “bouts” as clusters of calls separated by longer silent periods (O’Connell-Rodwell et al., 2012, 2024). (3) The antiphonal probability approach, adapted from Wasserman (1977) and building on the exact time window defined by Leong et al. (2003), compares the number of calls expected by chance within this boundary to the number actually observed, thereby assessing whether vocal activity increases following an initial call (Soltis et al., 2005a). Despite their widespread use, these frameworks rely on different assumptions about temporal structure and responsiveness, which can lead to different classifications of the same vocal events. Consequently, one method may classify a vocalization as coordinated turn-taking, while another regards it as independent or part of a broader calling bout. Cross-species research adds to the problem by employing entirely different frameworks (e.g., Noriega et al., 2019; Yeates et al., 2001), making it difficult to determine whether observed patterns reflect genuine species variation or depend on methodological differences.

Taken together, these challenges suggest that our current understanding of elephant vocal coordination and, more broadly, temporal communication in mammals may be shaped as much by analytical choice as by the underlying biological processes. Different methodological frameworks may therefore lead to contrasting interpretations of the same vocal interactions. This raises the central research question: to what extent do different analytical frameworks influence the classification and interpretation of temporally coordinated vocal events in African elephants? We hypothesized that applying these frameworks to the same dataset would yield different classifications of vocal events, thereby leading to contrasting interpretations of the presence and extent of coordinated communication.

Here, we compare three widely used approaches, as outlined above, applied to vocal data from a semi-free-ranging elephant group to assess how methodological differences influence the identification of temporally coordinated vocal events. Applying these frameworks to a common dataset, we assess how they capture temporal structure and how methodological choices shape the detection and interpretation of coordinated vocal events, underscoring the value of standardized definitions and analytical frameworks within elephant communication and across species. Aligning definitions and frameworks is crucial for robust cross-study comparisons, for uncovering general principles of mammalian vocal coordination, and for advancing our understanding of how temporal structure supports social communication in a long-lived, socially complex species.

Study subjects and housing

For this analysis, we used a dataset from a semi-free herd of African savanna elephants at Adventures with Elephants (AWE), Rory Hensman Conservation and Research Unit (RHCRU), Bela Bela, South Africa. The 300-hectare habitat allows free movement during the day, while elephants are stabled at night. The herd comprised three adult females, two adult males, and two calves born at the facility (Table 2). Elephants are managed “hands on” through positive reinforcement training, routine veterinary care, and are habituated to human presence.

Data collection

We used a standardized subgroup-separation context to elicit frequent contact rumbles and to minimize confounding visual cues. This design generated a clear temporal structure for evaluating alternative analytic frameworks. The resulting dataset provides repeated, comparable call–response opportunities that are directly relevant to our question about temporal coordination.

The herd was divided into two subgroups, with one observer assigned to each (leading to 28 subgroup arrangements; see Supplementary Tables S1; S2 in Supplementary File 1). For each trial, handlers positioned the subgroups at sites approximately 200 m apart with no line of sight between them. These distances were estimated in the field rather than systematically measured and may therefore have varied across trials. Each observer remained with their subgroup and collected audio and video recordings simultaneously. For each subgroup, a microphone was mounted on a tripod and positioned approximately 20 m from the animals, respectively. Because the elephants could move within their respective locations, the microphone-to-animal distance varied during recording. Exact microphone-to-animal and inter-microphone distances were not recorded, however, the distance between the microphones broadly corresponded to the estimated separation between the subgroups. Before each session, all recording devices were synchronized using an auditory and visual cue to ensure temporal alignment across recordings. Each separation and recording period lasted 10 minutes.

Between November 4 and 28, 2018, acoustic and video recordings were conducted during daytime hours (07:00-16:00), comprising a total of 18 recording sessions distributed across this period.

Acoustic recordings were made using two identical setups with omni-directional Neumann KM 183 microphones, modified to capture frequencies below 20 Hz, connected to a 722 Sound Devices HDD recorder (this combination provides a flat frequency response down to 10 Hz). Simultaneous video recordings were obtained with two Sony PJ650 cameras, each operated by one experimenter.

Data preparation

Audio recordings were processed using S_TOOLS-STx (Acoustics Research Institute, Austrian Academy of Sciences, Vienna) and down-sampled to 3 kHz for further annotation. The analyses focused on rumbles only. Each rumble was assigned a unique identifier composed of the experiment number, context (separation), experimenter, and a sequential call number (e.g., E14sAN.0004). The start and end points, the rumble class (single rumble or part of multiple overlapping rumbles), recording quality (a subjective rating based on structural clarity and background noise), caller identity, and experimenter name were documented. All 459 annotated rumbles were extracted using a custom script in STx and exported as CSV files for analysis along with associated metadata.

Call durations and inter-call intervals were calculated using the start and end points of each rumble. All three analytical frameworks were applied to the same annotated dataset of rumbles. Preprocessing steps, including the handling of overlapping calls and the exclusion of self-responses, were applied consistently where appropriate, with specific adjustments described for each method below.

Descriptive statistics and temporal categorization

Analyses were conducted in R (v. 4.4.1) with the significance threshold set at p = 0.05. Visualizations were produced in Python (v. 3.12.4) using Matplotlib (Hunter, 2007) and Seaborn (Waskom, 2021). No latency values were available for the first call in a recording session, leaving 428 calls available for latency-derived calculations. Latencies were classified into temporal categories following Leong et al. (2003), which we refer to here as the “ quartile-based method”. In this approach, intervals were defined as the time between the end of one rumble and the start of the next. Overlapping rumbles were assigned negative values and categorized as “overlapping”. This definition allows negative latency values for overlapping calls, which were retained to capture simultaneous vocal activity. Quartiles were calculated, and each call was assigned to one of four categories - overlapping (Figure 1A), adjacent (Figure 1B), intermittent, or single - based on the results. The first vocalization of each recording session was classified as a single vocalization serving as the starting point of the session, unless subsequent vocalizations overlapped with it, in which case it was classified as overlapping.

A chi-square (χ 2) test was then conducted to examine the distribution of categories across individuals.

Call durations and temporal categories

To assess whether overlap influences call duration, we classified the first call in each overlapping sequence as overlapping, regardless of its latency to the preceding call. All calls not classified as overlapping were classified as non-overlapping for this analysis, independent of their temporal category.

To examine whether call duration differs between overlapping and non-overlapping vocalizations, we fitted linear mixed-effects models using the lmer function from the R package ‘lme4’ (Bates et al., 2015), with significance testing implemented via lmerTest. Call duration (s) was included as the response variable, vocalization type (overlapping vs. non-overlapping) was specified as a fixed effect, and individual identity and recording session were included as random intercepts to account for repeated measures and non-independence of observations.

In a second analysis, call duration was compared among the four temporal call categories (single, adjacent, intermittent, and overlapping) using an analogous linear mixed-effects model with call type specified as a fixed effect and individual identity and recording session included as random intercepts.

Self-responses and antiphonal calling

Consecutive calls by the same individual without interjections from others were defined as “self-responses” and excluded from antiphonal calling analyses. The latter followed Wasserman’s (1977) approach, as adapted by Soltis et al. (2005a), comparing observed and expected response rates within the previously calculated time window for a response (overlapping or adjacent) after another individual’s call. For each individual, the expected number of answer rumbles was calculated according to the adapted analysis by Soltis et al. (2005a) as follows:

where N S was the number of rumbles produced by the focal individual, t was the total recording time, and

which represented the upper-bound amount of answerable time. N o was the number of rumbles produced by all other individuals, d was the mean rumble duration, and x was the 25 s response window. This calculation assumes that answerable time windows do not overlap and were therefore summed in full even when they overlapped in time.

Separate χ 2 tests (df = 1) were conducted for each individual to compare the observed and expected numbers of responses.

Bout criterion interval

Additionally, we analyzed the temporal clustering of rumbles using a bout criterion interval (BCI), based as closely as possible on the methodological approach described by O’Connell-Rodwell et al. (2012). The BCI represents the transition between temporally clustered calls within bouts and the longer pauses separate successive vocal bouts. Overlapping calls, for which the subsequent call began before the preceding call ended, were assigned an inter-call interval of 0 s for this analysis. We first assessed whether positive inter-call intervals differed from the exponential distribution expected if calls were randomly distributed using a Kolmogorov-Smirnov test. Because the rate parameter of the exponential distribution was estimated from the observed data, statistical significance was assessed using a parametric bootstrap with 10, 000 iterations. We then constructed a log-survivorship curve across the full range of observed inter-call intervals, and a segmented linear regression was fitted to the association between log-survivorship and latency using the R package segmented (v1.3-2; Muggeo, 2003). Accordingly, the BCI was identified as the breakpoint in slope estimated by the segmented regression. Intervals equal to or shorter than the estimated BCI were classified as within-bout intervals, whereas longer intervals were classified as between-bout intervals and marked the beginning of a new vocal bout.

Descriptive overview of data

During the separation context, 459 rumbles were recorded from seven individuals (Table 2), of which 86 (19%) were from unidentified callers. Shan produced most calls (n = 115; 25% of all rumbles), followed by Chichuru (n = 77; 17%) and Chova (n = 69; 15%).

Rumble durations ranged from just over one second (1.04 s) to 12.44 s. The majority of calls were relatively short in duration, with 75% lasting less than 6 s. The median duration was 4.96 s, indicating that half of all rumbles fell below this value. Overall, the distribution of call durations was centered around a mean of 5.08 ± 1.71 s. This indicates a relatively consistent pattern of call durations within the dataset, although some variability was observed.

Classification of temporal categories

Out of the 459 recorded rumbles, latency measurements to the preceding call were obtained for 428 instances. Latencies ranged from near-simultaneous overlaps to pauses lasting up to 760 s (≈12.5 min), with a mean interval of 52 s. Descriptive statistics for both raw and adjusted values are presented in Table 3.

Calls were classified into four temporal categories according to the quartile-based method by Leong et al. (2003): overlapping (latency< 0 s), adjacent (0–25 s), intermittent (25–71 s), and single (>71 s).

Distribution of temporal categories

Table 4 summarizes the distribution of rumbles across four temporal categories: overlapping, adjacent, intermittent, and single. Overlapping calls were the most frequent, accounting for 49% of all rumbles and 48% of calls from identified individuals. Adjacent calls were the least frequent, representing 14.2% and 15.5% of calls in the two datasets, respectively. A χ 2 test confirmed significant differences in category distribution (Table 4; full dataset: χ 2 = 148.85, df = 3, p< 0.001; identified individuals: χ 2 = 106.62, df = 3, p< 0.001).

Comparison between these two datasets showed no significant difference in category distribution (χ 2 = 0.673, df = 3, p = 0.88), indicating that excluding calls from unidentified individuals did not affect the overall pattern.

Comparison with previous studies

Table 5 compares the temporal category boundaries derived using the quartile-based method in the present study with those reported by Leong et al. (2003). Boundaries for adjacent calls were similar across studies, whereas the upper limit for intermittent calls was lower in the present dataset (71 s) than the 120 s reported by Leong et al. (2003).

Figure 1C illustrates the distribution of rumble vocalizations across four temporal categories for each identified individual. Calls from unknown individuals were excluded, as they likely represent contributions from multiple elephants and were therefore less informative for individual-level patterns. In total, 373 rumbles were analyzed. Patterns varied among individuals: Shan most frequently produced single calls, Zambezi predominantly produced intermittent calls, and the remaining individuals primarily produced overlapping vocalizations, with Messina reaching nearly 70% in this category.

Call duration analyses

Having established temporal categories and their distributions, we next examined how these corresponded with call durations (Figures 2A, B).

First, model assumptions for the two categories (overlapping and non-overlapping) were assessed visually, and no substantial deviations from normality or homoscedasticity were found. Call duration did not differ significantly between overlapping and non-overlapping vocalizations in the linear mixed-effects model (estimate = −0.25 ± 0.15 s, t = −1.71, p = 0.088). Estimated marginal mean durations were similar between call classes (overlapping: 4.75 s, 95% CI 3.89–5.61; non-overlapping: 4.50 s, 95% CI 3.64–5.36), and the estimated difference between groups was small (0.25 s, 95% CI −0.04 to 0.54; Cohen’s d = 0.20, 95% CI −0.08 to 0.49).

Second, model assumptions for the four temporal call categories were assessed visually, and no major deviations from normality or homoscedasticity were detected. When comparing call duration across the four categories, no significant differences were detected (Type III test: F (3, 342.24) = 1.25, p = 0.293). Estimated marginal mean durations were similar across categories (single: 4.41 s, 95% CI 3.54–5.28; adjacent: 4.63 s, 95% CI 3.74–5.51; intermittent: 4.51 s, 95% CI 3.63–5.39; overlapping: 4.76 s, 95% CI 3.89–5.62), and post-hoc Tukey-adjusted pairwise comparisons revealed no significant differences between any call-type pairs (p > 0.26 for all). The fixed effect of call category explained only a small proportion of the variance (marginal R 2 = 0.008; 95% bootstrap CI, 0.001–0.041), whereas including random effects considerably increased the explained variance (conditional R 2 = 0.403; 95% bootstrap CI, 0.177–0.597). Furthermore, random-effect variance was greater for individual identity than for recording session (ICC individual = 0.31; ICC recording session = 0.09), indicating that individual identity accounted for a considerable proportion of the variability in call duration.

Overall, both results showed that call duration showed little variation across temporal categories but was most strongly driven by individuals.

Self-responses

Not all rumbles represented potential communicative events between two individuals. In total, 121 “self-responses” were recorded, meaning that an individual produced at least two consecutive rumbles without any intervening vocalizations from another group member. Shan produced 58 self-responses, representing 47.9% of the total. This was more than twice the number recorded for Chichuru, who had the second highest count with 20 self-responses (16.5%). Together Shan and Chichuru accounted for 78 of the 121 (64.5%) observed self-responses, while, in contrast, Bela produced none.

Antiphonal probability analysis

Across the 35, 380 s of recorded observation, most elephants produced a higher number of rumbles occurring after another individual’s call than would be expected by random chance. Statistically significant deviations from chance levels were found for Chova (p = 0.005) and Messina (p = 0.037). Figure 3 illustrates this relationship, comparing predicted and observed numbers of rumbles occurring after another individual’s call per individual.

Bout criterion interval analysis

A Kolmogorov–Smirnov test confirmed that positive inter-call intervals (n = 307) differed significantly from the exponential distribution expected if calls were randomly distributed (D = 0.069, parametric bootstrap p = 0.016). The subsequent log-survivorship analysis identified a change in slope at an inter-call interval of approximately 124 s (123.57 s), which was identified as the bout criterion interval (BCI; Supplementary Figure S1). Intervals at or below this threshold were classified as within-bout intervals, whereas intervals longer than 124 s were classified as between-bout intervals and therefore marked the beginning of a new vocal bout. Of the 428 vocalizations for which latency to the preceding call could be calculated, 384 (89.7%) followed the preceding call within 124 s and were consequently classified as occurring within a vocal bout. The remaining 44 rumbles (approximately 10.3%) followed an interval longer than 124 s and marked the beginning of a new bout.

This exploratory study examined temporal vocalization patterns in a semi-free group of African savanna elephants during a standardized subgroup-separation context by applying multiple previously published methodologies (Leong et al., 2003; O’Connell-Rodwell et al., 2012, 2024; Soltis et al., 2005a) to the same dataset. The analytical frameworks differed substantially in how they classified temporal vocal interactions and, consequently, in the conclusions they supported regarding antiphonal signaling. Specifically, the quartile-based method, antiphonal probability analysis, and BCI approach yielded contrasting interpretations of temporal coordination, ranging from limited evidence of turn-taking to the predominance of extended group-level vocal bouts.

Comparative analysis of temporal categories

The quartile-based categories identified in this study diverged notably from those reported by Leong et al. (2003; Table 5), with category boundaries being significantly smaller on average, meaning that latencies between calls were shorter in the present study. Importantly, this comparison is based on the same analytical framework, indicating that differences in temporal categorization can arise even when identical methods are applied to different datasets. This discrepancy may be attributed to the study context: whereas Leong et al. (2003) observed elephants under relatively neutral conditions, the present study involved a herd that had been split into two subgroups. Although adjacent calls, which represent potential antiphonal responses under this framework, were the least common vocalization type in this study (Table 4), the shorter response times on average compared to the previous publication (Leong et al., 2003) may be explained by the high proportion of overlapping calls, which accounted for nearly 50% in this dataset. This high proportion of overlapping calls may be due to the separation of the two subgroups, leading to heightened arousal and increased urgency of communication. Supporting this interpretation, Armstrong and Johnson (2021) documented increased vocalizations following the separation of affiliated elephants. Similarly, Plotnik and de Waal (2014) found that stressful social contexts elicited increased vocal exchanges among group members in Asian elephants (Elephas maximus). A comparable context-dependent change in vocal activity has been observed in common marmosets (Callithrix jacchus). When focal animals were removed from their home cages containing their social partner, their trill rate increased (Landman et al., 2020), indicating that separation of affiliated individuals affects their vocal activity.

Nevertheless, although the category boundaries were shorter in the present study than in Leong et al. (2003), the antiphonal response windows ranging from 30–120 s or 25–124 s (present study) appear to be relatively long. These extended windows may reflect the flexibility of elephants in adapting their response times to different social or environmental contexts, such as varying levels of urgency and arousal. Additionally, unlike smaller species with faster response times due to their size and ecological constraints, elephants, as vocal production and vocal usage learners (Poole et al., 2005; Stoeger and Baotic, 2021), are capable of modulating their vocalization patterns. For instance, their ability to produce rapid vocal exchanges is evident during greeting events. Furthermore, given that vocalizing is an energetically costly behavior that increases metabolic rates in proportion to vocal effort, including duration and amplitude (Holt et al., 2015; Joshi et al., 2017), the relatively long duration of rumbles (Figure 2A) may necessitate recovery periods. This energetic constraint could contribute to the extended latencies observed between vocalizations, particularly under low to moderate arousal conditions.

However, the duration of overlapping rumbles did not differ significantly from temporally isolated calls (Figures 2A, B). Instead, variation in rumble duration may rather be explained by individual identity than temporal category, which aligns with a number of previous studies that have found social rank, context, body size, emotional state, and age to influence rumble durations (Baotic and Stoeger, 2017a; Soltis et al., 2005a, 2005b, 2014; Stoeger and Baotic, 2016).

Taken together, the findings suggest that herd separation in the current study may have intensified vocal output. Consequently, the quartile-based method is likely context-sensitive, and temporal boundaries derived from the observed distribution of calls may partly characterize the particular social or experimental situation rather than reflect stable response thresholds. Changes in calling rate and overlap may therefore alter the category boundaries and identified antiphonal calls even when the same analytical framework is applied.

Additionally, this method does not explicitly account for repeated observations within recording sessions, individuals, or group composition, all of which may affect temporal vocalization patterns. Therefore, the identification of communicative events may vary not only among contexts, but also among individuals, recording sessions, and group composition. Future studies could account for these sources of variation using mixed-effects or hierarchical models when analyzing antiphonal communication and compare latency distribution across contexts rather than exclusively relying on and re-applying dataset-specific quartile boundaries.

Antiphonal probability analysis

Using 25 s as the boundary for adjacent calls, we further tested for antiphonal calling patterns by examining whether individuals produced more vocalizations within this interval after another individual’s call than expected by chance.

A χ 2 test indicated that, out of the seven individuals, only two, Messina and Chova (Figure 3), produced significantly more vocalizations within 25 s following another individual’s call than expected by chance from their individual calling rates and the estimated available response opportunities. This contrasts with the findings of Soltis et al. (2005a), who reported a significant increase in calls among most individuals. Furthermore, response probability in their study was strongly influenced by the affiliative relationship between callers and responders, as responses were most likely to occur between affiliated pairs. The results in the present study suggest that potential antiphonal calling was not distributed uniformly across individuals as Nuanedi, Shan, Chichuru, Zambezi, and Bela did not differ significantly from chance expectations. Under this analytical framework, these results suggest that antiphonal communication appears less prominent in the present dataset, whereas overlapping calls, rather than antiphony, constitutes the most common temporal pattern (Table 4; Figure 1C). However, especially Bela’s result should be interpreted cautiously because of the small sample size and the consequently low expected response count.

Furthermore, the antiphonal probability analysis is conservative because the calculation of expected responses assumes that answerable time windows do not overlap, meaning that when calls occur in temporal clusters, several response windows may overlap in real time, but their full durations are added when calculating the maximum amount of answerable time without subtracting the temporal overlap. This consequently overestimates the proportion of recorded time that is considered answerable and, therefore, the number of responses expected to occur by chance. Accordingly, the analysis is biased against the detection of a significant increase in vocalizations following another individual’s rumble. This asymmetry between inflated expected response counts and the limitation of potential responses to a single dyadic interaction with the directly preceding call makes detection of above-chance answers relatively conservative, particularly during periods of heightened vocal activity.

While the exclusion of calls by unidentified individuals were necessary to obtain individual-level results, it likely further affected the detection of observed responses. Considering these limitations, the results of this analysis should be interpreted cautiously and should not necessarily be taken as evidence for or against the presence of antiphonal communication of individual elephants within this group. Differences in the number of calls, statistical power of individual tests, unidentified callers as well as the distribution of overlapping response opportunities may all have influenced the individual results. While this approach simplifies the analysis, it may not fully capture the complexity of temporal vocal interactions in elephants.

The present analysis further considers each individual’s overall probability of responding to any other identified caller but does not specifically analyze dyadic interactions or social relationships, and whether responses are more likely to occur between certain individuals. This may obscure selective antiphonal interactions between closely bonded individuals, as observed by Soltis et al. (2005a). The influence of social relationships on temporal coordination is a phenomenon that has been observed in multiple other taxa. For example, male chimpanzees (Pan troglodytes schweinfurthii) were more likely to join pant hoot choruses of strongly affiliated males (Fedurek et al., 2013). Similarly, stronger social bonds between bonobos (Pan paniscus) predicted the frequency of turn-taking interactions and overlap-avoidance between individuals (Levréro et al., 2019).

Taken together, these examples indicate that response probability may be structured by social relationships between dyadic pairs rather than occurring uniformly at a group level. Investigating this possibility requires reliable identification of callers and responders, independent measures of each dyadic relationship strength, as well as sufficient observations across dyads, data that can be difficult to obtain when recording large elephant groups in the field. Antiphonal probability analyses are therefore sensitive to data completeness and study design, as missing information on caller identity or dyadic relationships may obscure significant patterns or reduce statistical power. Additionally, the quartile-based boundary used to define adjacent and potential antiphonal calls may itself be context-dependent, as discussed in section 4.1.

Identification of vocal bouts

While quartile-based categories offer one method for defining temporal boundaries, this study also employs the bout criterion interval (BCI) as an alternative approach to identify communicative events as structured bouts. The BCI, derived via log-survivorship analysis, identifies the threshold at which tightly clustered calls (bouts) transition into extended periods of vocal inactivity. In the present study, the BCI defined all vocalizations occurring within 124 s as belonging to the same group-level calling bout. This interval is substantially longer than the BCI reported by O’Connell-Rodwell et al. (2012) for wild elephants departing a water hole, which was 1.5 s for wild female family groups.

However, in addition to the notably differing context between the studies, Sibly et al. (1990) cautioned that successive points in a log-survivorship plot are statistically interdependent, because each point is derived from a cumulative number of intervals exceeding a given duration, for example, an interval exceeding 15 s is also counted among intervals exceeding 10 s, 5 s, and so on. Instead, they suggest log-frequency models may present a non-cumulative alternative as they treat each interval independently. However, log-frequency analysis comes with its own limitations, such as the influence of histogram bin width selection on bout criterion estimates. Maximum-likelihood mixture models provide another alternative that avoids subjective bin width selection. Rekdahl et al. (2015) applied a mixture model to inter-call intervals of humpback whales (Megaptera novaeangliae) social calls to estimate a bout criterion and subsequently examined variation in bout use according to call types, social context, and group composition with generalized linear mixed models. While this study analyzed bouts on an individual-level, it illustrates how data-driven bout criterion can be combined with different biologically relevant variables while accounting for repeated measures.

Despite these methodological limitations, the 124 s BCI was substantially longer than the 71 s boundary between intermittent and isolated vocalizations obtained by applying the quartile-based method to the present dataset (Table 5). While this agreement does not constitute independent validation, it indicates that the two approaches identify a similar transition from clustered to isolated vocal activity. Based on this limit, approximately 89% of all calls in the present dataset were classified as part of a group-level vocal bout.

Overall, the analyses revealed inconsistencies in how the potential presence of antiphonal communication is identified and interpreted across studies. The first study to define a specific time frame described adjacent calls as those occurring within 30 s of a previous call (Leong et al., 2003). This cutoff was later adopted by subsequent studies without further testing (Soltis et al., 2005a; Leighty et al., 2008). Our results demonstrate that such fixed thresholds may not generalize across datasets and that applying an unvalidated temporal boundary may lead to biased classifications and alter the resulting biological interpretation. Recording situations, behavioral context, group composition, and the level of arousal likely affect call timing, however, the present study further shows that differences in analytical frameworks themselves can be a key source of variation in results and contrasting interpretations of the same vocal behavior. Consequently, future research would benefit from combining complementary frameworks, rather than relying on one universally applicable method or threshold.

For example, mixture models may be used to test whether inter-call intervals support distinct temporal populations and, when these populations are sufficiently separable, to estimate a model-based bout criterion (Rekdahl et al., 2015). Permutation procedures can assess whether observed response timing differs from patterns expected under an appropriate chance model, whereas mixed-effects or hierarchical models can evaluate variation depending on individual, dyads, recording session, and context, while also accounting for repeated observations. Furthermore, Kershenbaum et al. (2016) provide a comprehensive overview of statistical models in animal acoustic communication and demonstrate how different sequence structures, including overlap, timing and repetition can inform model choice, for example, hidden Markov or network models.

Importantly, these approaches address different aspects of temporal organization and should therefore be viewed as complementary rather than interchangeable or universally applicable. Reporting effect sizes and validating findings across populations and recording contexts will further improve the robustness, comparability, and biological interpretation of temporal analyses in elephant communication.