A method to quantify social relationships between
captive odontocetes based on distances between
individuals during synchronous breathing
Kaori Tage, 2Masatoshi Tsunokawa, 3Hajime Ishikawa, 4Takashi F.
Matsuishi
1

1
2

Graduate School of Fisheries Sciences, Hokkaido University, Hakodate, Hokkaido, Japan;
Otaru Aquarium Co. Ltd., Otaru, Hokkaido, Japan; 3 Institute of Osaka Marine Research,
Taiji, Wakayama, Japan; 4 GCF, Faculty of Fisheries Sciences, Hokkaido University,
Hakodate, Hokkaido, Japan. Corresponding author: T. F. Matsuishi,
catm@fish.hokudai.ac.jp
Abstract. Quantifying behaviour among captive odontocetes is important for understanding the social
structure and managing the captive conditions. Based on frequent interactions, trainers of captive
cetaceans establish perceptions of relationships between animals. Distances between individual cetaceans
during synchronous breathing can be used to express social relationships among odontocetes. If theperceptions of trainers can be visualised, these diagrams represent graphically a useful tool to improveanimal care. The study aimed to both quantify social relationships among captive odontocetes, and tovisualise trainer perceptions, using the distance between individuals during synchronous breathing as a
metric of odontocetes social cohesion. Data were collected from three pools at three facilities housing
common bottlenose dolphins or harbour porpoises. Individuals distance for dyads (a pair of cetaceans in
an interactional situation) were calculated using a combination of video recordings, visual observations,and body measurements. Proximity relationships between individuals in each pool were visualised using
multidimensional scaling analysis (MDS). Mathematically predicted relationships among captive
odontocetes were consistent with trainer perceptions of social relationships. We demonstrated that MDS
can be used to visualise social relationships among captive odontocetes, and that these visualisations canbe used to assist trainers and animal management to improve captivity conditions.
Key Words: dolphin proximity, multidimensional scaling analysis, synchronous breathing.

Introduction. Dolphins may experience psychological stress in captivity due to the limitedsocial environment (Serres et al 2020). Psychological stress can be aggravated in confinedenvironments and limited social groups, such as captive conditions (Waples & Gales 2002).
This stress can be caused by social interactions, separation of individuals, or inappropriategroupings (Waples and Gales 2002; Serres et al 2020). These stressors may result in lossof social relationships potentially leading to disease (Waples & Gales 2002). However,psychological stress in captive dolphins might be tempered if individuals have strong social
bonds and can benefit from the support of conspecifics (Clegg et al 2017; Serres et al2020). The dyads observation at a training session, keeping individuals in the same pooland segregating the individuals with negative effects for reducing the stress in the groupare important for revealing the social relationships.
Social relationships among captive odontocetes should be monitored to establish andmaintain minimally stressful environments (Miller et al 2021). Introducing a new animal,
the death of another, or birth can change group structure and social relationships.
Understanding these relationships is important for an appropriate management of thecaptivity (Waples & Gales 2002; Serres et al 2020). Animal caretakers often possess deep
knowledge of the behaviour of individuals under their care because trainers' impressions
are based on a comprehensive assessment of the daily training and observations (Whitham& Wielebnowski 2013; Khadpekar et al 2018). However, the perceptions of relationships
among captive individuals and trainers are difficult to transfer to others. This is because

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sensory impressions have different assessment criteria for different people and are difficult
to quantify and convey to others. Depicting social relationships by means of social-structuremaps has the following advantages. It can visually show social relationships, making
conveying information through human communication easier. Long-term monitoring iseasier because structural changes can be shown quantitatively and visually. However, tobest achieve this requires the subjective impressions of trainers to be quantified.
Multidimensional scaling (MDS) is a social network analysis (Hanneman & Mark
2005). Social network analysis (SNA) can quantify the strength of relationships between
individuals (Rose & Croft 2015; Davis et al 2018) and patterns within populations (Farine& Whitehead 2015; Rose & Croft 2015; Snijders et al 2017). Relationships can be defined
based on interactions or associations defined by proximity (Rose & Croft 2015; Davis et al2018). SNA can depict social relationships among individuals within a group, illustrating
individual social connections, and the strength of preferential relationships with others(Rose & Croft 2015). MDS can quantify and visualise similarities within a group using a
proximity matrix representing the distance between pairs of cetaceans (dyads) ininteractional situations, the result of which depicts spatial relationships among individuals(Hout et al 2013).
MDS using individual distance (ID) was applied to captive Iberian wolves Canis lupus
signatus and successfully represented pack cohesion (Soriano et al 2020). ID represents
the minimum distance an animal routinely maintains between itself and other members of
the same species (Hediger 1950). It has been used to identify social relationships in various
animal groups, and can be influenced by relationships between members within a group(Kummer 1970; Warburton & Lazarus 1991) and familiarity, social rank, sex and age (Shuji
1995; Sakai et al 2010; Soriano et al 2020). Quantifying ID might assist with theidentification of social relationships among captive odontocetes. Synchronous breathing
occurs when two or more dolphins simultaneously breathe on the surface (Connor et al2006), which is considered as having a functional role in maintaining relationships withinswimming dyads, because it can be influenced by pod social structure, kinship level, age,and sex (Sakai et al 2010; Actis et al 2018; Serres et al 2021), therefore it can be used as
an index of cohesion and sociality among individuals (Actis et al 2018). This index could bea useful and easily measured tool to assess cetacean sociality when individuals can be
identified above water (Sakai et al 2010; Senigaglia & Whitehead 2012; Actis et al 2018).
Synchronous breathing of pairs might also be easy to observe from the water in aquaria
because the numbers of individuals in pools are low enough to enable accurate
identification. In the case of this study, the objective is to depict the trainers' perceptions
by using MDS, so it is necessary to measure a meaningful ID. In addition, in order tocalculate accurate IDs, it is necessary to select a moment when the IDs are not distorted
when viewed from above the water surface. Odontocete ID during synchronous breathinghas been well-studied (Connor et al 2006; Sakai et al 2010; Senigaglia & Whitehead 2012;
Actis et al 2018; Serres et al 2021). For wild Indo-Pacific bottlenose dolphins, Tursiops
aduncus, at Mikura Island, Japan, ID during synchronous breathing was shortest between
female and calf pairs, and shorter in female pairs than in male pairs, and relationships
changed depending on the sex or age of the pairs (Sakai et al 2010). Indo-Pacificbottlenose dolphins may have strong mother-offspring bonds and associate with otherfemales to help rear calves (Wang 2018). Social relationships among captive odontocetes
could be expressed in aquaria using ID during synchronous breathing. It is difficult to apply
the methods of previous research to the captivity condition, so these methods are needed
to be improved for use in aquaria.
Firstly, surface video could be used to record and observe synchronous breathing.
For wild odontocetes, this breathing has been observed using video taken from helicopters,boats, or on SCUBA (Connor et al 2006; Sakai et al 2010; Senigaglia & Whitehead 2012;
Actis et al 2018; Smultea et al 2018). Because the synchronous breathing rate of captive
odontocetes increases under stress, for example, when a diver is in a pool (Serres et al2021), it would be inappropriate to observe surface breathing behaviour in captivity.
Surface video is not easy in aquarium environments using a drone to obtain the video.
Therefore, it is necessary to track odontocetes above water and fix the cameras looking
down over a pool from above in the case of aquaria. Secondly, ID has been estimated fromAACL Bioflux, 2023, Volume 16, Issue 6.
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distances between animals’ body (Connor et al 2006; Sakai et al 2010; Senigaglia et al2012; Senigaglia & Whitehead 2012; Serres et al 2021). The image is distorted because
the video is typically recorded from seats, in an oblique position.
Moreover, an animal's size in images varies depending on where it was situated in an
aquarium, relatively to the camera, which involved coefficients of correction. Hence, IDs
determined from animals in images might differ from actual IDs. The study aimed todevelop a method based on video recordings above the surface to quantify and visualisesocial relationships among captive odontocetes consistently with trainers' perceptions. MDS
was applied for visualising trainers' perceptions. The ID of dyads at synchronous breathing
was calculated from surface video to obtain the proximity matrices for MDS. This method
was applied to three pools at two aquariums for experimental purposes and demonstrated
the examples that could be obtained. This experiment does not intend to examine captive
odontocetes' social structures in the pools.
Material and Method
Quantifying social relationships
Coordinate correction. To convert video image locations to actual locations on thesurface of pools, formulas to correct coordinates are presented. Video cameras were
installed as far as possible from the pools to record the entire pool surface (Figure 1).

Figure 1. Pool and camera positions.
The video was recorded while a levelling rod marked every 20 cm (TAJIMA, HRD-100, 1m) with plastic strings attached to either end, or a disc (30 cm diameter, 5 mm thick, white
acrylic) with two holes and plastic strings, was moved over the surface of the pool fromthe back to front (Y-axis) and left to right (X-axis), towards the video camera. Since thecorrection formula is obtained in each facility, it does not matter if the size of the scalediffers from facility to facility as long as the scale is large enough to be visible on the image.
These scales were moved the appropriate number of times to ensure that no excess ordeficiency depended on the pool size. The levelling rod was only used in the Otaru
aquarium, but the disc was used in the Dolphin Resort. The disc proved easier to record
than the levelling rod. Because disc diameter remained constant in all directions, the X andY axes could be recorded simultaneously when the disc moved over the entire pool. Stills
were captured from video using Adobe Premiere Pro v 14.7.0 (build 23). Images werechosen when the scale (levelling rod or disc) was not distorted on the water surface. XYpixel coordinates on the scale were acquired every 20 (levelling rod) or 30 cm (disc) from
captured images using ImageJ v 1.53e. Here, XY pixel coordinates on the captured images
were recorded. Midpoints of XY pixel coordinates every 20 or 30 cm on the scale were
calculated. The 20 or 30 cm in length was divided by the distance between acquired XY
pixel coordinates (z) to calculate how many centimetres one pixel represented (cm pixel-1).
Values of z are defined as representative values for each midpoint. The multiple regression
conversion equations of the X and Y axes (Zx and Zy) were derived using values for the
midpoint and z. The derivation of Zx and Zy and the calculation of multiple correlation
coefficients were performed using the regression analysis function in Microsoft Excel.
Values of zwere plotted on the contour maps for both X and Y axes toward the video camera
using the "akima" package (Akima 2020) in R studio 1.4.1103. Zx and Zy with larger
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multiple regression coefficients were modified by removing the outliers of z referring to thecontour maps since it was difficult to find values that did not fit on the contour lines until
all z values were plotted. Locations of odontocetes were converted from surface images
using Zx and Zy. Zx and Zy were represented as 𝐴𝑋𝑝 + 𝐵𝑌𝑝 + 𝐶 and 𝐴ʹ𝑋𝑝 + 𝐵ʹ𝑌𝑝 + 𝐶ʹ ,respectively, at the pixel coordinate (𝑋𝑝 , 𝑌𝑝 ) on images, so the coordinate (𝑋, 𝑌) on the
𝑋

𝑌

𝑝
𝑝
surface of the pool was represented by (∑𝑘=1
𝑍𝑥 , ∑𝑘=1
𝑍𝑦 ). Therefore, the coordinate (𝑋, 𝑌)

was calculated by the formulas:𝑋=𝐴
𝑋 (𝑋 + 1) + 𝑋𝑝 (𝐵𝑌𝑝 + 𝐶)
2 𝑝 𝑝

𝑌=

𝐵′
𝑌 (𝑌 + 1) + 𝑌𝑝 (𝐴′ 𝑋𝑝 + 𝐶 ′ )2 𝑝 𝑝

ID calculation. The odontocete shape was simplified into a pentagon (Figure 2), with theshortest distance between two odontocetes calculated as the distance between the
pentagon vertices. The pentagon was assumed to be bilaterally symmetrical with respect
to the beak-fluke axis on the horizontal plane.

Figure 2. (a)(b) Body Measurement (c) calculations to determine dolphin or porpoise
body shape (d) Coordinates to acquire vertices of a pentagon.
(a) and (b) (1) Body length (from the tip of the rostrum to the tip of the fluke), (2)rostrum–flipper width (from the tip of the rostrum to the midpoint of the maximum widthof left and right flippers), (3) rostrum–blowhole length (from the tip of the rostrum to the
middle of the blowhole), (4) flipper–flipper width (the maximum width between left andright flippers), and (5) fluke width (the maximum width of the fluke). (c) values tocalculate vertices of a pentagon: (6) length of the rostrum–right flipper segment (fromthe tip of the rostrum to the right point of the maximum width of left and right flippers),(7) length of the segment from the rostrum to the right fluke (the distance between the
tip of the rostrum and the midpoint of the maximum width of fluke); θp is the angle
formed by the body length axis (1) and the rostrum–right flipper axis (6); θf is the angle
formed by (1) body length axis and (7) the rostrum–right fluke axis. (d) (a, b) is thecoordinate of the tip of the rostrum; (aʹ, bʹ) is the coordinate of the middle of theblowhole; (α, β) is the coordinate of the right point of the left and right flipper axis; and(αʹ, βʹ) is the coordinate of the left point of the left and right flipper axis.
Measurement of odontocetes and calculation of vertices of the pentagons. Body
measurements of each animal were made to calculate vertices for individual pentagons foreach individual in each pool. Measurements include lengths of (1) body, (2) rostrum–flipper
segment, (3) rostrum–blowhole segment, (4) fluke, and (5) flipper–flipper segment (Figure

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2, (a) and (b)). Using measurements (1)–(5), cos 𝜃𝑝 , sin 𝜃𝑝 , cos 𝜃𝑓 , sin 𝜃𝑓 , the length of therostrum–right flipper segment (6) and the length of the rostrum–right fluke segment (7)of Figure 2 (c) were calculated using the equation in Table 1. Pentagon vertices (Figure2(d)) are calculated by the rotation matrix using values for (1), (3), (8), (9), cos 𝜃𝑝 , sin 𝜃𝑝 ,cos 𝜃𝑓 , and sin 𝜃𝑓 for each odontocete using equations in Table 1 (All trigonometric functions,notations and coordinates correspond to values in Figure 2), after calculating thecoordinates of the rostrum and middle of the blowhole from captured images using ImageJ.
Table 1
Body measurements and calculations used to acquire pentagon vertices

Body length
Rostrum-flipper
Rostrum-blowhole
Fluke
Flipper-flipper

Corresponding
notation infigures
(1)
(2)
(3)
(4)
(5)

Rostrum-right point of flipper

(6)

(5)
2
√((2)) + ( )2Rostrum-right point of fluke

(7)

(4)
2
√((1)) + ( )
2

(8)

(6)
(1)

(9)

(7)
(1)

Measurement/ Calculation
items

The ratio of the rostrum tothe right point of the flipper
segment against the bodylengthThe ratio of the rostrum tothe right point of the fluke
segment against the bodylengthcos 𝜃pcos 𝜃psin 𝜃psin 𝜃pcos 𝜃fcos 𝜃fsin 𝜃fsin 𝜃fCoordinate of rostrum
Coordinate of blowhole
Coordinate of the right pointof the maximum width of left
and right flippers
Coordinate of the left point of
the maximum width of left
and right flippers
Coordinate of the right pointof the maximum width of the
fluke
Coordinate of the left point of
the maximum width of the
fluke
Coordinate of the midpoint of
the maximum width of the
fluke(𝑎, 𝑏)(𝑎′ , 𝑏′ )AACL Bioflux, 2023, Volume 16, Issue 6.
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Measured or obtained
value/calculation
Measured value
Measured value
Measured value
Measured value
Measured value
2

2

(2)
(6)
(5)⁄2
(6)
(1)
(7)
(4)⁄2
(7)
Obtained value from the images
Obtained value from the images(𝛼, 𝛽){(𝑥m − 𝑎) cos 𝜃p − (𝑦m − 𝑏) sin 𝜃p } × (8) + 𝑎,(){(𝑥m − 𝑎) sin 𝜃p + (𝑦m − 𝑏) cos 𝜃p } × (8) + 𝑏(𝛼 ′ , 𝛽 ′ ){(𝑥m − 𝑎) cos 𝜃p − (𝑦m − 𝑏)(− sin 𝜃p )} × (8) + 𝑎,(){(𝑥m − 𝑎)(−sin 𝜃p ) + (𝑦m − 𝑏) cos 𝜃p } × (8) + 𝑏(𝑥, 𝑦){(𝑥 − 𝑎) cos 𝜃f − (𝑦m − 𝑏) sin 𝜃f } × (9) + 𝑎,
( m){(𝑥m − 𝑎) sin 𝜃f + (𝑦m − 𝑏) cos 𝜃f } × (9) + 𝑏(𝑥 ′ , 𝑦 ′ ){(𝑥 − 𝑎) cos 𝜃f − (𝑦m − 𝑏)(− sin 𝜃f )} × (9) + 𝑎,
( m){(𝑥𝑚 − 𝑎)(−sin 𝜃f ) + (𝑦m − 𝑏) cos 𝜃f } × (9) + 𝑏(𝑥m , 𝑦m )(1) × 𝑎′ − 𝑎 × ((1) − (3)) (1) × 𝑏′ − 𝑏 × ((1) − (3))
(
,
)
(3)
(3)

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Distance calculation. Since the rostrum and blowhole during synchronous breathing was
captured, it was assumed that the odontocetes were approximately on the same plane,assuming the wave on the water surface is negligible.
1. The vertices of each pentagon are defined as the convex points on the body ofodontocetes: the rostrum, both ends of the maximum width of the left and right flippers,
and both ends of the maximum width of the fluke (Figure 2(d)).
2. The shortest distance between two individuals is represented by the minimum distance
between the combinations of vertices in two pentagons because the odontocete shape
was simplified into a pentagon. There are 25 possible distances between two individuals
with 5 vertex combinations, of which only one is the shortest.
3. Cross product was calculated using each edge vector of one individual and the convex
points of the other individual, to discriminate if two animals were superimposed. The
positive or negative signs of the cross products of one vertex of the arbitrary pentagon
and each of the five sides of another pentagon are all matched when pentagons weresuperimposed. Distance is defined as zero cm when two pentagons partly overlap incross-product calculation results.
4. Thus, all ID values (dij) represent either the shortest distance between vertices of two
pentagons or zero cm (overlap).
Calculation of indices of mean ID for MDS. An index of the mean distance was definedfor each dyad, di, by calculating the mean ID during the synchronous breathing frequency(fi) found in whole observation period. Social relationships among odontocetes in each poolare described by MDS using the distance matrices of 𝑑𝑖 , where fi represents the number ofimages available for ID calculation. Each ID for each dyad is represented as dij, where 𝑗represents each synchronous breath. di is represented as:
𝑑𝑖 =

𝑓𝑖
1
∑ 𝑑𝑖𝑗
𝑓𝑖
𝑗=1

Describing social relationships by MDS. The distance matrix for all dyads was createdby di. Social relationships among captive odontocetes in each pool were described using
MDS from this distance matrix. MDS results were prepared using the "igraph" package(Csardi et al 2006) in R studio 1.4.1103. When the distance between dyads on the surface
at the synchronous breathing is shorter, the individuals are plotted closer in twodimensional space on MDS than those with a long distance on the surface. By assessing
the distance between dyads on a map, one obtains a quantitative measurement ofperceived similarities relatively to other individuals in two-dimensional space (Hanneman& Mark 2005; Hout et al 2013). MDS outcomes were investigated to determine if they wereconsistent with trainer perceptions. When illustrated in MDS, lines between individuals
represent relative IDs.
Interviews. Before analysing MDS, we interviewed trainers about the perceptions of social
relationships between odontocetes under their care. The results of interviews were used todetermine if the outcome of MDS with di matched their impressions. The trainer's daily
observations on the social relationships among captive odontocetes were investigated.
Applications. We tested whether this method, which expresses individual relationships by
MDS, is consistent with the trainer's perceptions. Data were collected for three pools at
three facilities (Table 2): the Dolphin Stadium and a Display pool in the Otaru Aquarium(Otaru, Hokkaido, Japan), and an 11.0 m diameter pool at the Dolphin Resort (Taiji,
Wakayama Prefecture Japan). Video cameras were placed where the entire surface pool
could be seen. The focus was fixed on the middle of the pool.

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Table 2
Camera installation locations, visual observations and recordings by facility
Pool
Otaru
Aquarium
Display pool
Otaru
Aquarium
Dolphin
Stadium
Dolphin Resort
11.0 m circularpool

Height(m)

Camera–pool (m)Observable pool size(m) L×W or diameter

Observation
time (min)

3.8

2.4

12.0

943

4.5

12.5

78.0×33.0

948

Study period(yyyy.mm.dd hh:mm)
2019.11.28 09:00-16:00
2019.11.29 08:30-16:00
2019.11.30 08:30-15:40
2020.11.28 08:50-16:00
2020.11.29 08:30-16:00
2020.11.30 08:30-16:00

7.7

11.0

11.0

1079

2021.07.13 11:50-16:00
2021.07.14 09:20-17:00
2021.07.15 09:10-17:00

Visual observations and video recordings. Visual observations and video recordings
were made in all pools outside training and dolphin showtimes. Video cameras were placed
where the entire pool could be seen. The focus was fixed on the middle of the pool. Cameras
were always at the same position throughout the data collection after installation. Different
cameras were used for different pools. At the Otaru Aquarium Dolphin Stadium andDolphin. Resort circular pool, odontocete behaviour and video of scales were filmed usinga camcorder (SONY FDR-AX 700) with a recording format 2160/30p 60 Mbps (XAVC S 4K)
and a circular polarising light filter (SONY VF-62CPAM2) mounted on a camera tripod(Velbon Medium Aluminium Tripod EX-547). A web video camera (Logitech HD Pro Webcam
C920 with USB2.0 and 12 m of extension cable KB-USB-R212), camera tripod (SLIK
Compact II), and recording software (Logitech Capture 1.10.110, 24 fps, 640 × 360
resolution) were used at the Otaru Aquarium Display pool. The time, pairs involved insynchronous breathing, and any notable events were recorded by an observer positioned
as far as possible from the dolphins because individual identification and determining any
lag in synchronous breathing were difficult to achieve from video imagery (Figure 3.). Video
images were used for ID calculation and to identify behaviour before synchronous
breathing, and visual observations were used to determine the individuals involved and fi,
the synchronous breathing frequency.
Synchronous breathing. We recognise three patterns (1–3) in synchronous breathing
based on whether two odontocetes: 1) swam parallel to each other and simultaneously
broke the surface; 2) did not swim parallel to each other but broke the surface
simultaneously in the same direction; or 3) first breathed separately despite swimming
parallel to each other, and then swam parallel to each other and broke the surface
simultaneously. In this study, cases in which individuals breathed synchronously but had
not swum parallel in the same direction, or where one individual had jumped during
synchronous breathing were excluded because breathing without the same movement falls
outside the definition of synchronous breathing.

Figure 3. Images captured from the video (a) the Otaru aquarium Display pool, (b) the
Otaru aquarium Dolphin Stadium, (c) Dolphin Resort circular pool.
The Otaru Aquarium Display pool. Two female (A, M) and two male (S, T) harbour
porpoises (Phocoena phocoena) at the Otaru Aquarium Display pool (12.0 m diameter)
were observed from 11–13 December 2019. Table 3 shows measurements of harbour
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porpoises in the pool. The video camera was installed at 3.8 m height and 2.4 m away fromthe pool (Table 2). The levelling rod was moved on the water surface seven times back tofront and six times left to right towards the web video camera. The results of multiple
regression conversion formulas for converting video image locations to actual locations on
the surface of pools are:𝑍𝑥 = 0.0019𝑋𝑝 + 0.014𝑌𝑝 – 0.30 (𝑅2 = 0.88),
𝑍𝑦 = 0.0080𝑌𝑝 + 0.0035𝑋𝑝 – 14 (𝑅2 = 0.81).
The total observation time was 943 min (Table 2). Visual observations and video recordings
identified patterns of synchronous breathing 1 and 2 for each dyad. Observed mean ID and
frequency of synchronous breathing are listed by dyads in Table 4. The total fi for all six
dyads was 713. The shortest 𝑑𝑖 was calculated for dyad AT, and the longest for dyad AM.
The highest fi was observed for dyad AT, and the lowest for dyads AS and ST.
Table 3
Measurements of Harbour porpoises in the Otaru Aquarium Display pool
Porpoise
Measurements (cm)
Sex
code
(1)
(2)
(3)
(4)
A
F
185
45
15
43
M
F
173
60
14
38
S
M
158
50
18
39
T
M
161
46
20
39
(1)–(5) correspond to notations in Figures 2. and Table 1. Porpoises were measured on 26
December 2019.

(5)
52
42
43
45

Table 4
Dyad di and fi values for the Otaru Aquarium Display pooldi (cm)
Dyad
fi
AM
148
100
AS
129
22
AT
69
249
MS
145
126
MT
128
194
ST
133
22
fi is the frequency of synchronous breathing; di is our index of mean ID for each dyad.

The Otaru Aquarium Dolphin Stadium. Three male (A, N, R) common bottlenose
dolphins (Tursiops truncatus) were housed in the Dolphin Stadium of the Otaru Aquarium(Table 5) within a rectangular pool 78.0 × 33.0 m. Observations were conducted from 28–
30 November 2020. The camcorder was installed at 4.5 m in height and 12.5 m away fromthe pool (Table 2). A levelling rod was moved over the water surface seven times back tofront and four times left to right towards the camcorder. The results of multiple regression
conversion formulas are:𝑍𝑥 = −0.000011𝑋𝑝 + 0.00057𝑌𝑝 + 0.041 (𝑅2 = 0.61)
𝑍𝑦 = 0.0021𝑌𝑝 – 0.000098𝑋𝑝 – 0.35 (𝑅2 = 0.30)
Table 5
Measurements of male bottlenose dolphins in the Otaru Aquarium Dolphin Stadium
Measurements (cm)
(1)
(2)
(3)
(4)
(5)
A
266
56
35
58
84
N
303
73
38
65
94
R
316
76
42
68
97
(1)–(5) correspond to notations in Figures 2 and Table 1. Dolphins were measured on 29 November
2020.
Dolphin code

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The total observation time was 498 min (Table 2). Visual observations and video
recordings identified patterns 1–3 of synchronous breathing for each dyad. Measurementsof male bottlenose dolphins in the Otaru Aquarium Dolphin Stadium were shown in Table
5. The total 𝑓𝑖 for all three dyads was 148. The shortest di was calculated for dyad NR, thelongest for dyad AN. Observed mean ID and frequency of synchronous breathing for the
Otaru Aquarium Dolphin Stadium are listed by dyads in Table 6. The highest fi was observed
for dyad NR, which was the lowest fi for dyad AN.

Dyad di and fi values for the Otaru Aquarium Dolphin Stadium

Table 5Dyaddi (cm)
fi
AN
312
15
AR
288
53
NR
230
80
fi is the frequency of synchronous breathing; di is our index of mean ID for each dyad.

Dolphin Resort circular pool. Four male (C, F, G, H) common bottlenose dolphins in thispool were observed from 13–16 July 2021. Measurements of the dolphins were shown in
Table 7. The camcorder was installed on the roof of an adjacent building at 7.7 m in heightand 11.0 m away from the pool (Table 2).
The disc was moved on the water surface eight times back to front and seven times
left to right towards the camcorder. The results of multiple regression conversion formulas
are:
𝑍𝑥 = −0.00000081𝑋𝑝 + 0.00010𝑌𝑝 + 0.18 (𝑅2 = 0.96),
𝑍𝑦 = 0.00041𝑌𝑝 + 0.000039𝑋𝑝 + 0.17 (𝑅2 = 0.61).
The total observation time was 1079 min (Table 2). Visual observations and video
recordings identified patterns 1–3 of synchronous breathing for each dyad. Observed mean
ID and frequency of synchronous breathing are listed by dyads in Table 8. The total fi forall six dyads was 454. The shortest di was calculated for dyad CF, and the longest wascalculated for the dyad CG. The highest fi was observed for dyad CF, and the lowest wasobserved for the dyad FG (Table 8).
Table 6
Measurements of male bottlenose dolphins in the Dolphin Resort 11.0 m diameter pool
Measurements (cm)
(1)
(2)
(3)
(4)
(5)
C
297
97
42
66
79
F
296
89
38
65
76
G
302
95
40
68
78
H
307
97
42
71
74
(1)–(5) correspond to notations in Figures 2 and Table 1. Dolphins were measured on 19 July
2021.
Dolphin code

Table 7
Dyad di and fi values for the Dolphin Resort 11.0 m diameter pool
Dyad

di (cm)

fi

CF
23
305
CG
73
6
CH
60
14
FG
49
4
FH
42
25
GH
32
100
fi is the frequency of synchronous breathing; di is our index of mean ID for each dyad.

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Results. MDS in each pool were described using the distance matrix of di.
Application in the Otaru Aquarium Display pool. The AT dyad had a high fi and shortestdi (dAT=69 cm, fAT=249 in 943min). M seldom coordinated synchronous breathing withother individuals (fAM=100, fMS=126, fMT=194). The fi of S and other individuals was low(fAS=129, fMS=126, fST=22). Assuming that physical distance reflects social distance, theaffiliative dyads were considered to have the shorter ID. Therefore, as revealed in the MDS
outcome (Figure 4.), the result of the relative distance relationships using di (our index ofmean ID for each dyad), A and T are relatively close, and M and S are relatively distant.

Figure 4. Outcome of MDS with di for the Otaru Aquarium Display pool.
Application in the Otaru Aquarium Dolphin Stadium. The NR dyad had a high 𝑓𝑖 andthe shortest di (dNR=230cm fNR=80 in 948 min). A had a seldom coordinated synchronous
breathing with other individuals (fAN=15, fAR=53). A did synchronous breathing far fromothers (dAN=312, dAR=288). In the interview, the trainer recognised that N and R had anaffiliative relationship, but A and N did not. According to the trainer's daily observations, A
and N often engaged in aggressive behaviours such as chasing or biting, while N and R
swam together. However, trainers also said, "A and N did not engage in aggressive
behaviours and kept their distance when the two were put together. Therefore, therelationships of the three animals were not completely without affinity only when all threewere put together. It would be difficult to house or train the dolphins in the same pool if
the three animals were not entirely compatible". The MDS outcome (Figure 5.), show that
A was distanced from R and N, which is consistent with the trainer’s perceptions.

Figure 5. Outcome of MDS with 𝒅𝒊 in the Otaru Aquarium Dolphin Stadium pool.
Application in the Dolphin Resort circular pool. The CF dyad had a high fi and theshortest di (dNR=23 cm, fNR=305 in 1079 min). H had a seldom coordinated synchronous
breathing with other individuals (fCH=14, fFH=25), except for G (fGH=100). The trainer
perceived "H to be the dominant specimen among the four dolphins, and C and F often
swim together". According to the trainer's daily observations, H had the least number of
tooth rake marks of the four animals and often bit other dolphins. The di (our index ofmean ID for each dyad) was calculated from dij (all IDs for each dyad) and fi (synchronous
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breathing frequency). The trainer also indicated that "it was once possible to perform
husbandry training with both G and H simultaneously, but with the increased social rankingof H this was now impossible; H had to be alone". The outcome of MDS (Figure 6), in which
H was placed farther from other individuals, was consistent with trainer perceptions.

Figure 6. Outcome of MDS with di in the Dolphin Resort circular pool.
Discussion. These results suggest that MDS using di successfully expresses social
relationships among captive odontocetes. The outcomes illustrated by MDS are consistent
with trainer perceptions based on visual observations of dolphin and porpoise behaviours
in pools. In this study, MDS was described using di (our index of mean ID for each dyad)
calculated from (our index of mean ID for each dyad) calculated from dij (all IDs for eachdyad) and fi (synchronous breathing frequency). Affiliative dyads typically have a shorterdi and a higher fi, like AT in the Otaru Aquarium Display pool. This indicates that the shorter
the ID during synchronous breathing, the higher the synchronous breathing frequency incaptive conditions, as in the wild (Connor et al 2006; Actis et al 2018). Social relationships
illustrated by MDS are consistent with trainer perceptions based on visual observations ofdolphin and porpoise behaviours in pools. These results suggest that MDS using 𝑑𝑖
successfully expresses social relationships among captive odontocetes, even where trainers
have not discerned social relationships because of new introductions, the death ofindividuals in a population, population reconstruction or a population that is new to a
trainer. In addition to verbal communication, MDS plots can assist trainers in determining
the proper dyads for the training, social order, and the change of social relationships withthe growth and maturation because quantified social relationships can be used to evaluate
the social structure or stability. The ID during synchronous breathing in wild odontocetes
is affected by kinship and sex (Sakai et al 2010; Serres et al 2021). Continued observations
might reveal the effects of calf development, new introductions and class changes on social
relationships. Captive dolphins can experience stress stemming from social interactions(Waples & Gales 2002; Clegg et al 2017; Serres et al 2020). Because social relationships
reported herein are manifest for a narrow window of time, prolonged and recurring
observations should be made, such as when a new individual is introduced into an aquarium
environment or after an individual's death. The method was applied for three to five captive
odontocetes in this study. The most accurate ID could be calculated using the fixed cameraand multiple regression conversion equations. The observation was conducted for threedays, but MDS could visualise trainers' perceptions even during a short-term observation.
Therefore, this method can apply to the larger group and provide snapshots of the dolphins
if only the individuals can be identified.
Conclusions. The study showed that MDS can describe social relationships among captive
odontocetes with di as an index of individual distance, and was consistent with trainer
perceptions of relationships between captive animals. MDS enables the quantification ofsocial relationships among captive odontocetes and visualises trainer perceptions. Ongoinganalysis will enable changes in relationships between captive cetaceans to be identified
early, and adjustments made to improve long-term animal welfare.

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Acknowledgements. The authors are grateful to the Otaru Aquarium and Dolphin Resort
trainer teams, who permitted this study in their facilities. We also thank Ms Suzuki H., theFuture University of Hakodate, for her kind assistance in the experiment. Dr Steve O'Shea
from Edanz (https://jp.edanz.com/ac) edited a draft of this manuscript. This research did
not receive any specific grant from funding agencies in the public, commercial, or nonprofit sectors.
Conflict of interest. The authors declare no conflict of interest.
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Received: 06 September 2023. Accepted: 25 November 2023. Published online: 15 December 2023.
Authors:
Kaori Tage, Graduate School of Fisheries Sciences, Hokkaido University 3-1-1 Minato, Hakodate, Hokkaido 0418611, Japan, e-mail: kaori.t.fnawp07@gmail.com
Masatoshi Tsunokawa, Otaru Aquarium Co., Ltd. 3-303 Shukutsu, Otaru, Hokkaido 047-0047, Japan, e-mail:mtsuno@otaru-aq.jp
Hajime Ishikawa, Institute of Osaka Marine Research 703-15 Moriura, Taiji, Wakayama 619-5172, Japan, email: ishikawa@dolphinresort.jp
Takashi Fritz Matsuishi, GCF, Faculty of Fisheries Sciences, Hokkaido University 3-1-1 Minato, Hakodate,
Hokkaido 041-8611, Japan, e-mail: catm@fish.hokudai.ac.jp
This is an open-access article distributed under the terms of the Creative Commons Attribution License, which
permits unrestricted use, distribution and reproduction in any medium, provided the original author and source
are credited.
How to cite this article:
Tage K., Tsunokawa M., Ishikawa H., Matsuishi T. F., 2023 A method to quantify social relationships between
captive odontocetes based on distances between individuals during synchronous breathing. AACL Bioflux
16(6):3227-3239.

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