Cite this article: Jolles JW, Weimar N,
Landgraf T, Romanczuk P, Krause J, Bierbach D.
2020 Group-level patterns emerge from
individual speed as revealed by an extremely
social robotic fish. Biol. Lett. 16: 20200436.
Received: 10 June 2020
Accepted: 26 August 2020
behaviour, biotechnology, systems biology
speed, collective behaviour, guppy, individual
differences, robot, social
Authors for correspondence:
Jolle W. Jolles
Electronic supplementary material is available
online at https://doi.org/10.6084/m9.figshare.
Group-level patterns emerge from
individual speed as revealed by an
extremely social robotic fish
Jolle W. Jolles1,2, Nils Weimar3, Tim Landgraf4,5, Pawel Romanczuk5,6,
Jens Krause3,5,6 and David Bierbach3,5,6
Department of Collective Behaviour, Max Planck Institute of Animal Behavior, Konstanz, Germany
Zukunftskolleg, University of Konstanz, Konstanz, Germany
Department of Biology and Ecology of Fishes, Leibniz-Institute of Freshwater Ecology and Inland Fisheries,
Department of Mathematics and Computer Science, Institute for Computer Science, Freie Universität Berlin,
Excellence Cluster ‘Science of Intelligence’, Technische Universität Berlin, Berlin, Germany
Faculty of Life Sciences, Thaer-Institute, Humboldt-Universität zu Berlin, Berlin, Germany
JWJ, 0000-0001-9905-2633; TL, 0000-0003-4951-5235; PR, 0000-0002-4733-998X;
JK, 0000-0002-1289-2857; DB, 0000-0001-7049-2299
Understanding the emergence of collective behaviour has long been a key
research focus in the natural sciences. Besides the fundamental role of
social interaction rules, a combination of theoretical and empirical work
indicates individual speed may be a key process that drives the collective
behaviour of animal groups. Socially induced changes in speed by interact-
ing animals make it difficult to isolate the effects of individual speed on
group-level behaviours. Here, we tackled this issue by pairing guppies
with a biomimetic robot. We used a closed-loop tracking and feedback
system to let a robotic fish naturally interact with a live partner in real
time, and programmed it to strongly copy and follow its partner’smove-
ments while lacking any preferred movement speed or directionality of its
own. We show that individual differences in guppies’movement speed
were highly repeatable and in turn shaped key collective patterns: a
higher individual speed resulted in stronger leadership, lower cohesion,
higher alignment and better temporal coordination of the pairs. By combining
the strengths of individual-based models and observational work with state-
of-the-art robotics, we provide novel evidence that individual speed is a key,
fundamental process in the emergence of collective behaviour.
Understanding the emergence of collective behavioural patterns has long been
a key research focus in the natural sciences. Considerable theoretical and exper-
imental work has accumulated that describes how complex collective patterns
may arise via relatively simple mechanisms [1,2], including the role of pheno-
typic heterogeneity within and among groups . A fundamental insight is
that social interaction rules at the individual level—such as avoiding
others that are too near and approaching those far away—can explain the
large-scale cohesion, coordination and decision-making of animal groups [2,4].
Most animals control their motion by modulating their speed and turning,
and this speed regulation has been shown to be crucial for the attraction and
avoidance behaviour when animals group and interact [5–7]. Hence, individual
speed may be an additional fundamental factor that underlies the emergence of
the global properties of groups. Indeed, both short-term changes and heterogen-
eity in speed have been linked to a range of group-level properties, such as group
© 2020 The Author(s) Published by the Royal Society. All rights reserved.
cohesion, structure, shape, coordination, and leadership by
theoretical analyses , computer simulations [1,4,9] and
empirical work [6,10–14]. Importantly, grouping individuals
may differ in their preferred and optimal movement speeds
yet must also coordinate and adjust their behaviour to success-
fully group together [3,15]. Such socially induced changes in
speed by individuals interacting with one another make it dif-
ficult to empirically isolate the effects of individual speed for
group-level properties. And while with agent-based simu-
lations one can separately model such effects and thereby
make important predictions for collective behaviour, they are
no substitute for empirical data of real animal groups .
Due to recent advances in the field of robotics, robotic indi-
viduals now not only realistically look and behave like
conspecifics, but also interact with live animals in a natural
way [16–19]. This sets the stage for manipulative experiments
where part of the group members can be controlled and pro-
grammed with theoretical models under investigation. Here,
we present results from such an experiment using live guppies
(Poecilia reticulata) swimming with an interactive biomimetic
fish-like robot (robofish) to examine the role of fish’s individ-
ual movement speed on collective behavioural patterns. We
combined high-definition video tracking and a closed-loop
feedback system that used interaction rules from well-known
agent-based models  to steer the robot interactively in real
time [20,21]. We programmed the robot to always follow its
partner and copy its behaviour, while excluding any preferred
swimming speed or directionality, thus enabling us to deter-
mine how individual differences in the guppies’movement
speed alone determined group-level properties, in terms of
leadership, cohesion, alignment and temporal coordination.
We used laboratory-reared descendants of wild-caught Trinida-
dian guppies that were housed in large, randomly out-bred
mixed-sex stock tanks under controlled laboratory conditions
(12 h : 12 h light : dark; 26°C). We randomly selected 20 naive
adult females (standard length ‘BL’: 31.7 ± 0.8 mm) and moved
them to individual holding tanks (40 × 20 × 25 cm). The follow-
ing week, we tested fish first without robofish to assess their
preferred movement speed (week 2) and then twice with the
robofish (week 3; trial 2 five days later). Throughout, fish were
fed twice daily ad libitum with TetraMin flake food.
The test arena consisted of a large white glass tank (88 cm ×
88 cm, water height 7.5 cm) that was illuminated from above and
enclosed to minimize potential external disturbances. Fish were
moved from their individual holding compartment to the exper-
imental tank where they were allowed to acclimatize for 1 min in
an opaque PVC cylinder in the corner of the tank. After the cylin-
der was raised, the fish filmed from above for 10 min, and its
movements automatically tracked at 30 fps using BioTracker
. For the trials with the robotic fish, we used a three-dimen-
sional-printed fish replica resembling a female guppy that was
connected via magnets to a two-wheeled robot below the tank
(see electronic supplementary material, figure S1 and for details
). The robot was controlled via a closed-loop system whereby
the movements of the fish were tracked and fed-back to the robot
control. The robot unit then adjusted its position and orientation
in real time (i.e. with 30 hertz) to result in natural response times.
Robofish was circling in front of the acclimatization cylinder and
as soon as the guppy was released from the cylinder started its
Robofish’s interactive behaviour was based on the zonal model
 and allowed the robot to copy the live fish’s motions and follow
at a similar speed without a preferred speed or directional prefer-
ence of their own (figure 1 and electronic supplementary material,
figure S2). We programmed robofish to orientate towards the live
fish’s position and stay at a distance between 10–15 cm away (∼4
BL, ‘optimal distance zone’), reflecting spacing observed in wild
guppies . This resulted in robofish following at the instan-
taneous speed exhibited by the live fish while it was in this
optimal distance zone. Robofish gradually decreased or increased
its speed when the focal fish got into the graduation zone (3–
10 cm) or beyond the optimal distance zone, respectively. If the
focal fish was at a distance less than 3 cm away, robofish stopped
moving forward but kept turning at its location to focus on the live
fish’s position. The maximum speed and acceleration of robofish
were set to reflect that observed for the guppies when alone
(25 cm s
and 2.5 cm s
respectively, see electronic supplemen-
tary material, figure S3), with its maximum turning rate being
greater than 360°/s.
Tracking data were checked for errors, processed to correct for
missing frames, and converted to millimetres. Subsequently, based
on the centroid of each individual (focal and robotic), we calcu-
lated speed and heading as well as inter-individual distance. For
each trial, we computed the fish’s median speed, the median
inter-individual distance, median difference in heading angle,
and proportion of time the focal fish was in front (when moving
greater than 0.5 cm s
;‘leadership’). In addition, we computed
their coordination by running temporal correlations of both indi-
viduals’change in speed and heading, with a higher correlation
indicating movement changes were better copied between them.
We used a linear-mixed modelling approach to investigate
relationships in the individual- and group-level metrics as well
as repeatability in behaviour. Further details of our methods
and statistics can be found in the electronic supplementary
There were large and significant among-individual differ-
ences in guppies’movement speed across the two robofish
trials (R= 0.70, 95% confidence interval (CI) = 0.38–0.88),
which correlated well with their movement speed when
tested alone (χ
= 9.70, p= 0.002, R2
mar ¼0:32, electronic sup-
plementary material, figure S4). Although the majority of
fish slowed down when tested with robofish (30/38 trials),
there was large among-individual variation in fish’s speed
relative to that expressed in the solo assay (0.62± 0.06, 95%
robo speed (cm s–1)
Figure 1. Tracking data (approx. 1 min) of a randomly selected representative
pair, with the speed of the robofish coloured blue (low) to yellow (high), show-
ing how it followed the position and movements of its partner by natural
changes in speed (see further electronic supplementary material, figure S2).
Inset shows a photo of robofish following a guppy. Data were subsetted to
a region where the guppy made a number of turns and changes in speed.
royalsocietypublishing.org/journal/rsbl Biol. Lett. 16: 20200436
CI = 0.15–1.29; a value of 1 would indicate no change in
speed), which was itself not linked to their solo speed (χ
0.155, p= 0.212, R
Robofish conformed extremely well to the speed of the
guppy partner (χ
= 87.04, p<0.001, R2
mar ¼0:92, electronic
supplementary material, figure S5) and consistently exhibited
a slightly slower speed (speed difference: −0.58 ± 0.07 cm s
As a consequence, robofish primarily occupied the following
position (38/38 trials, electronic supplementary material,
figure S6), an effect that strongly increased with the speed of
the focal fish (χ
= 40.77, p< 0.001, R2
mar ¼0:68), with the fastest
guppies leading more than 90% of the time (figure 2a,b).
Robofish was able to maintain good cohesion and align-
ment with its live partner, and naturally copied its changes
in speed and heading (median max correlation coefficients:
0.51 and 0.58, electronic supplementary material, figure S7).
As for leadership, we found that these group-level outcomes
were very well explained by the individual speed of the
guppy. Pairs in which the guppy had a high median speed
were considerably less cohesive (χ
mar ¼0:81), more aligned (χ
=13.66, p<0.001, R2
and more coordinated (χ
=41.33, p< 0.001, R2
than pairs with a much slower guppy (figure 2c–f).
Live guppies paired with an extremely social robotic fish
showed large and repeatable individual differences in move-
ment speeds that in turn strongly explained leadership, group
cohesion, alignment and movement coordination. By testing
all fish with the same robot using identical interaction rules
and lacked any preferred movement speed and directionality,
these results provide novel experimental evidence that suggest
that individual speed is a fundamental factor in the emergence
of collective behavioural patterns, in line with existing theoreti-
cal and empirical work [4,8,12–14]. As individual differences in
speed are associated with a broad range of phenotypic traits
observed among grouping animals, this may also help provide
a mechanistic explanation for the effect of phenotypic heterogen-
eity of group-level patterns , as has for example been shown
for size, hunger and parasitism [24,25].
We observed a very strong, positive link between speed
and leadership, both in terms of clearer front-back position-
ing the faster fish were moving, as well as fish being
overall more in front the higher their median movement
speed. This result is in line with predictions from model
simulations [4,12] and previous empirical work [11,12]. By
testing fish with an extremely social partner that always
tried to follow, we found that at higher speeds fish led
almost all the time. This shows how leaders depend on the
responsiveness of their followers in order to express their
own preference (see also ) and more generally highlights
how both individual speeds and high levels of social respon-
siveness are important for the collective performance of
groups . At lower speeds, leadership differences were
not as apparent, potentially because individuals have greater
turning freedom at lower speeds . The absolute speed at
which a group is moving may therefore be just as important
as relative differences in speed between individuals in shap-
ing group structure. Our experiments show that the observed
effects of speed emerge from the self-organized dynamics of
the coupled leader–follower system, i.e. that it does not
require any diverging preferences of the follower. An analogy
prop time in front
robofish relative y-position (cm) median speed (BL s–1)
> 0.5 cm s–1
> 0.5 BL s–1
inter-individual distance (cm)
median heading diff (deg)
inter-individual dist (cm)
median speed (BL s–1)median speed (BL s–1)
max temporal heading corr
median speed (BL s–1)
Figure 2. (a,c) Density plot of robofish’s relative y-position and distance to its live partner, and (b,d,e,f) scatterplots of fish’s median speed in relation to the leadership,
cohesion, alignment and temporal coordination of the pair. Plots aand cshow boththe full data (blue line), the data was subsetted to where the focal fish moved at >0.5 cm/s
(green line), and at >0.5 BL/s (yellow line). Colour scale indicates speed (blue = low; yellow= high) and solid lines show the polynomial functions fitted in our models.
royalsocietypublishing.org/journal/rsbl Biol. Lett. 16: 20200436
can be drawn to a physical system, where the follower can be
viewed as an ‘active particle’strongly coupled to the leader
through a spring-like social force with friction.
Pairs consisting of a guppy with a high median speed were
considerably less cohesive than those with low median speeds,
in line with previous work on schooling sticklebacks . To
avoid collisions, grouping animals may actively increase their
distance when moving at higher speeds. However, robofish
was not programmed with such a rule, suggesting that the
observed positive link between cohesion and speed is due to
speed mediating the use of social interaction rules: faster indi-
viduals moving farther before they can change their position
in response to their group mates. This suggests that a shift in
interaction rules, such as via changes in the environment, may
alter the relationship between group speed and cohesion (see
e.g. [28,29]). Individual speed also strongly drove the alignment
and temporal coordination of the pairs, in line with previous
empirical studies that found fast-moving groups tend to be
polarized and slow-moving groups to be disordered
[12,13,30]. Since in our study the robotic partner completely
lacked any alignment rules, our findings provide novel empiri-
cal evidence that individual speed is a key factor facilitating
group alignment and coordination. Although speed-mediated
changes in local interaction rules may help to explain these
effects [6,10], groups may be more likely to become disordered
at lower speeds because of larger potential angular fluctuations
at lower speeds, as is predicted from the theoretical analysis .
Given that rates of information flow have been shown to be
higher in faster-moving groups , our finding that faster
groups showed better coordination of movement changes can
therefore be explained by the higher (local) order that arises
with higher individual speeds.
The large individual differences in movement speed
during the robofish trials were highly repeatable (R = 0.70),
as compared to the average repeatability of 0.37 reported
by a large meta-analysis . As robofish always copied its
live partner’s speed and movements, and always used the
same interaction rules, the large variability in movement
speed among the pairs must be attributable to the speed of
the live fish, which was in turn well explained by fish’s
solo speed. Interestingly however, considerable speed vari-
ation among the fish remained. The reduction in movement
speed between the solo and robofish trials therefore likely
reflects socially mediated changes, with guppies that
slowed down more being more socially responsive and/or
less inclined to lead. This corroborates previous observational
work that found live fish pairs moved faster when led by fish
that were less socially plastic in their speeding changes .
Future work is needed to properly determine to what
extent this behavioural variation in ‘social speed’indicates
true individual differences in social responsiveness.
In summary, by closed-loop experiments of live guppies
swimming with a biomimetic robot that always followed and
naturally copied its partners’movements, we bridged the rea-
lity gap between computer simulations and real-world
observations and provide novel evidence that individual
speed is a fundamental factor for the emergence of collective
behaviour. By programming the robotic fish without any of
its own movement preferences, we had the unique opportunity
to investigate how individual behaviour leads to group-level
patterns without the potential influence of individual hetero-
geneity in group mates. Exciting interdisciplinary work lies
ahead to further investigate the role that individuals play in
animal groups and how that depends on the social feedback
among heterogeneous group members.
Ethics. All reported experiments comply with the current German law
approved by LaGeSo (G0117/16 to D.B.).
Data accessibility. Data accompanying this paper can be found in the
electronic supplementary material.
Authors’contributions. J.W.J., N.W. and D.B. designed the study; T.L.,
D.B., P.R. and J.K. developed robofish; N.W. and D.B. conducted
the experiment with help from J.W.J. J.W.J. performed the analysis;
J.W.J. and D.B. wrote the manuscript with feedback from all other
authors. All authors agree accountability for the content in this
paper and approved the final version of the manuscript.
Competing interests. We declare we have no competing interests.
Funding. We acknowledge support from the Alexander von Humboldt-
Stiftung (postdoctoral fellowship to J.W.J.), the Zukunftskolleg, Uni-
versity of Konstanz (postdoctoral fellowship to J.W.J.), the German
Research Foundation (BI 1828/2-1, LA 3534/1-1, RO 4766/2-1) and
Germany’s Excellence Strategy (EXC 2002/1 ‘Science of Intelligence’,
project number 390523135).
Acknowledgements. We thank two anonymous reviewers for their help-
ful feedback. We are also very grateful to Hauke Mönck and Hai
Nguyen for help with programming the robot.
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