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Novel tag-based method for measuring tailbeat frequency and variations in amplitude in fish

Novel tag-based method for measuring tailbeat frequency and variations in amplitude in fish The tailbeat frequency ( TBF) together with tailbeat amplitude ( TBA) of fish are tightly correlated with swimming speed. In addition, these parameters can be used as indicators of metabolic rate and general activity level, provided that appropriate calibration studies have been performed in the laboratory. If an implantable bio‑logger could meas‑ ure TBF and TBA, it would, therefore, have great potential as a tool to monitor swimming behaviours and bioenerget‑ ics over extended periods of time in free roaming fish within natural or farm environments. The purpose of this study was, therefore, to establish a method for deriving accurate TBF and variations in TBA from activity tags that log high‑ resolution acceleration data. We used 6 tagged Atlantic salmon (Salmo salar) of ≈1 kg and subjected them to two types of swim trials in a large swim tunnel system. Test speeds were either incrementally increased in 20‑min intervals −1 until steady swimming ceased, or constant speed of 60 cm s was given in a 4‑h sustained test. The TBFs were visu‑ ally observed by camera and compared with computed values from the activity tags. In the incremental trials the TBF increased linearly with swimming speed, while it remained constant during the 4 h of sustained swimming. The −1 TBFs measured by activity tags were within ± 0.1 beat s of the visual measurements across the swim speeds tested −1 between 30 to 80 cm s . Furthermore, TBF and its corresponding relative swim speed were consistent between trial type. The relative TBA increased with swimming speed as a power function, showing that the fish relies on changes in both amplitude and frequency of tail movements when swimming at higher speeds, while adjustments of amplitude only play a minor part at lower speeds. These results demonstrate that TBFs can be measured accurately via activity tags, and thus be used to infer swimming activities and bioenergetics of free roaming fish. Furthermore, it is also pos‑ sible to estimate changes in TBA via activity tags which allows for more nuanced assessments of swimming patterns in free roaming fish. Keywords Acceleration, Bioenergetics, Data storage tag, Fish behaviour, Monitoring, Swim speed *Correspondence: M. Hvas malthe.hvas@imr.no Full list of author information is available at the end of the article © The Author(s) 2023. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http:// creat iveco mmons. org/ licen ses/ by/4. 0/. The Creative Commons Public Domain Dedication waiver (http:// creat iveco mmons. org/ publi cdoma in/ zero/1. 0/) applies to the data made available in this article, unless otherwise stated in a credit line to the data. Warren‑Myers et al. Animal Biotelemetry (2023) 11:12 Page 2 of 13 pumped per heartbeat) play a greater part in control- Introduction ling cardiac output [61, 63]. As such, while heart rate still Biotelemetry and biosensing devices have been used increases between inactivity and high swimming inten- extensively in fish biological research for decades to sity, it becomes a crude predictor of swimming speeds obtain otherwise unobtainable individual-based knowl- and metabolic rates when assessing the entire range of edge of fish species in their natural environments [30, activity found in fish, particularly at intermediate levels. 45]. Various types of tags have been developed for a range Furthermore, heart rate can be drastically elevated owing of purposes that may be externally attached or implanted to various stressors, while the fish is mostly inactive, internally, and function either as data transmitters or and in those cases heart rate does not reflect swimming data storage tags [11, 13]. The purpose of tagging studies speeds at all, e.g., [37]. Tags that measure acceleration has typically been to gain fundamental knowledge of the have also been investigated for their applicability to esti- spatial and temporal distribution of wild fish, including mate swimming speeds and bioenergetics in fish. Similar foraging behaviours, migration patterns, and movements to heart rate, activity proxies derived from acceleration during reproduction events [2, 14, 25, 56]. Such work also data have been shown to somewhat correlate with swim- has broader applications in conservation efforts and pop - ming speeds and metabolic rates, at least when assessing ulation managements by documenting the environmental very low and very high activity levels, e.g., [9]. However, preferences as well as the potential vulnerabilities of fish these parameters also suffer from limitations in how species when subjected to anthropogenic interferences accurately they may predict swimming speeds and meta- [12, 13, 48, 55]. More recently, tags have also gained pop- bolic rates over the full range of activity levels in fish [9, ularity in aquaculture research as an approach to assess 22, 75, 76]. fish welfare in sea cage environments [17, 46, 51]. A potentially more precise candidate for inferring Parameters typically measured in tagging studies are swimming speeds and metabolic rates in free roam- movements over extended periods of time [30, 45] or ing fish is the tailbeat frequency (TBF). It is well-docu - activity levels [16, 18, 41], often in combination with data mented that TBFs are tightly and linearly correlated with of the physical environment, such as depth, temperature, swimming speeds in various fish species tested in the and oxygen saturation [56, 59, 74]. In recent years, along laboratory, and that metabolic rate is sensitive to changes with miniaturization and increased storage capacity of in swimming speeds. TBFs can thus function as prox- computer chips, commercially available tags have been ies for metabolic rates at different activity levels [35, 37, developed to measure more sophisticated physiological 60]. The TBF can be derived from acceleration measure - parameters such as heart rate in fish in addition to other ments, provided they are logged at a sufficiently high fre - parameters [6, 9]. quency (i.e., at least 2 × the expected maximum tailbeat Biosensors or telemetry devices can provide a valuable rate). However, there are few studies, where electronic link between highly controlled laboratory experiments tags have been used to calculate TBF, and these are to and the actual conditions experienced by free swim- our knowledge limited to older efforts on rainbow trout ming fish in their ambient environment. For instance, in (Oncorhynchus mykiss) and Japanese flounder (Paralich - the laboratory heart rate and acceleration of tagged fish thys olivaceus) [41, 42]. Interestingly, analogous work has can systematically be measured in resting conditions, at been done in birds, where wing beat frequency has been increasing activity levels, and in response to acute stress estimated via accelerometer tags [21, 65]. [9, 36, 37, 76]. Tag data can then be correlated with other In addition to the TBF, the tail beat amplitude (TBA) is parameters of interest, particularly the swimming speed required to obtain a full assessment of how the fish gen - and the metabolic rate of the fish [37, 76]. Once such cali- erates thrust at various activity levels. Estimates of TBA bration studies have been performed, it is then possible are generally more complicated to obtain and we are to infer additional information in free roaming tagged unaware of any previous efforts to compute a TBA from fish species subjected to less well-defined contexts. acceleration tags. We theorize that absolute values of Specifically, obtaining accurate estimates of swimming TBA will be difficult to obtain based on acceleration, but speeds and metabolic rates indirectly via tagging devices that it will be possible to acquire a measure of changes in would have tremendous potential in many areas of fish TBA over time by comparing the measured amplitudes in biological research, as they can describe the bioenerget- acceleration. Hence, it may be possible to derive relative ics and swimming patterns at a high temporal resolution changes in TBA from high frequency acceleration tags over prolonged timescales of fish in their ambient envi - together with TBF. ronment [24, 75]. To be sure that novel tag derived parameters can Heart rate may not be the most precise indicator of provide relevant information about free roaming fish, swimming speed or metabolic rate, at least in salmonid they first need to undergo proof of concept studies in species, because changes in the stroke volume (blood W arren‑Myers et al. Animal Biotelemetry (2023) 11:12 Page 3 of 13 controlled laboratory settings, where data collected from where physical data in absolute units are of interest re- tags are validated [7, 27, 62, 76]. As such, tag derived calibrations may be considered, e.g., [21]. However, in TBFs, therefore, require confirmation with visually the present study we only report frequencies and relative observed values at different swimming speeds before changes. they can be used in the field. In this study, we tested if a commercially available activity tag with a high frequency data logging capac- Tagging of fish ity could measure the TBF and TBA in Atlantic salmon Atlantic salmon weighing 1068 ± 26  g (Table  1) were −1 (Salmo salar) subjected to two types of swim tunnel tri- tagged after anesthetizing with 150  mg L Finquel als. In the first trial, we performed a critical swim speed for approximately 4  min and then placed inverted on −1 inspired test with incremental increases in flow speeds in a holding tray. During tag implantation, 75  mg L Fin- 20-min intervals to assess a range of swimming activities. quel was continuously flowing over the gills via a tube In the second trial, we used a sustained swimming test, to keep the fish sedated. A Technosmart axy-5 s tag was where fish were subjected to a constant flow speed for 4 h then inserted into the abdominal cavity through an inci- to evaluate the consistency of TBF and TBA over time at sion made aft of the pectoral fin. The incision was closed the same activity level. Our primary aims were to investi- with 2 to 3 stitches, gently dried and then a thin layer of gate how well values computed from tag measurements antibacterial Histoacryl was applied to further seal the correlated with visual measurements for TBF (this was wound. The tagging procedure for each fish was com - not possible for TBA as amplitude is difficult to gauge pleted in less than 5 min. A total of 8 fish were tagged for visually) and correlate computed TBF and TBA values this study. with swimming speeds. Swim tunnel system Methods To test the efficacy of measuring swimming performance Animal husbandry with activity tags, fish were swum individually in a 1905 l Atlantic salmon post smolts (Aquagen) were kept in large Brett-type swim tunnel setup as described previously indoor holding tanks (diameter: 3  m; volume: 5.3 m ) at by Remen et  al. [54]. In brief, the cylindrical swim sec- the Matre Research Station, Institute of Marine Research, tion was 248 cm long with an internal diameter of 36 cm. Norway. Tanks were supplied with 12 °C filtered seawater −1 Controlled water currents within the tunnel was gener- (34 ppt) via a flowthrough system (120 l  min ). A simu- ated with a motor driven propeller (Flygt 4630, 11° pro- lated natural photoperiod was provided, and fish were fed peller blade, Xylem Water Solutions Norge AS, Norway). commercial feed (4.5 mm pellet size; Skretting) in excess The swim tunnel was connected via a large hose to the each day via automated feeders. Fish were acclimated to same header tank as used to supply water to the fish these conditions for a minimum of 1  month before the tanks, allowing for a continuous flow through the setup experimental trials began. The experimental trials were which maintained a 12  °C test temperature and ensured performed in October and November 2020, and the use optimal oxygen levels at all times. A camera was deployed of animals was approved by the Norwegian Food Safety downstream behind the rear grid to record the trials and Authorities under ethics permit identification number for visual estimates of TBF without disturbing the fish. At the rear end, a removable top lid allowed easy access into the tunnel for adding and removing fish. High frequency acceleration tags Commercially available accelerometer Data Storage Tags (Technosmart axy-5  s activity tags, dimensions Table 1 Morphometric parameters of the tagged Atlantic 22 × 13 × 10  mm, weight 4.5  g, www. techn osmart. eu) salmon tested in the swim trials with incremental increases in swim speed or sustained speed for 4 h were used to obtain the acceleration data. This data was then used to estimate TBF values and relative changes Trial Fish Weight (g) Length (cm) Condition in TBA. In addition, the TBF estimates could be com- factor pared to visual TBF measurements. The tags were pro - Incremental A 1085 47.1 1.04 grammed in TechnoSmart X MANAGER software (v. B 1094 46.8 1.07 1.8.3) to log tri-axial acceleration (X, Y and Z) with a C 939 44.5 1.07 sampling frequency of 25 Hz within a range of G (± 4 G). Sustained D 1093 46.6 1.08 Tag outputs were set to 8-bit values, mapping measured E 1104 47.2 1.05 acceleration values within this range. The accelerometer F 1091 46.5 1.09 tags were pre-calibrated by the manufacturer. In cases, Warren‑Myers et al. Animal Biotelemetry (2023) 11:12 Page 4 of 13 Swim trials with an anaesthetic overdose of Finquel, fish weight The day before a swim trial, one tagged fish was trans - and fork length were recorded, and the activity tag was ferred to the swim tunnel for acclimation overnight at recovered. −1 a water flow rate of 20  cm  s . This flow rate is gener - The remaining two of the tagged fish did not cope ade - ally too low to initiate continuous swimming efforts in quately in the tunnel environment as they were reluctant Atlantic salmon of the size tested here and instead they to swim consistently for the full trial period. These were, typically balance on the floor of the tunnel. An overnight therefore, discarded from further analyses, providing 3 acclimation period is standard procedure in Atlantic replicates for each trial type. salmon swim trials to allow recovery of acute handling stress and acclimation to a novel environment before the onset of swim tests, e.g., [37]. Tag data extraction and post processing analysis Three tagged fish (A–C, Table  1.) were swum individu- Raw data time series were downloaded and converted ally on separate days following a typical critical swim from 8-bit binary values into acceleration values in G speed protocol, e.g., [5] with the exception that the fish (± 4 G) in X MANAGER and stored as data sets in.csv were removed from the tunnel before fatigue occurred, as file format. inferred from the transition between steady swimming to Because the tags measured acceleration, some con- the onset of burst and glide swimming behaviour. Start- siderations were made before extracting TBF and TBA. ing from the initial overnight resting current speed of When implanting tags in fish there will be an offset −1 20 cm  s , for each fish on the day of the swim trial at between the accelerometer’s sensing axes and the BODY 10:00 h, the water flow in the swim tunnel was increased coordinate system, i.e., the (imagined) coordinate sys- −1 by 10 cm  s every 20 min until the fish no longer swam tem fixed to the fish’s centre of gravity (Fig.  1). The off - steadily. Once the fish stopped swimming steadily and set between the longitudinal axes (i.e., X and X,b) will be began exhibiting burst and glide behaviour, signifying negligible compared with the offset between the other transition to partially anaerobically fuelled swimming axes if the tag is implanted, such that it rests against the and imminent fatigue, e.g., [72], it was removed from abdomen of the fish as is the common practice, e.g., [10]. the tunnel. The fish was then immediately euthanized By assuming that the tag remains stationary inside with an anaesthetic overdose of Finquel, whereafter the the fish and that the raw data means for the entire weight and fork length were recorded, and the activity tag duration of the measurements represent the stationary recovered. While fish were swimming at each different speed interval, TBF (time taken for 100 tail beats) were meas- ured manually using video camera footage and a stop- watch. Visual measurement of TBFs is a simple procedure when the fish is readily observed on camera. In addition, the swim trials were recorded, so that visual measure- ments could be confirmed later on. Three other tagged fish (D–F, Table  1) were similarly tested individually on separate days. However, here a sustained swimming speed test was used following a similar procedure to that of Hvas and Oppedal [31]. Starting from the initial overnight resting current speed −1 of 20 cm  s at 09:54  h, the waterflow was increased by −1 10 cm  s every 2  min, so that by 10:00  h the waterflow −1 −1 speed was 60  cm  s . A sustained speed of 60  cm  s was chosen here to represent an intermediate chal- lenge slightly above the expected optimal cruising speed for minimum cost of transport, but still well within the aerobic limit of Atlantic salmon [31, 38]. Each fish was Fig. 1 Illustration of how the accelerometer measurement axes of then swum at this flow rate for the next 4 h. During this the tag (X, Y and Z) relate to orientation axes of the fish (X,b, Y,b and time manual measurements of the TBF were made every Z,b). Assuming that X is aligned with X,b, pitch (Θ) will define the 30  min using the camera footage and a stopwatch simi- angle between X and the horizontal plane, while the roll (ɸ) and yaw lar to the incremental swim trials. After 4 h of swimming, (ψ) angles will define used to describe the deviation between the Y the fish was removed from the tunnel and euthanised and Y,b and Z and Z,b, respectively W arren‑Myers et al. Animal Biotelemetry (2023) 11:12 Page 5 of 13 acceleration offsets, the angular offsets for roll (ɸ ) and outside the expected TBF frequency band. An example of pitch (θ) and yaw (ψ) can be calculated using the effect of these processing steps is given in Fig. 2. The rotated and filtered acceleration time series were φ = arctan , (1) represented in the time domain. However, in this case the frequency components were of particular interest, thus   it was desirable to present the data also in the frequency domain to evaluate the signal’s frequency constituents   θ =−arctan � (2) and amplitude in G (1G = 9.81 m/s ). To do this, the data 2 2 A + A Y Z must first be transformed using specific signal process - ing methods. One such transform is the ’Fast Fourier and Transform’ (FFT) which returns the frequency compo- nents for the entire signal duration to which it is applied. ψ = arctan (3) While FFT is a proven method for determining the fre- quency composition of complex signals, it analyses the where A , A and A are the measured accelerations X Y Z whole period as one, and thus cannot capture changes in along the different axes. The measured accelerations can the frequency composition that occur during the signal then be rotated to the BODY coordinate system using period. To acquire this ability, a modified FFT approach      called the ’Short Time Fast Fourier Transform’ (STFFT) A cψ cθ −sψ cφ + cψ sθ sφ sψ sφ + cψ cθ sφ A X,b X      = was applied instead. The STFFT algorithm applies a roll -  A   sψ cθ cψ cφ + sψ sθ sφ −cψ sφ + sψ sθ cφ  A  Y ,b Y A −sθ cθ sφ cθ cφ A ing time window to the input signal, applies the FFT to Z,b Z (4) the data within this window and then shifts by a pre-set amount to overlap with itself before re-applying the FFT where s and c denote sine and cosine, respectively [20]. to the data within the new window. This is repeated for Following rotation, gravity was subtracted from the the entire duration of the signal. By choosing the appro- Z-axis and data were filtered using a 4th order Butter - priate window length and overlap, the frequency and worth bandpass filter with low and high frequency lim - amplitude content of the input signal can be analysed its of 0.8 and 5 Hz, respectively, to suppress signal noise with respect to time. Fig. 2 Eec ff t of processing steps, exemplified using data from Fish C. The leftmost column shows the raw measurements, the middle column data after rotation using Eq. 4, while the rightmost column shows the resulting data after subtracting gravity and smoothing through filtering Warren‑Myers et al. Animal Biotelemetry (2023) 11:12 Page 6 of 13 For the rotated acceleration data, the acceleration com- To summarize, this tag data extraction and post pro- ponent A is aligned with the expected direction of cessing analysis results in a processing flow consisting Y,b the tail beat (i.e., laterally outwards from the fish body), of five main steps as illustrated in Fig. 4 . hence any distinct tail beat frequency would be expected to appear in the frequency spectrum of A . STFFT using Y,b a 20  s window and 75% overlap was, therefore, applied to this axis. For each (overlapping) window, the highest frequency spectrum peak was considered to represent both TBF (placement on the frequency axis) and TBA (peak height) resulting in one TBF and TBA result per 5 s (Fig. 3). Unlike for TBF, the value obtained through STFFT for TBA will not represent the absolute value of the TBA as acquiring this parameter from accelerations entails inte- grating the acceleration time series twice, which tends to amplify measurement errors and inaccuracies. Moreover, since the tags were placed intraperitoneally, the conver- sion would also require translating and transforming accelerations measured in the abdomen to those exhib- ited by the tail of the fish, which would in turn depend strongly on the fish morphology and other unknown factors. However, provided that the tag position within the fish is fixed after implantation, variations in ampli - tude should also be expressed through variations in the height of the spectral peaks acquired through the STFFT. All analyses based on TBA were, therefore, made using the relative TBA, i.e., a measure of how much the TBA Fig. 4 Flow chart showing the processing procedure for acquiring changes between different speeds. tailbeat frequency ( TBF) and tailbeat amplitude ( TBA) data from the accelerometer tag measurements −1 Fig. 3 Example frequency spectrum from Fish C at 30 cm s . The horizontal axis denotes frequency, while the vertical axis denotes the proportion of the total measured acceleration that is calculated for the different frequency components. For a fish swimming at a steady speed, the former of these will correspond to the TBF, while the second will relate to the TBA W arren‑Myers et al. Animal Biotelemetry (2023) 11:12 Page 7 of 13 −1 Statistical analysis (Fig.  5A–C). Above 80  cm  s , steady swimming ceased For the incremental and sustained swim trials, correla- for fish B and C as they began to show initial signs of tions between observed TBFs taken via the camera foot- fatigue, so the swim trial for both these fish ended, while age and tag estimated TBFs, were tested using Pearson’s for fish A, erratic changes in swimming pattern did not −1 correlation coefficient. For the sustained swim trial, lin - occur until after 90 cm  s (Fig.  5A–C). For the 4-h sus- −1 ear regression using the mean hourly TBF estimates from tained swim speed tests at 60  cm  s , the fish exhibited tag measured data was used to test for any change in TBF consistent swimming behaviour for the full duration of over the 4-h period. To compare between swim trials, the test (Fig. 5D–F). −1 the ratio of TBF measured via the tags to BL s between In the incremental swim speed tests, the mean TBF −1 swim trial type at the flow speed of 60 cm  s was tested measured from camera observations ranged from 1.53 −1 −1 −1 using a one-way ANOVA. For all tests, the significant beats s ± 0.08 at 30  cm  s to 2.65 beats s ± 0.06 at −1 difference level was set at p < 0.05. All analyses were con- 80 cm  s , and the TBF derived from acceleration meas- −1 −1 ducted using SPSS 26 statistical software package. Data urements ranged from 1.40 beats s ± 0.05 at 30 cm  s −1 −1 are reported as mean ± standard error of the mean unless to 2.67 beats s ± 0.06 at 80  cm  s (Fig.  6A). There specified otherwise. was a strong linear correlation between the camera observed and tag estimated TBFs (Pearson’s r = 0.99, Results P < 0.001 (Fig. 6B). In the sustained swim trials, the over- Tailbeat frequency all mean TBF observed via the camera were 2.17 ± 0.07 −1 −1 In the incremental swim speed tests the TBF increased beats s and for the tag, 2.19 ± 0.03 beats s (Fig.  6C). −1 linearly with swimming speed from 30 to 80  cm  s There was a strong linear correlation between the mean Fig. 5 Incremental (A–C) and sustained (D–F) swim trials of tagged fish. For all graphs, black line represents tag estimated mean tailbeat frequency ( TBF) of 10 s subset measurements with 50% overlap between subsets. For fish A–C, red line indicates tag estimated mean TBF for each 20‑min interval at a specific current speed. Grey circles with a grey line indicate mean frequency of 3 visual estimates taken from camera recordings within each of those respective intervals. Error bars represents mean ± s.e.m. For fish D–F, vertical dashed lines indicate each hour from the start and end −1 point of the 4‑h sustained swim speed tests at 60 cm sec . Here, red line indicates tag estimated mean tail beat frequency for the complete trial, and grey circles with a grey line indicate visual point estimates of tailbeat frequency in 30‑min intervals Warren‑Myers et al. Animal Biotelemetry (2023) 11:12 Page 8 of 13 Fig. 6 Observed and tag computed tailbeat frequencies ( TBF) in the incremental swim speed trial (A) and the sustained swim trial (C), where error bars are mean ± s.e.m. Followed by correlation plots between tag estimated and observed TBF in their corresponding trials on the left panels (B and D) hourly camera observed and tag estimated TBFs (Pear- This relationship was best described with a power func - 2 2 son’s r = 0.88, P < 0.001) (Fig.  6D). Using tag estimated tion providing an R of 0.998. Furthermore, the changes TBF only, there was no significant change in the mean in TBF with increasing swimming speed were well- hourly TBF over the 4-h period showing that the TBF described by a linear regression, where R was 0.998 remained constant at constant swimming efforts over (Fig. 7B). The product of TBF and TBA across swimming time (F = 4.5, P = 0.06). speed could then provide a visualization of the relative 1,10 Using tag measured TBFs as a proxy for swimming increase in thrust generated by the fish, and this relation - speed in the sustained swim trial at the flow rate of ship followed a power function (R of 0.999) (Fig. 7C). −1 −1 60 cm  s the average tag TBF of 2.19 ± 0.03 beats s −1 equated to a swim speed of 1.28 ± 0.01 BL s (mean fork length of 46.8 ± 0.2  cm). This was consistent with the Discussion incremental swim trial during the 20  min period when In this study, we investigated whether commercially −1 the flow rate was also 60 cm  s as the average tag meas- available acceleration tags with a high frequency log- −1 ured TBF of 2.16 ± 0.07 beats s equated to a swim speed ging capacity could be used to accurately compute TBFs −1 of 1.30 ± 0.02 BL s (mean fork length 46.1 ± 0.8 cm). As in Atlantic salmon across a range of swimming speeds −1 such, when comparing the mean ratio of TBF to BL s at as well as providing consistent estimates over time at a this specific flow speed between the trial types, there was constant intermediate swimming speed. Since estimates −1 −1 no difference (TBF: BL. s : Incremental = 1.66 ± 0.07; of TBFs from tags were within ± 0.1 beats s of visual Sustained = 1.70 ± 0.03; F = 0.5, P = 0.5). counts across the assessed swimming speeds and trial 1,4 types, we conclude that acceleration tags effectively can be used to measure TBFs with enough accuracy to be Changes in tailbeat amplitude and thrust with increasing used as a proxy for swimming speeds and bioenergetics swimming speed in free roaming fish. In addition, we were able to compute There was a distinct relationship between the changes changes in relative tail beat amplitude (TBA) and found in relative TBA and the swimming speed of the fish that this parameter increases with swimming speed in (Fig.  7A), with the amplitude appearing to stay constant −1 a pattern resembling a power function. Combined, TBF for the lower speeds (30–40  cm ) and then increas- −1 and TBA derived from acceleration tags can thus provide ing substantially across the higher speeds (50–80  cm ). W arren‑Myers et al. Animal Biotelemetry (2023) 11:12 Page 9 of 13 −1 Fig. 7 Relative tail beat amplitudes at increasing current speeds as compared to 30 cm s fitted with a power function (A), and tailbeat frequency −1 at increasing current speeds fitted with a linear function (B). In C, the changes in thrust generated relative to 30 cm s is shown and fitted with a power function, where thrust is expressed as the product of the mean tailbeat amplitude and frequency at each current speed. Data in A and B are mean ± s.e.m additional assessments of how free roaming fish generate swimming speeds follow a power function [50]. This thrust in different scenarios. relationship reflects the hydrodynamics of swimming as the drag force increases in proportion to the square Tailbeat frequency as a proxy for swimming speed of the speed, meaning that the power required to over- and metabolic rate come drag increases with the cube of the speed [66, Acceleration tags have been used to infer swimming 70], making it energetically more and more expensive speeds and metabolic rates in fish on several occasions to increase swimming efforts further. For instance, in (e.g., [22, 57, 73, 75]. However, acceleration data has pre- Atlantic salmon the increase in aerobic metabolic rate viously mostly been sampled at lower frequencies, typi- between low and high swimming speeds approximates cally 1  Hz [3, 4, 76]. In consequence, categorization of a power function and increases with a factor of 3 to 6, swimming activity and associated energetic costs in such depending on the acclimation temperature [32]. Since the studies tends to be limited to crude categorizations, such metabolic rate response to increasing swimming speeds as resting, routine or burst swimming behaviours [1, 9]. is well-understood in fish and, moreover, is readily meas - By calculating the TBF from high resolution acceleration ured with swim tunnel respirometry in laboratory experi- tag data as in the present study, it would be possible to ments, robust calibration curves can be gathered, so that define a more fine-grained scale of swimming activity TBF tag data also can be used as a proxy of metabolic levels that would give greater precision in categorising rate. the movements of free roaming fish. This will be par - Our estimates of relative TBA as a function of swim- ticularly useful at intermediate activity levels, which are ming were best described by a power function, similar presumably the energetic states that fish occupy most of to the metabolic requirement at increasing swimming the time, for instance during foraging or migration which speeds. Meanwhile, the TBF increased linearly with are associated with optimal cruising speeds at minimum swimming speed. However, the drag forces increase transport costs [15, 71]. in proportion to the square of the speed, as discussed TBF tag data can also be expected to provide more above. To explain the observed propulsion of the fish, the accurate swimming speed estimates than other measur- amplitude, therefore, needed to increase relatively more able parameters, such as heart rate and instantaneous at higher speeds, as shown here. Furthermore, the prod- acceleration, since it is directly linked with the undula- uct of TBF and TBA can be used to estimate the relative tory locomotion. In the present study, TBF increased thrust generated by the fish. Owing to the patterns of −1 linearly from approximately 1.4 to 2.6 beats s with TBF and TBA with increasing swimming speed, thrust −1 increasing swimming speeds from 30 to 80 cm  s . Simi- was also best described as a power function. This reflects lar strong relationships between TBFs and swimming the above-mentioned hydrodynamics of swimming and speeds are well-documented in various fish species [35, corresponding metabolic requirements to overcome 37, 60], and highlights the potential for using previously increasing drag forces [66, 70]. Changes in TBA can, established regression lines to estimate swimming speeds therefore, provide additional information on how fish from TBF data in free-swimming tagged fish. generates thrust and contribute to making accelerom- The metabolic rate is highly sensitive to changes in eter tag data even more accurate in predicting swimming activity, and the energetic requirements at increasing speeds in ambient environments. Warren‑Myers et al. Animal Biotelemetry (2023) 11:12 Page 10 of 13 Limitations of tailbeat frequency tags to infer swimming and parasites [33, 67], and possibly exposure to toxic speeds and bioenergetics in fish substances in polluted environments [23, 49]. As such, While the correlations between TBF, swimming speed, when attempting to monitor the physiology and behav- and associated energetic costs are well-established, they iour of free-swimming fish, there will always be unknown are also context dependent and influenced by various factors that could alter correlations between TBF, swim- biological and environmental factors [35, 52, 60]. These ming speed and metabolic rate. Such uncertainties are must, therefore, be considered for proper interpretations an inherent challenge when studying animals outside the of TBF tag data from fish in ambient environments and laboratory. may limit the reliability of such tag data if parameters of unknown effects are involved. Thus, to fully exploit the Applications and further development of tailbeat possibility of TBF tags and to ensure the most accurate frequency tags data interpretation, a nuanced suite of lab-based calibra- We envision several useful applications with TBF tags in tion studies is ideally required on a per species basis. In future studies, particularly in aquaculture research with well-studied fish species, such as salmonids, it will be regard to fish welfare in salmon sea cages. Within these possible to amass correlation curves measured in many vast fish group sizes, the scope for detailed data acquisi - different contexts to strengthen data interpretations tion from tagged sentinel fish is large [17, 69], and vital of TBF tags. However, TBF tags may have less value as when moving towards the knowledge-based concept of a tool for energetic monitoring in less studied species, precision fish farming [19]. In this, TBF should allow for where swimming capacities and metabolic rates have recording behavioural modes and estimating the physical not been measured systematically. Nevertheless, it will demand of swimming in fish groups driven by environ - still be possible to describe the scope of TBFs used and mental features and social interactions (see [53] for estab- the frequency distribution to quantify general swimming lished observation methods). For example, in response patterns through time when studying new fish species. to high current speed, caged salmon change their group Apart from species differences in morphology and behaviour from circular schooling to a static group posi- physiology, the size of the fish is presumably the most tion directed against the inflowing water [40] which is important factor to influence TBF and its correlation likely to dampen current exposure within the fish school with swimming speed and metabolic rates. Specifically, [34]. Moreover, if an algorithm like the one used in this smaller fish can attain a higher TBF and swim at higher study were to be implemented in acoustic tags carrying −1 relative swimming speeds (e.g., body lengths s ), but accelerometers, these could be set to transmit the com- larger fish are able to swim faster in absolute units (e.g., puted tail beat rate in real time. This data could then be −1 cm s ) [35, 52]. The same TBF will, therefore, not cor - combined with measurements of absolute position [26] respond to the same swimming speed in fish of different and movement speed [27, 28] in the cage, which would size classes. It is thus important to consider size effects, enable more detailed studies of the link between TBF and especially if individuals remain tagged for prolonged energetic expenditure and actual movement in sea cages. periods and grow substantially in size. In addition, meta- Of fundamental interest, TBF can also be used to shed bolic rates also scale with size in a somewhat predictable new light into questions such as individual fish need for manner, where smaller individuals have a higher mass rest and switch in behavioural mode connected with vari- specific metabolic rate [43, 52]. ous photo-regimes and observed diel heart rate variation Since the metabolism of ectothermic fish is greatly with night and day length [69], recovery from exhaust- dependent on temperature this factor is also important ing operational procedures, such as mechanical parasite to consider. Typically, metabolic rates increase with a treatment [18], and whether adverse conditions such as factor of 2–3 per 10  °C, but thermal sensitivity depends high temperature [32] or internal processes as sexual on species, the specific portion of its thermal niche, and maturation or fasting will induce the urge for migration acclimation history [44]. Interestingly, the correlation and thus change in swimming pace or pattern. Sentinel between TBF and swimming speed is more consistent fish with TBF tags may also be important tools for docu - across temperatures than metabolic rate, except at ther- menting fish coping ability in novel aquaculture rearing mal extremes which pose a limit to maximum swimming technologies and systems. Possible applications in this capacity [32, 35]. Hence, TBF as a predictor of swimming area could include enabling continuous logging in harsh speed is less sensitive to fluctuations in temperature com - and remote ocean farming sites, serving as a compo- pared to metabolic rate. nent in early warning of negative buoyancy by increased Other factors worth considering include nutritional swimming speed in submerged salmon cages [58], as well states and body condition [39, 47], life-stages and par- as providing documentation and tuning of water current ticularly sexual maturation [29, 68], impacts of diseases exposure in closed containment systems [64]. W arren‑Myers et al. Animal Biotelemetry (2023) 11:12 Page 11 of 13 Tags that measure TBF also have potential for pro- use a singularity-free representation of rotation (e.g., viding new knowledge on fish species in the wild, for quaternions). instance during periods of migration to feeding or Selection of signal processing sliding window width spawning grounds, but also to generally obtain a more (20  s) and overlap (75%) was a trade-off between calcu - detailed understanding of natural activity patterns over lation robustness, computational demand and (timely) extended periods of time. Here, some practical consid- resolution for the results. For the signals measured in erations are methods of tag retrieval as high-frequency this study using a shorter window introduced more noise acceleration tags presently only function as implantable compared to longer windows due to the FFT averaging data storage tags. effect. Longer windows did not produce improved results While the TBA parameter computed in this study pro- while increasing computational demand. The parameters vided a relative measure of the changes in TBA rather used during processing are, therefore, considered a rea- than the absolute value (as was the case for TBF), it was sonable compromise. apparent that higher TBA-values correlated with higher The filtering bandpass parameters (0.8 and 5 Hz) were swimming speeds. Furthermore, the patterns observed chosen to suppress the effect of low and high frequency corresponded well with hydrodynamic predictions with contributions outside the range of the expected TBF for regard to thrust needed to overcome drag at increasing Atlantic salmon, e.g., [37]. These parameters are highly speeds. Although this parameter may not be as easy to species and size class specific and must be adapted link directly with energetics, it can be combined with accordingly with an appropriate TBF range (or for the TBF to estimate the relative thrust generated by the fish. general case). Finally, future tests using accelerometers This provides a unitless measure of swimming output to extract TBF and TBA should use sensor settings to that can be considered analogous to the cardiac output maximize the signal to noise ratio, i.e., the lowest possible which consists of heart rate multiplied by stroke volume. sensing range and the highest possible bit resolution. Similarly, stroke volume in fish is generally measured in The continuous development of more sophisticated relative changes, while heart rate implicitly is expressed implantable bio-loggers makes for an exciting future in as a frequency. Obtaining both TBA and TBF, there- fish biological research. Moreover, novel methods within fore, allow for a more holistic assessment of swimming biotelemetry and biosensors will help close the gap fur- energetics. ther between controlled laboratory trials and the more varied and unpredictable environments experienced by fish when allowed to swim around freely [8]. Managing data from tailbeat frequency tags The approach used in the present study to determine Acknowledgements The technical staff at the Matre Research station for providing excellent animal TBF and TBA is an adaptation of well-known signal husbandry. processing techniques. Data were successfully rotated into the BODY coordinate system, thus allowing direct Author contributions This study was conceived and designed by all authors. Experimental trials comparison of A data based on the assumption that Y,b were performed by MH, analyses of tag data were done by ES and MF. First the mean of all recorded data represents the accelera- draft was written by FW‑M with all co ‑authors providing thorough feedback tion offset. This assumption is only valid if the tags do before approving the final version. All authors read and approved the final manuscript. not shift within the peritoneal cavity during data capture. Future trials can address this by suturing tags in place for Funding improved implantation control and easier result compar- This research was funded through the Research Council of Norway, EXPOSED Aquaculture Research Centre, grant number 237790. Martin Føre acknowl‑ ison between individuals. Alternatively, the offsets can be edges the financial support from Salmar ASA/Salmar Aker Ocean AS. periodically re-calculated, compared to previous values and updated accordingly. Data availability Raw data will be made available upon request. Furthermore, care must be taken when calculating the offsets (Eqs.  1, 2 and 3). Accurate offset calculations pre - T T Declarations clude that [A , A , A ] ≉0. If [A , A , A ] ≈0, i.e., below X Y Z X Y Z the signal noise level, A , A and A should be ini- X,b Y,b Z,b Ethics approval and consent to participate tialized to 0. Furthermore, for θ = 90°, Eq.  4 is singular The use of animals was approved by the Norwegian Food Safety Authorities under ethics permit identification number 24444. (i.e., the denominator becomes 0) and cannot be solved. In free-swimming fish, this may occur when the fish is Consent for publication free to manoeuvre in all three dimensions (although All authors have agreed to publish this work as presented here. salmon are unlikely to moving at as steep angles as Competing interests θ = 90°). Future implementations of this approach The authors declare no competing interests. should, therefore, either include a singularity check or Warren‑Myers et al. Animal Biotelemetry (2023) 11:12 Page 12 of 13 Author details 17. 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Novel tag-based method for measuring tailbeat frequency and variations in amplitude in fish

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Copyright © The Author(s) 2023
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2050-3385
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10.1186/s40317-023-00324-3
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Abstract

The tailbeat frequency ( TBF) together with tailbeat amplitude ( TBA) of fish are tightly correlated with swimming speed. In addition, these parameters can be used as indicators of metabolic rate and general activity level, provided that appropriate calibration studies have been performed in the laboratory. If an implantable bio‑logger could meas‑ ure TBF and TBA, it would, therefore, have great potential as a tool to monitor swimming behaviours and bioenerget‑ ics over extended periods of time in free roaming fish within natural or farm environments. The purpose of this study was, therefore, to establish a method for deriving accurate TBF and variations in TBA from activity tags that log high‑ resolution acceleration data. We used 6 tagged Atlantic salmon (Salmo salar) of ≈1 kg and subjected them to two types of swim trials in a large swim tunnel system. Test speeds were either incrementally increased in 20‑min intervals −1 until steady swimming ceased, or constant speed of 60 cm s was given in a 4‑h sustained test. The TBFs were visu‑ ally observed by camera and compared with computed values from the activity tags. In the incremental trials the TBF increased linearly with swimming speed, while it remained constant during the 4 h of sustained swimming. The −1 TBFs measured by activity tags were within ± 0.1 beat s of the visual measurements across the swim speeds tested −1 between 30 to 80 cm s . Furthermore, TBF and its corresponding relative swim speed were consistent between trial type. The relative TBA increased with swimming speed as a power function, showing that the fish relies on changes in both amplitude and frequency of tail movements when swimming at higher speeds, while adjustments of amplitude only play a minor part at lower speeds. These results demonstrate that TBFs can be measured accurately via activity tags, and thus be used to infer swimming activities and bioenergetics of free roaming fish. Furthermore, it is also pos‑ sible to estimate changes in TBA via activity tags which allows for more nuanced assessments of swimming patterns in free roaming fish. Keywords Acceleration, Bioenergetics, Data storage tag, Fish behaviour, Monitoring, Swim speed *Correspondence: M. Hvas malthe.hvas@imr.no Full list of author information is available at the end of the article © The Author(s) 2023. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http:// creat iveco mmons. org/ licen ses/ by/4. 0/. The Creative Commons Public Domain Dedication waiver (http:// creat iveco mmons. org/ publi cdoma in/ zero/1. 0/) applies to the data made available in this article, unless otherwise stated in a credit line to the data. Warren‑Myers et al. Animal Biotelemetry (2023) 11:12 Page 2 of 13 pumped per heartbeat) play a greater part in control- Introduction ling cardiac output [61, 63]. As such, while heart rate still Biotelemetry and biosensing devices have been used increases between inactivity and high swimming inten- extensively in fish biological research for decades to sity, it becomes a crude predictor of swimming speeds obtain otherwise unobtainable individual-based knowl- and metabolic rates when assessing the entire range of edge of fish species in their natural environments [30, activity found in fish, particularly at intermediate levels. 45]. Various types of tags have been developed for a range Furthermore, heart rate can be drastically elevated owing of purposes that may be externally attached or implanted to various stressors, while the fish is mostly inactive, internally, and function either as data transmitters or and in those cases heart rate does not reflect swimming data storage tags [11, 13]. The purpose of tagging studies speeds at all, e.g., [37]. Tags that measure acceleration has typically been to gain fundamental knowledge of the have also been investigated for their applicability to esti- spatial and temporal distribution of wild fish, including mate swimming speeds and bioenergetics in fish. Similar foraging behaviours, migration patterns, and movements to heart rate, activity proxies derived from acceleration during reproduction events [2, 14, 25, 56]. Such work also data have been shown to somewhat correlate with swim- has broader applications in conservation efforts and pop - ming speeds and metabolic rates, at least when assessing ulation managements by documenting the environmental very low and very high activity levels, e.g., [9]. However, preferences as well as the potential vulnerabilities of fish these parameters also suffer from limitations in how species when subjected to anthropogenic interferences accurately they may predict swimming speeds and meta- [12, 13, 48, 55]. More recently, tags have also gained pop- bolic rates over the full range of activity levels in fish [9, ularity in aquaculture research as an approach to assess 22, 75, 76]. fish welfare in sea cage environments [17, 46, 51]. A potentially more precise candidate for inferring Parameters typically measured in tagging studies are swimming speeds and metabolic rates in free roam- movements over extended periods of time [30, 45] or ing fish is the tailbeat frequency (TBF). It is well-docu - activity levels [16, 18, 41], often in combination with data mented that TBFs are tightly and linearly correlated with of the physical environment, such as depth, temperature, swimming speeds in various fish species tested in the and oxygen saturation [56, 59, 74]. In recent years, along laboratory, and that metabolic rate is sensitive to changes with miniaturization and increased storage capacity of in swimming speeds. TBFs can thus function as prox- computer chips, commercially available tags have been ies for metabolic rates at different activity levels [35, 37, developed to measure more sophisticated physiological 60]. The TBF can be derived from acceleration measure - parameters such as heart rate in fish in addition to other ments, provided they are logged at a sufficiently high fre - parameters [6, 9]. quency (i.e., at least 2 × the expected maximum tailbeat Biosensors or telemetry devices can provide a valuable rate). However, there are few studies, where electronic link between highly controlled laboratory experiments tags have been used to calculate TBF, and these are to and the actual conditions experienced by free swim- our knowledge limited to older efforts on rainbow trout ming fish in their ambient environment. For instance, in (Oncorhynchus mykiss) and Japanese flounder (Paralich - the laboratory heart rate and acceleration of tagged fish thys olivaceus) [41, 42]. Interestingly, analogous work has can systematically be measured in resting conditions, at been done in birds, where wing beat frequency has been increasing activity levels, and in response to acute stress estimated via accelerometer tags [21, 65]. [9, 36, 37, 76]. Tag data can then be correlated with other In addition to the TBF, the tail beat amplitude (TBA) is parameters of interest, particularly the swimming speed required to obtain a full assessment of how the fish gen - and the metabolic rate of the fish [37, 76]. Once such cali- erates thrust at various activity levels. Estimates of TBA bration studies have been performed, it is then possible are generally more complicated to obtain and we are to infer additional information in free roaming tagged unaware of any previous efforts to compute a TBA from fish species subjected to less well-defined contexts. acceleration tags. We theorize that absolute values of Specifically, obtaining accurate estimates of swimming TBA will be difficult to obtain based on acceleration, but speeds and metabolic rates indirectly via tagging devices that it will be possible to acquire a measure of changes in would have tremendous potential in many areas of fish TBA over time by comparing the measured amplitudes in biological research, as they can describe the bioenerget- acceleration. Hence, it may be possible to derive relative ics and swimming patterns at a high temporal resolution changes in TBA from high frequency acceleration tags over prolonged timescales of fish in their ambient envi - together with TBF. ronment [24, 75]. To be sure that novel tag derived parameters can Heart rate may not be the most precise indicator of provide relevant information about free roaming fish, swimming speed or metabolic rate, at least in salmonid they first need to undergo proof of concept studies in species, because changes in the stroke volume (blood W arren‑Myers et al. Animal Biotelemetry (2023) 11:12 Page 3 of 13 controlled laboratory settings, where data collected from where physical data in absolute units are of interest re- tags are validated [7, 27, 62, 76]. As such, tag derived calibrations may be considered, e.g., [21]. However, in TBFs, therefore, require confirmation with visually the present study we only report frequencies and relative observed values at different swimming speeds before changes. they can be used in the field. In this study, we tested if a commercially available activity tag with a high frequency data logging capac- Tagging of fish ity could measure the TBF and TBA in Atlantic salmon Atlantic salmon weighing 1068 ± 26  g (Table  1) were −1 (Salmo salar) subjected to two types of swim tunnel tri- tagged after anesthetizing with 150  mg L Finquel als. In the first trial, we performed a critical swim speed for approximately 4  min and then placed inverted on −1 inspired test with incremental increases in flow speeds in a holding tray. During tag implantation, 75  mg L Fin- 20-min intervals to assess a range of swimming activities. quel was continuously flowing over the gills via a tube In the second trial, we used a sustained swimming test, to keep the fish sedated. A Technosmart axy-5 s tag was where fish were subjected to a constant flow speed for 4 h then inserted into the abdominal cavity through an inci- to evaluate the consistency of TBF and TBA over time at sion made aft of the pectoral fin. The incision was closed the same activity level. Our primary aims were to investi- with 2 to 3 stitches, gently dried and then a thin layer of gate how well values computed from tag measurements antibacterial Histoacryl was applied to further seal the correlated with visual measurements for TBF (this was wound. The tagging procedure for each fish was com - not possible for TBA as amplitude is difficult to gauge pleted in less than 5 min. A total of 8 fish were tagged for visually) and correlate computed TBF and TBA values this study. with swimming speeds. Swim tunnel system Methods To test the efficacy of measuring swimming performance Animal husbandry with activity tags, fish were swum individually in a 1905 l Atlantic salmon post smolts (Aquagen) were kept in large Brett-type swim tunnel setup as described previously indoor holding tanks (diameter: 3  m; volume: 5.3 m ) at by Remen et  al. [54]. In brief, the cylindrical swim sec- the Matre Research Station, Institute of Marine Research, tion was 248 cm long with an internal diameter of 36 cm. Norway. Tanks were supplied with 12 °C filtered seawater −1 Controlled water currents within the tunnel was gener- (34 ppt) via a flowthrough system (120 l  min ). A simu- ated with a motor driven propeller (Flygt 4630, 11° pro- lated natural photoperiod was provided, and fish were fed peller blade, Xylem Water Solutions Norge AS, Norway). commercial feed (4.5 mm pellet size; Skretting) in excess The swim tunnel was connected via a large hose to the each day via automated feeders. Fish were acclimated to same header tank as used to supply water to the fish these conditions for a minimum of 1  month before the tanks, allowing for a continuous flow through the setup experimental trials began. The experimental trials were which maintained a 12  °C test temperature and ensured performed in October and November 2020, and the use optimal oxygen levels at all times. A camera was deployed of animals was approved by the Norwegian Food Safety downstream behind the rear grid to record the trials and Authorities under ethics permit identification number for visual estimates of TBF without disturbing the fish. At the rear end, a removable top lid allowed easy access into the tunnel for adding and removing fish. High frequency acceleration tags Commercially available accelerometer Data Storage Tags (Technosmart axy-5  s activity tags, dimensions Table 1 Morphometric parameters of the tagged Atlantic 22 × 13 × 10  mm, weight 4.5  g, www. techn osmart. eu) salmon tested in the swim trials with incremental increases in swim speed or sustained speed for 4 h were used to obtain the acceleration data. This data was then used to estimate TBF values and relative changes Trial Fish Weight (g) Length (cm) Condition in TBA. In addition, the TBF estimates could be com- factor pared to visual TBF measurements. The tags were pro - Incremental A 1085 47.1 1.04 grammed in TechnoSmart X MANAGER software (v. B 1094 46.8 1.07 1.8.3) to log tri-axial acceleration (X, Y and Z) with a C 939 44.5 1.07 sampling frequency of 25 Hz within a range of G (± 4 G). Sustained D 1093 46.6 1.08 Tag outputs were set to 8-bit values, mapping measured E 1104 47.2 1.05 acceleration values within this range. The accelerometer F 1091 46.5 1.09 tags were pre-calibrated by the manufacturer. In cases, Warren‑Myers et al. Animal Biotelemetry (2023) 11:12 Page 4 of 13 Swim trials with an anaesthetic overdose of Finquel, fish weight The day before a swim trial, one tagged fish was trans - and fork length were recorded, and the activity tag was ferred to the swim tunnel for acclimation overnight at recovered. −1 a water flow rate of 20  cm  s . This flow rate is gener - The remaining two of the tagged fish did not cope ade - ally too low to initiate continuous swimming efforts in quately in the tunnel environment as they were reluctant Atlantic salmon of the size tested here and instead they to swim consistently for the full trial period. These were, typically balance on the floor of the tunnel. An overnight therefore, discarded from further analyses, providing 3 acclimation period is standard procedure in Atlantic replicates for each trial type. salmon swim trials to allow recovery of acute handling stress and acclimation to a novel environment before the onset of swim tests, e.g., [37]. Tag data extraction and post processing analysis Three tagged fish (A–C, Table  1.) were swum individu- Raw data time series were downloaded and converted ally on separate days following a typical critical swim from 8-bit binary values into acceleration values in G speed protocol, e.g., [5] with the exception that the fish (± 4 G) in X MANAGER and stored as data sets in.csv were removed from the tunnel before fatigue occurred, as file format. inferred from the transition between steady swimming to Because the tags measured acceleration, some con- the onset of burst and glide swimming behaviour. Start- siderations were made before extracting TBF and TBA. ing from the initial overnight resting current speed of When implanting tags in fish there will be an offset −1 20 cm  s , for each fish on the day of the swim trial at between the accelerometer’s sensing axes and the BODY 10:00 h, the water flow in the swim tunnel was increased coordinate system, i.e., the (imagined) coordinate sys- −1 by 10 cm  s every 20 min until the fish no longer swam tem fixed to the fish’s centre of gravity (Fig.  1). The off - steadily. Once the fish stopped swimming steadily and set between the longitudinal axes (i.e., X and X,b) will be began exhibiting burst and glide behaviour, signifying negligible compared with the offset between the other transition to partially anaerobically fuelled swimming axes if the tag is implanted, such that it rests against the and imminent fatigue, e.g., [72], it was removed from abdomen of the fish as is the common practice, e.g., [10]. the tunnel. The fish was then immediately euthanized By assuming that the tag remains stationary inside with an anaesthetic overdose of Finquel, whereafter the the fish and that the raw data means for the entire weight and fork length were recorded, and the activity tag duration of the measurements represent the stationary recovered. While fish were swimming at each different speed interval, TBF (time taken for 100 tail beats) were meas- ured manually using video camera footage and a stop- watch. Visual measurement of TBFs is a simple procedure when the fish is readily observed on camera. In addition, the swim trials were recorded, so that visual measure- ments could be confirmed later on. Three other tagged fish (D–F, Table  1) were similarly tested individually on separate days. However, here a sustained swimming speed test was used following a similar procedure to that of Hvas and Oppedal [31]. Starting from the initial overnight resting current speed −1 of 20 cm  s at 09:54  h, the waterflow was increased by −1 10 cm  s every 2  min, so that by 10:00  h the waterflow −1 −1 speed was 60  cm  s . A sustained speed of 60  cm  s was chosen here to represent an intermediate chal- lenge slightly above the expected optimal cruising speed for minimum cost of transport, but still well within the aerobic limit of Atlantic salmon [31, 38]. Each fish was Fig. 1 Illustration of how the accelerometer measurement axes of then swum at this flow rate for the next 4 h. During this the tag (X, Y and Z) relate to orientation axes of the fish (X,b, Y,b and time manual measurements of the TBF were made every Z,b). Assuming that X is aligned with X,b, pitch (Θ) will define the 30  min using the camera footage and a stopwatch simi- angle between X and the horizontal plane, while the roll (ɸ) and yaw lar to the incremental swim trials. After 4 h of swimming, (ψ) angles will define used to describe the deviation between the Y the fish was removed from the tunnel and euthanised and Y,b and Z and Z,b, respectively W arren‑Myers et al. Animal Biotelemetry (2023) 11:12 Page 5 of 13 acceleration offsets, the angular offsets for roll (ɸ ) and outside the expected TBF frequency band. An example of pitch (θ) and yaw (ψ) can be calculated using the effect of these processing steps is given in Fig. 2. The rotated and filtered acceleration time series were φ = arctan , (1) represented in the time domain. However, in this case the frequency components were of particular interest, thus   it was desirable to present the data also in the frequency domain to evaluate the signal’s frequency constituents   θ =−arctan � (2) and amplitude in G (1G = 9.81 m/s ). To do this, the data 2 2 A + A Y Z must first be transformed using specific signal process - ing methods. One such transform is the ’Fast Fourier and Transform’ (FFT) which returns the frequency compo- nents for the entire signal duration to which it is applied. ψ = arctan (3) While FFT is a proven method for determining the fre- quency composition of complex signals, it analyses the where A , A and A are the measured accelerations X Y Z whole period as one, and thus cannot capture changes in along the different axes. The measured accelerations can the frequency composition that occur during the signal then be rotated to the BODY coordinate system using period. To acquire this ability, a modified FFT approach      called the ’Short Time Fast Fourier Transform’ (STFFT) A cψ cθ −sψ cφ + cψ sθ sφ sψ sφ + cψ cθ sφ A X,b X      = was applied instead. The STFFT algorithm applies a roll -  A   sψ cθ cψ cφ + sψ sθ sφ −cψ sφ + sψ sθ cφ  A  Y ,b Y A −sθ cθ sφ cθ cφ A ing time window to the input signal, applies the FFT to Z,b Z (4) the data within this window and then shifts by a pre-set amount to overlap with itself before re-applying the FFT where s and c denote sine and cosine, respectively [20]. to the data within the new window. This is repeated for Following rotation, gravity was subtracted from the the entire duration of the signal. By choosing the appro- Z-axis and data were filtered using a 4th order Butter - priate window length and overlap, the frequency and worth bandpass filter with low and high frequency lim - amplitude content of the input signal can be analysed its of 0.8 and 5 Hz, respectively, to suppress signal noise with respect to time. Fig. 2 Eec ff t of processing steps, exemplified using data from Fish C. The leftmost column shows the raw measurements, the middle column data after rotation using Eq. 4, while the rightmost column shows the resulting data after subtracting gravity and smoothing through filtering Warren‑Myers et al. Animal Biotelemetry (2023) 11:12 Page 6 of 13 For the rotated acceleration data, the acceleration com- To summarize, this tag data extraction and post pro- ponent A is aligned with the expected direction of cessing analysis results in a processing flow consisting Y,b the tail beat (i.e., laterally outwards from the fish body), of five main steps as illustrated in Fig. 4 . hence any distinct tail beat frequency would be expected to appear in the frequency spectrum of A . STFFT using Y,b a 20  s window and 75% overlap was, therefore, applied to this axis. For each (overlapping) window, the highest frequency spectrum peak was considered to represent both TBF (placement on the frequency axis) and TBA (peak height) resulting in one TBF and TBA result per 5 s (Fig. 3). Unlike for TBF, the value obtained through STFFT for TBA will not represent the absolute value of the TBA as acquiring this parameter from accelerations entails inte- grating the acceleration time series twice, which tends to amplify measurement errors and inaccuracies. Moreover, since the tags were placed intraperitoneally, the conver- sion would also require translating and transforming accelerations measured in the abdomen to those exhib- ited by the tail of the fish, which would in turn depend strongly on the fish morphology and other unknown factors. However, provided that the tag position within the fish is fixed after implantation, variations in ampli - tude should also be expressed through variations in the height of the spectral peaks acquired through the STFFT. All analyses based on TBA were, therefore, made using the relative TBA, i.e., a measure of how much the TBA Fig. 4 Flow chart showing the processing procedure for acquiring changes between different speeds. tailbeat frequency ( TBF) and tailbeat amplitude ( TBA) data from the accelerometer tag measurements −1 Fig. 3 Example frequency spectrum from Fish C at 30 cm s . The horizontal axis denotes frequency, while the vertical axis denotes the proportion of the total measured acceleration that is calculated for the different frequency components. For a fish swimming at a steady speed, the former of these will correspond to the TBF, while the second will relate to the TBA W arren‑Myers et al. Animal Biotelemetry (2023) 11:12 Page 7 of 13 −1 Statistical analysis (Fig.  5A–C). Above 80  cm  s , steady swimming ceased For the incremental and sustained swim trials, correla- for fish B and C as they began to show initial signs of tions between observed TBFs taken via the camera foot- fatigue, so the swim trial for both these fish ended, while age and tag estimated TBFs, were tested using Pearson’s for fish A, erratic changes in swimming pattern did not −1 correlation coefficient. For the sustained swim trial, lin - occur until after 90 cm  s (Fig.  5A–C). For the 4-h sus- −1 ear regression using the mean hourly TBF estimates from tained swim speed tests at 60  cm  s , the fish exhibited tag measured data was used to test for any change in TBF consistent swimming behaviour for the full duration of over the 4-h period. To compare between swim trials, the test (Fig. 5D–F). −1 the ratio of TBF measured via the tags to BL s between In the incremental swim speed tests, the mean TBF −1 swim trial type at the flow speed of 60 cm  s was tested measured from camera observations ranged from 1.53 −1 −1 −1 using a one-way ANOVA. For all tests, the significant beats s ± 0.08 at 30  cm  s to 2.65 beats s ± 0.06 at −1 difference level was set at p < 0.05. All analyses were con- 80 cm  s , and the TBF derived from acceleration meas- −1 −1 ducted using SPSS 26 statistical software package. Data urements ranged from 1.40 beats s ± 0.05 at 30 cm  s −1 −1 are reported as mean ± standard error of the mean unless to 2.67 beats s ± 0.06 at 80  cm  s (Fig.  6A). There specified otherwise. was a strong linear correlation between the camera observed and tag estimated TBFs (Pearson’s r = 0.99, Results P < 0.001 (Fig. 6B). In the sustained swim trials, the over- Tailbeat frequency all mean TBF observed via the camera were 2.17 ± 0.07 −1 −1 In the incremental swim speed tests the TBF increased beats s and for the tag, 2.19 ± 0.03 beats s (Fig.  6C). −1 linearly with swimming speed from 30 to 80  cm  s There was a strong linear correlation between the mean Fig. 5 Incremental (A–C) and sustained (D–F) swim trials of tagged fish. For all graphs, black line represents tag estimated mean tailbeat frequency ( TBF) of 10 s subset measurements with 50% overlap between subsets. For fish A–C, red line indicates tag estimated mean TBF for each 20‑min interval at a specific current speed. Grey circles with a grey line indicate mean frequency of 3 visual estimates taken from camera recordings within each of those respective intervals. Error bars represents mean ± s.e.m. For fish D–F, vertical dashed lines indicate each hour from the start and end −1 point of the 4‑h sustained swim speed tests at 60 cm sec . Here, red line indicates tag estimated mean tail beat frequency for the complete trial, and grey circles with a grey line indicate visual point estimates of tailbeat frequency in 30‑min intervals Warren‑Myers et al. Animal Biotelemetry (2023) 11:12 Page 8 of 13 Fig. 6 Observed and tag computed tailbeat frequencies ( TBF) in the incremental swim speed trial (A) and the sustained swim trial (C), where error bars are mean ± s.e.m. Followed by correlation plots between tag estimated and observed TBF in their corresponding trials on the left panels (B and D) hourly camera observed and tag estimated TBFs (Pear- This relationship was best described with a power func - 2 2 son’s r = 0.88, P < 0.001) (Fig.  6D). Using tag estimated tion providing an R of 0.998. Furthermore, the changes TBF only, there was no significant change in the mean in TBF with increasing swimming speed were well- hourly TBF over the 4-h period showing that the TBF described by a linear regression, where R was 0.998 remained constant at constant swimming efforts over (Fig. 7B). The product of TBF and TBA across swimming time (F = 4.5, P = 0.06). speed could then provide a visualization of the relative 1,10 Using tag measured TBFs as a proxy for swimming increase in thrust generated by the fish, and this relation - speed in the sustained swim trial at the flow rate of ship followed a power function (R of 0.999) (Fig. 7C). −1 −1 60 cm  s the average tag TBF of 2.19 ± 0.03 beats s −1 equated to a swim speed of 1.28 ± 0.01 BL s (mean fork length of 46.8 ± 0.2  cm). This was consistent with the Discussion incremental swim trial during the 20  min period when In this study, we investigated whether commercially −1 the flow rate was also 60 cm  s as the average tag meas- available acceleration tags with a high frequency log- −1 ured TBF of 2.16 ± 0.07 beats s equated to a swim speed ging capacity could be used to accurately compute TBFs −1 of 1.30 ± 0.02 BL s (mean fork length 46.1 ± 0.8 cm). As in Atlantic salmon across a range of swimming speeds −1 such, when comparing the mean ratio of TBF to BL s at as well as providing consistent estimates over time at a this specific flow speed between the trial types, there was constant intermediate swimming speed. Since estimates −1 −1 no difference (TBF: BL. s : Incremental = 1.66 ± 0.07; of TBFs from tags were within ± 0.1 beats s of visual Sustained = 1.70 ± 0.03; F = 0.5, P = 0.5). counts across the assessed swimming speeds and trial 1,4 types, we conclude that acceleration tags effectively can be used to measure TBFs with enough accuracy to be Changes in tailbeat amplitude and thrust with increasing used as a proxy for swimming speeds and bioenergetics swimming speed in free roaming fish. In addition, we were able to compute There was a distinct relationship between the changes changes in relative tail beat amplitude (TBA) and found in relative TBA and the swimming speed of the fish that this parameter increases with swimming speed in (Fig.  7A), with the amplitude appearing to stay constant −1 a pattern resembling a power function. Combined, TBF for the lower speeds (30–40  cm ) and then increas- −1 and TBA derived from acceleration tags can thus provide ing substantially across the higher speeds (50–80  cm ). W arren‑Myers et al. Animal Biotelemetry (2023) 11:12 Page 9 of 13 −1 Fig. 7 Relative tail beat amplitudes at increasing current speeds as compared to 30 cm s fitted with a power function (A), and tailbeat frequency −1 at increasing current speeds fitted with a linear function (B). In C, the changes in thrust generated relative to 30 cm s is shown and fitted with a power function, where thrust is expressed as the product of the mean tailbeat amplitude and frequency at each current speed. Data in A and B are mean ± s.e.m additional assessments of how free roaming fish generate swimming speeds follow a power function [50]. This thrust in different scenarios. relationship reflects the hydrodynamics of swimming as the drag force increases in proportion to the square Tailbeat frequency as a proxy for swimming speed of the speed, meaning that the power required to over- and metabolic rate come drag increases with the cube of the speed [66, Acceleration tags have been used to infer swimming 70], making it energetically more and more expensive speeds and metabolic rates in fish on several occasions to increase swimming efforts further. For instance, in (e.g., [22, 57, 73, 75]. However, acceleration data has pre- Atlantic salmon the increase in aerobic metabolic rate viously mostly been sampled at lower frequencies, typi- between low and high swimming speeds approximates cally 1  Hz [3, 4, 76]. In consequence, categorization of a power function and increases with a factor of 3 to 6, swimming activity and associated energetic costs in such depending on the acclimation temperature [32]. Since the studies tends to be limited to crude categorizations, such metabolic rate response to increasing swimming speeds as resting, routine or burst swimming behaviours [1, 9]. is well-understood in fish and, moreover, is readily meas - By calculating the TBF from high resolution acceleration ured with swim tunnel respirometry in laboratory experi- tag data as in the present study, it would be possible to ments, robust calibration curves can be gathered, so that define a more fine-grained scale of swimming activity TBF tag data also can be used as a proxy of metabolic levels that would give greater precision in categorising rate. the movements of free roaming fish. This will be par - Our estimates of relative TBA as a function of swim- ticularly useful at intermediate activity levels, which are ming were best described by a power function, similar presumably the energetic states that fish occupy most of to the metabolic requirement at increasing swimming the time, for instance during foraging or migration which speeds. Meanwhile, the TBF increased linearly with are associated with optimal cruising speeds at minimum swimming speed. However, the drag forces increase transport costs [15, 71]. in proportion to the square of the speed, as discussed TBF tag data can also be expected to provide more above. To explain the observed propulsion of the fish, the accurate swimming speed estimates than other measur- amplitude, therefore, needed to increase relatively more able parameters, such as heart rate and instantaneous at higher speeds, as shown here. Furthermore, the prod- acceleration, since it is directly linked with the undula- uct of TBF and TBA can be used to estimate the relative tory locomotion. In the present study, TBF increased thrust generated by the fish. Owing to the patterns of −1 linearly from approximately 1.4 to 2.6 beats s with TBF and TBA with increasing swimming speed, thrust −1 increasing swimming speeds from 30 to 80 cm  s . Simi- was also best described as a power function. This reflects lar strong relationships between TBFs and swimming the above-mentioned hydrodynamics of swimming and speeds are well-documented in various fish species [35, corresponding metabolic requirements to overcome 37, 60], and highlights the potential for using previously increasing drag forces [66, 70]. Changes in TBA can, established regression lines to estimate swimming speeds therefore, provide additional information on how fish from TBF data in free-swimming tagged fish. generates thrust and contribute to making accelerom- The metabolic rate is highly sensitive to changes in eter tag data even more accurate in predicting swimming activity, and the energetic requirements at increasing speeds in ambient environments. Warren‑Myers et al. Animal Biotelemetry (2023) 11:12 Page 10 of 13 Limitations of tailbeat frequency tags to infer swimming and parasites [33, 67], and possibly exposure to toxic speeds and bioenergetics in fish substances in polluted environments [23, 49]. As such, While the correlations between TBF, swimming speed, when attempting to monitor the physiology and behav- and associated energetic costs are well-established, they iour of free-swimming fish, there will always be unknown are also context dependent and influenced by various factors that could alter correlations between TBF, swim- biological and environmental factors [35, 52, 60]. These ming speed and metabolic rate. Such uncertainties are must, therefore, be considered for proper interpretations an inherent challenge when studying animals outside the of TBF tag data from fish in ambient environments and laboratory. may limit the reliability of such tag data if parameters of unknown effects are involved. Thus, to fully exploit the Applications and further development of tailbeat possibility of TBF tags and to ensure the most accurate frequency tags data interpretation, a nuanced suite of lab-based calibra- We envision several useful applications with TBF tags in tion studies is ideally required on a per species basis. In future studies, particularly in aquaculture research with well-studied fish species, such as salmonids, it will be regard to fish welfare in salmon sea cages. Within these possible to amass correlation curves measured in many vast fish group sizes, the scope for detailed data acquisi - different contexts to strengthen data interpretations tion from tagged sentinel fish is large [17, 69], and vital of TBF tags. However, TBF tags may have less value as when moving towards the knowledge-based concept of a tool for energetic monitoring in less studied species, precision fish farming [19]. In this, TBF should allow for where swimming capacities and metabolic rates have recording behavioural modes and estimating the physical not been measured systematically. Nevertheless, it will demand of swimming in fish groups driven by environ - still be possible to describe the scope of TBFs used and mental features and social interactions (see [53] for estab- the frequency distribution to quantify general swimming lished observation methods). For example, in response patterns through time when studying new fish species. to high current speed, caged salmon change their group Apart from species differences in morphology and behaviour from circular schooling to a static group posi- physiology, the size of the fish is presumably the most tion directed against the inflowing water [40] which is important factor to influence TBF and its correlation likely to dampen current exposure within the fish school with swimming speed and metabolic rates. Specifically, [34]. Moreover, if an algorithm like the one used in this smaller fish can attain a higher TBF and swim at higher study were to be implemented in acoustic tags carrying −1 relative swimming speeds (e.g., body lengths s ), but accelerometers, these could be set to transmit the com- larger fish are able to swim faster in absolute units (e.g., puted tail beat rate in real time. This data could then be −1 cm s ) [35, 52]. The same TBF will, therefore, not cor - combined with measurements of absolute position [26] respond to the same swimming speed in fish of different and movement speed [27, 28] in the cage, which would size classes. It is thus important to consider size effects, enable more detailed studies of the link between TBF and especially if individuals remain tagged for prolonged energetic expenditure and actual movement in sea cages. periods and grow substantially in size. In addition, meta- Of fundamental interest, TBF can also be used to shed bolic rates also scale with size in a somewhat predictable new light into questions such as individual fish need for manner, where smaller individuals have a higher mass rest and switch in behavioural mode connected with vari- specific metabolic rate [43, 52]. ous photo-regimes and observed diel heart rate variation Since the metabolism of ectothermic fish is greatly with night and day length [69], recovery from exhaust- dependent on temperature this factor is also important ing operational procedures, such as mechanical parasite to consider. Typically, metabolic rates increase with a treatment [18], and whether adverse conditions such as factor of 2–3 per 10  °C, but thermal sensitivity depends high temperature [32] or internal processes as sexual on species, the specific portion of its thermal niche, and maturation or fasting will induce the urge for migration acclimation history [44]. Interestingly, the correlation and thus change in swimming pace or pattern. Sentinel between TBF and swimming speed is more consistent fish with TBF tags may also be important tools for docu - across temperatures than metabolic rate, except at ther- menting fish coping ability in novel aquaculture rearing mal extremes which pose a limit to maximum swimming technologies and systems. Possible applications in this capacity [32, 35]. Hence, TBF as a predictor of swimming area could include enabling continuous logging in harsh speed is less sensitive to fluctuations in temperature com - and remote ocean farming sites, serving as a compo- pared to metabolic rate. nent in early warning of negative buoyancy by increased Other factors worth considering include nutritional swimming speed in submerged salmon cages [58], as well states and body condition [39, 47], life-stages and par- as providing documentation and tuning of water current ticularly sexual maturation [29, 68], impacts of diseases exposure in closed containment systems [64]. W arren‑Myers et al. Animal Biotelemetry (2023) 11:12 Page 11 of 13 Tags that measure TBF also have potential for pro- use a singularity-free representation of rotation (e.g., viding new knowledge on fish species in the wild, for quaternions). instance during periods of migration to feeding or Selection of signal processing sliding window width spawning grounds, but also to generally obtain a more (20  s) and overlap (75%) was a trade-off between calcu - detailed understanding of natural activity patterns over lation robustness, computational demand and (timely) extended periods of time. Here, some practical consid- resolution for the results. For the signals measured in erations are methods of tag retrieval as high-frequency this study using a shorter window introduced more noise acceleration tags presently only function as implantable compared to longer windows due to the FFT averaging data storage tags. effect. Longer windows did not produce improved results While the TBA parameter computed in this study pro- while increasing computational demand. The parameters vided a relative measure of the changes in TBA rather used during processing are, therefore, considered a rea- than the absolute value (as was the case for TBF), it was sonable compromise. apparent that higher TBA-values correlated with higher The filtering bandpass parameters (0.8 and 5 Hz) were swimming speeds. Furthermore, the patterns observed chosen to suppress the effect of low and high frequency corresponded well with hydrodynamic predictions with contributions outside the range of the expected TBF for regard to thrust needed to overcome drag at increasing Atlantic salmon, e.g., [37]. These parameters are highly speeds. Although this parameter may not be as easy to species and size class specific and must be adapted link directly with energetics, it can be combined with accordingly with an appropriate TBF range (or for the TBF to estimate the relative thrust generated by the fish. general case). Finally, future tests using accelerometers This provides a unitless measure of swimming output to extract TBF and TBA should use sensor settings to that can be considered analogous to the cardiac output maximize the signal to noise ratio, i.e., the lowest possible which consists of heart rate multiplied by stroke volume. sensing range and the highest possible bit resolution. Similarly, stroke volume in fish is generally measured in The continuous development of more sophisticated relative changes, while heart rate implicitly is expressed implantable bio-loggers makes for an exciting future in as a frequency. Obtaining both TBA and TBF, there- fish biological research. Moreover, novel methods within fore, allow for a more holistic assessment of swimming biotelemetry and biosensors will help close the gap fur- energetics. ther between controlled laboratory trials and the more varied and unpredictable environments experienced by fish when allowed to swim around freely [8]. Managing data from tailbeat frequency tags The approach used in the present study to determine Acknowledgements The technical staff at the Matre Research station for providing excellent animal TBF and TBA is an adaptation of well-known signal husbandry. processing techniques. Data were successfully rotated into the BODY coordinate system, thus allowing direct Author contributions This study was conceived and designed by all authors. Experimental trials comparison of A data based on the assumption that Y,b were performed by MH, analyses of tag data were done by ES and MF. First the mean of all recorded data represents the accelera- draft was written by FW‑M with all co ‑authors providing thorough feedback tion offset. This assumption is only valid if the tags do before approving the final version. All authors read and approved the final manuscript. not shift within the peritoneal cavity during data capture. Future trials can address this by suturing tags in place for Funding improved implantation control and easier result compar- This research was funded through the Research Council of Norway, EXPOSED Aquaculture Research Centre, grant number 237790. Martin Føre acknowl‑ ison between individuals. Alternatively, the offsets can be edges the financial support from Salmar ASA/Salmar Aker Ocean AS. periodically re-calculated, compared to previous values and updated accordingly. Data availability Raw data will be made available upon request. Furthermore, care must be taken when calculating the offsets (Eqs.  1, 2 and 3). Accurate offset calculations pre - T T Declarations clude that [A , A , A ] ≉0. If [A , A , A ] ≈0, i.e., below X Y Z X Y Z the signal noise level, A , A and A should be ini- X,b Y,b Z,b Ethics approval and consent to participate tialized to 0. Furthermore, for θ = 90°, Eq.  4 is singular The use of animals was approved by the Norwegian Food Safety Authorities under ethics permit identification number 24444. (i.e., the denominator becomes 0) and cannot be solved. In free-swimming fish, this may occur when the fish is Consent for publication free to manoeuvre in all three dimensions (although All authors have agreed to publish this work as presented here. salmon are unlikely to moving at as steep angles as Competing interests θ = 90°). Future implementations of this approach The authors declare no competing interests. should, therefore, either include a singularity check or Warren‑Myers et al. Animal Biotelemetry (2023) 11:12 Page 12 of 13 Author details 17. 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Journal

Animal BiotelemetrySpringer Journals

Published: Mar 24, 2023

Keywords: Acceleration; Bioenergetics; Data storage tag; Fish behaviour; Monitoring; Swim speed

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