FishDiveR: Wavelet analyses and machine learning provide robust classification of animal behaviour from time-depth data

FishDiveR: Wavelet analyses and machine learning provide robust classification of animal behaviour from time-depth data | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Method Article FishDiveR: Wavelet analyses and machine learning provide robust classification of animal behaviour from time-depth data Calvin S. Beale, Jenna L. Hounslow, Angela J.E. Beer, Matias Braccini, and 10 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6907076/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 22 Jan, 2026 Read the published version in Movement Ecology → Version 1 posted 9 You are reading this latest preprint version Abstract 1. Biologging devices have revolutionised our understanding of aquatic animal movement by enabling the collection of detailed depth and temperature time-series. The advent of pop-up satellite archival tags has been particularly impactful, facilitating the collection of tens of thousands of depth time-series (DTS) datasets, with deployment periods ranging from days to years. Datasets from recovered tags are more detailed than those transmitted via satellite, yet both are commonly reported with rudimentary histograms of time-at-temperature and time-at-depth. Such histograms often fail to capture the complex temporal dynamics of vertical movements that are available from the high sampling frequency time-series in recovered tags. 2. This study describes a robust and effective method for the quantitative analysis of large DTS datasets collected from archival tags, utilising continuous wavelet transformation (CWT), Principal Component Analysis (PCA), and k-means clustering. CWT was employed to detect key periodic patterns within the data. Daily wavelet components were calculated across different wavelet periods (e.g., 5-min through 24-h) and reduced via PCA to characterise daily vertical movement behaviour while preserving variance. Finally, unsupervised k-means clustering was used to classify vertical movement behaviours according to their wavelet components and depth summary statistics. 3. This approach efficiently processed large quantities of data, and validation using simulated data demonstrated its robustness and versatility, with assigned behaviour clusters matching the original simulated behaviour types with high accuracy (97.7%). For the empirical data, distinct behavioural clusters were identified across a wide range of species, including an oceanic manta ray Mobula birostris , whale shark Rhincodon typus , Atlantic cod Gadus morhua , and largetooth sawfish Pristis pristis . Down sampling of the DTS revealed the method to be somewhat insensitive to the sampling frequency of tags, maintaining 83.9% accuracy as sampling frequency decreased from one to 15-minutes. 4. These results not only underscore the method's efficacy but also highlight its broad applicability in diverse settings. To facilitate uptake of this approach, an R package FishDiveR , tailored for the implementation of this analytical methodology has been developed. Behaviour classification k-means clustering satellite archival tags principal component analysis R package vertical movement sampling frequency Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 1. Background The advent of animal-attached time-depth recorders (TDRs), and more recently, transmission of this data via satellite (e.g., Pop-up satellite archival tags - PSATs) has revolutionised the study of aquatic species [ 1 – 4 ]. Over the past three decades, this growing body of work has highlighted diverse and complex vertical movements of some of the most intractable species occupying nearshore, coastal, and pelagic environments [ 5 – 7 ]. For example, depth time-series (DTS) data have revealed how changes in both large- and meso-scale oceanographic conditions influence the vertical distribution of marine predators [ 7 – 9 ], as well as identifying scaling laws in marine predator search behaviour [ 1 ]. Vertical movement is generally considered to be a powerful representation of animal behaviour, since pronounced gradients in environmental conditions, such as temperature, light, and dissolved oxygen, are encountered over small scales (< 100m), unlike horizontal movements where similar gradients may occur over 100s to 1000s of kilometres [ 3 ]. In an applied context, vertical movement data are contributing to our understanding of the behaviour of aquatic species, shedding light on how environmental conditions influence the utilisation of the water column. This has significant implications for fisheries management and conservation, as it can contribute to the identification of critical habitats and migratory corridors while also mitigating human impacts such as bycatch or vessel collisions [ 10 ]. Since the first introduction of the technology in 1997 [ 11 ], and the continued use of TDRs, thousands of these devices have been deployed globally, recording DTS for extended durations (e.g., 1246 days; [ 12 ]), generating millions of records of vertical movement data with unprecedented detail. Despite this, much of these data remains underutilised for fine-scale behavioural analysis due to the challenges associated with processing, storing, analysing, visualising, and interpreting such large datasets [ 13 ]. Nearly three decades after their first development, most studies still primarily rely on histograms of time-at-depth and temperature-at-depth (e.g., [ 14 ]). These histograms, while useful for summarising the overall distribution of time spent at various depths or temperatures, cannot resolve finer temporal dynamics and detailed patterns that may contain behavioural signals. Further, this approach does not capture the continuous nature of vertical movements and the specific timing and frequency of behaviours (e.g., [ 14 ]), which are critical for understanding their ecological and biological significance [ 15 ]. For air-breathing aquatic species such as marine turtles (e.g., Natator depressus ), vertical movements are often analysed as discrete “dives” extracted from TDR data, with the return to the surface delineating the end of a vertical movement period, which can subsequently be characterised and categorised into distinct dive types with associated behaviours (see [ 16 ]). Although many gill-breathing aquatic species such as epipelagic fishes can show similar patterns of movement [ 17 ], these species may not be surface-oriented and often exhibit complex and sometimes apparently unpredictable patterns of depth change (see [ 7 , 9 ]). For example, oceanic whitetip sharks ( Carcharhinus longimanus ) remain surface oriented in waters < 28 o C, but rarely approach the surface above this temperature [ 7 ]. The lack of a quantitative, standardised, and widely available method for analysing DTS of gill-breathing species has limited behavioural studies in fishes. Given the repetitive nature of vertical movements by many fishes, fast Fourier transformation [ 18 ], has significantly advanced the interpretation of data by identifying dominant frequencies within time-series. Although this has revealed important insights into the environmental variables driving these behaviours [ 19 – 21 ], a limitation of this analysis is that it provides only a single, discrete decomposition of frequencies, reducing the capacity to segment time-series data where distinct dominant frequencies may occur over time (e.g., differentiate periods that contain a diel signal from those that do not) – a critical factor for detecting shifts in vertical movements [ 22 ]. In contrast, continuous approaches to time-series analyses, such as continuous wavelet transformation (CWT), offer a non-stop representation of the frequency components within a dataset, making them a more appropriate analytical technique for examining non-stationary time-series [ 23 ]. The ability of CWT to capture both the frequencies and the timing of their occurrence within a dataset should ultimately allow for the identification of temporal patterns in vertical movements [ 24 ]. Whereas time-series methods such as FFT or CWT may effectively characterise vertical movements and provide behavioural insight, animals often engage in persistent behavioural states [ 25 ], resulting in distinct, repeatable, movement patterns. This distinction enables the classification of time-series data into discrete categories corresponding to behavioural states, based on inherent similarities in the data. For instance, state-space models and Hidden Markov Models (HMMs) have been used to infer travelling and area-restricted search behaviours from horizontal movements in satellite tracking data [ 26 , 27 ]. Similarly, unsupervised machine learning methods, including clustering techniques, have been utilised to classify behaviour from accelerometer data, based on recurring features within the data identified from a CWT ([ 28 , 29 ]). However, despite the potential of using a similar approach with depth data, no standardised workflow integrating CWT (or other time-series methods) and discrete classification has been developed to date. This study introduces a novel, standardised approach for the quantitative analysis of vertical movement time-series from aquatic species equipped with TDRs, such as PSATs. The effectiveness of the method is demonstrated through simulated vertical movement data and real-world case studies involving an oceanic manta ray Mobula birostris , Atlantic cod Gadus morhua , largetooth sawfish Pristis pristis , and whale shark Rhincodon typus , showcasing its ability to uncover behavioural patterns in species with different behavioural strategies. 2. Methods 2.1 Methodological workflow This study introduces a novel quantitative methodology for classifying vertical movement patterns from the depth data of gill-breathing aquatic species. The approach focusses on analysing DTS data sampled at regular intervals, commonly obtained from TDRs, including PSATs. The analysis uses continuous wavelet transformation followed by principal component analysis and k-means clustering to classify 24-hour periods of vertical movement and assist in the interpretation of complex vertical movement patterns. The method combines selected depth summary statistics and principal component scores within the data flow (Fig. 1 ) to improve clustering outcomes. 2.2 Feature extraction 2.2.1 Depth summary statistics The DTS data were separated into 24-h segments starting at midnight to maintain consistency across datasets and facilitate classification of patterns of vertical movement. A suite of 10 daily and seven diel depth statistics were calculated for each 24-h segment, including mean depth, mean absolute vertical velocity, and depth skewness amongst others (Table S1 ). Time of sunset and sunrise was derived using the R package ‘suncalc’ [ 30 ], according to daily latitude and longitude. The diel statistics were calculated by subtracting the depth statistics during the day from depth statistics at night, and then standardised by dividing by the maximum depth on that day. These daily depth summary statistics ( DSS ) formed the first of two sets of features used in the subsequent k-means clustering (Fig. 1 ). 2.2.2 Wavelet components Wavelet analysis CWT was applied using the R package ‘WaveletComp’ [ 31 ] to deconstruct the high-sampling frequency DTS into two-dimensional periodic components ( sensu [ 23 ]). This method facilitated the investigation of behaviours across various time frames by transforming the DTS into time-frequency space. The lower wavelet period was set to 5-min or 10-min, based on the depth sampling frequency, to ensure that short duration vertical movements were captured accurately. An upper period of 24-h was selected to limit the analysis to daily behaviour patterns such as diel vertical migration, excluding longer-scale patterns not relevant to the study's objectives. The wavelet period range (5-min to 24-h) was divided into 12 sub-octaves per octave, resulting in 99 distinct wavelet periods, to achieve sufficient temporal resolution and capture ecologically relevant periods (e.g., 24-h, 12-h, and 6-h) corresponding to natural cycles such as day-night changes and tidal rhythms. The wavelet power spectrum was visualised to highlight temporal dynamics within the data, along with the mean wavelet power per period to highlight the dominant periods. For each 24-h segment, wavelet summary statistics (WSS) consisting of the mean and variance of power and mean amplitude – were calculated for each period within the wavelet period range (99 periods between 5-min and 24-h), yielding a total of 297 individual summary statistics (three variables across 99 periods). While additional summary statistics can be calculated by the CWT for each period, preliminary analysis revealed the three chosen variables captured most of the variance in the dataset. Principal component analysis for data dimensionality reduction To manage the high dimensionality and collinearity inherent in the 297 WSS calculated for each 24-h period, while retaining the essential characteristics of the vertical movement behaviours, a principal component analysis (PCA) was performed using the R package ‘FactoMineR’ [ 32 ]. Principal components (PCs) were retained first according to Kaisers rule (Eigenvalue ≥ 1; [ 33 ]), and second according to PCs contributing to ≥ 70% of the cumulative variance [ 34 ]. To facilitate interpretation of the retained PCs, mean loadings of the WSS on each PC were visualised. The scores of the retained PCs derived from the WSS are hereafter referred to as wavelet components ( WCs , see Fig. 1 ). WCs were then combined with the DSS to create a suite of ~ 20 features (dependent on number of WC s retained) as input data for unsupervised machine learning classification (see Fig. 1 ). 2.3 K-means unsupervised machine learning The features ( n = 20; combined DSS and WCs ), were first standardised to ensure that each feature contributed equally to the clustering process, regardless of its original scale. K-means clustering was chosen as it is a widely used (e.g., [ 35 , 36 ]), efficient method for partitioning data into distinct groups (clusters) based on similarity [ 37 , 38 ]. Values of k (number of clusters) ranging from 2 to 15 were utilised to explore potential groupings. The optimal number of clusters was determined using the ‘elbow’ method [ 39 ], and the silhouette width method [ 40 ], which was subsequently used in the k-means clustering. To interpret vertical movement behaviours represented by the clusters, the standardised mean values for each feature (for k clusters) were visually compared. Finally, representative examples for each cluster were visualised by selecting days ( n = 3, where available) closest to the centre of each cluster. 2.4 Simulation of vertical movement data To evaluate the robustness and accuracy of the methodology, a 180-day DTS of vertical movement data was simulated with a 1-min sampling frequency. Given the absence of an existing framework for simulating the vertical movement data of gill-breathing species, a series of parameters was developed to control vertical movement over time. The objective was to generate DTS data resembling those recorded from PSATs deployed on oceanic manta rays as illustrated in the results, as they display four commonly observed vertical movement behaviours: diel vertical migration (DVM), reverse diel vertical migration (RDVM), shallow movement, and bounce diving (see [ 4 ]). Fixed sunrise and sunset times of 06:00 and 18:00, respectively, were assumed for all days. Each vertical movement behaviour was controlled with parameters for mean and standard deviation for shallow depth, time at depth, surface interval, and bottom depth limits (Table S2). Hourly changes in bottom depth were simulated using a random walk, allowing a maximum depth variation of 2.5%. To balance variability with periods of repetitive behaviour, a fixed probability of 25% was set for the behaviour to transition to a different behaviour at midnight, acknowledging that vertical movement behaviours typically persist for several days (e.g., [ 25 ]). 2.5 Application to real-world data To demonstrate the applicability of the described methodology, feature extraction (2.1.1) and k-means unsupervised machine learning (2.1.2) were applied to real-world datasets chosen to represent each of two pelagic species, an oceanic manta ray and a whale shark, and two benthic species, an Atlantic cod and a largetooth sawfish. For detailed tagging methods, specifications, and programming, see Table S3. 2.6 Robustness to varying depth sampling frequency Historically, DTS have been recorded across a range of sampling frequencies from 1-s to > 10-min. To assess the robustness and applicability of the method across different depth sampling frequencies, the method was applied to an iteratively thinned empirical dataset (87-days from an oceanic manta ray). This dataset was resampled to create new DTS with sampling frequencies ranging from 5 to 30-min, increasing in 5-min intervals. The full suite of analyses described in sections 2.2 and 2.3 was performed on each resampled dataset. The sampling frequency of the original DTS was 5-s; however, a 1-min depth sampling frequency was used for comparisons due to computational and file-size limitations. The overall accuracy of cluster assignments was compared between each sampling frequency (5 to 30-min) and the benchmark 1-min depth sampling frequency. The proportion of days accurately assigned to the same behaviour cluster across different sampling frequencies was evaluated. Since true behaviour types are not known in real-world data, a modified confusion matrix approach was employed to evaluate all possible assignments of clusters via performance metrics (Equations 1–3) [ 41 ]: $$\:\text{P}\text{r}\text{e}\text{c}\text{i}\text{s}\text{i}\text{o}\text{n}\:=\:\frac{\text{T}\text{r}\text{u}\text{e}\:\text{P}\text{o}\text{s}\text{i}\text{t}\text{i}\text{v}\text{e}\text{s}}{\text{T}\text{r}\text{u}\text{e}\:\text{P}\text{o}\text{s}\text{i}\text{t}\text{i}\text{v}\text{e}\text{s}\:+\:\text{F}\text{a}\text{l}\text{s}\text{e}\:\text{P}\text{o}\text{s}\text{i}\text{t}\text{i}\text{v}\text{e}\text{s}}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\text{E}\text{q}\text{n}1\right)$$ $$\:\text{R}\text{e}\text{c}\text{a}\text{l}\text{l}\:=\:\frac{\text{T}\text{r}\text{u}\text{e}\:\text{P}\text{o}\text{s}\text{i}\text{t}\text{i}\text{v}\text{e}\text{s}}{\text{T}\text{r}\text{u}\text{e}\:\text{P}\text{o}\text{s}\text{i}\text{t}\text{i}\text{v}\text{e}\text{s}\:+\:\text{F}\text{a}\text{l}\text{s}\text{e}\:\text{N}\text{e}\text{g}\text{a}\text{t}\text{i}\text{v}\text{e}\text{s}}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\text{E}\text{q}\text{n}2\right)$$ $$\:\text{F}1\:\text{s}\text{c}\text{o}\text{r}\text{e}=2\frac{\text{P}\text{r}\text{e}\text{c}\text{i}\text{s}\text{i}\text{o}\text{n}\:\text{*}\:\text{R}\text{e}\text{c}\text{a}\text{l}\text{l}}{\text{P}\text{r}\text{e}\text{c}\text{i}\text{s}\text{i}\text{o}\text{n}\:+\:\text{R}\text{e}\text{c}\text{a}\text{l}\text{l}}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\text{E}\text{q}\text{n}3\right)$$ Precision (Eq. 1) measured the proportion of correctly matched cluster assignments (consistent days) out of all assignments, whereas recall (Eq. 2) measured the proportion of correctly matched cluster assignments out of all days that should have been matched (consistent days at the benchmark frequency). The F1 score (Eq. 3), as the harmonic mean of precision and recall, provided a single metric to evaluate the accuracy of each cluster assignment [ 41 ]. Overall accuracy (macro F1), calculated as the proportion of correct cluster assignments out of the total number of assignments, was also used to evaluate performance across different sampling frequencies. By calculating the F1 scores and overall accuracy relative to the 1-min benchmark, it was possible to assess the accuracy maintained as the sampling frequency decreased. This analysis also allowed the evaluation of the impact of decreased sampling frequency on individual clusters, identifying behaviours that were more susceptible to misclassification at lower sampling frequencies. In this context, "true positives" (TP), "false positives" (FP), and "false negatives" (FN) refer to the accuracy of cluster assignments between different sampling frequencies, rather than comparisons to a known ground truth. A TP occurs when a day in the down-sampled dataset is correctly matched to the same cluster as in the 1-min benchmark dataset. A FP is defined as a day is incorrectly assigned to a cluster that does not correspond to its cluster in the benchmark dataset. A FN occurs when a day should have been assigned to the correct cluster but was incorrectly classified. To ensure consistent and accurate cluster assignments across different sampling frequencies, a systematic approach was adopted to map clusters and evaluate their performance; cluster assignments can vary due to the random initialization of centroids in k-means clustering, leading to inconsistent cluster labels across different sampling frequencies. For example, cluster one in one dataset might correspond to cluster three in another dataset. To address this variability, all possible mappings were evaluated before selecting the one that maximized the F1 scores between the 1-min benchmark dataset and down-sampled datasets to facilitate accurate comparison. 2.7 FishDiveR R-Mark package To facilitate broad adoption of this methodology, an open-source R-Mark package ‘FishDiveR’ has been developed. This package integrates each step of the methodology as a separate function, along with various plotting functions to analyse and visualise vertical movement data. FishDiveR is available at https://github.com/calvinsbeale/FishDiveR 3. Results 3.1 Simulation testing The simulated 180-days DTS data (Fig. 2 A) were processed into 24-h segments starting at midnight. The wavelet power spectrum (Fig. 2 B) revealed the highest mean power concentrated around three periods: 24-h, 8-h, and 1-h. Based on the wavelet power distribution, four distinct types of vertical movement patterns were identified in the wavelet power spectrum, each representing a different pattern of behaviour in the simulated data, consistent with the patterns visible in the DTS (Fig. 2 A). PCA conducted on WSS – mean power, mean amplitude, and variance of power – initially identified 10 WCs with eigenvalues ≥ 1. Subsequent reduction retained three WCs , which collectively accounted for 90.85% of the cumulative variance (Table S4). Contrasting mean wavelet loadings were observed for the three WCs across the 99 wavelet periods (Fig. 3 ). Each WC reflects a specific aspect of the vertical movement patterns, exhibiting high wavelet loadings at different timescales and capturing the variance in behaviour across the range of periods selected. Specifically, WC1 shows high loadings for high-frequency vertical movements (between 5-min and 1-h), WC2 for longer-duration vertical movements (between 1-h and 8-h), and WC3 for diel behaviour patterns (around 12-h). Initial clustering of features ( n = 20; combined WCs and DSS ) indicated that four or five clusters were appropriate (Fig. 4 ). Silhouette width was greatest for five clusters, which was chosen for k-means clustering, and each 24-h segment of vertical movement data was assigned to a cluster (Table S5). The separation of clustered segments across the three WCs was clear among clusters one through four, whereas clusters four and five overlapped (Fig. 5 A). The mean standardised values of the 20 features derived from each cluster reflect the deviation of each cluster's mean from the dataset's overall mean, which showed clear separation of clusters among variables (Fig. 5 B). For example, in cluster four, the standardised mean depth of -1.86, indicated shallower depths compared to the overall mean, whereas cluster two had a standardised mean depth of 0.73, indicating deeper depths relative to the overall mean (Table S6). Visualisation of the days closest to the centre of each cluster group (Fig. S1 ) highlighted differences among clusters one through four as visible differences in vertical movement patterns, depth ranges, and diel patterns. Clusters four and five, however, appeared visually identical. On inspection of all 24-h segments, the assigned clusters matched the original simulated behaviours on all but six segments, resulting in a 97.7% accuracy rate. The six incorrectly clustered segments constituted cluster five. Mean standardised values primarily separated clusters four and five by vertical velocity. Inspection of the DTS coloured by cluster assignment (Fig. S2) indicated cluster five was only found at the transitions of behaviour when large changes in depth occurred at either the start or end of the 24-h segment. When four clusters were selected based on the elbow method, the days in cluster five were subsumed into cluster four, and 24-h segments were assigned to clusters matching the original simulated behaviours with 100% accuracy (Table S5). 3.2 Real world application While the DTS from the four case studies displayed markedly different vertical movement patterns, all wavelet spectra indicated repetitive vertical movements (high power) on a range of periods (Fig. 6 ). Some periodicities of high-power periods were unique to individual species, whereas others were common amongst all species (e.g., 24-h). Additionally, changes in the periodicity that corresponded to high-power were evident throughout deployments of all species (Fig. 6 , A-D). All species exhibited a similar number of WCs with eigenvalues ≥ 1, ranging between 18 and 22 (Table S7). The number of WCs contributing to ≥ 90% of the cumulative variance ranged between 9 and 12. To reduce overlap in WCs and simplify cluster description, the minimum number of WCs that contributed to ≥ 75% of the cumulative variance were used in the k-means clustering. The retained WCs accounted for the following cumulative variances: oceanic manta ray = 76.65% (6 WCs ), whale shark = 76.69% (4 WCs ), Atlantic cod = 77.01% (4 WCs ), and largetooth sawfish = 78.75% (6 WCs ) (Table S7, for mean wavelet power loadings see Figs S3-6). Notably, the Atlantic cod had the largest percentage variance within WC 1 at 55.1%, compared to 34.8–36.3% in the other three species. The appropriate number of clusters (k) was explicit for whale shark and Atlantic cod, based on a peak in silhouette width at four and three clusters, respectively (Figs S7B, S8B). The oceanic manta ray and largetooth sawfish both had high silhouette width at two or three clusters, which then dropped sharply before gradually increasing as k increased (Figs S9B, S10B). The elbow method suggested points of inflection at five and four clusters, respectively. K-means feature values were key for explaining differences between clusters (Figs S7-10D). For example, oceanic manta ray cluster three had a depth kurtosis of 8.24 compared to a maximum of -0.29 in other clusters, indicating it was key in distinguishing this cluster. Whale shark cluster one had a mean absolute vertical velocity of 3.24, compared to a maximum of -0.75 in other clusters, indicating it was crucial to distinguishing this cluster. WC s were also critical in distinguishing clusters by highlighting the dominant frequencies at which vertical movements occurred. For example, cluster three of the Atlantic cod dataset was represented by a positive value of WC 1 and negative values of WC 2, WC 3, and WC 4, indicating higher-than-average wavelet power on short frequency periods (10-mins to 1.5-h), and lower-than-average wavelet power on medium to long frequency periods (1.5 to 24-h). Visualisation of the three 24-hr periods closest to the centre of the cluster revealed a strong resemblance of days within each cluster by the naked eye, with 24-hr periods contained within other clusters appearing dissimilar. Some known vertical movement patterns were identifiable, such as extreme deep diving in the oceanic manta ray (Fig. 7 A, Cluster 3), or the sedentary behaviour of Atlantic cod, characterised only by tidal movement (Fig. 7 C, Cluster 2). For distribution of clusters within each species’ DTS, see Figs S11-14. 3.3 Minimum depth sampling frequency requirements The down-sampled DTS revealed a loss in detail of vertical movements as sampling frequency decreased; wavelet spectra also showed reduced detail and lower levels of wavelet power (Fig. 8 ). Down-sampling highlighted the risk of rapid vertical movements being lost. For example, cluster three originally consisted of a single day with a short (< 30-min) vertical movement to 750 m. When the sampling frequency was reduced to 30-min, no depth data were recorded below 300 m (Fig. 8 D). Despite this, the day was still accurately assigned to cluster three. Overall accuracy of cluster assignments varied across sampling frequencies, with accuracy gradually decreasing to 83.9% at a sampling frequency of 15-min, and further dropping to a low of 64.3% at a frequency of 25-min (Fig. 9 ). This decline in accuracy was primarily due to cluster one being merged into another cluster. The accuracy of assignments for cluster one dropped to 54.5% at the 10-min and 15-min sampling frequencies, respectively. 4. Discussion This study presents FishDiveR, a robust methodology for rapidly processing and classifying the vertical movements captured in continuous DTS data from diverse aquatic species. It successfully classified 180 days of simulated DTS data and 543 days of recovered archival tag DTS data, demonstrating that FishDiveR can classify vertical movement patterns across species with differing life histories, from pelagic species such as oceanic manta rays and whale sharks to benthic species such as Atlantic cod and largetooth sawfish. The method detects both large-scale vertical movements, such as DVM commonly seen in manta rays, as well as small-scale variations like the tidal signal in Atlantic cod during sedentary phases. This flexibility ensures FishDiveR can accommodate diverse vertical movement behaviours, allowing users to tailor the analysis by adding or removing features as needed before classification. FishDiveR will introduce a broad range of users to quantitative analysis of depth data by establishing a user-friendly, standardised methodology that can be implemented on regular desktop computers. Moreover, by integrating continuous wavelet transformations, principal component analysis, and unsupervised k-means clustering, FishDiveR is applicable to both contemporary high-frequency recovered data (sampling frequency up to 1-second) and legacy low-frequency data (sampling frequency generally > 10-mins). Finally, the method’s flexibility makes it applicable to diverse species with differing life histories, from pelagic to benthic environments. FishDiveR provides a robust, efficient, and reproducible analysis, processing the large datasets created by high frequency sampling in minutes, while accurately classifying vertical movement patterns. FishDiveR identified dominant frequencies in vertical movements (such as DVMs or rapid oscillatory diving, e.g., Fig. 7 B, cluster 2 and 7A, cluster 2, respectively) in both simulated and real data and classified each 24-h segment into discrete vertical movement patterns, irrespective of benthic or pelagic lifestyle. This capability surpasses that of alternative techniques such as FFT (e.g., [ 19 , 21 ]). For example, FFT may indicate the presence of DVM, but not its temporal occurrence (or spatial occurrence when combined with estimates of animal position), requiring manual post-processing. Utilising unsupervised machine learning, FishDiveR automates the process of classification, avoiding the errors associated with manual methods, such as the 57% disagreement between classifiers manually labelling behaviours in a dataset [ 42 ]. Manual classification is not only prone to subjectivity but is also time consuming, often taking weeks to label thousands of dives, whereas FishDiveR can classify a 180-day dataset in minutes. FishDiveR’s quantitative workflow ensures reproducibility by automating classification. It also enhances analysis flexibility by allowing users to compare clustering results with different k-means features . By adjusting the features ( DSS or WCs ) and observing how they impact cluster assignments, users can refine their understanding of distinct vertical movement behaviours. Compared to other unsupervised techniques commonly used for classifying behavioural states from movement data, such as HMMs [ 26 ], FishDiveR offers a simpler, more accessible workflow. Although HMMs are effective for time-series data with stochastic state transitions, they require careful model specification and parameter tuning which can be computationally intensive and require statistical expertise [ 27 ]. FishDiveR, by using CWT, focuses on detecting periodic behaviours, though it does not account for state persistence or autocorrelation. Features extracted by FishDiveR could theoretically be incorporated into HMMs to better model transitions between behavioural states. Accurate identification of patterns in vertical movement relies on the sampling frequency of the data [ 43 , 44 ]. Frequency of sampling must balance the need to capture sufficient data to avoid losing crucial information with practical constraints such as battery life, data storage, and the planned deployment duration [ 45 ]. Researchers are also constrained by the bandwidth limitations of data transmission via satellite when tag recovery is not guaranteed. Comparisons of cluster results at reduced sampling frequencies revealed that FishDiveR maintains high accuracy with depth sampling frequencies as low as 30-min; however, care should be taken to acknowledge the potential loss of information on behaviours occurring over shorter durations. This finding can inform the choice of sampling frequency for future studies and highlights the opportunity for reanalysing three decades of existing tagging data using FishDiveR. Although the current version of FishDiveR is designed for continuous time-series data, future iterations may expand its capabilities to handle time-series with gaps, addressing a common challenge in satellite transmitted datasets. The simulated data provided a useful evaluation of the methodology; however, limitations arose due to the absence of a standardised approach for generating simulated vertical movement data. Specifically, the simulation parameters only aimed to replicate four common vertical movement behaviours: diel vertical migration (DVM), reverse diel vertical migration (RDVM), shallow movement, and bounce diving (see [ 4 ]). Notably, the simulated vertical movement behaviours only transitioned at midnight, a situation that does not necessarily reflect real-world conditions (see [ 46 ]). The simulation revealed that abrupt transitions between different vertical movement behaviours could lead to the identification of a movement cluster that was not present in the simulated data. This artefact resulted from the abnormally high vertical velocities during transitions, which are not typical of real data. In the analysis of real-world data, the clusters produced by FishDiveR corresponded to well-known behaviours of the study species, including DVM, RDVM, crepuscular movement, rapid oscillatory diving, and inactive/dormant behaviours [ 47 – 50 ]. The successful classification of datasets from both benthic and pelagic animals highlights FishDiveR’s applicability to a diverse range of species. The range of depth statistics used, and the equal weighting of k-means features , allow FishDiveR to classify vertical movements over large depth ranges such as DVM or ‘extreme’ dives ≥ 500m in oceanic manta rays, and over small depth ranges, such as diel behaviour near the seabed and selective tidal stream transport in Atlantic cod [ 51 ]. This level of classification would previously have required a time-consuming in-depth analysis of the individual datasets. A key strength of FishDiveR lies in its ability to identify multiple clusters that would have been generalised into a single class of behaviour if only summary statistics had been applied (e.g., [ 14 ]). For example, variations in DVM occurring in the whale shark dataset were identified as distinct clusters, where traditional methods would have likely grouped them into a single DVM cluster. Indeed, FishDiveR distinguished different forms of DVM based on both surface proportion and night-time activity. Similarly, it identified differences in RDVM in the oceanic manta ray based on vertical velocities and surface proportion. These differentiations in vertical movements align with the diversity in DVM patterns documented in planktonic and nektonic prey organisms [ 10 ], including nocturnal, twilight, and reverse-diel-migrations [ 52 ]. Such detailed classification underscores FishDiveR's capability to provide a robust analysis of vertical movements that traditional methods might overlook. However, while the classification of vertical movements offers functional insights, it is important to acknowledge that the identified “behaviours” are typically not validated and rely on inferences from other studies [ 4 , 53 ]. Therefore, the ability of FishDiveR to detect distinct “behaviours” is contingent upon the current understanding of species-specific vertical movements. Continued efforts in studying these movements using multi-sensor tags and additional techniques (e.g., prey mapping via acoustic methods) are strongly recommended to advance this field [ 4 ]. Future iterations of FishDiveR will aim to accommodate non-continuous time series, which are common in satellite-transmitted datasets and when sampling frequency changes during deployment. This will further increase the software’s application to both existing and future PSAT datasets. Additionally, FishDiveR could be adapted to analyse the vertical movements of other taxa that move in three-dimensional space, such as birds in flight as revealed by altitude loggers [ 54 ]. Similar to aquatic species, the vertical movements of flying birds could reveal key behavioural patterns related to migration, foraging, and response to environmental changes. The software also holds potential for cross-species meta-analysis, highlighting shared behavioural patterns and their environmental drivers through quantitative, multivariate comparisons ( sensu [ 55 ]). These extensions underscore the versatility of FishDiveR, making it a potentially valuable tool for researchers in both marine and aerial ecology. 5. Conclusion This novel workflow represents a significant advance over both manual classification and the use of depth summaries by enabling the identification of dynamic behaviours through the precise capture of their timing and frequency. The accompanying R package, FishDiveR, streamlines the analysis of large depth time-series data, enabling efficient processing of large datasets to uncover complex behavioural patterns with only a basic knowledge of R programming. This makes it a valuable tool for ecologists, conservationists, and managers studying aquatic and potentially avian fauna. Declarations Ethics approval Research was conducted in Indonesia with permission under Surat Izin Penelitian Nomor 69A/SIP/IV/FR/8/2022, and with Murdoch University animal ethics permit number RW3318/21. Consent for publication Not applicable Availability of data and materials R-Mark FishDiveR package code is currently available in its development version for peer review at: https://github.com/calvinsbeale/FishDiveR R-Mark code for simulation of diving behaviour, analysis of the four empirical datasets, and the down-sampling and comparison of different sampling intervals of oceanic manta ray tag data, along with the data from the simulated vertical movement dataset, the four empirical datasets, and the data required for the down-sampling and comparison of different sampling intervals is uploaded for peer review with this manuscript here: https://www.dropbox.com/scl/fo/3zjedmuhzrfzti7ftn4hr/AOZV0Aq4-BNfLPdU3ogNVlE?rlkey=4sx8zeqxrpwf94w04kkavopwx&st=13ukpwl2&dl=0 Competing interests The authors declare that they have no competing interests. Funding We thank MAC3 Impact Philanthropies, the Henry Foundation, the Save the Blue Foundation, Daniel Roozen, and Katrine Bosley for their generous financial support of Conservation International satellite tagging programs. Finally, we extend special thanks to the Harbig Family Foundation for their generous financial support. Author contributions (CRediT author statement): Calvin S. Beale: Conceptualisation, Methodology, Software, Formal analysis, Investigation, Writing – Original Draft, Writing – Review & Editing. Jenna L. Hounslow: Writing – Review & Editing. Angela J.E. Beer: Writing – Review & Editing. Matias Braccini: Writing – Review & Editing. Mark V. Erdmann: Funding acquisition. Alastair Harry: Writing – Review & Editing. Neil R. Loneragan: Writing – Review & Editing. Mark Meekan: Writing – Review & Editing. Stephen J. Newman: Writing – Review & Editing. David Righton: Writing – Review & Editing. Ferawati Runtuboy: Writing – Review & Editing. Michael J. Travers: Writing – Review & Editing. Serena Wright: Writing – Review & Editing. Adrian C. Gleiss: Conceptualisation, Methodology, Writing – Review & Editing. Acknowledgements We acknowledge and appreciate the assistance RISTEK-BRIN to obtain this research permit, along with BALITBANGDA Papua Barat and Pemerintah Daerah Raja Ampat. We would like to thank both the University of Papua (UNIPA) and the Maritime and Fisheries Polytechnic of Sorong for their help in arranging research permits, collaboration, and research opportunities. We also thank the Raja Ampat Marine Protected Area Management Authority (UPTD BLUD KKPD Raja Ampat) for supporting this research. Additionally, we would like to thank Desert Star Systems for providing tag data from bluefin tuna for testing FishDiveR. References Sims DW, Southall EJ, Humphries NE, Hays GC, Bradshaw CJA, Pitchford JW et al. Scaling laws of marine predator search behaviour. Nature [Internet]. 2008 [cited 2024 Jul 11];451:1098–102. 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Supplementary Files FishDiveRSupplementaryMaterialsrevised20250621.docx Cite Share Download PDF Status: Published Journal Publication published 22 Jan, 2026 Read the published version in Movement Ecology → Version 1 posted Editorial decision: Revision requested 12 Sep, 2025 Reviews received at journal 10 Sep, 2025 Reviews received at journal 17 Aug, 2025 Reviewers agreed at journal 15 Aug, 2025 Reviewers agreed at journal 25 Jul, 2025 Reviewers invited by journal 16 Jul, 2025 Editor assigned by journal 24 Jun, 2025 Submission checks completed at journal 24 Jun, 2025 First submitted to journal 16 Jun, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6907076","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Method Article","associatedPublications":[],"authors":[{"id":486218702,"identity":"051ab5cc-d1d0-4bcf-8499-7f369a2423dd","order_by":0,"name":"Calvin S. 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Gleiss","email":"","orcid":"","institution":"Murdoch University","correspondingAuthor":false,"prefix":"","firstName":"Adrian","middleName":"C.","lastName":"Gleiss","suffix":""}],"badges":[],"createdAt":"2025-06-16 15:38:20","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6907076/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6907076/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1186/s40462-025-00622-w","type":"published","date":"2026-01-22T15:58:04+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":87107522,"identity":"dfea7171-b2be-4a5f-92b7-0b1ad3554506","added_by":"auto","created_at":"2025-07-19 15:51:01","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":576049,"visible":true,"origin":"","legend":"\u003cp\u003eOverview of the methodological workflow. A) An animal is tagged with a time-depth recorder. During pre-processing, the tag data are cropped and inspected for depth sensor drift. B) Feature extraction: depth summary statistics (DSS) are calculated. Concurrently, principal component analysis is applied to wavelet summary statistics from continuous wavelet transformation. Wavelet components and DSS are combined and standardised as k-means features. C) K-means unsupervised machine learning is applied, and the optimal number of clusters is determined. Clustered depth time-series data are visualised. D) To facilitate the identification of vertical movement patterns as behaviours, the user inspects the mean values that define each cluster and examines 24-hour time-series plots of the days that best represent each cluster. *Final number of features is dependant on number of retained wavelet components during analysis (see section 2.2.2).\u003c/p\u003e","description":"","filename":"image1.png","url":"https://assets-eu.researchsquare.com/files/rs-6907076/v1/07cb393ffbbfc80cafcea016.png"},{"id":87107523,"identity":"a5d39a5a-514f-400e-859f-295a8a06d69e","added_by":"auto","created_at":"2025-07-19 15:51:01","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":684279,"visible":true,"origin":"","legend":"\u003cp\u003eSimulated data – The 180-day vertical movement dataset with a depth sampling frequency of 1-minute. Data were generated to mimic data from oceanic manta rays, containing four commonly recorded vertical movement behaviours: diel vertical migration, reverse diel vertical migration, shallow movement, and bounce diving. A) Simulated depth time-series. B) Continuous wavelet transform power spectrum corresponding to the depth time-series. Y-axis indicates the wavelet period on which power is calculated, with a lower period of 5-minutes and an upper period of 24-hours, using 12 sub-octaves, on a logarithmic scale. Areas of high wavelet power (red) indicate repetitive signals on that period at that time; for example, there is high wavelet power on the 24-hour period indicating a strong repetitive pattern of 24-hour vertical movement during days 10 through 18.\u003c/p\u003e","description":"","filename":"image2.png","url":"https://assets-eu.researchsquare.com/files/rs-6907076/v1/33e866b93b081fc1a3737ff0.png"},{"id":87107525,"identity":"ac4dbe0d-7aae-4a81-ad8d-26391862638a","added_by":"auto","created_at":"2025-07-19 15:51:01","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":280758,"visible":true,"origin":"","legend":"\u003cp\u003eSimulated data – Mean wavelet power loadings of wavelet components (WCs) one through three across the wavelet period range (lower period of 5-minutes to upper period of 24-hours). Each WC reflects a specific aspect of the vertical movement patterns, dominating at different timescales and capturing the variance in behaviour across the period range. Specifically, WC1 captures high-frequency vertical movements (between 5-minutes and 1-hour), WC2 captures longer duration vertical movements (between 1-hour and 8-hours), and WC3 encompasses diel behaviour patterns (surrounding 12-hours). Note x-axis is on a logarithmic scale.\u003c/p\u003e","description":"","filename":"image3.png","url":"https://assets-eu.researchsquare.com/files/rs-6907076/v1/daa9ac1245a1369cd31ace51.png"},{"id":87107949,"identity":"670e20e5-cd89-41d0-b84f-a75e3a808699","added_by":"auto","created_at":"2025-07-19 15:59:01","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":187284,"visible":true,"origin":"","legend":"\u003cp\u003eSimulated data – Determining the optimal number of clusters (k) to use in k-means analysis. A) The elbow method shows a bend at four and five clusters based on within-cluster sum of squares. B) Silhouette width analysis identifies five as the optimal number of clusters. The red dashed lines highlight potential choices of k, with both methods suggesting four or five clusters, and silhouette width specifically supporting five for optimal clustering.\u003c/p\u003e","description":"","filename":"image4.png","url":"https://assets-eu.researchsquare.com/files/rs-6907076/v1/1716644d2750faa6cf8cc7fa.png"},{"id":87107536,"identity":"900ef6ec-8efc-444f-ae10-94e833b0f0df","added_by":"auto","created_at":"2025-07-19 15:51:01","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":326076,"visible":true,"origin":"","legend":"\u003cp\u003eSimulated data – Separation of clusters among the first three wavelet components (WCs) and depth summary statistics (DSS). A) 3D plot of the first three WCs shows distinct separation between clusters one through four, with overlap between clusters four and five. B) Bar plot of mean standardised values of k-means features (n = 20) per cluster, highlighting the differences in DSS and WCs across clusters.\u003c/p\u003e","description":"","filename":"image5.png","url":"https://assets-eu.researchsquare.com/files/rs-6907076/v1/d4287d087e3e5fcb48e5cb9b.png"},{"id":87107538,"identity":"4cc122b6-b281-45b5-9eda-fda5c35f3f42","added_by":"auto","created_at":"2025-07-19 15:51:01","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":973082,"visible":true,"origin":"","legend":"\u003cp\u003eDepth time-series and corresponding continuous wavelet transformation power spectra from recovered tags deployed on two pelagic and two benthic species. A) Oceanic manta ray Mobula birostris, Indonesia: 87-days, 5-second sampling frequency. B) Whale shark Rhincodon typus, Christmas Island, Australia: 87-days, 1-minute sampling frequency. C) Atlantic cod Gadus morhua, English Channel, UK: 308-days, 10-minute sampling frequency. D) Largetooth sawfish Pristis pristis, Australia: 61-days, 1-second sampling frequency. High wavelet power (red) indicates repetitive vertical movement patterns. Note: y-axes show wavelet periods from 5-min to 24-hr (A, B, D) and 10-min to 24-hr (C), on a logarithmic scale. Depth y-axes in panels A and C are plotted on a semi-logarithmic scale.\u003c/p\u003e","description":"","filename":"image6.png","url":"https://assets-eu.researchsquare.com/files/rs-6907076/v1/5db32f370843454b74c84cdb.png"},{"id":87107954,"identity":"fa3c7b51-cd0c-4fb7-b8d6-9df6ba8784e9","added_by":"auto","created_at":"2025-07-19 15:59:02","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":682366,"visible":true,"origin":"","legend":"\u003cp\u003eDepth time-series extracts from recovered archival tags from four species. The three 24-hour segments closest to the centre (i.e., most representative) of each cluster are plotted (note oceanic manta ray cluster three contained only one segment). Each segment is coloured by its corresponding cluster and grouped vertically by species in each panel. The y-axis, representing depth is freely scaled among clusters within each panel and across the different panels. Shading indicates night-time periods. A) Oceanic manta ray Mobula birostris. B) Whale shark Rhincodon typus. C) Atlantic cod Gadus morhua. D) Largetooth sawfish Pristis pristis.\u003c/p\u003e","description":"","filename":"image7.png","url":"https://assets-eu.researchsquare.com/files/rs-6907076/v1/b2184940e0a9a73b422e27cc.png"},{"id":87107544,"identity":"a2ef913c-5d41-456a-bed5-18d61d0add93","added_by":"auto","created_at":"2025-07-19 15:51:02","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":676544,"visible":true,"origin":"","legend":"\u003cp\u003eImpact of sampling frequency on depth time-series and wavelet power spectra, and the resultant impact on classification of vertical movement behaviours. Comparative depth sampling frequencies for a 30-day period of oceanic manta ray Mobula birostris dataset illustrate how decreased sampling frequencies impact clustering. Higher sampling frequencies (≥20-min; B \u0026amp; C) provide finer-scale details and more accurate cluster assignments, whereas lower sampling frequencies (\u0026lt;20-min; D) capture essential vertical movements but reduce accuracy of cluster assignments. As sampling frequency decreases, there is a loss of detail in vertical movement and a reduction in wavelet power across various periods. The depth y-axes are fixed to illustrate the loss of data as the sampling frequency decreases. Each 24-hour segment is coloured by cluster assignment. The robustness of the methodology is demonstrated by the consistent cluster assignments across varying sampling frequencies. Note: wavelet period is plotted on a logarithmic scale.\u003c/p\u003e","description":"","filename":"image8.png","url":"https://assets-eu.researchsquare.com/files/rs-6907076/v1/c76b130ad95faf2813ab01e2.png"},{"id":87107545,"identity":"08420f52-c4e7-434e-b4ab-79921cb49923","added_by":"auto","created_at":"2025-07-19 15:51:02","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":269625,"visible":true,"origin":"","legend":"\u003cp\u003eClassification performance (cluster assignment) of oceanic manta ray Mobula birostris dataset at different depth sampling frequencies (x-axis) compared to cluster assignments for the benchmark dataset (1-minute depth sampling frequency). Performance was evaluated for each cluster (F1 score) and overall (macro F1 score) for each depth sampling frequency.\u003c/p\u003e","description":"","filename":"image9.png","url":"https://assets-eu.researchsquare.com/files/rs-6907076/v1/8c4b6160663b20e9f307f41f.png"},{"id":101151820,"identity":"b3433cda-2b7b-41f0-bf36-fa9672b76d9a","added_by":"auto","created_at":"2026-01-26 16:06:13","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":5607903,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6907076/v1/63cc6967-2db6-4f48-853f-800491df79bd.pdf"},{"id":87107953,"identity":"a1840510-1478-4128-a432-c38c6a5d1a2f","added_by":"auto","created_at":"2025-07-19 15:59:01","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":3412910,"visible":true,"origin":"","legend":"","description":"","filename":"FishDiveRSupplementaryMaterialsrevised20250621.docx","url":"https://assets-eu.researchsquare.com/files/rs-6907076/v1/6c5e4b8b1b92395856e89ba9.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"FishDiveR: Wavelet analyses and machine learning provide robust classification of animal behaviour from time-depth data","fulltext":[{"header":"1. Background","content":"\u003cp\u003eThe advent of animal-attached time-depth recorders (TDRs), and more recently, transmission of this data via satellite (e.g., Pop-up satellite archival tags - PSATs) has revolutionised the study of aquatic species [\u003cspan additionalcitationids=\"CR2 CR3\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. Over the past three decades, this growing body of work has highlighted diverse and complex vertical movements of some of the most intractable species occupying nearshore, coastal, and pelagic environments [\u003cspan additionalcitationids=\"CR6\" citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. For example, depth time-series (DTS) data have revealed how changes in both large- and meso-scale oceanographic conditions influence the vertical distribution of marine predators [\u003cspan additionalcitationids=\"CR8\" citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e], as well as identifying scaling laws in marine predator search behaviour [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. Vertical movement is generally considered to be a powerful representation of animal behaviour, since pronounced gradients in environmental conditions, such as temperature, light, and dissolved oxygen, are encountered over small scales (\u0026lt;\u0026thinsp;100m), unlike horizontal movements where similar gradients may occur over 100s to 1000s of kilometres [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. In an applied context, vertical movement data are contributing to our understanding of the behaviour of aquatic species, shedding light on how environmental conditions influence the utilisation of the water column. This has significant implications for fisheries management and conservation, as it can contribute to the identification of critical habitats and migratory corridors while also mitigating human impacts such as bycatch or vessel collisions [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eSince the first introduction of the technology in 1997 [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e], and the continued use of TDRs, thousands of these devices have been deployed globally, recording DTS for extended durations (e.g., 1246 days; [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]), generating millions of records of vertical movement data with unprecedented detail. Despite this, much of these data remains underutilised for fine-scale behavioural analysis due to the challenges associated with processing, storing, analysing, visualising, and interpreting such large datasets [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. Nearly three decades after their first development, most studies still primarily rely on histograms of time-at-depth and temperature-at-depth (e.g., [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]). These histograms, while useful for summarising the overall distribution of time spent at various depths or temperatures, cannot resolve finer temporal dynamics and detailed patterns that may contain behavioural signals. Further, this approach does not capture the continuous nature of vertical movements and the specific timing and frequency of behaviours (e.g., [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]), which are critical for understanding their ecological and biological significance [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eFor air-breathing aquatic species such as marine turtles (e.g., \u003cem\u003eNatator depressus\u003c/em\u003e), vertical movements are often analysed as discrete \u0026ldquo;dives\u0026rdquo; extracted from TDR data, with the return to the surface delineating the end of a vertical movement period, which can subsequently be characterised and categorised into distinct dive types with associated behaviours (see [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]). Although many gill-breathing aquatic species such as epipelagic fishes can show similar patterns of movement [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e], these species may not be surface-oriented and often exhibit complex and sometimes apparently unpredictable patterns of depth change (see [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e, \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]). For example, oceanic whitetip sharks (\u003cem\u003eCarcharhinus longimanus\u003c/em\u003e) remain surface oriented in waters\u0026thinsp;\u0026lt;\u0026thinsp;28\u003csup\u003eo\u003c/sup\u003eC, but rarely approach the surface above this temperature [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. The lack of a quantitative, standardised, and widely available method for analysing DTS of gill-breathing species has limited behavioural studies in fishes.\u003c/p\u003e\u003cp\u003eGiven the repetitive nature of vertical movements by many fishes, fast Fourier transformation [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e], has significantly advanced the interpretation of data by identifying dominant frequencies within time-series. Although this has revealed important insights into the environmental variables driving these behaviours [\u003cspan additionalcitationids=\"CR20\" citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e], a limitation of this analysis is that it provides only a single, discrete decomposition of frequencies, reducing the capacity to segment time-series data where distinct dominant frequencies may occur over time (e.g., differentiate periods that contain a diel signal from those that do not) \u0026ndash; a critical factor for detecting shifts in vertical movements [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]. In contrast, continuous approaches to time-series analyses, such as continuous wavelet transformation (CWT), offer a non-stop representation of the frequency components within a dataset, making them a more appropriate analytical technique for examining non-stationary time-series [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]. The ability of CWT to capture both the frequencies and the timing of their occurrence within a dataset should ultimately allow for the identification of temporal patterns in vertical movements [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eWhereas time-series methods such as FFT or CWT may effectively characterise vertical movements and provide behavioural insight, animals often engage in persistent behavioural states [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e], resulting in distinct, repeatable, movement patterns. This distinction enables the classification of time-series data into discrete categories corresponding to behavioural states, based on inherent similarities in the data. For instance, state-space models and Hidden Markov Models (HMMs) have been used to infer travelling and area-restricted search behaviours from horizontal movements in satellite tracking data [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e, \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e]. Similarly, unsupervised machine learning methods, including clustering techniques, have been utilised to classify behaviour from accelerometer data, based on recurring features within the data identified from a CWT ([\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]). However, despite the potential of using a similar approach with depth data, no standardised workflow integrating CWT (or other time-series methods) and discrete classification has been developed to date.\u003c/p\u003e\u003cp\u003eThis study introduces a novel, standardised approach for the quantitative analysis of vertical movement time-series from aquatic species equipped with TDRs, such as PSATs. The effectiveness of the method is demonstrated through simulated vertical movement data and real-world case studies involving an oceanic manta ray \u003cem\u003eMobula birostris\u003c/em\u003e, Atlantic cod \u003cem\u003eGadus morhua\u003c/em\u003e, largetooth sawfish \u003cem\u003ePristis pristis\u003c/em\u003e, and whale shark \u003cem\u003eRhincodon typus\u003c/em\u003e, showcasing its ability to uncover behavioural patterns in species with different behavioural strategies.\u003c/p\u003e"},{"header":"2. Methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\u003ch2\u003e2.1 Methodological workflow\u003c/h2\u003e\u003cp\u003eThis study introduces a novel quantitative methodology for classifying vertical movement patterns from the depth data of gill-breathing aquatic species. The approach focusses on analysing DTS data sampled at regular intervals, commonly obtained from TDRs, including PSATs. The analysis uses continuous wavelet transformation followed by principal component analysis and k-means clustering to classify 24-hour periods of vertical movement and assist in the interpretation of complex vertical movement patterns. The method combines selected depth summary statistics and principal component scores within the data flow (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e) to improve clustering outcomes.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e\u003ch2\u003e2.2 \u003cem\u003eFeature\u003c/em\u003e extraction\u003c/h2\u003e\u003cdiv id=\"Sec5\" class=\"Section3\"\u003e\u003ch2\u003e2.2.1 \u003cem\u003eDepth summary statistics\u003c/em\u003e\u003c/h2\u003e\u003cp\u003eThe DTS data were separated into 24-h segments starting at midnight to maintain consistency across datasets and facilitate classification of patterns of vertical movement. A suite of 10 daily and seven diel depth statistics were calculated for each 24-h segment, including mean depth, mean absolute vertical velocity, and depth skewness amongst others (Table \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003e). Time of sunset and sunrise was derived using the R package \u0026lsquo;suncalc\u0026rsquo; [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e], according to daily latitude and longitude. The diel statistics were calculated by subtracting the depth statistics during the day from depth statistics at night, and then standardised by dividing by the maximum depth on that day. These daily \u003cem\u003edepth summary statistics\u003c/em\u003e (\u003cem\u003eDSS\u003c/em\u003e) formed the first of two sets of \u003cem\u003efeatures\u003c/em\u003e used in the subsequent k-means clustering (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e).\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec6\" class=\"Section3\"\u003e\u003ch2\u003e2.2.2 \u003cem\u003eWavelet components\u003c/em\u003e\u003c/h2\u003e\u003cp\u003e\u003cem\u003eWavelet analysis\u003c/em\u003e\u003c/p\u003e\u003cp\u003eCWT was applied using the R package \u0026lsquo;WaveletComp\u0026rsquo; [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e] to deconstruct the high-sampling frequency DTS into two-dimensional periodic components (\u003cem\u003esensu\u003c/em\u003e [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]). This method facilitated the investigation of behaviours across various time frames by transforming the DTS into time-frequency space. The lower wavelet period was set to 5-min or 10-min, based on the depth sampling frequency, to ensure that short duration vertical movements were captured accurately. An upper period of 24-h was selected to limit the analysis to daily behaviour patterns such as diel vertical migration, excluding longer-scale patterns not relevant to the study's objectives.\u003c/p\u003e\u003cp\u003eThe wavelet period range (5-min to 24-h) was divided into 12 sub-octaves per octave, resulting in 99 distinct wavelet periods, to achieve sufficient temporal resolution and capture ecologically relevant periods (e.g., 24-h, 12-h, and 6-h) corresponding to natural cycles such as day-night changes and tidal rhythms. The wavelet power spectrum was visualised to highlight temporal dynamics within the data, along with the mean wavelet power per period to highlight the dominant periods. For each 24-h segment, \u003cem\u003ewavelet summary statistics (WSS)\u003c/em\u003e consisting of the mean and variance of power and mean amplitude \u0026ndash; were calculated for each period within the wavelet period range (99 periods between 5-min and 24-h), yielding a total of 297 individual summary statistics (three variables across 99 periods). While additional summary statistics can be calculated by the CWT for each period, preliminary analysis revealed the three chosen variables captured most of the variance in the dataset.\u003c/p\u003e\u003cp\u003e\u003cem\u003ePrincipal component analysis for data dimensionality reduction\u003c/em\u003e\u003c/p\u003e\u003cp\u003eTo manage the high dimensionality and collinearity inherent in the 297 \u003cem\u003eWSS\u003c/em\u003e calculated for each 24-h period, while retaining the essential characteristics of the vertical movement behaviours, a principal component analysis (PCA) was performed using the R package \u0026lsquo;FactoMineR\u0026rsquo; [\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e]. Principal components (PCs) were retained first according to Kaisers rule (Eigenvalue\u0026thinsp;\u0026ge;\u0026thinsp;1; [\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e]), and second according to PCs contributing to \u0026ge;\u0026thinsp;70% of the cumulative variance [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e]. To facilitate interpretation of the retained PCs, mean loadings of the \u003cem\u003eWSS\u003c/em\u003e on each PC were visualised. The scores of the retained PCs derived from the \u003cem\u003eWSS\u003c/em\u003e are hereafter referred to as \u003cem\u003ewavelet components\u003c/em\u003e (\u003cem\u003eWCs\u003c/em\u003e, see Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). \u003cem\u003eWCs\u003c/em\u003e were then combined with the \u003cem\u003eDSS\u003c/em\u003e to create a suite of ~\u0026thinsp;20 \u003cem\u003efeatures\u003c/em\u003e (dependent on number of \u003cem\u003eWC\u003c/em\u003es retained) as input data for unsupervised machine learning classification (see Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e).\u003c/p\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Sec7\" class=\"Section2\"\u003e\u003ch2\u003e2.3 K-means unsupervised machine learning\u003c/h2\u003e\u003cp\u003eThe \u003cem\u003efeatures\u003c/em\u003e (\u003cem\u003en\u003c/em\u003e\u0026thinsp;=\u0026thinsp;20; combined \u003cem\u003eDSS\u003c/em\u003e and \u003cem\u003eWCs\u003c/em\u003e), were first standardised to ensure that each \u003cem\u003efeature\u003c/em\u003e contributed equally to the clustering process, regardless of its original scale. K-means clustering was chosen as it is a widely used (e.g., [\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e, \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e]), efficient method for partitioning data into distinct groups (clusters) based on similarity [\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e, \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e]. Values of k (number of clusters) ranging from 2 to 15 were utilised to explore potential groupings. The optimal number of clusters was determined using the \u0026lsquo;elbow\u0026rsquo; method [\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e], and the silhouette width method [\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e], which was subsequently used in the k-means clustering. To interpret vertical movement behaviours represented by the clusters, the standardised mean values for each \u003cem\u003efeature\u003c/em\u003e (for \u003cem\u003ek\u003c/em\u003e clusters) were visually compared. Finally, representative examples for each cluster were visualised by selecting days (\u003cem\u003en\u003c/em\u003e\u0026thinsp;=\u0026thinsp;3, where available) closest to the centre of each cluster.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e\u003ch2\u003e2.4 Simulation of vertical movement data\u003c/h2\u003e\u003cp\u003eTo evaluate the robustness and accuracy of the methodology, a 180-day DTS of vertical movement data was simulated with a 1-min sampling frequency. Given the absence of an existing framework for simulating the vertical movement data of gill-breathing species, a series of parameters was developed to control vertical movement over time. The objective was to generate DTS data resembling those recorded from PSATs deployed on oceanic manta rays as illustrated in the results, as they display four commonly observed vertical movement behaviours: diel vertical migration (DVM), reverse diel vertical migration (RDVM), shallow movement, and bounce diving (see [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]). Fixed sunrise and sunset times of 06:00 and 18:00, respectively, were assumed for all days.\u003c/p\u003e\u003cp\u003eEach vertical movement behaviour was controlled with parameters for mean and standard deviation for shallow depth, time at depth, surface interval, and bottom depth limits (Table S2). Hourly changes in bottom depth were simulated using a random walk, allowing a maximum depth variation of 2.5%. To balance variability with periods of repetitive behaviour, a fixed probability of 25% was set for the behaviour to transition to a different behaviour at midnight, acknowledging that vertical movement behaviours typically persist for several days (e.g., [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]).\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e\u003ch2\u003e2.5 Application to real-world data\u003c/h2\u003e\u003cp\u003eTo demonstrate the applicability of the described methodology, \u003cem\u003efeature\u003c/em\u003e extraction (2.1.1) and k-means unsupervised machine learning (2.1.2) were applied to real-world datasets chosen to represent each of two pelagic species, an oceanic manta ray and a whale shark, and two benthic species, an Atlantic cod and a largetooth sawfish. For detailed tagging methods, specifications, and programming, see Table S3.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec10\" class=\"Section2\"\u003e\u003ch2\u003e2.6 Robustness to varying depth sampling frequency\u003c/h2\u003e\u003cp\u003eHistorically, DTS have been recorded across a range of sampling frequencies from 1-s to \u0026gt;\u0026thinsp;10-min. To assess the robustness and applicability of the method across different depth sampling frequencies, the method was applied to an iteratively thinned empirical dataset (87-days from an oceanic manta ray). This dataset was resampled to create new DTS with sampling frequencies ranging from 5 to 30-min, increasing in 5-min intervals. The full suite of analyses described in sections \u003cspan refid=\"Sec4\" class=\"InternalRef\"\u003e2.2\u003c/span\u003e and \u003cspan refid=\"Sec7\" class=\"InternalRef\"\u003e2.3\u003c/span\u003e was performed on each resampled dataset.\u003c/p\u003e\u003cp\u003eThe sampling frequency of the original DTS was 5-s; however, a 1-min depth sampling frequency was used for comparisons due to computational and file-size limitations. The overall accuracy of cluster assignments was compared between each sampling frequency (5 to 30-min) and the benchmark 1-min depth sampling frequency. The proportion of days accurately assigned to the same behaviour cluster across different sampling frequencies was evaluated. Since true behaviour types are not known in real-world data, a modified confusion matrix approach was employed to evaluate all possible assignments of clusters via performance metrics (Equations 1\u0026ndash;3) [\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e]:\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\:\\text{P}\\text{r}\\text{e}\\text{c}\\text{i}\\text{s}\\text{i}\\text{o}\\text{n}\\:=\\:\\frac{\\text{T}\\text{r}\\text{u}\\text{e}\\:\\text{P}\\text{o}\\text{s}\\text{i}\\text{t}\\text{i}\\text{v}\\text{e}\\text{s}}{\\text{T}\\text{r}\\text{u}\\text{e}\\:\\text{P}\\text{o}\\text{s}\\text{i}\\text{t}\\text{i}\\text{v}\\text{e}\\text{s}\\:+\\:\\text{F}\\text{a}\\text{l}\\text{s}\\text{e}\\:\\text{P}\\text{o}\\text{s}\\text{i}\\text{t}\\text{i}\\text{v}\\text{e}\\text{s}}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\left(\\text{E}\\text{q}\\text{n}1\\right)$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equb\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equb\" name=\"EquationSource\"\u003e\n$$\\:\\text{R}\\text{e}\\text{c}\\text{a}\\text{l}\\text{l}\\:=\\:\\frac{\\text{T}\\text{r}\\text{u}\\text{e}\\:\\text{P}\\text{o}\\text{s}\\text{i}\\text{t}\\text{i}\\text{v}\\text{e}\\text{s}}{\\text{T}\\text{r}\\text{u}\\text{e}\\:\\text{P}\\text{o}\\text{s}\\text{i}\\text{t}\\text{i}\\text{v}\\text{e}\\text{s}\\:+\\:\\text{F}\\text{a}\\text{l}\\text{s}\\text{e}\\:\\text{N}\\text{e}\\text{g}\\text{a}\\text{t}\\text{i}\\text{v}\\text{e}\\text{s}}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\left(\\text{E}\\text{q}\\text{n}2\\right)$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equc\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equc\" name=\"EquationSource\"\u003e\n$$\\:\\text{F}1\\:\\text{s}\\text{c}\\text{o}\\text{r}\\text{e}=2\\frac{\\text{P}\\text{r}\\text{e}\\text{c}\\text{i}\\text{s}\\text{i}\\text{o}\\text{n}\\:\\text{*}\\:\\text{R}\\text{e}\\text{c}\\text{a}\\text{l}\\text{l}}{\\text{P}\\text{r}\\text{e}\\text{c}\\text{i}\\text{s}\\text{i}\\text{o}\\text{n}\\:+\\:\\text{R}\\text{e}\\text{c}\\text{a}\\text{l}\\text{l}}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\left(\\text{E}\\text{q}\\text{n}3\\right)$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003ePrecision (Eq.\u0026nbsp;1) measured the proportion of correctly matched cluster assignments (consistent days) out of all assignments, whereas recall (Eq.\u0026nbsp;2) measured the proportion of correctly matched cluster assignments out of all days that should have been matched (consistent days at the benchmark frequency). The F1 score (Eq.\u0026nbsp;3), as the harmonic mean of precision and recall, provided a single metric to evaluate the accuracy of each cluster assignment [\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e]. Overall accuracy (macro F1), calculated as the proportion of correct cluster assignments out of the total number of assignments, was also used to evaluate performance across different sampling frequencies. By calculating the F1 scores and overall accuracy relative to the 1-min benchmark, it was possible to assess the accuracy maintained as the sampling frequency decreased. This analysis also allowed the evaluation of the impact of decreased sampling frequency on individual clusters, identifying behaviours that were more susceptible to misclassification at lower sampling frequencies.\u003c/p\u003e\u003cp\u003eIn this context, \"true positives\" (TP), \"false positives\" (FP), and \"false negatives\" (FN) refer to the accuracy of cluster assignments between different sampling frequencies, rather than comparisons to a known ground truth. A TP occurs when a day in the down-sampled dataset is correctly matched to the same cluster as in the 1-min benchmark dataset. A FP is defined as a day is incorrectly assigned to a cluster that does not correspond to its cluster in the benchmark dataset. A FN occurs when a day should have been assigned to the correct cluster but was incorrectly classified. To ensure consistent and accurate cluster assignments across different sampling frequencies, a systematic approach was adopted to map clusters and evaluate their performance; cluster assignments can vary due to the random initialization of centroids in k-means clustering, leading to inconsistent cluster labels across different sampling frequencies. For example, cluster one in one dataset might correspond to cluster three in another dataset. To address this variability, all possible mappings were evaluated before selecting the one that maximized the F1 scores between the 1-min benchmark dataset and down-sampled datasets to facilitate accurate comparison.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e\u003ch2\u003e2.7 FishDiveR R-Mark package\u003c/h2\u003e\u003cp\u003eTo facilitate broad adoption of this methodology, an open-source R-Mark package \u0026lsquo;FishDiveR\u0026rsquo; has been developed. This package integrates each step of the methodology as a separate function, along with various plotting functions to analyse and visualise vertical movement data. FishDiveR is available at \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://github.com/calvinsbeale/FishDiveR\u003c/span\u003e\u003cspan address=\"https://github.com/calvinsbeale/FishDiveR\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/div\u003e"},{"header":"3. Results","content":"\u003cdiv id=\"Sec13\" class=\"Section2\"\u003e\u003ch2\u003e3.1 Simulation testing\u003c/h2\u003e\u003cp\u003eThe simulated 180-days DTS data (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eA) were processed into 24-h segments starting at midnight. The wavelet power spectrum (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eB) revealed the highest mean power concentrated around three periods: 24-h, 8-h, and 1-h. Based on the wavelet power distribution, four distinct types of vertical movement patterns were identified in the wavelet power spectrum, each representing a different pattern of behaviour in the simulated data, consistent with the patterns visible in the DTS (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eA).\u003c/p\u003e\u003cp\u003ePCA conducted on \u003cem\u003eWSS\u003c/em\u003e \u0026ndash; mean power, mean amplitude, and variance of power \u0026ndash; initially identified 10 \u003cem\u003eWCs\u003c/em\u003e with eigenvalues\u0026thinsp;\u0026ge;\u0026thinsp;1. Subsequent reduction retained three \u003cem\u003eWCs\u003c/em\u003e, which collectively accounted for 90.85% of the cumulative variance (Table S4). Contrasting mean wavelet loadings were observed for the three \u003cem\u003eWCs\u003c/em\u003e across the 99 wavelet periods (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e). Each \u003cem\u003eWC\u003c/em\u003e reflects a specific aspect of the vertical movement patterns, exhibiting high wavelet loadings at different timescales and capturing the variance in behaviour across the range of periods selected. Specifically, \u003cem\u003eWC1\u003c/em\u003e shows high loadings for high-frequency vertical movements (between 5-min and 1-h), \u003cem\u003eWC2\u003c/em\u003e for longer-duration vertical movements (between 1-h and 8-h), and \u003cem\u003eWC3\u003c/em\u003e for diel behaviour patterns (around 12-h).\u003c/p\u003e\u003cp\u003eInitial clustering of \u003cem\u003efeatures\u003c/em\u003e (\u003cem\u003en\u003c/em\u003e\u0026thinsp;=\u0026thinsp;20; combined \u003cem\u003eWCs\u003c/em\u003e and \u003cem\u003eDSS\u003c/em\u003e) indicated that four or five clusters were appropriate (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e). Silhouette width was greatest for five clusters, which was chosen for k-means clustering, and each 24-h segment of vertical movement data was assigned to a cluster (Table S5). The separation of clustered segments across the three \u003cem\u003eWCs\u003c/em\u003e was clear among clusters one through four, whereas clusters four and five overlapped (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eA). The mean standardised values of the 20 \u003cem\u003efeatures\u003c/em\u003e derived from each cluster reflect the deviation of each cluster's mean from the dataset's overall mean, which showed clear separation of clusters among variables (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eB). For example, in cluster four, the standardised mean depth of -1.86, indicated shallower depths compared to the overall mean, whereas cluster two had a standardised mean depth of 0.73, indicating deeper depths relative to the overall mean (Table S6).\u003c/p\u003e\u003cp\u003eVisualisation of the days closest to the centre of each cluster group (Fig. \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003e) highlighted differences among clusters one through four as visible differences in vertical movement patterns, depth ranges, and diel patterns. Clusters four and five, however, appeared visually identical. On inspection of all 24-h segments, the assigned clusters matched the original simulated behaviours on all but six segments, resulting in a 97.7% accuracy rate. The six incorrectly clustered segments constituted cluster five. Mean standardised values primarily separated clusters four and five by vertical velocity. Inspection of the DTS coloured by cluster assignment (Fig. S2) indicated cluster five was only found at the transitions of behaviour when large changes in depth occurred at either the start or end of the 24-h segment. When four clusters were selected based on the elbow method, the days in cluster five were subsumed into cluster four, and 24-h segments were assigned to clusters matching the original simulated behaviours with 100% accuracy (Table S5).\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec14\" class=\"Section2\"\u003e\u003ch2\u003e3.2 Real world application\u003c/h2\u003e\u003cp\u003eWhile the DTS from the four case studies displayed markedly different vertical movement patterns, all wavelet spectra indicated repetitive vertical movements (high power) on a range of periods (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e). Some periodicities of high-power periods were unique to individual species, whereas others were common amongst all species (e.g., 24-h). Additionally, changes in the periodicity that corresponded to high-power were evident throughout deployments of all species (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e, A-D).\u003c/p\u003e\u003cp\u003eAll species exhibited a similar number of \u003cem\u003eWCs\u003c/em\u003e with eigenvalues\u0026thinsp;\u0026ge;\u0026thinsp;1, ranging between 18 and 22 (Table S7). The number of \u003cem\u003eWCs\u003c/em\u003e contributing to \u0026ge;\u0026thinsp;90% of the cumulative variance ranged between 9 and 12. To reduce overlap in \u003cem\u003eWCs\u003c/em\u003e and simplify cluster description, the minimum number of \u003cem\u003eWCs\u003c/em\u003e that contributed to \u0026ge;\u0026thinsp;75% of the cumulative variance were used in the k-means clustering. The retained \u003cem\u003eWCs\u003c/em\u003e accounted for the following cumulative variances: oceanic manta ray\u0026thinsp;=\u0026thinsp;76.65% (6 \u003cem\u003eWCs\u003c/em\u003e), whale shark\u0026thinsp;=\u0026thinsp;76.69% (4 \u003cem\u003eWCs\u003c/em\u003e), Atlantic cod\u0026thinsp;=\u0026thinsp;77.01% (4 \u003cem\u003eWCs\u003c/em\u003e), and largetooth sawfish\u0026thinsp;=\u0026thinsp;78.75% (6 \u003cem\u003eWCs\u003c/em\u003e) (Table S7, for mean wavelet power loadings see Figs S3-6). Notably, the Atlantic cod had the largest percentage variance within \u003cem\u003eWC\u003c/em\u003e1 at 55.1%, compared to 34.8\u0026ndash;36.3% in the other three species.\u003c/p\u003e\u003cp\u003eThe appropriate number of clusters (k) was explicit for whale shark and Atlantic cod, based on a peak in silhouette width at four and three clusters, respectively (Figs S7B, S8B). The oceanic manta ray and largetooth sawfish both had high silhouette width at two or three clusters, which then dropped sharply before gradually increasing as k increased (Figs S9B, S10B). The elbow method suggested points of inflection at five and four clusters, respectively.\u003c/p\u003e\u003cp\u003eK-means \u003cem\u003efeature\u003c/em\u003e values were key for explaining differences between clusters (Figs S7-10D). For example, oceanic manta ray cluster three had a depth kurtosis of 8.24 compared to a maximum of -0.29 in other clusters, indicating it was key in distinguishing this cluster. Whale shark cluster one had a mean absolute vertical velocity of 3.24, compared to a maximum of -0.75 in other clusters, indicating it was crucial to distinguishing this cluster. \u003cem\u003eWC\u003c/em\u003es were also critical in distinguishing clusters by highlighting the dominant frequencies at which vertical movements occurred. For example, cluster three of the Atlantic cod dataset was represented by a positive value of \u003cem\u003eWC\u003c/em\u003e1 and negative values of \u003cem\u003eWC\u003c/em\u003e2, \u003cem\u003eWC\u003c/em\u003e3, and \u003cem\u003eWC\u003c/em\u003e4, indicating higher-than-average wavelet power on short frequency periods (10-mins to 1.5-h), and lower-than-average wavelet power on medium to long frequency periods (1.5 to 24-h).\u003c/p\u003e\u003cp\u003eVisualisation of the three 24-hr periods closest to the centre of the cluster revealed a strong resemblance of days within each cluster by the naked eye, with 24-hr periods contained within other clusters appearing dissimilar. Some known vertical movement patterns were identifiable, such as extreme deep diving in the oceanic manta ray (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003eA, Cluster 3), or the sedentary behaviour of Atlantic cod, characterised only by tidal movement (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003eC, Cluster 2). For distribution of clusters within each species\u0026rsquo; DTS, see Figs S11-14.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec15\" class=\"Section2\"\u003e\u003ch2\u003e3.3 Minimum depth sampling frequency requirements\u003c/h2\u003e\u003cp\u003eThe down-sampled DTS revealed a loss in detail of vertical movements as sampling frequency decreased; wavelet spectra also showed reduced detail and lower levels of wavelet power (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e). Down-sampling highlighted the risk of rapid vertical movements being lost. For example, cluster three originally consisted of a single day with a short (\u0026lt;\u0026thinsp;30-min) vertical movement to 750 m. When the sampling frequency was reduced to 30-min, no depth data were recorded below 300 m (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003eD). Despite this, the day was still accurately assigned to cluster three.\u003c/p\u003e\u003cp\u003eOverall accuracy of cluster assignments varied across sampling frequencies, with accuracy gradually decreasing to 83.9% at a sampling frequency of 15-min, and further dropping to a low of 64.3% at a frequency of 25-min (Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e). This decline in accuracy was primarily due to cluster one being merged into another cluster. The accuracy of assignments for cluster one dropped to 54.5% at the 10-min and 15-min sampling frequencies, respectively.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e"},{"header":"4. Discussion","content":"\u003cp\u003eThis study presents FishDiveR, a robust methodology for rapidly processing and classifying the vertical movements captured in continuous DTS data from diverse aquatic species. It successfully classified 180 days of simulated DTS data and 543 days of recovered archival tag DTS data, demonstrating that FishDiveR can classify vertical movement patterns across species with differing life histories, from pelagic species such as oceanic manta rays and whale sharks to benthic species such as Atlantic cod and largetooth sawfish. The method detects both large-scale vertical movements, such as DVM commonly seen in manta rays, as well as small-scale variations like the tidal signal in Atlantic cod during sedentary phases. This flexibility ensures FishDiveR can accommodate diverse vertical movement behaviours, allowing users to tailor the analysis by adding or removing \u003cem\u003efeatures\u003c/em\u003e as needed before classification.\u003c/p\u003e\u003cp\u003eFishDiveR will introduce a broad range of users to quantitative analysis of depth data by establishing a user-friendly, standardised methodology that can be implemented on regular desktop computers. Moreover, by integrating continuous wavelet transformations, principal component analysis, and unsupervised k-means clustering, FishDiveR is applicable to both contemporary high-frequency recovered data (sampling frequency up to 1-second) and legacy low-frequency data (sampling frequency generally\u0026thinsp;\u0026gt;\u0026thinsp;10-mins). Finally, the method\u0026rsquo;s flexibility makes it applicable to diverse species with differing life histories, from pelagic to benthic environments.\u003c/p\u003e\u003cp\u003eFishDiveR provides a robust, efficient, and reproducible analysis, processing the large datasets created by high frequency sampling in minutes, while accurately classifying vertical movement patterns. FishDiveR identified dominant frequencies in vertical movements (such as DVMs or rapid oscillatory diving, e.g., Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003eB, cluster 2 and 7A, cluster 2, respectively) in both simulated and real data and classified each 24-h segment into discrete vertical movement patterns, irrespective of benthic or pelagic lifestyle. This capability surpasses that of alternative techniques such as FFT (e.g., [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e, \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]). For example, FFT may indicate the presence of DVM, but not its temporal occurrence (or spatial occurrence when combined with estimates of animal position), requiring manual post-processing. Utilising unsupervised machine learning, FishDiveR automates the process of classification, avoiding the errors associated with manual methods, such as the 57% disagreement between classifiers manually labelling behaviours in a dataset [\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e]. Manual classification is not only prone to subjectivity but is also time consuming, often taking weeks to label thousands of dives, whereas FishDiveR can classify a 180-day dataset in minutes. FishDiveR\u0026rsquo;s quantitative workflow ensures reproducibility by automating classification. It also enhances analysis flexibility by allowing users to compare clustering results with different k-means \u003cem\u003efeatures\u003c/em\u003e. By adjusting the \u003cem\u003efeatures\u003c/em\u003e (\u003cem\u003eDSS\u003c/em\u003e or \u003cem\u003eWCs\u003c/em\u003e) and observing how they impact cluster assignments, users can refine their understanding of distinct vertical movement behaviours.\u003c/p\u003e\u003cp\u003eCompared to other unsupervised techniques commonly used for classifying behavioural states from movement data, such as HMMs [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e], FishDiveR offers a simpler, more accessible workflow. Although HMMs are effective for time-series data with stochastic state transitions, they require careful model specification and parameter tuning which can be computationally intensive and require statistical expertise [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e]. FishDiveR, by using CWT, focuses on detecting periodic behaviours, though it does not account for state persistence or autocorrelation. \u003cem\u003eFeatures\u003c/em\u003e extracted by FishDiveR could theoretically be incorporated into HMMs to better model transitions between behavioural states.\u003c/p\u003e\u003cp\u003eAccurate identification of patterns in vertical movement relies on the sampling frequency of the data [\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e, \u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e]. Frequency of sampling must balance the need to capture sufficient data to avoid losing crucial information with practical constraints such as battery life, data storage, and the planned deployment duration [\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e]. Researchers are also constrained by the bandwidth limitations of data transmission via satellite when tag recovery is not guaranteed. Comparisons of cluster results at reduced sampling frequencies revealed that FishDiveR maintains high accuracy with depth sampling frequencies as low as 30-min; however, care should be taken to acknowledge the potential loss of information on behaviours occurring over shorter durations. This finding can inform the choice of sampling frequency for future studies and highlights the opportunity for reanalysing three decades of existing tagging data using FishDiveR. Although the current version of FishDiveR is designed for continuous time-series data, future iterations may expand its capabilities to handle time-series with gaps, addressing a common challenge in satellite transmitted datasets.\u003c/p\u003e\u003cp\u003eThe simulated data provided a useful evaluation of the methodology; however, limitations arose due to the absence of a standardised approach for generating simulated vertical movement data. Specifically, the simulation parameters only aimed to replicate four common vertical movement behaviours: diel vertical migration (DVM), reverse diel vertical migration (RDVM), shallow movement, and bounce diving (see [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]). Notably, the simulated vertical movement behaviours only transitioned at midnight, a situation that does not necessarily reflect real-world conditions (see [\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e]). The simulation revealed that abrupt transitions between different vertical movement behaviours could lead to the identification of a movement cluster that was not present in the simulated data. This artefact resulted from the abnormally high vertical velocities during transitions, which are not typical of real data.\u003c/p\u003e\u003cp\u003eIn the analysis of real-world data, the clusters produced by FishDiveR corresponded to well-known behaviours of the study species, including DVM, RDVM, crepuscular movement, rapid oscillatory diving, and inactive/dormant behaviours [\u003cspan additionalcitationids=\"CR48 CR49\" citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e50\u003c/span\u003e]. The successful classification of datasets from both benthic and pelagic animals highlights FishDiveR\u0026rsquo;s applicability to a diverse range of species. The range of depth statistics used, and the equal weighting of k-means \u003cem\u003efeatures\u003c/em\u003e, allow FishDiveR to classify vertical movements over large depth ranges such as DVM or \u0026lsquo;extreme\u0026rsquo; dives\u0026thinsp;\u0026ge;\u0026thinsp;500m in oceanic manta rays, and over small depth ranges, such as diel behaviour near the seabed and selective tidal stream transport in Atlantic cod [\u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e51\u003c/span\u003e]. This level of classification would previously have required a time-consuming in-depth analysis of the individual datasets.\u003c/p\u003e\u003cp\u003eA key strength of FishDiveR lies in its ability to identify multiple clusters that would have been generalised into a single class of behaviour if only summary statistics had been applied (e.g., [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]). For example, variations in DVM occurring in the whale shark dataset were identified as distinct clusters, where traditional methods would have likely grouped them into a single DVM cluster. Indeed, FishDiveR distinguished different forms of DVM based on both surface proportion and night-time activity. Similarly, it identified differences in RDVM in the oceanic manta ray based on vertical velocities and surface proportion. These differentiations in vertical movements align with the diversity in DVM patterns documented in planktonic and nektonic prey organisms [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e], including nocturnal, twilight, and reverse-diel-migrations [\u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e52\u003c/span\u003e]. Such detailed classification underscores FishDiveR's capability to provide a robust analysis of vertical movements that traditional methods might overlook.\u003c/p\u003e\u003cp\u003eHowever, while the classification of vertical movements offers functional insights, it is important to acknowledge that the identified \u0026ldquo;behaviours\u0026rdquo; are typically not validated and rely on inferences from other studies [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e, \u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e53\u003c/span\u003e]. Therefore, the ability of FishDiveR to detect distinct \u0026ldquo;behaviours\u0026rdquo; is contingent upon the current understanding of species-specific vertical movements. Continued efforts in studying these movements using multi-sensor tags and additional techniques (e.g., prey mapping via acoustic methods) are strongly recommended to advance this field [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eFuture iterations of FishDiveR will aim to accommodate non-continuous time series, which are common in satellite-transmitted datasets and when sampling frequency changes during deployment. This will further increase the software\u0026rsquo;s application to both existing and future PSAT datasets. Additionally, FishDiveR could be adapted to analyse the vertical movements of other taxa that move in three-dimensional space, such as birds in flight as revealed by altitude loggers [\u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e54\u003c/span\u003e]. Similar to aquatic species, the vertical movements of flying birds could reveal key behavioural patterns related to migration, foraging, and response to environmental changes. The software also holds potential for cross-species meta-analysis, highlighting shared behavioural patterns and their environmental drivers through quantitative, multivariate comparisons (\u003cem\u003esensu\u003c/em\u003e [\u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e55\u003c/span\u003e]). These extensions underscore the versatility of FishDiveR, making it a potentially valuable tool for researchers in both marine and aerial ecology.\u003c/p\u003e"},{"header":"5. Conclusion","content":"\u003cp\u003eThis novel workflow represents a significant advance over both manual classification and the use of depth summaries by enabling the identification of dynamic behaviours through the precise capture of their timing and frequency. The accompanying R package, FishDiveR, streamlines the analysis of large depth time-series data, enabling efficient processing of large datasets to uncover complex behavioural patterns with only a basic knowledge of R programming. This makes it a valuable tool for ecologists, conservationists, and managers studying aquatic and potentially avian fauna.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch3\u003eEthics approval\u0026nbsp;\u003c/h3\u003e\n\u003cp\u003eResearch was conducted in Indonesia with permission under Surat Izin Penelitian Nomor 69A/SIP/IV/FR/8/2022, and with Murdoch University animal ethics permit number RW3318/21.\u003c/p\u003e\n\u003ch3\u003eConsent for publication\u003c/h3\u003e\n\u003cp\u003eNot applicable\u003c/p\u003e\n\u003ch3\u003eAvailability of data and materials\u003c/h3\u003e\n\u003cp\u003eR-Mark FishDiveR package code is currently available in its development version for peer review at: https://github.com/calvinsbeale/FishDiveR\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eR-Mark code for simulation of diving behaviour, analysis of the four empirical datasets, and the down-sampling and comparison of different sampling intervals of oceanic manta ray tag data, along with the data from the simulated vertical movement dataset, the four empirical datasets, and the data required for the down-sampling and comparison of different sampling intervals is uploaded for peer review with this manuscript here: https://www.dropbox.com/scl/fo/3zjedmuhzrfzti7ftn4hr/AOZV0Aq4-BNfLPdU3ogNVlE?rlkey=4sx8zeqxrpwf94w04kkavopwx\u0026amp;st=13ukpwl2\u0026amp;dl=0\u0026nbsp;\u003c/p\u003e\n\u003ch3\u003eCompeting interests\u003c/h3\u003e\n\u003cp\u003eThe authors declare that they have no competing interests.\u003c/p\u003e\n\u003ch3\u003eFunding\u003c/h3\u003e\n\u003cp\u003eWe thank MAC3 Impact Philanthropies, the Henry Foundation, the Save the Blue Foundation, Daniel Roozen, and Katrine Bosley for their generous financial support of Conservation International satellite tagging programs. Finally, we extend special thanks to the Harbig Family Foundation for their generous financial support.\u003c/p\u003e\n\u003ch3\u003eAuthor contributions (CRediT author statement):\u003c/h3\u003e\n\u003cp\u003e\u003cstrong\u003eCalvin S. Beale:\u003c/strong\u003e Conceptualisation, Methodology, Software, Formal analysis, Investigation, Writing \u0026ndash; Original Draft, Writing \u0026ndash; Review \u0026amp; Editing. \u003cstrong\u003eJenna L. Hounslow:\u003c/strong\u003e Writing \u0026ndash; Review \u0026amp; Editing. \u003cstrong\u003eAngela J.E. Beer:\u003c/strong\u003e Writing \u0026ndash; Review \u0026amp; Editing. \u003cstrong\u003eMatias Braccini:\u003c/strong\u003e Writing \u0026ndash; Review \u0026amp; Editing. \u003cstrong\u003eMark V. Erdmann:\u0026nbsp;\u003c/strong\u003eFunding acquisition. \u003cstrong\u003eAlastair Harry:\u003c/strong\u003e Writing \u0026ndash; Review \u0026amp; Editing. \u003cstrong\u003eNeil R. Loneragan:\u003c/strong\u003e Writing \u0026ndash; Review \u0026amp; Editing. \u003cstrong\u003eMark Meekan:\u003c/strong\u003e Writing \u0026ndash; Review \u0026amp; Editing. \u003cstrong\u003eStephen J. Newman:\u003c/strong\u003e Writing \u0026ndash; Review \u0026amp; Editing. \u003cstrong\u003eDavid Righton:\u003c/strong\u003e Writing \u0026ndash; Review \u0026amp; Editing. \u003cstrong\u003eFerawati Runtuboy:\u003c/strong\u003e Writing \u0026ndash; Review \u0026amp; Editing. \u003cstrong\u003eMichael J. Travers:\u003c/strong\u003e Writing \u0026ndash; Review \u0026amp; Editing. \u003cstrong\u003eSerena Wright:\u003c/strong\u003e Writing \u0026ndash; Review \u0026amp; Editing. \u003cstrong\u003eAdrian C. Gleiss:\u003c/strong\u003e Conceptualisation, Methodology, Writing \u0026ndash; Review \u0026amp; Editing.\u003c/p\u003e\n\u003ch3\u003eAcknowledgements\u003c/h3\u003e\n\u003cp\u003eWe acknowledge and appreciate the assistance RISTEK-BRIN to obtain this research permit, along with \u003cem\u003eBALITBANGDA Papua Barat\u0026nbsp;\u003c/em\u003eand\u003cem\u003e\u0026nbsp;Pemerintah Daerah Raja Ampat.\u003c/em\u003e We would like to thank both the University of Papua (UNIPA) and the Maritime and Fisheries Polytechnic of Sorong for their help in arranging research permits, collaboration, and research opportunities. We also thank the Raja Ampat Marine Protected Area Management Authority (UPTD BLUD KKPD Raja Ampat) for supporting this research. 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Available from: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://onlinelibrary.wiley.com/doi/full/\u003c/span\u003e\u003cspan address=\"https://onlinelibrary.wiley.com/doi/full/\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1002/ecs2.4825\u003c/span\u003e\u003cspan address=\"10.1002/ecs2.4825\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"movement-ecology","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"move","sideBox":"Learn more about [Movement Ecology](http://movementecologyjournal.biomedcentral.com/)","snPcode":"40462","submissionUrl":"https://submission.nature.com/new-submission/40462/3","title":"Movement Ecology","twitterHandle":"@BioMedCentral","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"BMC/SO AJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Behaviour classification, k-means clustering, satellite archival tags, principal component analysis, R package, vertical movement, sampling frequency","lastPublishedDoi":"10.21203/rs.3.rs-6907076/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6907076/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003e1. Biologging devices have revolutionised our understanding of aquatic animal movement by enabling the collection of detailed depth and temperature time-series. The advent of pop-up satellite archival tags has been particularly impactful, facilitating the collection of tens of thousands of depth time-series (DTS) datasets, with deployment periods ranging from days to years. Datasets from recovered tags are more detailed than those transmitted via satellite, yet both are commonly reported with rudimentary histograms of time-at-temperature and time-at-depth. Such histograms often fail to capture the complex temporal dynamics of vertical movements that are available from the high sampling frequency time-series in recovered tags.\u003c/p\u003e\u003cp\u003e2. This study describes a robust and effective method for the quantitative analysis of large DTS datasets collected from archival tags, utilising continuous wavelet transformation (CWT), Principal Component Analysis (PCA), and k-means clustering. CWT was employed to detect key periodic patterns within the data. Daily wavelet components were calculated across different wavelet periods (e.g., 5-min through 24-h) and reduced via PCA to characterise daily vertical movement behaviour while preserving variance. Finally, unsupervised k-means clustering was used to classify vertical movement behaviours according to their wavelet components and depth summary statistics.\u003c/p\u003e\u003cp\u003e3. This approach efficiently processed large quantities of data, and validation using simulated data demonstrated its robustness and versatility, with assigned behaviour clusters matching the original simulated behaviour types with high accuracy (97.7%). For the empirical data, distinct behavioural clusters were identified across a wide range of species, including an oceanic manta ray \u003cem\u003eMobula birostris\u003c/em\u003e, whale shark \u003cem\u003eRhincodon typus\u003c/em\u003e, Atlantic cod \u003cem\u003eGadus morhua\u003c/em\u003e, and largetooth sawfish \u003cem\u003ePristis pristis\u003c/em\u003e. Down sampling of the DTS revealed the method to be somewhat insensitive to the sampling frequency of tags, maintaining 83.9% accuracy as sampling frequency decreased from one to 15-minutes.\u003c/p\u003e\u003cp\u003e4. These results not only underscore the method's efficacy but also highlight its broad applicability in diverse settings. To facilitate uptake of this approach, an R package \u003cem\u003eFishDiveR\u003c/em\u003e, tailored for the implementation of this analytical methodology has been developed.\u003c/p\u003e","manuscriptTitle":"FishDiveR: Wavelet analyses and machine learning provide robust classification of animal behaviour from time-depth data","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-07-19 15:50:56","doi":"10.21203/rs.3.rs-6907076/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-09-12T15:04:34+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-09-10T08:34:56+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-08-18T02:05:36+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"40349828639149317353160351521827047744","date":"2025-08-15T11:29:22+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"233140232727747743576718148196396315572","date":"2025-07-25T09:52:37+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-07-16T09:02:39+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-06-24T13:18:50+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-06-24T13:17:54+00:00","index":"","fulltext":""},{"type":"submitted","content":"Movement Ecology","date":"2025-06-16T15:34:16+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"movement-ecology","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"move","sideBox":"Learn more about [Movement Ecology](http://movementecologyjournal.biomedcentral.com/)","snPcode":"40462","submissionUrl":"https://submission.nature.com/new-submission/40462/3","title":"Movement Ecology","twitterHandle":"@BioMedCentral","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"BMC/SO AJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"9571e49a-7a21-4b43-b223-586fcecadfa9","owner":[],"postedDate":"July 19th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2026-01-26T16:02:46+00:00","versionOfRecord":{"articleIdentity":"rs-6907076","link":"https://doi.org/10.1186/s40462-025-00622-w","journal":{"identity":"movement-ecology","isVorOnly":false,"title":"Movement Ecology"},"publishedOn":"2026-01-22 15:58:04","publishedOnDateReadable":"January 22nd, 2026"},"versionCreatedAt":"2025-07-19 15:50:56","video":"","vorDoi":"10.1186/s40462-025-00622-w","vorDoiUrl":"https://doi.org/10.1186/s40462-025-00622-w","workflowStages":[]},"version":"v1","identity":"rs-6907076","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6907076","identity":"rs-6907076","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}