The α-acoustic indices were studied under three experimental conditions: a controlled environment (with artificial tracks only), in situ playbacks (with artificial tracks played back over natural sounds), and a natural environment (only with natural sounds) (Figure 1).

Fourteen α-acoustic diversity indices were calculated for tracks from the controlled environment, in situ playbacks, and natural environment: two intensity indices, eleven complexity indices, and one soundscape index. The used indices are summarized in Table 1, along with their bibliographic references: (1) the peak-to-peak sound pressure level (SPL_pp); (2) the root mean square sound pressure level (SPL_rms); (3) the amplitude index, calculated as the median of the amplitude envelope (M = AI); (4) the bioacoustic index, which measures the area under the power spectrum (BI = Bio); (5) the temporal entropy (TE = H_t), which measures the envelope complexity; (6) the spectral entropy (also named the Shannon spectral entropy and Pielou’s evenness index, SE = S = H_f), which measures the spectral complexity; (7) the Gini–Simpson spectral entropy (also named the Simpson spectral entropy, Gini–Simpson spectral index, or Simpson spectral index, GS), which is derived from the spectral entropy; (8) the acoustic entropy index (also named total entropy or acoustic entropy, H), which measures both the envelope and spectrum; (9) the acoustic richness index (also named acoustic richness, AR), which measures the envelope complexity and intensity; (10) the acoustic diversity index (ADI = H’), which measures the spectrum complexity; (11) the acoustic evenness index (AEI = Aeve = AE), which applies the Gini index to a frequency spectrum; (12) the number of peaks in a frequency spectrum (also named frequency peak number, NP); (13) the acoustic complexity index (ACI); and (14) the normalized difference soundscape index (NDSI), which measures the ratio between two frequency bands (Table 1, Equations (S1) to (S10)). All the indices were calculated in R software version 3.6.1. (R Core Team, 2019) with the libraries seewave, signal, sound, and soundecology. The functions used are detailed in Table 1.

Prior to analysis, the files recorded by the hydrophone in the controlled environment were subsampled at 44.1 kHz to be comparable with the soundtracks recorded during the in situ playbacks, and in the natural environment.

The indices were calculated for the 50–2000 Hz frequency band. For the NDSI, the so-called “anthropophony band” was the band of interest (fish sounds, 50–2000 Hz), while the so-called “biophony band” was the band occupied by benthic invertebrate snaps (mainly snapping shrimps, 2.5–8.5 kHz). Out of the eleven tested complexity indices, specific settings were necessary for three of them (ACI, ADI, and AEI). To examine the effect of the settings on the ADI and AEI, the following frequency bandwidths and threshold were tested: 10, 50, 100, 500, and 1000 Hz; −10, −25, −50, and −75 dB. These tests were realized on the three datasets (controlled, in situ playbacks, and natural environments). The effect of settings was not tested on the ACI as previously done by Bolgan et al. (2018). For the ADI and AEI, two “optimal” settings, obtained from the controlled environment, were kept because one of them was more representative of the sound abundance, while the other was more representative of the sound type richness. Consequently, the following settings were used for the calculations: FFT window = 2048, window name = Hanning, size of frequency bands (for the ADI and AEI) = step = 100 and 500 Hz, threshold (for the ADI and AEI) = −25 and −50 dB (referred to as “ADI_v1, ADI_v2, AEI_v1, and AEI_v2” throughout the document; v1 = 100 Hz and −50 dB, and v2 = 500 Hz and −25 dB), overlap = 75%, number of windows (for the ACI) = 120 for 1 min files and 360 for 3 min files.

The indices were calculated for each file, i.e., each block from the controlled environment (Figure 2), five replicates of each block for the in situ playbacks, and 108 files of 1 min for the natural environment (Figure 2). In addition, for the in situ playbacks, a second analysis was realized: the indices were calculated for each “background block” (i.e., natural acoustic environment without playbacks) and for each “playback block” (i.e., blocks with both natural acoustic environment and playback sounds) from each replicate. Then, the values from each “background block” were subtracted from those of the adjacent “playback block” to obtain a delta, referred to as “delta sounds” throughout the document. For graphical visualization, the deltas of all the replicates were averaged together.

The values of the different indices were standardized between 0 and 1 with the formula “standardized(x) = [(x − min(x)) (max(x) − min(x))⁻¹]”. These standardized values were plotted as “bubble graphs”. Standard Z-scores greater than |3| were considered as outliers. The correlation between each index with both the sound abundance and the sound type richness was assessed using Spearman's rank correlation ρ with the associated p-values corrected with the Benjamini–Yekutieli method. This method was used rather than the Benjamini–Hochberg method because of the non-independence of the tests. Then, the coefficient of multiple correlation (R) was calculated for each index (Equation (1)). For the in situ playbacks, both the artificial abundance/richness (from the stimuli) and the total abundance/richness (including both stimuli and natural sounds) were examined. (1) R i , a , d 2 = ρ a , i 2 + ρ d , i 2 − 2 ρ a , i ρ d , i ρ a , d 1 − ρ a , d 2 Calculation of the coefficient of multiple correlation (R). i = index; a = sound abundance; d = sound type richness.

In the controlled environment, no index was significantly correlated with the sound type richness (Table 2). The ACI, GS, H, and SE showed positive correlations with the sound type richness that were, however, not statistically significant (Table 2). The ADI, M, and TE were strongly correlated with the sound abundance (ρ = 0.95, 0.90, and 0.90, p = 0.0062, 0.036, and 0.036), while a negative correlation was observed for the AEI (ρ = −0.95, P = 0.0062; Table 2). The correlation between the sound abundance and ADI was observed with a threshold of −50 dB, but not with smaller (−10 or −25 dB) or higher thresholds (−75 dB) (ρ = 0.95, p = 0.0044; Table S3). No effect of the step (i.e., the size of the frequency bands) was observed. No correlation was observed with the default settings. The same results were obtained for the AEI (Figure 3, Table S4).

In the in situ playbacks, M and TE were both correlated with the playback sound abundance (both ρ = 0.82, both p < 0.0001; Table S5), and total sound abundance (i.e., playback and natural fish sounds) (ρ = 0.84 and 0.80, both p < 0.0001; Table 3). In contrast, NP was negatively correlated with the total sound abundance (ρ = −0.56, P = 0.0032; Table 3). When considering the “delta sounds”, only M was correlated with the sound abundance (ρ = 0.90, p < 0.0001; Table S6). In all cases, the ADI never correlated with the sound abundance or sound type richness (Tables S7–S9). Similar observations were obtained for the AEI, but with negative signs (Tables S10–S12).

In the natural environment, when considering the optimal settings, no index showed any statistically significant correlation with the sound abundance (Figure 4, Table 4). Four indices (ADI_v1, NP, SPL_rms, and TE) were negatively correlated with the sound type richness (ρ = −0.43, −0.52, −0.35, and −0.57, all p < 0.001), while six indices (ACI, AEI_v1, BI, M, NDSI, and SPL_pp) were positively correlated with the sound type richness (ρ = 0.53, 0.43, 0.36, 0.55, 0.35, and 0.47, all p < 0.05; Figure 4, Table 4). In the natural environment, the sound abundance and sound type richness were not independent (ρ = 0.53, p < 0.0001). When considering a broader range of settings, the ADI was positively correlated with the sound abundance (ρ = 0.33 to 0.34, all p < 0.006), but only with a low threshold (−10 dB) and low step values (10, 50, and 100 Hz). With this low threshold (−10 dB), a positive correlation with the sound type richness was found (ρ = 0.29, p = 0.031), but only with low step values (10 and 100 Hz). In contrast, with high thresholds (−50 and −75 dB), the correlations between the sound type richness and ADI were generally all negative (−0.51 < ρ < −0.34, all p < 0.004) (Table S13). Similar results were obtained for the AEI (Table S14). When using a low threshold (−10 dB) with low step values (10, 50, and 100 Hz), the AEI appeared to be negatively correlated with the sound abundance (ρ = −0.32, p = 0.012), while with higher thresholds, it was generally positively correlated with the sound type richness (0.36 < ρ < 0.51, all p < 0.004) (Table S14).

In both the controlled environment and in situ playbacks, no index was correlated with the sound type richness. M and TE were correlated with the sound abundance in both the controlled environment and in situ playbacks. Similarly, the ADI and AEI were also correlated with the sound abundance, but only in the controlled environment. In the natural environment, the opposite was observed: no index was correlated with the sound abundance, but many (ACI, ADI, AEI, BI, M, NDSI, NP, SPL_rms, SPL_pp, and TE) were correlated with the sound type richness. These results are therefore contradictory and can lead to misinterpretation.

The controlled experiments showed that the indices were correlated with the sound abundance but not with the sound type richness, implying that they are sensitive to the number of sounds but are not capable of distinguishing the different types of fish sounds. In the in situ playbacks, the indices were not able to capture those differences, both in terms of the sound abundance and sound type diversity of the played-back and naturally occurring fish sounds. This is of critical importance, because it clearly shows that indices are incapable of discerning subtle modifications of a subset of a soundscape (i.e., fish frequency band), being intended, rather, to describe soundscape phenomena over a wide and often diverse frequency bandwidth. The disappearance of a species or arrival of an invasive species within the fish frequency band would therefore be difficult to assess, unless it produced mass phenomena. Marine coastal soundscapes are always noisy and distinct from terrestrial soundscapes because they show limited frequency partitioning. In contrast, in terrestrial soundscapes, frequency partitioning is often linked to species or a group of animals (Figure 5) (Krause, 2012). Coastal biological soundscapes are dominated by a broad band range (>30 kHz) of short transient snaps of invertebrates, with a low frequency resolution (Lossent et al., 2017) and a narrow (<2 kHz) low-frequency band occupied mainly by fish sounds. Coastal soundscapes, especially in coral reefs, are therefore characterized by mass biophonic phenomena with little frequency partitioning (Figure 5).

In some terrestrial environments, indices are not suitable for biodiversity monitoring without prior removal of biasing sounds, such as the anthropophony (Fairbrass et al., 2017) or anuran sounds in tropical forests (Eldridge et al., 2018). In a study on terrestrial soundscapes conducted in Japan, the comparison between acoustic indices and acoustic richness (i.e., the number of different sounds produced by animals) under different sonic conditions (e.g., presence or absence of wind, rain, and anthropophony) revealed that only two (AR and TE) out of the eleven tested indices reflected the measured richness across all the sonic conditions. Moreover, none of these indices correlated with the measured richness when masked by broadband insect stridulations (Ross et al., 2021). In our study, the indices were affected by background noise (Figure 1). In coral reefs, the major contributor to background noise is the biophony, such as sounds from snapping shrimps that are always present (Johnson et al., 1947; Au and Banks, 1998). Although their peak frequency is above 2 kHz, these sounds are usually broadband sounds and overlap the fish band (0.05–2 kHz). These broadband sounds affect indices, particularly those detecting peaks, such as NP. In addition, in coral reefs, a diurnal “background noise” band around 400 to 500 Hz is present and composed of transient short pulses attributed to Pomacentridae sounds (Figure 1) (Staaterman et al., 2013; Raick et al., 2023). This mass phenomenon in the fish band influences the indices. In the Polynesian Islands, the intensity of this “fish noise” was higher in shallow reefs than in deeper reefs (Raick et al., 2023), but the indices did not show the same trends depending on the depth. For example, the ACI and SPL_pp, which were positively correlated with the sound type richness, were higher at shallow depths, while the contrary was found for the SPL_rms, which was negatively correlated with the sound type richness. The indices that were positively correlated with the sound type richness, i.e., the number of fish sound types that were clearly identified and into which the detected sounds were classified, did not reflect this sound type richness, but they did quantify biological mass phenomena (e.g., the Pomacentridae sounds in shallow reefs). Consequently, none of the acoustic indices tested can inform on fish acoustic diversity. Even a combination of indices (Williams et al., 2022) within such a small, poorly stratified frequency band dominated by biophonic background noise cannot inform on fish sound acoustic diversity because it is not suitable for depicting subtle changes in sound types.

In addition, there was no correlation between most of the indices and the measured sound abundance in the natural environment. This is because the number of sounds in the background noise was higher than the number of sounds manually selected to measure the abundance and richness, i.e., those with a high signal-to-noise ratio allowing for the identification and classification of sounds into types. When testing the settings of the ADI and AEI, the only threshold that showed a link with the sound abundance was −10 dB, while in the controlled environment, this threshold was −50 dB, which implies an influence of the presence of mass acoustic phenomena. Moreover, to establish a link with the sound abundance, the ADI and AEI frequency bands (i.e., steps) had to be small (bandwidths of 10 to 100 Hz). Small bands also better correlated with the sound type richness, but both positively and negatively depending on the threshold. However, indices that work on frequency bands, such as the AEI or ADI, are appropriate when soundscapes are divided into bands, which is not the case in marine coastal soundscapes (or only partly the case). Indeed, coastal marine soundscapes, contrary to terrestrial soundscapes, are generally divided into a few overlapping bands: a low-frequency band (mainly fish sounds, some crustacean sounds, and sometimes whale sounds) and a high-frequency band (transient benthic sounds, and occasionally small cetacean sounds) (Figure 4). The band occupied by fish sounds (mainly below 2 kHz) is narrow and shows little frequency partitioning. Contrary to terrestrial environments, frequency bands in coastal marine soundscapes provide only poor ecologically relevant information on diversity.

Moreover, the use of the tested indices to assess fish sound diversity is problematic because fish sounds are typically drum-like sounds, of similar frequencies, composed of pulses or (pseudo-)harmonic sounds. If the frequency bands chosen in the settings are too small, such sounds would be detected in several bands. Bands would therefore “decompose” a sound type in different bands but would not be representative of different fish sound types. The type of fish sounds (e.g., knocks and herbivorous sounds vs. grunts, buzzes, and chirps) has been shown to impact some indices’ values (Bolgan et al., 2018; Dimoff et al., 2021). Similarly, in fish and frogs, indices have been suggested to be more limited with harmonic sounds than with single-pulsed sounds (Bolgan et al., 2018; Indraswari et al., 2020). Therefore, as dominating fish sounds are not the same everywhere, this can impact the indices and comparisons between sites. For example, in French Polynesia, the proportion of pulse series is known to vary between the photic and mesophotic reefs (Raick et al., 2023). Therefore, caution is needed when comparing the values of indices from one environment to another.

These different considerations lead to the conclusion that acoustic indices are not appropriate for studying fish sound diversity in marine coastal environments such as coral reefs. Indices, for example, may be used to report on the anthropophony, to study the geophony, to focus on high-frequency sounds produced by benthic invertebrates, or to study fish mass phenomena, but such usage was not inspected in the present study.

In this study, the use of manually chosen settings compared to default settings considerably increased the values of the correlations. Depending on the settings used, indices such as the ADI or the AEI could be correlated with the sound abundance or with the sound type richness. In addition, the sign of the correlation changed depending on the settings and, more importantly, the threshold used: low (around −10 dB) or high (under −50 dB). The same observations were made by Bohnenstiehl et al. (2018) with the ACI. They found negative correlations between the ACI and sound abundance of harmonic fish calls with a low frequency resolution (47–94 Hz), and positive correlations with a high frequency resolution (23 Hz). This is in agreement with other studies showing the high sensitivity of the ACI to settings such as the frequency resolution (Bolgan et al., 2018; Dimoff et al., 2021). When comparing the results of the controlled experiment in this study with those reported in 2018 for similar tracks (Bolgan et al., 2018), the correlation between the ACI and the sound abundance is completely different (ρ = 0.66 vs. ρ = −0.05). The differences could be due to slight changes in the software used (R vs. SoundscapeMeter (Farina et al., 2012)), which measure different ACI metrics (e.g., ACI_f vs. ACI_tot) and allow slightly different settings (e.g., presence or absence of a noise filter). In addition, the settings that allow the best representation of the sound abundance and sound type richness vary depending on the environment, e.g., temperate seas vs. coral reefs (Dimoff et al., 2021). This high sensitivity of the settings would pose a risk if acoustic diversity indices were to be widely used for habitat management or for informing on marine spatial planning.

TE was one of the two indices correlated with the sound abundance in both the controlled environment and in situ playbacks. In the natural environment, this index was the most impacted by biological “background” noise (i.e., the highest correlation observed with the sound type richness). The higher performance of TE compared to other indices and the impact of background noise have been underlined in terrestrial environments too (Ross et al., 2021). TE is known to perform well in the presence of a geophony (Ross et al., 2021) and anthropophony (Depraetere et al., 2012; Ross et al., 2021), which appear as temporally invariable low-frequency patterns in the soundscape (Pieretti et al., 2011). On the other hand, TE is known to be affected by background noise, the sound duration, and overlap (Gasc et al., 2017).

Correlations between H and the fish sound type richness were not observed, not even in the natural environment, where many of the indices were impacted by biological “background” noise. Similar observations were made in temperate reefs (Harris et al., 2016). These results are not caused by the absence of a link but by the intrinsic calculation of the index. H is designed to have low values for pure tones and high values for almost silent soundscapes or, on the contrary, noisy soundscapes across frequency bands. In the in situ playbacks, the values of H were always higher when the loudspeaker was silent. In addition, when the number of sound types emitted by the loudspeaker was increased from 1 to 2, H increased, but when the number of sounds was increased from 2 to 3, H decreased (Figure S1). This was observed for all the sound abundances tested. This shows that this index is not representative of the sound type richness because there is no linear relation between them.

The ADI and AEI were only correlated with the sound abundance in the controlled environment. In Indonesian coral reefs, the ADI and AEI were correlated with fish species richness (19% to 24% of the deviance explained), when calculated for a higher-frequency band: 1.2–11 kHz (Peck et al., 2021), which is the frequency band covered by benthic invertebrates’ snapping sounds (Nedelec et al., 2015; Raick et al., 2021). Similar to what is observed with H, low values of the AEI could relate to a near-silent, saturated, or windy terrestrial soundscape, while high values of the ADI could relate to a completely silent or a noisy soundscape.

At low frequencies (band: 0.1–1.2 kHz), Peck et al. (2021) found that only the ACI was affected by fish abundance (38% of the deviance explained). However, the use of the ACI in coral reefs is known to be impacted by a masking effect (Dimoff et al., 2021), for example, in chorus events (Staaterman et al., 2017). Therefore, a single fish species can have a considerable effect on indices because they respond to mass phenomena (Staaterman et al., 2017; Bolgan et al., 2018). Moreover, when considering higher-frequency bands, typically dominated by snapping shrimps’ broadband sounds, indices such as the ACI saturate at high snap rates (Bohnenstiehl et al., 2018).

Using simulated bird recordings, Gasc et al. (2015) showed that some indices are affected by the sound duration in comparison to the file duration (S/R ratio; H, SE, TE, M, and ACI), background noise (H, SE, TE, M, AR, and ACI), type of sound (NP and ACI), relative amplitude (AR), and overlap (H, SE, TE, M, and ACI) (Gasc et al., 2015). Therefore, to correctly reflect the acoustic biodiversity, particularly of a group of animals, indices should be insensitive to the (1) S/R ratio, (2) background noise, (3) type of sound (i.e., should be equally sensitive to different types of sounds (e.g., pulse series vs. upsweeps)), (4) relative amplitude of the sounds, and (5) sound overlap (Gasc et al., 2015).