Proceedings of the Royal Society B: Biological Sciences
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The influence of body size on the intermittent locomotion of a pelagic schooling fish

Takuji Noda

Takuji Noda

Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan

[email protected]

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Ko Fujioka

Ko Fujioka

National Research Institute of Far Seas Fisheries, FRA, Shizuoka 424-8633, Japan

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Hiromu Fukuda

Hiromu Fukuda

National Research Institute of Far Seas Fisheries, FRA, Shizuoka 424-8633, Japan

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Hiromichi Mitamura

Hiromichi Mitamura

Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan

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Kotaro Ichikawa

Kotaro Ichikawa

Field Science Education and Research Center, Kyoto University, Kyoto 606-8502, Japan

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Nobuaki Arai

Nobuaki Arai

Field Science Education and Research Center, Kyoto University, Kyoto 606-8502, Japan

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    Abstract

    There is a potential trade-off between grouping and the optimizing of the energetic efficiency of individual locomotion. Although intermittent locomotion, e.g. glide and upward swimming (GAU), can reduce the cost of locomotion at the individual level, the link between the optimization of individual intermittent locomotion and the behavioural synchronization in a group, especially among members with different sizes, is unknown. Here, we continuously monitored the schooling behaviour of a negatively buoyant fish, Pacific bluefin tuna (N = 10; 21.0 ∼ 24.5 cm), for 24 h in an open-sea net cage using accelerometry. All the fish repeated GAU during the recording periods. Although the GAU synchrony was maintained at high levels (overall mean = 0.62 for the cross-correlation coefficient of the GAU timings), larger fish glided for a longer duration per glide and more frequently than smaller fish. Similar-sized pairs showed significantly higher GAU synchrony than differently sized pairs. Our accelerometry results and the simulation based on hydrodynamic theory indicated that the advantage of intermittent locomotion in energy savings may not be fully optimized for smaller animals in a group when faced with the maintenance of group cohesion, suggesting that size assortative shoaling would be advantageous.

    1. Background

    Living in groups provides various advantages [1], such as a reduced energetic cost of locomotion [24], reduced vulnerability to predators [5] and increased foraging opportunities [6]. Group-living animals must synchronize their behaviour to maintain group cohesion [7]. However, there is the potential cost of the synchronizing behaviour [8,9], as individuals may have different optimal activity budgets and movement abilities (speed, turning, etc.) due to their own morphological and physiological constraints. Because similar-sized individuals tend to have similar activity budgets and movement abilities [10], synchrony is best maintained by individuals that are similar in size [11,12]. Differently sized individuals must adjust to suboptimal activity rhythms to maintain synchrony with the group [7,11,12].

    At the individual level, animals exhibit diverse behavioural strategies to reduce the cost of locomotion. One of the important behavioural strategies to reduce the cost of locomotion is intermittent locomotion, which is employed by many different species of animals, including invertebrates and vertebrates living in aerial, terrestrial and aquatic environments [1315]. During intermittent locomotion, individuals intersperse phases of gliding and active propulsion and can greatly minimize their energy usage compared with during continuous horizontal movement [14,1618]. However, because gliding is passive movement using the gravity and the hydrodynamic force acting on the body, the direction and speed of gliding would be more restricted than active propulsions using their appendages freely for accelerating/decelerating or manoeuvring (see electronic supplementary material, appendix A3 for the empirical support based on our study using a gyroscope data logger [19]). Therefore, if differently sized animals perform their intermittent locomotion at their own optimal timing in a group, the group would split apart because optimal activity rhythms may differ among the individuals. Thus, it is hypothesized that the intermittent locomotion in a group is generally synchronized among individuals, while the difference in size affects the partition of energy/time used for the different activities in intermittent locomotion.

    To test the hypothesis, we focused on glide and upward swimming (GAU) of a negatively buoyant pelagic fish [16]. More specifically, Pacific bluefin tuna, Thunnus orientalis (PBT), were considered as a model species because they exhibit GAU [18] while generally constructing schools [20]. Observing the natural GAU of multiple PBT requires a relatively large space. When considering the tail-beat interval of the fish in a fraction of a second, rapid changes in GAU may exist. Therefore, monitoring the movement at a temporal resolution of at least 1 s (thereby identifying the change of the behavioural state) is effective for understanding the GAU performance of schooling individuals. Thus, we monitored the GAU of schooling PBT in a semi-natural environment using an open-sea net cage for 24 h and acceleration/depth data loggers attached to the body of fish (accelerometry), and we investigated the synchronization of the movement of GAU and intra-school variations. We also performed a simulation based on hydrodynamic theory to support the results from accelerometery. Our work is set out to uncover the implications of body size for the synchronization of intermittent locomotion in a group.

    2. Material and methods

    Fieldwork was conducted in August of 2013, and the open-sea net cages (12 × 12 m square and 6 m depth) were monitored near Kaminokae in Kochi, Japan (33°16′54″ N; 133°14′48″ E). During this period, fishermen caught wild PBT less than 1 year of age that were migrating northward along the Kuroshio Current off the coast of Kochi (8–16 km from the coastline), two to three months after hatching in the area near the Nansei Islands [21]. After the fishermen brought live tuna back to our net cages, we selected only healthy looking, alive fish with no apparent damage to their bodies and eyes. Then, we carefully released the fish into one of the net cages (the entire procedure took less than 20 s). The fish were kept in the net cage for several days and fed two to three times a day, which allowed for recovery from the stress and trauma due to fishing. On the day of the experiment, the fish stocked in the net cage were hooked with bait (but no barb) by professional fishermen. We quickly examined the condition of the fish again, and then we attached multi-sensor data loggers to the dorsal musculature of only healthy-looking fish by piercing two cable ties after quickly measuring the fork length (FL) and total length (TL). The tagged fish were carefully released into another net cage of the same size (the surgical procedure took less than 60 s). Fish were allowed at least 29 h to recover from the surgery before the start of the data logging. During the experiment, all the fish were fasted.

    The acceleration data loggers (ORI-380D3GT; 12 mm diameter, 45 mm length; 10 g in air; Little Leonardo Ltd, Tokyo, Japan) were attached to 10 fish (FL: 22.2 ± 1.0 cm, ranging from 21.0 cm to 24.5 cm; electronic supplementary material, table S1). The data loggers measured three-axis acceleration (±8 g) at 20 Hz, depth and temperature at 1 Hz and 12 bits resolution continuously for approximately 40 h. The data were recorded for 24 h (16:00 to 15:59 of the next day) and used for the analysis. After recovering the data loggers from all the fish, all the data loggers were shaken together to record the time stamp for measuring the time drift of each logger from the start of the recording, which revealed less than a 4 s difference among the 10 data loggers. The depth sensors were calibrated before the experiment by hanging the data loggers to known depths ranging from 0 to 8 m at 1 m intervals. The acceleration data showed that all the fish vigorously swam during the recording hours. When the fish were recaptured, there was no apparent damage to their eyes and bodies, except for a little friction and pierced holes on their skins caused by the attachment of the data loggers. The speed calculated using the accelerometer values in our experiment (approx. 2 FL s−1, see below) was similar to a previous report [22] that monitored the speed of 15 cm-sized fish in a tank via video recording (without tagging). Thus, the effect of the tagging was considered relatively low. The water temperature during the recording hours was almost constant (28.1–29.5°C).

    (a) Data analysis

    The data were analysed using a custom-written program in Igor Pro (WaveMetrics Inc., Lake Oswego, OR, USA), and Python 2.7.8 with pandas, and the matplotlib library were used for the time-series analysis and visualization. The statistical analysis was performed using R Statistical Computing Software (v. 2.13.0, R Foundation for Statistical Computing, Vienna, Austria).

    The accelerometer simultaneously measured the dynamic acceleration caused by tail-beat movement and static acceleration caused by gravity change. The two components were separated by two band low-pass filters (0.95/1.2 Hz, IFDL v. 4.0; WaveMetrics Inc.) based on the assumption that the high- and low-frequency components corresponded to dynamic and static acceleration, respectively [23]. The pitch angle (the angle of the fish body axis relative to horizontal) was calculated from the static component of the acceleration data in the longitudinal direction (measured at 20 Hz), and then the data were resampled at 1 Hz. To correct for any difference in the pitch recorded by the data logger and the true pitch of the fish due to the attachment error of the accelerometer, we regressed the vertical velocity, calculated over 1 s, against the pitch angle of the fish (at vertical velocity = 0 m s−1 presumed to be 0°), and the angle was subtracted from any pitch estimates [24]. Then, the speed data were obtained using the vertical velocity/sine (pitch). There was a possibility of errors in speed estimation based on the body angle and the rate of change of depth when the angle approached 0° or 90°; therefore, data points with the swim speed calculated using the body angle less than 10° or more than 80° were excluded from the analyses. Anomalous swim speeds of more than 1.0 m s−1 (approx. 5 FL s−1), possibly resulting from other errors, were excluded from the analysis.

    Swaying acceleration was obtained from the dynamic acceleration in the transversal direction and was indicative of tail beating. Gliding was considered as a lack of an oscillating signal in the swaying acceleration [25]. To identify the pattern of GAU from the acceleration data, a wavelet analysis using the Morlet mother function (min cycle = 0.05 s, max cycle = 1.00 s, ω0 = 10) [26] was first applied to the swaying acceleration for every second, and the periodicity and amplitude for every second was obtained. Then, the dominant cycle for every second was calculated. All the swimming with active propulsion was considered upward swimming for the simple description following ‘GAU’, even though this may not have always been the case when fish swam upward. During upward swimming, there was clear periodicity of approximately 0.2 s in the acceleration signals (electronic supplementary material, figure S2). During gliding, the amplitudes of the periodicity of 0.05–1.00 s were relatively low (electronic supplementary material, figure S2), as there was no clear periodicity of 0.05–1.00 s in the movement. Thus, GAU could be identified for every second by setting a threshold for the amplitude of the dominant cycle (electronic supplementary material, figure S2; the threshold value of 0.1 for the amplitude was used; see electronic supplementary material, appendix A1 for the determination of the threshold value). A period with the amplitude of the dominant cycle > 0.1 was considered upward swimming, and a period with the amplitude of the dominant cycle ≦ 0.1 was considered gliding. Finally, the pattern of timing and the duration of GAU were converted to a binary time series (0 as upward swimming and 1 as gliding) for the cross-correlation analysis to calculate the level of GAU synchrony among individuals (see the following sections).

    (b) Assessment of individual movement via locomotive variables

    The movement of individuals was assessed by deriving the following locomotive variables: hourly mean of glide duration per glide, tail-beat frequency (TBF) while active propulsion, vectoral dynamic body acceleration (VeDBA) while active propulsion, speed during glide, speed while active propulsion, mean depth change per glide, hourly total glide duration and number of glides. VeDBA was calculated as the scalar value of the vector summation of x, y and z dynamic accelerations, and the mean values over 1 s were obtained. The VeDBA, as the indicator of locomotion effort, may be a better proxy for the oxygen consumption than ODBA in teleost fish [27]. In addition, to account for the possibility of the fish swimming downward by active propulsion instead of gliding, the ratio of the glide detection rate according to the wavelet analysis on the acceleration data, to the glide detection rate according to the depth change rate (hereafter, glide detection rate by wavelet over depth change) was also calculated. The threshold for the depth change rate was 0.15 m s−1 (see electronic supplementary material, appendix A2 for the determination of the threshold value).

    The total cost of GAU in 24 h for each individual was estimated as (total VeDBA during active propulsion for 24 h) + (basal cost for 24 h), similar to appendix S1 in [25]. The standard metabolic rate (SMR) was assumed to be approximately 0.3× routine metabolic rate [18,28]. Thus, the basal cost was calculated as 0.3× (mean VeDBA for each individuals) × (time for 24 h).

    (c) Assessment of the level of glide and upward swimming synchrony

    The level of GAU synchrony was assessed by calculating the cross-correlation between the binary time series of GAU patterns for every pair among individuals at hourly basis. Cross-correlation can be used as a measure of similarity of two time series, as a function of the lag of one relative to the other. The recorded time of the data logger could not be perfectly synchronized due to the time drift of the data loggers. While the GAU patterns were identified at a temporal resolution of 1 s, the time deviation per hour of the logger was theoretically smaller than 1 s (time-keeping accuracy of the real-time clock used in the logger was maximum approx. 125 ppm at 25°C). Therefore, although the time deviation may increase with elapsed hours, setting an appropriate time lag in the cross-correlation analysis for the GAU patterns at hourly basis would allow for the assessment of the level of GAU synchrony. In particular, the maximum value of the cross-correlation coefficient (hereafter, cross-correlation coefficient), calculated among the different lags (less than ±4 s) was selected (figure 1). After the cross-correlation coefficients among all the combinations of pairs (45 pairs in total; hereafter cross-correlation coefficients by all pairs) were calculated, the mean cross-correlation values of all the combinations of pairs between the focal fish and the rest of the fish (hereafter cross-correlation coefficients by individuals) were obtained for each focal fish (i.e. nine pairs for each fish).

    Figure 1.

    Figure 1. (a) Glide event patterns of two fish as identified each second; examples are shown for ID27 (bottom) and ID40 (top) for 15 min. The timing of the glide events was generally synchronized between the two fish, but there were also some glide events that were observed for one fish but not for the other fish (e.g. see the box of broken line), which in turn resulted in the difference in the number of glides during a given period. (b) The enlarged graph of (a). The glide event identified each second is indicated as a bar with the width of 1 s, and the glide duration was represented as the total widths of the consecutive bars. One glide was defined as the consecutive glide events identified each second. Note that the glide durations were different between the two fish, although the timing of the glides was generally synchronized. The glide duration of ID27 (23.5 cm in FL) was generally longer than ID40 (21.0 cm in FL). (c) The cross-correlation analysis of the glide patterns between two fish each hour with different time lags. The examples shown correspond to ID27 and ID40 during 0:00:00 ∼ 0:59:59. Here, the time lags ranging from −10 to 10 min are represented. (d) The enlarged graph of (c). The time lags ranging from −10 to 10 s are represented. Note that there is a clear peak in the cross-correlation coefficient at the time lag of −1 s.

    (d) Statistics

    To uncover the implications of body size for the intra-school variances of GAU performance and the synchronization of GAU movement, the ordinary least squares regression (OLS) analysis was applied between the size of the fish and the overall mean of the hourly locomotive variables and level of GAU synchrony. The OLS analysis was also applied between the size difference in FL and the overall mean of the hourly level of GAU synchrony. However, because the locomotive variables and the level of GAU synchrony changed with the time of day, it was also important to understand the effect of size on the GAU performance under the control of the time of day. Therefore, the contribution of the time of day (hour) as well as the size of individuals (FL) on the locomotor variables and the level of GAU synchrony were also statistically investigated by the generalized additive mixed models (for detailed procedure, see electronic supplementary material, appendix A4).

    (e) Simulation

    To understand the effect of body size on the synchronization of intermittent locomotion, we performed a simulation based on hydrodynamic theory. According to Takagi et al. [18], the energetically ideal speed and angle for GAU and horizontal swimming speed can be theoretically determined based on the hydrodynamic and morphological characteristics of PBT (body surface area, submerged weight and drag and lift coefficients).

    (i) Determination of speed and angle for glide and upward swimming and horizontal swimming speed

    Suppose there are two differently sized fish (Fish L: 24.5 cm in FL and 26.2 cm in TL simulating ID04, Fish S: 21.0 cm in FL and 22.7 cm in TL simulating ID40), and each fish performs one GAU in a vertically restricted space (6 m in depth), such as the net cage used in our experiment. The speeds and angles for gliding and upward swimming, and horizontal swimming speeds of both fish were determined as follows. The fish of 20–30 cm in TL may have 1.5 (TL s−1) for their glide speed [18], assuming the angle of attack is 0° and that the fish do not modulate their angle of attack during gliding. Therefore, the glide speeds (UG) for Fish L and Fish S were determined as 0.393 m s−1 and 0.341 m s−1, respectively. These speeds were actually similar to the values obtained in this study (figure 3g,h). The glide angle with size may be obtained as the following linear equation (the equation was estimated from fig. 8 in [18] assuming the angle of attack was 0°):

    Display Formula
    2.1
    Using TL and the above equation, the glide angles (α) for Fish L and Fish S were determined as 50.780° and 49.643°, respectively. When assuming the energy based on SMR is 30% of the total energy spent during motion, the most efficient upward swimming speed can be 1.4 times the glide speed [18]. Therefore, the upward swimming speeds (UB) for Fish L and Fish S were determined as 0.550 m s−1 and 0.477 m s−1, respectively (2.1 TL s−1 for both fish). These speeds were also similar to values obtained in this study (figure 3i,j).

    When assuming that the pectoral fins are extended during the tail beating, the ratio of the coefficient of the lift force during upward swimming to the coefficient of the lift force during gliding (denoted as l1) could be 0.5, and the ratio of the coefficient of the lift force during horizontal swimming to the coefficient of the lift force during gliding (denoted as l0) could be 0.5 [18]. The upward swimming angle (β) can be derived by the following equation (modified from the eqn (13) in [18]):

    Display Formula
    2.2

    Therefore, using the above equation and using the values of glide angle (α), glide speed (UG), upward swimming speed (UB) and l1, the upward swimming angles (β) for Fish L and Fish S were determined as 51.709° and 50.610°, respectively. Furthermore, the horizontal swimming speeds (U0) can be derived by the following equation (the same as eqn (37) in [18]):

    Display Formula
    2.3

    Therefore, using equation (2.3) and the values of glide angle (α), glide speed (UG) and l0, the horizontal swimming speeds (U0) for Fish L and Fish S were determined as 0.699 m s−1 (2.668 TL s−1) and 0.598 m s−1 (2.636 TL s−1), respectively. The determined values for Fish L and Fish S are summarized in electronic supplementary material, table S2.

    (ii) Simulation scenario

    As determined above, the larger fish has higher optimum GAU swimming speeds (in m s−1) than the smaller fish. The differences in the angles for gliding and upward swimming are relatively small between the two fish. Because gliding is less energetically expensive than active swimming, a fish should modulate the number and duration of glides to minimize total energy expenditure. Thus, when two differently sized fish perform one GAU by maintaining their group cohesion, the larger fish with higher GAU speeds can optimize their movement, whereas smaller fish with lower GAU speeds may suboptimize its GAU.

    We exclusively considered a situation that when one larger fish (Fish L) optimized its own GAU, the other smaller fish (Fish S) would follow Fish L by changing the time allocation of its glide, upward swimming and horizontal swimming. In particular, the smaller fish would allocate its horizontal swimming with higher speed, instead of GAU, for some ratio (horizontal swimming ratio (HSR)) of the horizontal distance covered by the GAU of the larger fish (electronic supplementary material, figure S6). For simplicity, we assumed that the HSR was equally allocated for both glide and upward swimming. We also considered that the smaller fish would allocate its vertical movement during GAU for some ratio (vertical swimming ratio (VSR)) of the vertical distance covered by the GAU of the larger fish (electronic supplementary material, figure S6). It was assumed that the smaller fish moved the same vertical distance for gliding as for upward swimming in its GAU, which enabled the fish to move back to the same vertical position (the sea surface).

    Here, the following two types of distances were considered to be minimized, as indicative of group cohesion. In case 1 (FinalDist), the smaller fish reduced the distance between the two fish at the endpoint, when the larger fish finished its own GAU. In case 2 (MeanDist), the smaller fish reduced the mean distance between the two fish during their GAU until the larger fish finished its own GAU. The simulation was conducted by changing HSR and VSR at a 1% interval. The situation when the smaller fish reached the endpoint of the GAU of the larger fish earlier than the larger fish (i.e. the smaller fish used more time/distance for horizontal swimming and less time/distance for GAU), which would never happen, assuming the smaller fish tried to perform GAU to save energy, was omitted from the analysis.

    3. Results

    (a) Overall pattern of grouping

    All the fish exhibited typical GAU repeatedly during the recorded 24 h (figures 1 and 2). The depth profiles of all the fish exhibited similar trends (electronic supplementary material, figure S1). The mean cross-correlation coefficients by individuals showed that the synchrony of GAU was maintained at high levels during the entire period (overall mean ± s.d. = 0.62 ± 0.16; N = 2160; figure 2). Other results and discussion regarding the overall pattern of grouping are described in electronic supplementary material, appendix A5.

    Figure 2.

    Figure 2. Patterns of (a) the hourly total number of glides, (b) the hourly mean glide duration per glide and (c) the hourly total glide duration of all individuals represented by different colours or line styles (only for the online version). The IDs of the fish in the right box were ordered by the size of the fish (the size of the fish increases from the bottom to the top). The patterns of (d) the hourly mean cross-correlation coefficient of the focal fish and the other nine fish (in total, nine pairs for each fish). The night-time and daytime are represented by the black and white zones in the bottom of figures, respectively.

    (b) Intra-school variations in movement

    Larger fish had significantly increased values than smaller fish for the total glide duration, the number of glides, the mean glide duration per glide, the depth change per glide, and the glide detection rate by wavelet over depth change (electronic supplementary material, tables S4 and S5; figures 2 and 3). In particular, the smallest fish (ID40) glided for 33% shorter duration per glide, 53% shorter duration per hour and 36% less number per hour, than the largest fish (ID04) (figure 3a,c). The vertical distance moved by the smallest fish during gliding was 75% of the largest fish (figure 3f). The largest fish glided for almost 90% of its total number of descending occasions, while the smallest fish glided for only half of its total number of descending occasions (figure 3k). Speeds (m s−1) during gliding and active propulsion of larger fish were significantly higher than smaller fish, while speed during active propulsion, represented in FL s−1, decreased with increasing fish size (electronic supplementary material, tables S4 and S5; figure 3g,i,j). If the size difference was smaller, the level of GAU synchrony, indicated by the cross-correlation coefficients by all pairs, was higher (electronic supplementary material, tables S4 and S5; figure 3l). The TBF scaled with size (TBF = 2.44 FL−1.30; R2 = 0.64; N = 10) and the 95% confidence intervals for the exponent (−2.08; −0.50) bracketed the expected value of −1.00 [29] (figure 3d was represented without log-transform for x- and y-axes to compare with other locomotive variables). The VeDBA of smaller fish showed significantly increased values than larger fish (electronic supplementary material, tables S4 and S5; figure 3e), and the total cost of GAU within 24 h of the smallest fish was 161% of the largest fish (electronic supplementary material, table S1). Key results are summarized in electronic supplementary material, table S3.

    Figure 3.

    Figure 3. The size of the fish in fork length (FL) is represented in the x-axis. The overall mean (y-axis) of: (a) the hourly mean glide duration per glide, (b) the hourly total glide duration, (c) the hourly total number of glides, (d) the hourly mean tail-beat frequency (TBF), (e) the hourly mean vectoral dynamic body acceleration (VeDBA), (f) the hourly mean depth change per glide, (g) the hourly mean speed during gliding (m s−1), (h) the hourly mean speed during gliding (FL s−1), (i) the hourly mean speed during active propulsion (m s−1), (j) the hourly mean speed during active propulsion (FL s−1), (k) the hourly glide detection rate by wavelet over depth change and (l) the hourly cross-correlation coefficient by all pairs. The error bars represent the standard error of the hourly mean. Significant linear regression relationships are also shown (see also electronic supplementary material, table S4 for the results of ordinary least squares regression analysis).

    (c) Simulation

    In case 1 (FinalDist), the minimum distance (0.027 m) was obtained when HSR and VSR were 30% and 77%, respectively (figure 4). In case 2 (MeanDist), the minimum distance (0.665 m) was obtained when HSR and VSR were 5% and 87%, respectively (figure 4). In both cases, the results suggested that the smaller fish had to compromise its GAU to maintain group cohesion. Although it was unknown whether the fish would decrease FinalDist, MeanDist or other measures in real situations, the decreased ratio (75%) of mean depth change per glide for the smallest fish (ID40) compared with the largest fish (ID04), shown by the accelerometry results, was closer to the VSR of FinalDist.

    Figure 4.

    Figure 4. A simulation scenario (detailed illustration: electronic supplementary material, figure S6) was considered when one larger fish (Fish L: 24.5 cm in fork length (FL)) optimized its own glide and upward swimming (GAU) in a vertically restricted environment (6 m depth), the other smaller fish (Fish S: 21.0 cm in FL) would follow Fish L by changing the time allocation of its horizontal swimming and GAU to maintain group cohesion. The smaller fish would allocate its horizontal swimming for some ratio (horizontal swimming ratio (HSR; x-axis)) of the horizontal distance covered by the larger fish, and its vertical movement during GAU for some ratio (vertical swimming ratio (VSR; y-axis)) of the vertical distance covered by the GAU of the larger fish. The energetically ideal speeds and angles for GAU and horizontal swimming speeds for both fish were determined based on hydrodynamic theory (for the calculation, see Material and methods). The following two types of distances were considered to be minimized, as indicative of group cohesion. (a) In case 1 (FinalDist), the smaller fish reduced the distance between the two fish at the endpoint, when the larger fish finished its own GAU. (b) In case 2 (MeanDist), the smaller fish reduced the mean distance between the two fish during their GAU movement until the larger fish finished its own GAU. The calculated distance is shown in colour. In both cases, the results indicated that the smaller fish had to compromise its GAU to maintain group cohesion.

    4. Discussion

    Our accelerometry results and the simulation based on hydrodynamic theory indicated that individuals in a group modulated the partition of energy/time used for the different activities in intermittent locomotion (i.e. GAU), possibly according to size-related differences of GAU performance, while maintaining group cohesion. The trend in the size-related differences was even confirmed under the effect of time of day. In particular, larger fish glided for longer durations and more frequently than smaller fish. Although the TBF–size relationship was not different from the expected scaling relationship [29], size-related differences based on the body morphology and hydrodynamic characteristics of the fish would affect differences of speed (and angle) during GAU [18]. Larger fish glided and swam upward at faster speeds (m s−1), using more vertical space for their GAU. Smaller fish with slower speeds (m s−1) for their GAU used less vertical space, and instead may use horizontal swimming for more time/distance or even swim downward by active propulsion to follow larger fish, as shown by the decreased glide detection rate by wavelet over depth change in smaller fish.

    Although living in groups provides various advantages [1], it would be potentially disadvantageous for smaller fish to synchronize their intermittent locomotion with the other members in a group, as smaller fish must reduce the duration and number of gliding to maintain the group cohesion. In addition, smaller fish would use more energy than larger fish, as shown in the lower total cost of GAU within 24 h. Previously, Notemigonus crysoleucas swam in a swim tunnel, and the gliding and coasting durations and the energy usage among different spatial positions in a school were monitored for a limited duration (15 min). The results suggested that the energy savings from the collective use of schooling and intermittent locomotion were sacrificed [30]. However, the link between the optimization of individual intermittent locomotion and the behavioural synchronization in a group, especially among members of different sizes, has not been investigated. Our experiment continuously monitored fish for 24 h under semi-natural conditions and the simulation based on hydrodynamic theory showed the advantage of intermittent locomotion in energy savings may be not fully optimized for smaller fish in a group when faced with maintaining group cohesion.

    The level of GAU synchrony between pairs may also be influenced by the size-related differences in GAU performance. The level of GAU synchrony was large when the size difference between the individuals of the pairs was small and vice versa. This may be because similar-sized individuals tend to have similar GAU performance (speed and angle), whereas individuals that differ in size have different GAU performance. Thus, as shown for other animals [11,12], the synchrony would be best maintained by individuals of similar sizes, even for the intermittent locomotion of PBT.

    The sub-optimality of the GAU for smaller fish in a group, shown in the accelerometer experiment using a net cage, may also be observed in the open ocean. Because the space in the net cage was restricted, the fish would need to turn many times to avoid collisions with the net. Their glide duration may have been shorter than without the cage. However, because the mechanism of sub-optimality of the GAU for smaller fish in a group is based on the difference of GAU performance among individuals resulting from the body morphology and hydrodynamic characteristics, the mechanism would also be valid in nature as long as the fish perform GAU while maintaining group cohesion. While our simulation assumed vertically restricted space, the vertical restriction in space was used only for restricting the movement of larger fish. On the other hand, in the open ocean where more individuals can freely join and leave groups, smaller fish in a group may potentially leave the group and construct or join another group similar in size [7] because similar-sized individuals tend to have similar GAU performance; otherwise growth of smaller fish may be hindered according to higher energetic cost maintaining group cohesion [9]. Size assortment of groups is observed in many animals, presumably to reduce the predation risk and foraging competition [1]. Size assortment of groups may also result from the cost of behavioural synchrony among individuals that differ in size [9], because differently sized individuals tend to have different activity budgets and movement abilities [10]. Our results showed that synchronizing the GAU in a group is costly for smaller individuals and the GAU synchrony was more tightly maintained for individuals similar in size, suggesting an additional mechanism of size assortment of shoals based on intermittent locomotion. Because the performance of intermittent locomotion can be determined based on the body morphology and hydrodynamic characteristics [18,31], intra-group variations of intermittent locomotion may be even observed in other animals, hence potentially affecting their group dynamics.

    As shown from the accelerometer experiment and the simulation, body size can be a key factor affecting intra-group differences of GAU performance and the synchronization of the activities. However, there may be the other factors. For example, energy savings by intermittent locomotion may not be equal among the members of a group depending on the spatial position [30], as the hydrodynamic advantages are different among the spatial positions in a group [24], resulting in differences in GAU performance. The reduced speed (FL s−1) during active propulsion in larger fish of our data may partly result from the difference of hydrodynamic advantages among the spatial positions. In addition, it is possible that fish modulated their angle of attack during gliding, potentially resulting in the difference in the speed/angle change during gliding [18]. Furthermore, because the synchronization of activity requires the sensory perception of the activity of other individuals, the distance among individuals may affect the GAU performance in a group. If the distance is larger, the sensory perception of the activity of other individuals may be delayed, resulting in delayed timing for GAU synchronization with other individuals. The relative order of spatial position in a group may also affect the activity recognition of other individuals, potentially affecting the timing difference of GAU among individuals. Rules determining the initiators and followers of GAU in a group are unknown. The difference of GAU performance of individuals may even be a trade-off among various biotic (e.g. nutritional state, aerobic capacity, ages and predator defence) and physical factors (e.g. hypoxia, light level and temperature). Thus, further studies are needed to understand the relationships among the spatial positions in a school, intra-school movement, activity synchrony and various biotic and physical conditions, which would elucidate the costs and benefits of schooling and how school dynamics can emerge from the local interactions among individuals.

    5. Conclusion

    Our accelerometry experiment using a negatively buoyant pelagic fish and the simulation based on hydrodynamic theory demonstrated that synchronizing activities with other group members may cause a deviation from optimal intermittent locomotion for small individuals in a group, suggesting the implication of body size on assortment of shoals due to kinematics (i.e. the performance of intermittent locomotion).

    Ethics

    All procedures for the experiment were approved by the Animal Research Committee of Kyoto University (permit number: Informatics 25–7).

    Data accessibility

    All data used are presented in the electronic supplementary material.

    Authors' contributions

    All authors contributed to the design of the experimental study and fieldwork to collect data. T.N. analysed and interpreted data, and prepared the manuscript. All authors contributed to the final version. All authors read and approved the final manuscript.

    Competing interests

    The authors declare that they have no competing interests.

    Funding

    This research was supported by cooperative research organization for the Promotion Program of International Fisheries stock assessment from the Fisheries Agency of Japan, JSPS KAKENHI grant nos. 25712022 and 16J05814 and joint research fund with Biologging Solutions Inc.

    Acknowledgements

    We thank A. Takahashi and Y. Kawabata for the lending of acceleration data loggers. We acknowledge the Fisherman Cooperative Association of Kaminokae, great fishermen Y. Deki and T. Oki, colleagues M. Ishikawa, K. Kikuchi, H. Yamane, T. Hori, J. Takagi, C.A. Farwell and the staff of Fukuya Hotel for supporting the fieldwork.

    Footnotes

    Published by the Royal Society. All rights reserved.

    References