A Complexity-Entropy Based Approach for the Detection of Fish Choruses

Automated acoustic indices to infer biological sounds from marine recordings have produced mixed levels of success. The use of such indices in complex marine environments, dominated by several anthropogenic and geophonic sources, have yet to be understood fully. In this study, we introduce a noise resilient method based on complexity-entropy (hereafter named C-H) for the detection of biophonic sounds originating from fish choruses. The C-H method was tested on data collected in Changhua and Miaoli (Taiwan) during the spring in both 2016 and 2017. Miaoli was exposed to continual shipping activity, which led to an increase of ~10 dB in low frequency ambient noise levels (5–500 Hz). The acoustic dataset was successively analyzed via the acoustic complexity index, the acoustic diversity index and the bioacoustic index. The C-H method was found to be strongly correlated with fish chorusing (Pearson correlation: rH < −0.9; rC > 0.89), and robust to noise originating from shipping activity or natural sources, such as wind and tides (rH and rC were between 0.22 and −0.19). Other indices produced lower or null correlations with fish chorusing due to missed identification of the choruses or sensitivity to other sound sources. In contrast to most acoustic indices, the C-H method does not require a prior setting of frequency and amplitude thresholds, and is therefore, more user friendly to untrained technicians. We conclude that the use of the C-H method has potential implications in the efficient detection of fish choruses for management or conservation purposes and could help with overcoming the limitations of acoustic indices in noisy marine environments.


Introduction
Underwater sound exists throughout the world's oceans. Recently, the issue of an increasing contribution from human activities into the marine environment has received increased focus from scientists and international institutions [1-3]. Augmented noise input from human activities in the ocean originates mainly from continual shipping, offshore and coastal construction and industrialization, and such noise has been found to produce severe negative impacts on marine species [4][5][6][7][8][9][10]. To quantify the abundance, behavior and diversity of species in relation to noise effects, one must develop efficient and reliable monitoring tools. Recently, passive acoustic monitoring (PAM) has been used for the long-term monitoring of marine biodiversity and as a proxy for population health [11][12][13][14]. The implementation of PAM has resulted in the collection of vast datasets [15]. Nevertheless, extracting significant details regarding marine communities or specific species remains a challenging task [16,17].

Data Measurements
Passive acoustic recorders were deployed in two regions, Changhua (A1) and Miaoli (N1), located approximately 4.5 km off the Eastern Taiwan Strait (ETS) (Figure 1). A1 and N1 are 90 km apart located in the Taiwan Strait and are composed of sandy bottoms and hard sedimentary rocks at 20 to 25 m of depth. Monitoring duration, depth of recorders and geographical coordinates of both recording stations are reported in Table 1. The recordings were performed utilizing wildlife acoustics SM3M (sensitivity −164.5 dB re 1 µPa; flat frequency response (±0.1 dB) between 0.1 to 10 kHz). Acoustic files of 60 min were recorded continuously with a sampling frequency of 48 kHz, wav format, encompassing ~3840 h and ~1.3 TB of acoustic recordings. Diverse sources of sounds affect the composition of the acoustic environment of both areas. The northeast monsoon in winter and the southwest monsoon in summer are the primary factors affecting the wind and current variations around Taiwan [45]. Every year the ETS experiences several tropical storms, accompanied by strong wind speeds. These extreme meteorological conditions cause the sea's tidal level rise and flooding to occur, thus triggering sediment transport and noise due to the collision of sediment grains. Noise from maritime activities is also present at the study sites. In particular, Long Feng fishing harbor is situated 5 km from N1, causing dense vessel activity in that area. Fishes at both A1 and N1 are the major contributors to the biological sounds. Sciaenidae species are found abundantly at the ETS and are known to produce choruses [46,47]. These species are commonly addressed as croakers or drums. The chorusing is carried-out for attracting mates during spawning, communication and social cohesion. Indo-pacific humpback dolphins and bottlenose dolphins are also known to inhabit the ETS [48,49].

Data Measurements
Passive acoustic recorders were deployed in two regions, Changhua (A1) and Miaoli (N1), located approximately 4.5 km off the Eastern Taiwan Strait (ETS) (Figure 1). A1 and N1 are 90 km apart located in the Taiwan Strait and are composed of sandy bottoms and hard sedimentary rocks at 20 to 25 m of depth. Monitoring duration, depth of recorders and geographical coordinates of both recording stations are reported in Table 1. The recordings were performed utilizing wildlife acoustics SM3M (sensitivity −164.5 dB re 1 µPa; flat frequency response (±0.1 dB) between 0.1 to 10 kHz). Acoustic files of 60 min were recorded continuously with a sampling frequency of 48 kHz, wav format, encompassing~3840 h and~1.3 TB of acoustic recordings. Diverse sources of sounds affect the composition of the acoustic environment of both areas. The northeast monsoon in winter and the southwest monsoon in summer are the primary factors affecting the wind and current variations around Taiwan [45]. Every year the ETS experiences several tropical storms, accompanied by strong wind speeds. These extreme meteorological conditions cause the sea's tidal level rise and flooding to occur, thus triggering sediment transport and noise due to the collision of sediment grains. Noise from maritime activities is also present at the study sites. In particular, Long Feng fishing harbor is situated 5 km from N1, causing dense vessel activity in that area. Fishes at both A1 and N1 are the major contributors to the biological sounds. Sciaenidae species are found abundantly at the ETS and are known to produce choruses [46,47]. These species are commonly addressed as croakers or drums. The chorusing is carried-out for attracting mates during spawning, communication and social cohesion. Indo-pacific humpback dolphins and bottlenose dolphins are also known to inhabit the ETS [48,49].

The Complexity-Entropy Method
The information content of a system is typically computed from a probability distribution P describing the distribution of some observable quantity. An information measure can primarily be viewed as a quantity that characterizes that given probability distribution. Shannon entropy is utilized as a measure to quantify the information content of a system. Given any arbitrary probability distribution P = p i : i = 1, . . . , M , the Shannon's logarithmic information, is regarded as the measure of the uncertainty associated with the physical process described by P. When S[P] = 0, it is possible to predict with complete certainty, which of the possible outcomes i (the probabilities of which are given by p i ) will actually take place. In this instance, the underlying process described by the probability distribution is the maximum compared to a uniform distribution [50].
Nevertheless, an entropy measure cannot quantify the degree of structure or patterns present in a process [51]. Moreover, it was shown that measures of complexity can quantify the degree of correlation structures. This kind of information is not discriminated by randomness measures. The opposite extremes are perfect order and maximal randomness (for example, a periodic sequence and white noise). The statistical complexity measure (C) introduced by Lamberti et al. [52] can provide a wide range of possible degrees of correlation structure between these extremes. Statistical complexity can detect essential correlation structures and provides important additional information regarding the characteristics of the underlying probability distribution, which entropy cannot detect. Statistical complexity (C) is a function of P and is defined through the product [53]  ]/2 as the Jensen-Shannon divergence, and Q 0 , a normalization constant being the inverse of the maximum possible value of J[P, P e ]. This value is obtained when one of the components of P, say p m = 1, and the remaining components are equal to zero. The Jensen-Shannon divergence quantifies the difference between the probability distribution P and P e [54]. C is not a trivial function of the entropy because it depends on two different probabilities' distributions: the one associated with the system under analysis, P, and the uniform distribution, P e . Furthermore, for each given value of the normalized permutation entropy H s [P] ∈ [0, 1], there is a range of possible values of complexity, C min ≤ C ≤ C max . The usual procedure for evaluating the bounds C min and C max is given in Martin et al., 2006 [55]. Thus, it is clear that important additional information related to the correlational structure between the components of the physical system is provided by evaluating C.
To calculate H S and C, an associated probability distribution should be constructed. The probability distribution is evaluated by using the method introduced by Bandt and Pompe [40]. This method considers the time causality of the system dynamics, performed by employing a suitable partition based on ordinal patterns obtained by comparing neighboring values of the original series. For a given time series x(t) N t = 1 , of an embedding dimension d > 1, and an embedding delay time τ, the ordinal pattern of order d generated by has to be considered. To each time s, we assign a d-dimensional vector that results from the evaluation of the time series at times s − (d − 1) τ, . . . , s − τ, s. Clearly, the higher the value of d, the more the information about the past that is incorporated into the ensuing vectors. By the ordinal pattern of order d related to time s, we mean the permutation π = (r 0 , r 1 , . . . , r D−1 ) of (0, 1, . . . , d − 1) defined by In this manner, the vector defined by Equation (3) is converted into a unique symbol π. For instance, if we assume a time series {7, 3, 4, 5, 2, 9, . . . } with embedding dimension d = 4 and embedding delay τ = 1, the state space is divided into 4! partitions, and 24 mutually exclusive permutation symbols are considered. The first four-dimensional vector is (7,3,4,5). According to Equation (3), this vector corresponds to (x s−3 , x s−2 , x s−1 , x s ), Following Equation (4), it yields x s−3 ≥ x s ≥ x s−1 ≥ x s−2 . Then, the ordinal pattern which satisfies Equation (4) will be (3, 0, 1, 2). The second four-dimensional vector is (3, 4, 5, 2) and (1, 2, 3, 0) will be its associated permutation, and so on. For all the D! possible permutations π i of order d, their associated relative frequencies can be naturally computed by the number of times this particular order sequence is found in the time series divided by the total number of sequences. Thus, an ordinal pattern probability distribution P = p(π i ), i = 1, . . . , d! is obtained from the time series. Determining the embedding dimension d and the time delay τ are necessary to evaluate the appropriate probability distribution, particularly for d, which determines the number of accessible states given by d!. Moreover, it was established that the length N of the time series must satisfy the condition N d! in order to obtain reliable statistics [56]. For practical purposes, Bandt and Pompe suggested d = 3, . . . , 7 and embedding delay τ = 1 [40].
The above discussed, the normalized Shannon entropy H S -Equation (2), and the statistical complexity C-Equation (1), are calculated using the permutation probability distribution P = p(π i ), i = 1, . . . , d! . Defined in this manner, these quantifiers are typically referred to as permutation entropy (H) and permutation statistical complexity (C) [57]. The H and C produce complementary information about two distinct properties of a data set. Permutation entropy quantifies the degree of disorder inherent in a process, where more predictable signals, which demonstrate a tendency to repeat just a few fluctuation patterns, have lower permutation entropy than less predictable signals (which tend to exhibit all the possible fluctuation patterns). For a given entropy value, the statistical complexity quantifies the degree to which there exists privileged fluctuation patterns among those patterns accessible to the system. By calculating these quantities for a given time series, both randomness and the degree of correlational structures in the fluctuations of the system are evaluated simultaneously [41]. Complexity and entropy were evaluated using the R package 'statcomp' (Version 0.0.1.1000) [58] using the command global-complexity(), for embedding dimension d = 6, and to evaluate the C max and C min , command limit_curves(d, fun = 'min/max') is utilized (R code is provided in Supplementary Materials Section S7).

Computation of Acoustic Indices
In this study, we utilized three AIs, namely ACI [29], ADI [30,31] and BI [32], to explore the detection capability of fish chorusing and to verify the robustness of these indices to anthropogenic noise. ACI measures the sound intensity in different, short duration frequency bins, yielding high ACI values for biophony from fish calls and low values in the presence of constant sounds originating from anthropophony from shipping and ambient noise. ADI calculates the Shannon's diversity index to evaluate spectrum complexity along width-prefixed frequency bins and evaluates the degree of variation of energy along frequencies of a selected portion of the spectrogram, thus yielding high ADI values when biophony occurs. BI is the area under the power spectrum curve across the specified range of frequencies occupied by the biophony and is used to describe the proportion of this acoustic space that occupies a recording. These acoustic indices were calculated using the R (version 3.4.1) [59] package 'soundecology' (version 1.3.2) [60]. ACI and BI were applied to the frequency range 10-3500 Hz with an Fast Fourier Transform (FFT) of 2048 points (frequency resolution 39.06 Hz; temporal resolution 0.026 s) and a cluster size of 60 s for ACI computations. For calculating ADI, the maximum frequency was set to 3500 Hz, fixing a resolution of 200 Hz and a threshold of −50 dB.

Data Analysis and Statistics
Spectrograms and sound pressure levels (SPLs) were computed using PAMGuide [61] with an FFT size of 1024 points and a 1-s time segment averaged to 60-s resolution via the Welch method. Mean (RMS), median and 95th percentile SPLs were calculated for the frequency bands 50 to 200 Hz and 500 to 2500 Hz, which were chosen as reference bands for quantifying low frequency anthropogenic noise and fish chorusing, respectively. Most of the fish chorusing was observed in the frequency band 500 to 2500 Hz, hence this was chosen as a reference band for chorusing activity and to avoid the effect of anthropophony occurring at other frequencies. To explore the circadian pattern of the fish chorusing, the hourly RMS (mean), SPL (500-2500 Hz) and standard deviation (SD) were evaluated at A1 and N1 for both years.
To assess the fish chorus detection of AIs and C-H, we firstly compared hourly mean SPL 500-2500Hz with hourly AIs and C-H of two recording days (h24) at A1, precisely, on 4 and 26 April 2016. Successively, we analyzed four days characterized by different levels of fish chorusing and noise: (a) intense dawn and dusk chorusing with sediment-generated noise; (b) mild dawn and dusk chorusing with vessel and sediment-generated noise; (c) mild dawn chorus with noise from 18 vessels (observed during 24 h); (d) absence of chorusing with continual, sediment-generated noise. Hourly ACI, ADI, BI and C-H were used for the analyses. A complexity-entropy plane H × C was built to show the variation of the complexity as a function of its entropy. This plane was utilized to study changes in the dynamics (randomness and correlation structure) occurring in the acoustic recordings.
Successively, AIs and C-H methods were extended to the complete monitoring at A1 and N1, during the spring periods of the years 2016 and 2017 (Table 2), with the aim of comparing their ability to infer fish choruses in long-term analysis. All indices and SPL were normalized by subtracting the minimum in the series, then dividing by the new maximum of that series. A Pearson correlation was applied to verify the relationship between indices and SPL 500-2500Hz , at three time periods: Dawn (00:00-05:00), Dusk (18:00-23:00) and 06:00-17:00. A second Pearson correlation between hourly mean SPL 500-2500Hz and indices was also performed on the entire acoustic dataset without considering the hour of the day as a grouping factor. Due to the fact that some of the noise affected the 500 to 2500 Hz frequency band, which was used as reference for chorusing activity, a complementary Pearson correlation was performed between indices and SPL obtained from the frequency band of 50 to 200 Hz. SPL  Hz was selected to be representative of the noise disturbance for both vessels and sediment transportation but not of fish calls. This step was intended to assess whether indices' results were influenced by noise. In order to minimize the chance of including noise in SPL 500-2500Hz and to make this measure a better proxy of fish choruses, we used the SPL value only during the fish chorusing hours (i.e., 00:00-05:00 and 18:00-23:00) and used zero in the remnant hours of the day.
Furthermore, we verified the accuracy of the AIs and the C-H method by manually listening to the acoustic recordings for the fish choruses and by annotating the presence (1) or absence (0) of choruses. For this purpose, we chose 10 days (n = 240 h) of acoustic files for which we computed the response of the AIs and the C-H method. A confusion matrix [62] was built to summarize the performance of the indices based on the binary classification, and was formed by two dimensions: (1) fish chorus (presence/absence); (2) chorus detected by the acoustic index (yes/no). The threshold of detection was chosen to be >0.5 for ACI, ADI, BI and C, and <0.5 for H. This classification created: (a) true positives (TP); i.e., the index detected the chorus when the chorus was actually present; (b) false positives (FP); i.e., the index detected the chorus when the chorus was not present; (c) true negatives (TN); i.e., the index did not detect the chorus when the chorus was not present; (d) false negatives (FN); i.e., the index did not detect the chorus when the chorus was present.
Based on those metrics, the accuracies and errors are given by Equations (5) and (6): Error Finally, at location A1 and N1 for the monitoring duration mentioned in Table 1, the four-dimensional plot constructed represents hourly variation (z-axis) of H (x-axis) and C (y-axis), and the corresponding hourly mean SPL 500-2500Hz (fourth dimension) is represented as a color bar.

General Soundscape Features
The underwater noise levels at monitoring regions A1 and N1 were dominated by fish chorusing at~500 to 2500 Hz (Figure 2, labelled as X). Diverse noise inputs were recorded at A1 in 2017 ( Figure 2b): pile driving at~10 to 30 Hz (labelled as A); fishing boats passing in close proximity of the hydrophone (labelled as C) at~10 to 150 Hz; and high waves and currents causing impact of sediment particles with the PAM recorder, resulting in noise at~10 to 70 Hz (labelled as B). Sound levels at N1 were heavily influenced at~50 to 200 Hz by continual vessel noise throughout the acoustic monitoring period (Figure 2c,d, labelled as Y). Table 3 shows mean (RMS), median and 95th percentile SPLs. Due to continual shipping activity, the low frequency  sound levels at N1 (95th percentile) werẽ 10 dB higher than in A1.
Finally, at location A1 and N1 for the monitoring duration mentioned in Table 1, the fourdimensional plot constructed represents hourly variation (z-axis) of H (x-axis) and C (y-axis), and the corresponding hourly mean SPL500-2500Hz (fourth dimension) is represented as a color bar.

General Soundscape Features
The underwater noise levels at monitoring regions A1 and N1 were dominated by fish chorusing at ~500 to 2500 Hz (Figure 2, labelled as X). Diverse noise inputs were recorded at A1 in 2017 ( Figure  2b): pile driving at ~10 to 30 Hz (labelled as A); fishing boats passing in close proximity of the hydrophone (labelled as C) at ~10 to 150 Hz; and high waves and currents causing impact of sediment particles with the PAM recorder, resulting in noise at ~10 to 70 Hz (labelled as B). Sound levels at N1 were heavily influenced at ~50 to 200 Hz by continual vessel noise throughout the acoustic monitoring period (Figure 2c,d, labelled as Y). Table 3 shows mean (RMS), median and 95th percentile SPLs. Due to continual shipping activity, the low frequency (50-200 Hz) sound levels at N1 (95th percentile) were ~10 dB higher than in A1.             ACI produced spurious peaks from~00:00 to 19:00 on 9 April (Figure 4b) and from~09:00 to~15:00 on 26 April (Figure 4h). ACI failed to detect the dusk and dawn choruses. In particular, this technique displayed a deep decrease at~03:00 on the 26th, corresponding to the dawn chorus, and it showed low values corresponding to dusk choruses of both days. ACI showed decreasing values with noise at low frequencies (10-300 Hz), and higher values with fish calls when not grouped in dense choruses.

Fish Chorus Detection Performance of AIs and the C-H Method
On 9 and 26 April, the ADI values (Figure 4c,i) exhibited peaks at the chorusing hours, similar to SPLs. Nevertheless, additional false peaks occurred at~06:00 to 10:00 on the 9 and at~07:00 on 26 April.
The BI detected dusk choruses peaking at~20:00 on both the 9 and 26 April. It failed to detect the dawn chorus on 9 April, but produced a false peak at~06:00. On 26 April, BI detected the dawn chorus~03:00 but produced other peaks at~07:00 (Figure 4d,j).
C and H produced peaks and dips, respectively, during the same time periods of the peaks in SPL. In particular, during the fish chorusing hours, C produced peaks similar to those of SPLs, mostly at dawn but also at dusk (Figure 4e (milder on the 4 April, more prominent on the 26 April). Intense chorusing activity occurred around dusk (17:00-21:00). As a result, SPL500-2500Hz peaked during these periods.   To have complete comprehension of the results, we investigated the properties of the C-H method by applying it to four distinct cases characterized by noise occurrence (Figure 5), discussed as follows.
Case 1: Intense dawn and dusk chorusing and sediment-generated noise. Figure 5a depicts the dawn and dusk chorusing (~113 dB) and noise due to sediment transport (Figure 5a, label A). C and H produced peaks and dips during the dawn and dusk chorusing hours (Figure 5e,i). Beyond the chorusing hours, H and C remained invariant to any other noise occurring in the recording. It can be observed on the C-H plane that, during the chorusing periods, H and C fall on the left-side of the plane (Figure 5m, label F), and the periods without chorusing are gathered on the right-side of the plane (Figure 5m, label N).

Case 2:
Mild dawn and dusk chorusing with vessel and sediment-generated noise. Figure 5b demonstrates the point about noise from vessel reaching higher frequencies and covering fish sounds when it is high amplitude (labelled as B and D) and from sediment transportation (labelled as C). The dawn chorusing from~00:00 to 05:00 was detected by H and C from~02:00 (Figure 5f,j). H and C scantly responded to the dusk chorusing and to vessel noise at~17:00 (label D). H and C, however, did not respond to vessel noise (Label B) and high-intensity sediment noise at~12:00 tõ 14:00 (Label C), respectively. On the C-H plane, the C and H during dawn chorus hours (Figure 5n, label F) were separated from the hours when chorusing was absent (Figure 5n, label N).
Case 3: Mild dawn chorus with noise from~18 vessels. Figure 5c shows a 24-h recording with dawn chorusing between~02:00 to 04:00 with~18 vessel passages in the background. H and C responded to the chorusing (Figure 5g,k), and outside chorusing hours, remained relatively constant (H ≈ 0.85 and C ≈ 0.27). As a result, the chorusing hours on the C-H plane were isolated from the others (Figure 5o).

Case 4:
Absence of chorusing with continual, sediment-generated noise. Figure 5d shows the continual sediment noise. H remained high, at~0.88, whereas C was low at 0.2, throughout the 24 h (Figure 5h,l). On the C-H plane, H and C for all periods were accumulated on the right-side of the plane (Figure 5p).
Similarly, we tested the AIs on the four cases ( Figure 6). The ACI dipped when the fish calls became dense (Figure 6e-g) and thus was not able to catch the main fish chorusing hours, increasing for some intense and intermittent sediment-generated noise (Figure 6f). The ADI was high during the fish chorusing (Figure 6i,j) and non-chorusing hours (Figure 6j,k), but lowered for intense noise from vessels and sediments (Figure 6i,j). The BI was not consistent with fish chorusing and increased with vessel and sediment noise (Figure 6m-o). Similarly, we tested the AIs on the four cases ( Figure 6). The ACI dipped when the fish calls became dense (Figure 6e-g) and thus was not able to catch the main fish chorusing hours, increasing for some intense and intermittent sediment-generated noise (Figure 6f). The ADI was high during the fish chorusing (Figure 6i,j) and non-chorusing hours (Figure 6j,k), but lowered for intense noise from vessels and sediments (Figure 6i,j). The BI was not consistent with fish chorusing and increased with  When extending the analysis to the entire dataset, the Pearson correlations between the normalized hourly means of the results from indices and SPLs gave various results (Supplementary Figures S4 and S5). At both A1 and N1, ACI, ADI and BI produced inconsistent and lower r values, during and beyond the chorusing hours. The C positively correlated with both the dawn and dusk chorus with r > 0.9 (Supplementary Figures S4d,i, and S5d,i) and H negatively correlated with chorusing, thereby yielding r < −0.9 (Supplementary Figures S4e,j, and S5e,j).
Results from the second Pearson correlation between hourly means SPL500-2500Hz and indices are shown in Table 3. A highly significant correlation with SPL500-2500Hz was found for H (−0.9 < r < −0.98; p ≈ 1) and C (0.89 < r < 0.95; p ≈ 0) for both sites and duration of monitoring (as in Table 2). ADI had correlation 0.61 < r < 0.81; p < 0.001, which was followed by BI's (0.4 < r < 0.79; p < 0.001). A particularly weak linear relationship was found with ACI (−0.31 < r < −0.11). Weak or null correlations were found between hourly means SPL50-200Hz and indices, with higher r presented by ADI in N1 (r = −0.41; p ≈ 0.19). In particular, C and H showed an r close to zero.
The confusion matrix created from the manual annotation of fish choruses in 240 acoustic files revealed high accuracy rates of H and C (95% and 83%, respectively; Figure 7j,k). The other AIs When extending the analysis to the entire dataset, the Pearson correlations between the normalized hourly means of the results from indices and SPLs gave various results (Supplementary Figures S4 and S5). At both A1 and N1, ACI, ADI and BI produced inconsistent and lower r values, during and beyond the chorusing hours. The C positively correlated with both the dawn and dusk chorus with r > 0.9 (Supplementary Figures S4d,i and S5d,i) and H negatively correlated with chorusing, thereby yielding r < −0.9 (Supplementary Figures S4e,j and S5e,j).
Results from the second Pearson correlation between hourly means SPL 500-2500Hz and indices are shown in Table 3. A highly significant correlation with SPL 500-2500Hz was found for H (−0.9 < r < −0.98; p ≈ 1) and C (0.89 < r < 0.95; p ≈ 0) for both sites and duration of monitoring (as in Table 2). ADI had correlation 0.61 < r < 0.81; p < 0.001, which was followed by BI's (0.4 < r < 0.79; p < 0.001). A particularly weak linear relationship was found with ACI (−0.31 < r < −0.11). Weak or null correlations were found between hourly means SPL  and indices, with higher r presented by ADI in N1 (r = −0.41; p ≈ 0.19). In particular, C and H showed an r close to zero.
The confusion matrix created from the manual annotation of fish choruses in 240 acoustic files revealed high accuracy rates of H and C (95% and 83%, respectively; Figure 7j,k). The other AIs registered lower levels of accuracy (ACI: 60%, ADI: 59% and BI: 73%, respectively) and higher error rates (Figure 7g,i). registered lower levels of accuracy (ACI: 60%, ADI: 59% and BI: 73%, respectively) and higher error rates (Figure 7g,i).

Discussion
In this study, we introduced a technique based on the C-H method for detecting fish choruses and compared its detection performance with AIs, such as ACI, ADI and BI. It was shown that the chosen AIs were not consistent for detecting the fish chorusing, instead producing spurious detections, during chorusing hours. AIs resulted in low detection accuracy rates, whereas the

Discussion
In this study, we introduced a technique based on the C-H method for detecting fish choruses and compared its detection performance with AIs, such as ACI, ADI and BI. It was shown that the chosen AIs were not consistent for detecting the fish chorusing, instead producing spurious detections, during chorusing hours. AIs resulted in low detection accuracy rates, whereas the introduced, C-H method showed accuracies of 95% and 83%. Moreover, H and C were significantly correlated with the fish chorusing. The C was found to be positively correlated with the fish chorusing, whereas H was negatively correlated, thus resulting in |r| > 0.9.
In this study, ACI decreased in the presence of dense fish chorusing activity (Figure 6e at~02:00 and~20:00; Figure 6f at~04:00; Figure 6g at~03:00). Nevertheless, ACI increased when there was mild chorusing activity (Figure 6f at~00:00-01:00 and~18:00-19:00; Figure 6g at~00:00-01:00). Hence, ACI was able to detect the chorusing by increasing values when the fish started to aggregate songs but, as the chorus intensified, ACI tended to severely decrease. Studies in [23,33] noticed similar behavior of ACI, leading to the consideration that it fails to detect situations where calls or songs are so dense and undiscernible that they are interpreted by the index as a continuous sound. Indeed, ACI was designed to detect variation in intensities over time (milliseconds) but not constant sounds, such as vessel noise or compact fish choruses. ACI was found to decrease for the two loud vessel transits (Figure 6f at~08:00 and~17:00) and to relatively remain invariant (ACI ≈ 3800) for the transit of~18 vessels in the background (Figure 6g). Contrarily, a study in [26] found that ACI increased for vessel noise. Further, ACI tended to decrease for mild sediment noise of short durations (~15 min) (Figure 6e at~09:00; Figure 6h at~18:00). When the sediment noise became louder and longer, however, ACI was not able to filter it (Figure 6f at~12:00-14:00; Figure 6h at~05:00-07:00). Studies have utilized amplitude [26] and frequency filters [26,56] for improving the detection capability of ACI, but such refining was sometimes insufficient to catch the peak of the chorus faithfully [21].
ADI increased for the dawn and dusk fish chorusing activity (Figure 6i-k). Accordingly, ADI showed r ≥ 0.6 during the chorusing hours (Table 4). ADI remained high for vessel transits (Figure 6j at~17:00; Figure 6k). The study in [26] also demonstrated that ADI was influenced by vessel noise and responded to some sediment noise by producing peaks (Figure 6i at~12:00-13:00 and at~10:00-18:00). It is evident from Figure 6l that, for sediment noise occurring throughout the 24-h recording period, ADI exhibited random low and high values.
Long-term analysis of data from AIs failed to detect chorusing periods effectively and produced spurious detections beyond chorusing hours (Supplementary Figure S6). AIs work on the principle of evaluating energy and its variations in the recordings measured in terms of power spectrum and Shannon's entropy in the specified frequency range or over a selected amplitude threshold [20,61,63]. Nevertheless, when dealing with fish songs and long-term recordings, selecting these parameters can be elusive because it is likely that anthropophony will occur in the specified frequency range (as in Figure 5). Recently, a study [64] utilized an unsupervised clustering approach for detection of fish chorusing in a quiet environment. Those unsupervised techniques require prior knowledge of the fish calls. This may not be a reliable method for determining long-term fish chorusing trends in a natural habitat, where many fish species still remain unidentified.
The C-H method tested in this study was found to be efficient in addressing fish chorusing even in the presence of anthrophonies and geophonies. Consequently, it proved to be a useful tool to extract fish chorusing from acoustic recordings. This method does not require a specified amplitude threshold and frequency range. Rather, it works on the principle of extracting the information by attempting to quantify the randomness and correlations present in the acoustic recordings. Because, H is negatively correlated with the chorusing, it produces a dip during the chorusing hours. Contrarily, C is positively correlated with the fish chorusing; hence, it peaks during the chorusing hours, resembling the peaks in SPL (Figures 4-7). The C-H method requires one to choose the embedding dimension 3 ≤ d ≤ 7, and the selection of d is simple and flexible. It is shown that C and H remains robust to varying d (see Supplementary Figure S3), and it is recommended to utilize higher d = 6, 7 to retrieve more information, such as correlation structure and randomness from the acoustic recordings [50].
On the C-H plane (Figure 5m), the white noise located on the extreme right of the plane suggests that it is highly random (high H ≈ 0.93) and has no correlation structure (low C ≈ 0.13). The sine series is located on the extreme left of the plane, exhibiting determinism (low H ≈ 0.34) and increased correlation structure (high C ≈ 0.31). In the time period during the absence of fish chorusing, C and H lie on the right side of the plane. Similar to the position of white noise on the plane, as the fish chorusing starts, C and H tend to move left of the plane (Figure 5m-p). When the chorusing intensifies, C and H move close to the position of the sine signal (Figure 5m-p). This behavior occurs because fish chorusing will increase the correlation structure (C increases) and decrease the randomness (H decreases) in the background noise.
As the intensity and the duration of the chorus diminish, H (randomness) increases and C (correlation structure) tends to decrease. As a result, H and C move towards the right side of the plane (Figure 5m-p). In the absence of the fish chorusing, H and C remain relatively constant (Figure 5h,l,p). For instance, in a 24-h recording, where~18 vessels transited and the dawn chorus occurred, the C-H method was robust to vessel passage and was able to detect the dawn chorus effectively (Figure 5c,g,k,o). On another day, C-H slightly responded to the vessel transit, which was heard for~2 h (Figure 5f,j). This increase occurred because the long-duration vessel transit is composed of continual tones, which cause C in the acoustic time series to increase and H to reduce.
Our long-term data collected is well suited for understanding these AIs in terms of the robustness to different anthrophony and geophony. Several sources of anthrophony exist in the long-term recordings, including noises from various short-duration industrial and construction activities, seismic survey air gun blasting, noise from fishing vessels with various types of engines and long-duration noise from constant distant shipping. Together, that all forms an ideal complex marine soundscape to evaluate the performance of AIs in detection of fish choruses. The establishment of efficient AIs for studying the variation of the dawn and dusk fish-chorusing trend will enable better understanding of species-specific ecology and behavior, based on acoustically derived information, such as abundance of calls, temporal occurrence and seasonal variability. The validation of ad hoc indices for automatic detection of biophony in marine environments could further facilitate the evaluation of the impact of anthropogenic disturbances [21,33]. This study shows the importance of application of effective AIs in establishing long-term biophony trends.

Conclusions
Marine acoustic biological activity could function as a highly suitable proxy for addressing trends in biodiversity levels and the functionalities of the ecosystems. In order to do so, adapted automatic information procedures able to discern biological sounds from other sources (anthropogenic or geophonic) are, today, in strong demand. The C-H method was herein tested in marine environments and intended to fill the gaps left by other indices that were ideated and firstly used for terrestrial sites. The C-H method was found to be strongly correlated with fish chorusing and not influenced by noise originating from shipping activity or natural sources, such as wind and tides. Future studies could apply C-H to terrestrial or freshwater recordings, where it could potentially be of help, particularly in those environments characterized by periodic overlapping choruses (such as bird dawn choruses) or where sounds produce high saturation of the spectrograms. The C-H method may also be extended for the detection of cetacean vocalizations, but other research is needed to verify this approach on different targets. Placed beside other existing acoustic indices, the C-H method could represent a complementary measure to determine changes in the composition of animal communities and help managers and decision-makers monitor wildlife.