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A variable refractory period increases collective
performance in noisy environments
Violette Chiara
a,1
, Patrick Arrufat
a
, and Rapha€
el Jeanson
a,2
a
Centre de Recherches sur la Cognition Animale (UMR5169), Centre de Biologie Int
egrative, Universit
e de Toulouse, CNRS, Universit
e Paul Sabatier, 31062
Toulouse, France
Edited by Bert H€
olldobler, Arizona State University, Tempe, AZ; received August 30, 2021; accepted January 24, 2022
Synchronized oscillations are found in all living systems, from cells
to ecosystems and on varying time scales. A generic principle
behind the production of oscillations involves a delay in the
response of one entity to stimulations from the others in the sys-
tem. Communication among entities is required for the emergence
of synchronization, but its efficacy can be impaired by surrounding
noise. In the social spider Anelosimus eximius, individuals coordi-
nate their activity to catch large prey that are otherwise inaccessi-
ble to solitary hunters. When hunting in groups, dozens of spiders
move rhythmically toward their prey by synchronizing moving
and stopping phases. We proposed a mechanistic model imple-
menting individual behavioral rules, all derived from field experi-
ments, to elucidate the underlying principles of synchronization.
We showed that the emergence of oscillations in spiders involves
a refractory state, the duration of which depends on the relative
intensity of prey versus conspecific signals. This flexible behavior
allows individuals to rapidly adapt to variations in their vibrational
landscapes. Exploring the model reveals that the benefits of syn-
chronization resulting from improved accuracy in prey detection
and reduced latency to capture prey more than offset the cost of
the delay associated with immobility phases. Overall, our study
shows that a refractory period whose duration is variable and
dependent on information accessible to all entities in the system
contributes to the emergence of self-organized oscillations in
noisy environments. Our findings may inspire the design of artifi-
cial systems requiring fast and flexible synchronization between
their components.
cooperation jself-organization jsynchronization jspider jswarm
Oscillations are ubiquitous in biological systems, from biochem-
ical reactions in cells to predator–prey interactions in ecosys-
tems and on time scales ranging from fractions of a second to years.
Considerable attention has been given to the study of the underly-
ing mechanisms, from the simplest to the most complex systems,
and a limited number of common elements have been recognized
as essential for giving rise to temporal oscillations (1–3). Basically,
there are two broad categories of mechanisms leading to the pro-
duction of oscillations on a collective scale: either the entities of the
system have their own rhythm and the oscillations require the
adjustment of their phases, or the entities of the system have no
intrinsic rhythmic activity and the oscillations result from the ability
of one element to excite another component of the system. In both
cases, the production of oscillations relies on the interactions
between the components of the system. Communication is essential
for regulating interactions between entities and for the expression
of feedback loops that are necessary for the emergence of collective
behaviors in self-organized systems, which are notably characterized
by an absence of centralized control (4). Achieving optimal collec-
tive performance therefore requires minimizing the negative impact
of noise on communication to increase the signal-to-noise ratio and
improve the quality of information processing.
A critical ingredient for generating oscillatory behavior is the
existence of a sufficiently large delay in the response of the excit-
able entities making up the system. In cellular systems for
instance, the presence of intermediate steps in feedback loops
generate delays that are sources of oscillations in the production
of gene transcripts (5). This delay may also take the form of a
refractory period that requires an entity that has just been excited
to remain inactive for a certain time before returning to its origi-
nal state (6). Such a mechanism explains, for example, the genesis
of the heartbeat with cells alternating between phases of activity
and inactivity (7) or, on another scale, the propagation of the
Mexican wave, where spectators in stadiums stand up and sit
down in a coordinated manner (8). Most studies aimed at gener-
ating synchronization in artificial systems (e.g., robotic swarms)
use agents with periodic behavior (9), but the implementation of
a refractory period coupled with the mutual excitability of entities
represents an interesting alternative to coordinate the activities of
a multitude of interacting elements.
Understanding the genesis of oscillations in animal groups
requires characterizing the signals involved in social interactions
and identifying the individual behavioral rules that generate the
feedback and delays necessary for the production of rhythmic
behavior on a collective scale. Groups of animals exhibit synchro-
nized behaviors leading to the propagation of regular waves of
activity or signaling in a variety of contexts. A paradigmatic exam-
ple is found in fireflies, where males delay the emission of their
light signal in response to a signal from a conspecific, leading
assemblies to flash rhythmically (10). One remarkable example of
synchronization leading to collective oscillations is found in the
social spider Anelosimus eximius during cooperative hunts (Movie
Significance
In biological and artificial systems, synchronization is an
important means of achieving coordination. During hunting,
social spiders alternate their moving and stopping phases in
unison as they move toward their prey. We combined field-
work and modeling to investigate the behavioral rules that
lead to the emergence of synchronized oscillations in hunt-
ing groups. We showed that an individual's decision to
move depends on the relative intensity of vibrations emitted
by the prey and the moving spiders. This rule allows the
group to adapt quickly to any change in prey size or the
number of spiders involved in the hunt. Such synchroniza-
tion ensures that the spiders can locate their prey without
being disturbed by signals from conspecifics and thus
improves hunting performance.
Author contributions: V.C. and R.J. designed research; V.C. and R.J. performed
research; V.C., P.A., and R.J. contributed new reagents/analytic tools; V.C. and R.J.
analyzed data; and V.C. and R.J. wrote the paper.
The authors declare no competing interest.
This article is a PNAS Direct Submission.
This article is distributed under Creative Commons Attribution-NonCommercial-
NoDerivatives License 4.0 (CC BY-NC-ND).
1
Present address: Grupo Ecolox
ıa Animal (Lab 97), Torre CACTI, Centro de
Investigaci
on Mari~
na, Universidade de Vigo, 36310 Pontevedra, Spain.
2
To whom correspondence may be addressed. Email: raphael.jeanson@univ-tlse3.fr.
This article contains supporting information online at http://www.pnas.org/lookup/
suppl/doi:10.1073/pnas.2115103119/-/DCSupplemental.
Published March 7, 2022.
PNAS 2022 Vol. 119 No. 12 e2115103119 https://doi.org/10.1073/pnas.2115103119 j
1of9
ECOLOGY
S1). Among the 50,000 species of spiders described so far, about
20 have evolved toward permanent sociality (11). These species
are characterized by a series of traits that include cooperation in
prey capture, web construction, colony defense, and brood care
(12, 13). A. eximius inhabits tropical rainforests of northern South
America, and colonies can comprise thousands of individuals (12,
14). Nests, which can measure several meters in width and length,
are typically composed of a horizontal basket-shaped silken sheet
and a network of vertical threads, connected to the vegetation,
used to intercept flying prey (Fig. 1A). Spiders cooperate during
hunting, and collectively, they can catch very large prey, up to 700
times the weight of an individual spider (15). When approaching
the prey, spiders rapidly synchronize their displacements by alter-
nating phases of mobility and immobility (16) (Fig. 1 and Movie
S1). Many solitary spiders that hunt alone also exhibit pausing
behaviors (17–19), the challenge with social spiders is to explain
the coordination of the many hunters leading to the emergence of
synchronized waves of moves. Although this collective behavior
was a source of inspiration in the field of swarm intelligence to
develop model of optimization (20), the mechanisms underlying
the emergence of the periodic oscillations in hunting spiders still
remains poorly understood.
Spiders live in a vibrational world (21). They are exposed to
multiple vibrations whether these are produced by conspecifics
and involved in the regulation of social interactions or whether
they are produced by prey struggling in the web and used by
the spiders to orient themselves during the hunt. We proposed
that social spiders use vibrational information to coordinate the
behavioral transition between movement and immobility phases
during collective hunting. Our hypothesis was that they switch
between behavioral states depending on the surrounding noise
produced by the moving spiders relative to the signal emitted
by the prey. We developed a numerical model implementing
only behavioral rules measured in field experiment to validate
our hypothesis. We then used this model to identify the
respective contribution of the rules driving the emergence of
oscillations and to explore how synchronization is beneficial
during group hunting in a noisy environment.
Results
Individual Behaviors. We performed field experiments in French
Guiana. Collective hunts were triggered with a custom vibrating
lure that elicits behaviors in spiders similar to those observed
when a prey falls into the web: individuals rapidly develop
synchronized oscillations between phases of mobility and
immobility. The use of a lure, instead of live prey, allowed us to
stimulate the same groups of spiders several times without their
motivation being affected by the consumption of the prey (Fig.
1B). When spiders are engaged in a hunt, they continue to
move synchronously for a few seconds when the vibrations tem-
porarily stop or when the natural prey escapes (Fig. 1C). By
placing or removing the lure from the web, we were able to dis-
tinctly quantify the response of spiders to vibrations produced
by conspecifics or by the lure. We used a timestep of 0.08 s to
analyze video-recorded hunting.
Probability of moving in response to vibrations. We aimed at
determining how immobile spiders reacted to the vibrations pro-
duced by one or more moving spiders or by the lure. We used
the behavioral response of spiders to vibrational stimuli to infer
how the signal produced by the lure or conspecifics was attenu-
ated when propagating on the web. Earlier work documented a
sigmoidal relationship between the intensity of the stimulus and
the neuronal response to vibrations in spiders (22). Therefore,
we modeled the behavioral response of spiders to the vibrations
Vusing a sigmoidal function: the probability of moving P
move
increases exponentially at low stimulus intensity and at a deceler-
ating rate at large intensity. This gives the following:
Pmove ¼1
1þeσVðÞ
,[1]
where σis a constant.
Since attenuation of vibrations with distance on a web is
exponential (23), the intensity of the signal at a distance dfrom
the source of vibrations is the following:
V¼V0ekd,[2]
where V
0
is the intensity of vibrations at the origin, and kis a
constant that determines how fast vibrations are attenuated.
Therefore, we had to determine the values of V
0
and kfor
vibrations produced either by the spiders or by the lure.
We assumed that an individual detected the local vibration,
whether produced by a single spider or by a combination of spi-
ders. Because vibrations are approximately additive, the inten-
sity of the vibrations V
spider
produced by Nmoving spiders that
are perceived by a stopped spider is given by the following:
Vspider ¼∑N
i¼1V0spiders ekspiderdi,[3]
where V0spider is the intensity of spider vibrations at the origin
(the vibrations at the origin being assumed identical for all
moving spiders), d
i
the distance between the stopped spider
and each moving spider i, and k
spider
the coefficient of attenua-
tion of spider vibrations.
From Eqs. 1and 3, the probability of moving for a stopped
individual in response to Nmoving spiders is thus given by the
following:
Pmove,spider ¼1
1þeσspiders∑N
i¼1V0spider ekspiderdi
:[4]
In order to estimate the parameters V0spider ,k
spider
, and σ
spider
,we
analyzed by eye four hunting sequences, each lasting 10 to 14 s
0 6 12 18 24 30 36 42 48 54 60
Time (s)
0
5
10
15
20
25
30
35
40
45
Moving spiders
AB
C
Fig. 1. Collective hunting in social spiders. (A) Web of the socia l spide r
A. eximius in French Guiana. (B) A dead fly connected to a vibration genera-
tor was brought into contact with the web to trigger collective hunting
behavior in a group of social spiders. (C) Activity patterns in a group of spi-
ders engaged in a hunt triggered by the lure. Individuals alternate synchro-
nously between moving and stopping when hunting. The colored areas indi-
cate when the lure was contacting the web. (Copyright R. Jeanson/CNRS.)
2of9 jPNAS Chiara et al.
https://doi.org/10.1073/pnas.2115103119 A variable refractory period increases collective performance in noisy environments
and involving 26 to 46 spiders (SI Appendix, Fig. S1). When the
lure was absent, we identified each moment (t
0
) when one or
more spiders (initiators) moved spontaneously after all spiders
had been stopped for at least one timestep. We then deter-
mined whether the spiders that were immobile at timestep (t
0
)
started moving at the next step (t
1
) in response to the vibrations
produced by the initiator(s). For each individual, this allowed
us to obtain the probability that it started moving in response
to the movements of Nspiders by considering their distance.
We used a maximum log-likelihood approach to find the values
of the parameters V0spider ,k
spider
, and σ
spider
(Eq. 4) that maxi-
mize the probability of observing the experimental data (Fig.
2Aand SI Appendix, Fig. S2). In absence of the lure, the best fit
was obtained with V0spider =0.71, k
spider
=0.18 cm
1
and σ
spider
=
1.62.
We next aimed at estimating the response of spiders to the
lure. We needed to identify events where all spiders were
motionless before the lure was activated in order to measure
the spiders’ response only to the lure and not to conspecifics.
We used 18 hunting sequences with a mean of 30 spiders
(minimum =13, maximum =78) that were immobile for at
least 0.08 s. After all spiders had stopped, we determined
which individuals moved in the timestep beginning with the
movement of the first spider after the lure had approached
the web. As we did to model the response to spider vibra-
tions, we modeled the response to lure with a sigmoid func-
tion:
Pmove,lure ¼1
1þeσlureV0lure eklure d
ðÞ
,[5]
where dis the spider’s distance to the lure, V0lure is the intensity
of lure vibration at the origin, and k
lure
the coefficient of attenu-
ation of lure vibration.
Fitting our experimental dataset with Eq. 5, we obtained
V0lure =5.74, k
lure
=0.05 cm
1
, and σ
lure
=4.42 (Fig. 2B).
We then used the parameters obtained for both fits to calcu-
late the intensity of the signal produced by moving spiders or
by the lure. The comparison between the observed proportions
of spiders that moved as a function of signal intensity and the
corresponding theoretical probabilities revealed quantitative
agreement for both spider and lure response, which means that
we satisfactorily modeled the behavioral responses of spiders to
stimuli (Fig. 2 Aand B). At any distance from a focal individ-
ual, the intensity of the signal produced by the lure was greater
than the strength of the signal produced by one moving spider
(Fig. 2C). The individual probability of moving decreased with
the distance from the source of vibration and was greater in
response to the lure than to a single moving spider (Fig. 2D).
Probability of stopping in presence and absence of the lure. In
the absence of the lure, we detected no correlation between the
time spent moving and the maximum intensity of spider vibra-
tions perceived during the move (Pearson correlation test: t=
1.377, df =856, r=0.047, and P=0.169) (SI Appendix, Fig.
S3). This suggested that the activity of other spiders had no
influence on the probability of stopping. The durations of
moves were twice as long in the presence than in the absence of
the lure (log-rank test: χ
2
=6.3, df =1, and P=0.01). The sur-
vival curves for the duration of moves recorded in the presence
or absence of the lure were plotted on a log-linear scale and fit-
ted with linear regressions (Fig. 3A). The slope of each regres-
sion line gave the individual probability per unit time that a
moving spider would stop when the lure was active or not
(Fig. 3A).
Spontaneous probability of moving in absence of vibrations. We
assessed the individual probability of moving spontaneously
(i.e., not in response to any external vibration) when all spiders
AB
CD
Fig. 2. Individual response to signal intensity. Probabilities of moving in response to vibrations produced by spiders (A) or the lure (B). The dots (n=830
for the spiders, n=550 for the lure) give the observed events (move or not) as a function of the intensity of the signal received by a stopped individual
at the preceding timestep (the positions of the dots were shifted along the y-axis for illustrative purpose). The triangles indicate the experimental propor-
tion ±95% CI of spiders that moved as a function of signal strength by 0.5 interval. The lines give the predicted probabilities obtained with Eq. 4for spi-
ders (V0spider =0.71, k
spider
=0.18 cm
1
, and σ
spider
=1.62) and Eq. 5for the lure (V0lure =5.74, k
lure
=0.05 cm
1
, and σ
lure
=4.42). (C) Predicted intensity of
the signal perceived by a spider as a function of its distance from the lure or a single moving spider. (D) Predicted probability of moving in response to
the lure or a single moving spider as a function of the distance to the immobile spider.
ECOLOGY
Chiara et al.
A variable refractory period increases collective performance in noisy environments
PNAS j3of9
https://doi.org/10.1073/pnas.2115103119
were stopped in absence of the lure. We plotted on a log-linear
scale the survival curves of the durations of the phases of
silence recorded in the four hunting sequences used to quantify
the response of spiders to vibrations (Fig. 3B). The slope gives
the probability per unit of time that at least one spider started
to move. Assuming that each spider was equally likely to start
moving spontaneously, the individual probability of moving per
unit of time was given by the slope divided by the number of
spiders likely to move. Using a number of spiders of 25 (i.e.,
the average number of individuals involved in the sequences
used to calculate the slope), we obtained an individual proba-
bility of moving spontaneously per unit of time equaling 2.63
10
4
ms
1
.
Characterization of the refractory state. After a spider stopped,
we needed to identify what condition had to be met for it to
return to an excitable state and respond again to vibrations
emitted by its conspecifics. We considered the vibrational infor-
mation emitted by conspecifics or by the lure that was received
by each spider at each timestep (0.08 s) of its stop to determine
whether a refractory state existed and, if so, whether its expres-
sion was dependent on the presence of the lure. In the absence
of the lure, ∼70% of the stops preceding an individual’s move
were characterized by a period of at least 0.08 s where all spi-
ders were immobile (Fig. 4A). In contrast, when the lure was
active, less than 10% of the stops contained a period when all
spiders were stopped (Fig. 4B). We then used Eq. 3to calculate
the intensity of the signal produced by moving individuals that
a stationary spider perceived for each timestep during its stop
in absence or presence of the lure. The values of the lowest spi-
der signal intensity recorded during one timestep during each
stop was greater in the presence of the lure than in its absence
(Fig. 4C). This implied that the spiders did not resume their
movement until the vibrations of the conspecifics were very
low, whereas in the presence of the lure, the spiders could
resume their movement even if they perceived relatively higher
vibrations from the conspecifics. Last, we calculated the ratio of
the intensity of the signal produced by the lure divided by the
intensity of the signal produced by moving spiders at each time-
step when a spider was stopped. A stopped spider experienced
a minimum ratio of the lure signal over the spider signal
greater than 0.5 in 99% of the observed cases (n=438) (Fig.
4D). This meant that during almost every stop in the presence
of the lure, the signal intensity of the lure received by the
stopped spider was more than one-half the signal strength pro-
duced by moving spiders for a least one timestep. Based on
these results, we proposed the rule that an individual that had
just stopped entered a refractory state and could not resume
movement as long as the strength of the signal emitted by the
lure was less than one-half the strength of the signal produced
by the mobile spiders. When the lure was absent, this meant
that the spiders all had to observe a phase of silence to allow
them to become active again. Therefore, the duration of the
refractory phase was not fixed and could vary depending on the
vibrational landscape perceived by a stopped spider.
Spider velocity. The speed of spiders was obtained by dividing
the distance of each move (i.e., distance between the positions
of two successive stops) by the duration of the movement. We
detected no difference in spider’s velocity in presence or
absence of the lure (Student’s ttest on log transformed data:
t
760.43
=1.38, P=0.17). Pooling the data recorded in pres-
ence and absence of the lure, the experimental distribution of
velocities was fitted with a lognormal distribution (geometric
mean ×/SD =0.17 ×/0.93, n=1,241) (SI Appendix, Fig. S4A).
Orientation of spider movement in relation to the lure. For each
moving spider, we determined the orientation of its move with
respect to the lure (i.e., the value of the angle between the
starting and ending position of its move and the position of the
lure). When the lure was not active, we used the coordinates of
its last active position. In our experimental conditions where we
rapidly alternated the presence and absence of the lure and
moved the lure between two successive stimulations, we
detected a marginal difference in the angular distribution of
movements when the lure was present or not (Watson–Wheeler
test: W =6.834, df =2, and P=0.033). Although the spiders
tended to move predominantly in a forward direction, the dis-
tribution of angles obtained under our experimental conditions
revealed that their movements did not go in a straight line
toward the prey and showed frequent reorientations (SI
Appendix, Fig. S4B).
Emergence of Oscillations. We developed a two-dimensional spa-
tially explicit agent–based model written in R to explore the
contribution of social interactions on the emergence of synchro-
nization during collective hunting (SI Appendix, Fig. S5).
AB
Fig. 3. (A) Survival curves of the durations of moves in presence (n=858)
and absence (n=383) of the lure. Colored bands are 95% CI. (B) Survival
curve of the durations of the phases of silence (n=34).
AB
CD
Fig. 4. Influence of the presence of the lure on the decision to move. (A
and B) Proportion of stops where 0, 1, 2, or 3 spiders were active in
absence (n=1,179) or presence (n=471) of the lure. (C) Lowest intensity
of the signal produced by spiders (Signal
Spiders
) perceived during one time-
step by an individual when stopped in presence or absence of the lure. (D)
Histogram of the minimum value of the ratio of lure signal divided by spi-
der signal perceived by stopped individuals during one timestep before
resuming movement (n=438).
4of9 jPNAS Chiara et al.
https://doi.org/10.1073/pnas.2115103119 A variable refractory period increases collective performance in noisy environments
To compare simulations and observations, we analyzed 12-s
portions of hunting sequences (n=20) to characterize activity
patterns in hunting groups of different sizes (mean =30 spi-
ders, minimum =12, and maximum =60). Each of the 20
sequences included episodes where the lure was active or not.
For each sequence, we calculated a score of synchronization for
the periods when the lure was inactive and a score for the peri-
ods when the lure was active (Materials and Methods). This
score of synchronization ranges between 1 and 1 (0 =no syn-
chronization, 1 =maximum synchronization). Next, we ran sim-
ulations where the initial positions of the spiders corresponded
to the same spatial coordinates as the spiders tracked in the
experiments. For each simulated sequence, the lure was active
at the same timestep and at the same position as in the experi-
ments. In our model, a spider could either be stopped (inactive)
or moving (active) (SI Appendix, Fig. S5). At the beginning of
each simulation, individuals were initialized in the inactive
state. At each timestep (0.08 s/cycle), the velocity of each active
individual was drawn randomly from the lognormal distribution
fitted from the experimental data (SI Appendix, Fig. S4A). For
each movement of a spider, the value of the angle of its move-
ment relative to the position of the lure was drawn from the
experimental distribution (SI Appendix, Fig. S4B). Moving spi-
ders had a constant probability of stopping per unit time, the
value of which depended on the presence or absence of the
lure (Fig. 3A). When an individual just stopped, it entered a
refractory state and could not become active (neither spontane-
ously nor in response to vibrations) as long as the amount of
lure’s vibrations was lower than one-half the amount of spiders’
vibrations (Fig. 4Dand SI Appendix, Fig. S5). A stopped indi-
vidual that exited its refractory state became activable and
could start moving either spontaneously or in response to the
vibrations produced by the spiders or the lure. The probability
of moving for a stopped spider in response to vibrations was
given by Eqs. 4and 5. In absence of the lure, a stopped individ-
ual must not perceive any spider vibration during at least one
timestep to get out of its refractory state. When the lure was
switched off, the spiders moved toward the previous position of
the lure. We performed a total of 20 simulations for each of the
20 observed sequences.
At the individual level, longer stopping times were obtained in
the absence than in the presence of the lure in the simulations,
just as was observed in the experiments, though the difference in
the simulated data were more pronounced than in the observed
data (SI Appendix,Fig.S6Aand B). It is important to note that
our simulations reproduced the observed patterns while no rule
governing the duration of stops in the presence of vibration was
explicitly implemented but only a rule governing the refractory
period and the probability of responding to the lure or to other
spiders.
At the collective level, the intensity of synchronization was
greater when the lure was inactive than active in both experi-
ments (paired Student’s ttest: t
19
=7, P<0.001) and simula-
tions (linear mixed model [LMM]: F
1,779
=3,864.1, P<0.001)
(Fig. 5Aand SI Appendix, Figs. S1 and S7A). Similarly, we
found that the periods between successive peaks of spider activ-
ity were longer in the absence than in the presence of the lure
in both experiments (LMM: t
1,230.25
=33.93, P<0.001) and
simulations (LMM: F
1,3738
=6,753.4, P<0.001) (Fig. 5B). Our
model being validated, we then aimed to examine the contribu-
tion of the different identified rules and associated values in
the emergence of synchronization. The exploration of the
model showed that both the refractory state and the social
amplification associated with the increase in the probability of
moving as a function of the number of active individuals were
necessary for the emergence of synchronized oscillations (Fig.
5Cand SI Appendix, Fig. S7B). Simulations implementing a
relaxation of the rule controlling the exit of the refractory state
in the absence of lure and allowing spiders to resume move-
ment even if other spiders are moving (i.e., no full silence) still
exhibited a higher degree of synchronization in the absence of
lure than in the presence of lure, even though the difference
progressively diminished when the spider signal below which an
individual can leave the refractory state was increased (Fig.
5D). Similarly, varying the ratios of the lure signal to the spider
signal beyond which the spider can leave the refractory state
did not abolish the greater synchrony observed in the absence
of the lure. The gradual increase in the level of synchrony in
the presence of the lure when the ratio was increased is
explained by the fact that more spiders must be silent to allow
the refractory state to end (Fig. 5E). All these results demon-
strate that the rules identified are robust and do not depend
strictly on the values of the parameters. Finally, we examined
the impact the implementation of a refractory state of a fixed
duration on the intensity of the synchronization (all other
parameters values being those measured experimentally).
Under this condition, similar levels of synchronization were
obtained in the presence and absence of the lure, which is
inconsistent with empirical observations (Fig. 5F). To reach a
synchronization intensity similar to that of our experiments, a
fixed refractory period of at least 1.04 s would be required,
which is much higher than the average stop duration found in
our experiments in presence (median: 0.16 s) or in absence of
the lure (median: 0.48 s) (Fig. 5Fand SI Appendix, Figs. S6A
and S7C). Overall, our analysis revealed that the synchronized
oscillations in hunting groups of spiders emerged spontane-
ously from the existence of a refractory state, the duration of
which depended on the behavior of the conspecifics and was
variable (SI Appendix, Fig. S6C).
Benefits of Synchronization. It is generally accepted that synchro-
nization of spiders hunting in groups reduces vibrational noise,
thereby improving the ability of the spiders to locate the epi-
center of the vibrations emitted by the prey (16, 24). A massive
and rapid accumulation of spiders on the prey is all the more
important as the webs of A. eximius are not sticky and the risk
is high of the prey escaping before being seized by spiders (15).
However, the advantages of synchronization in spider groups
have not been explicitly addressed, as it is not possible, on an
experimental basis, to prevent spiders from synchronizing dur-
ing hunting. We therefore used our numerical model to study
the extent to which coordinated alternation between phases of
movement and pause is possibly beneficial to hunting spiders.
We compared two extreme situations where the detection of
prey position by spiders was or was not impacted by noise from
moving spiders (SI Appendix, Fig. S8). Combined with the study
of the influence of noise, we also explored the impact of the
presence or absence of the refractory state on the movement of
spiders. When noise had no impact, the spiders were able to
accurately locate the prey position and move directly to it with-
out being disturbed by the vibrations emitted by the conspe-
cifics. This gives the best theoretical performance that can be
used as a reference to assess how the presence of vibratory
noise and the implementation of a refractory state influence
the efficiency of the group. When noise was influential, we
assumed that spider vibrations above a given threshold
decreased an individual’s ability to locate the epicenter of the
lure’s vibrations and that spiders oriented themselves randomly
on the web. Based on our experimental results, we considered
that the spider moved directly toward the prey when the vibra-
tion intensity of the prey was greater than or equal to one-half
that of the spiders and randomly otherwise.
We explored the time taken for 50% of the group to reach
the prey for each condition in groups of 10 to 100 individuals
and in the presence of prey signal of increasing intensity (i.e.,
to mimic prey of increasing size) (Fig. 6). Whatever the size of
ECOLOGY
Chiara et al.
A variable refractory period increases collective performance in noisy environments
PNAS j5of9
https://doi.org/10.1073/pnas.2115103119
the group, spiders reached the prey within 40 s when noise was
not influential in the absence of a refractory state. Under this
condition, spiders could always detect the prey and determine
its position regardless of the intensity of the conspecifics’ vibra-
tions without needing to stop (Fig. 6A). In the absence of a det-
rimental influence of noise, the implementation of a refractory
state led to an increase in the time required for 50% of the
group to reach the prey, highlighting the detrimental influence
of pausing behaviors in hunting efficiency (Fig. 6B). The time
to reach the prey varied with group size and prey signal
strength because the duration of the refractory state, which
depends on the signal-to-noise ratio, was greater when the prey
signal was weak or the spiders were numerous and therefore
noisy. The combination of the presence of noise and the
absence of a refractory strongly impaired spiders’ orientation
and their ability to reach the prey, except for small group size
and large prey signal (Fig. 6C). The implementation of a refrac-
tory state when noise was influential significantly improved
hunting performance (Fig. 6 Dand E). These simulations,
which incorporate the behavioral rules observed in spiders, pre-
dict that if the number of spiders recruited to the hunt scales
with prey signal strength (25, 26), then the time to reach the
prey is relatively constant and hunting efficiency is maintained.
In the scenario where the angle of movement was determined
upon exiting the refractory state (Fig. 6D), not when the spider
began to move (Fig. 6E), spiders reached the prey faster
(because the amount of noise perceived by a spider changed
between the time it left the refractory state and the time it
started moving again). Finally, the implementation of a refrac-
tory period of fixed duration [set here at 0.16 s, which is equal
to the median duration of the stops in the presence of the lure
in the experiments (SI Appendix, Fig. S7)] had severe conse-
quence on the latency to contact the prey (Fig. 6E). Overall,
our results provide strong evidence that a refractory state of
variable duration allows spiders to significantly minimize the
negative consequences of the noise inevitably produced by mov-
ing conspecifics and thus proves to be an effective behavioral
strategy for optimizing hunting success.
Discussion
Our study showed that the key mechanism driving the emer-
gence of synchronization during hunting in social spiders is the
decision rule for leaving the refractory state, which depends on
the signal-to-noise ratio. Compared to other biological systems
where synchronization involves a refractory period whose dura-
tion is relatively fixed and not influenced by external conditions
(27–29), the duration of the refractory phase in social spiders is
variable and modulable in response to variations in the signal-
to-noise ratio. Our exploration of the model revealed that a
long refractory period relative to the duration of activity would
be required to generate synchronization, which is not consistent
with empirical observations and was found to be detrimental to
collective performance. The existence of a refractory state of a
variable duration gives spiders the unique advantage of being
able to behave flexibly in response to the many factors that can
Fig. 5. Synchronization in experiments and simulations. Boxplots of (A) scores of synchronization and (B) periods between activity peaks in experimental
(n=20) and simulated hunting sequences when the lure was alternately present or absent. We simulated each of the 20 observed sequences 20 times. At
the beginning of each simulation, the spatial coordinates of the individuals were identical to those of the spiders in the corresponding observed
sequence. In A, each point on the boxplots of the simulated data gives the median of the scores obtained in the 20 simulations. Each gray line connects
the scores of synchronization obtained in the same hunting sequence in presence and absence of the lure. In B, the values of the periods between the
activity peaks were pooled for all peaks in all simulations. (C) Score of synchronization in simulations (n=20 for each of the 20 hunting sequences) where
the refractory state was implemented (+) or not () and when the probability of moving varied (+) or not () as a function of the number of active spi-
ders (social interactions). Horizontal line in each box represents the median, and the Lower and Upper hinges indicate the first and third quartiles. Lower
and higher whiskers extend to the most extreme values within 1.5 interquartile ranges from the first and third quartiles, respectively. (D) Score of syn-
chronization in simulations for different intensities of spider signal below which an individual can leave the refractory state in absence of the lure.
Dashed lines indicate the experimental values. (E) Score of synchronization in simulations for different ratios of the lure signal over the spider signal
beyond which the spider can leave the refractory state. Dashed lines indicate the experimental. (F) Score of synchronization in simulations implementing
a refractory period of a fixed duration. From (D–F), each point gives the median score obtained for 20 simulations of each of the 20 hunting sequences.
See SI Appendix, Fig. S7 for an illustration of representative activity patterns for the different conditions tested.
6of9 jPNAS Chiara et al.
https://doi.org/10.1073/pnas.2115103119 A variable refractory period increases collective performance in noisy environments
potentially influence the transmission of vibrational signals
across the web. These factors include prey species and size,
which can produce vibrations of different frequencies or inten-
sities (23) or abiotic conditions that can alter the mechanical
properties of the silk (30). For example, synchronization
occurred when hunting moths but not grasshoppers possibly
because the later produce more intense vibrations (15). The
behavioral rules involved in collective hunting should therefore
allow spiders to optimize prey capture by dynamically adapting
to any changes occurring during the hunt, such as distance to
prey or the number of conspecifics engaged in the hunt.
In social spiders, oscillations during collective hunting have
been documented in A. eximius, but mentions of synchronized
movements have also been made in two other species (13, 31).
Solitary spiders could potentially constitute a largely unsuspected
reservoir of collective behaviors that deserve further attention.
Indeed, the vast majority of species of spiders are solitary at
adulthood, but most, if not all, show a transient tolerant and gre-
garious phase during their early developmental stage (32). By
living in groups, juvenile spiders may face the same constraints
as social spiders and may have developed strategies to optimize
collective capture of prey, as suggested by anecdotal reference to
the existence of synchrony in groups of juveniles of the subsocial
species Amaurobius ferox (33). Experimental efforts should be
made to document the existence of oscillations in solitary species
and to identify whether the underlying behavioral rules are uni-
versally shared across species, whether transiently or perma-
nently social.
In other biological systems also composed of excitable enti-
ties, such as neuronal assemblies or cardiac tissue, variations in
the duration of refractory periods can result in electrophysiological
alterations. In the heart, for example, differences in refractoriness
between atrial cells can trigger arrhythmias because proximal
regions can be re-excited, when they should not, due to the lack of
uniformity of excitability recovery (34, 35). In systems whose func-
tional properties depend closely on temporal stability and unifor-
mity of refractory periods, the duration of the refractoriness relies
primarily, if not solely, on the entity itself. In other words, the exit
from the refractory period depends on the time already spent in
this state and not on the behavior of other entities. The stability of
such systems therefore requires a strict control in the expression of
the refractory period at the individual level. This differs from the
contribution of the refractory period at work in the system we
studied here, where the exit from the refractory state does not
depend on the history of each individual (i.e., the time spent in the
refractory period) but is conditioned by the immediate behavior of
the whole group. Indeed, the information about the state of the
system propagates throughout the network and is almost immedi-
ately accessible to all units, although the intensity of the informa-
tion available varies according to individuals and their location on
the web. By integrating all available information, the system com-
ponents can therefore synchronize quickly without paying the cost
of the long immobility delays that a fixed refractory period would
impose.
In conclusion, the mechanisms unraveled in our study provide
flexibility and robustness at the collective level while avoiding the
ABC
DE
F
Fig. 6. Prey capture efficiency. Each panel indicates the time required for 50% of the group to reach the prey as function of group size and prey signal
intensity (varying V0lure in Eq. 5). Spiders obeyed or not a refractory state (refractory versus no refractory) and were influenced or not by the noise (noise
versus no noise) produced by the moving spiders. The lure was active during the entire simulation. Simulations implementing an absence of refractory
period and noise gives the best theoretical performance (A). Band Cgive the latency to reach the prey when only the refractory period or only the noise
was implemented. In the presence of a refractory state and noise, spiders determined the noise level and the angle of their move toward the prey either
when leaving the refractory state (D) or when starting to move (E). For all conditions, the duration of the refractory state was variable and ended when
the strength of the signal emitted by the prey was more than one-half the strength of the signal produced by the mobile spiders except in (F), where the
duration of the refractory period was fixed and equal to 0.16 s. Spiders that did not reach their prey within 120 s received a +120 value. The dotted line
indicates the value of V0lure measured experimentally.
ECOLOGY
Chiara et al.
A variable refractory period increases collective performance in noisy environments
PNAS j7of9
https://doi.org/10.1073/pnas.2115103119
risks of desynchronization inherent to the errors or inaccuracies
of individual components. From an engineering point of view, our
findings are relevant to design self-organizing procedures to
enable the cooperation of a multitude of agents in decentralized
artificial systems such as swarm robots (9, 36). The implementa-
tion of a variable refractory period, whose expression is condi-
tional on the noise-to-signal ratio, has the potential to be an
original bioinspired strategy of communication to achieve reliable,
fast, and flexible coordination in noisy environments while mini-
mizing the complexity of operations at the individual level.
Materials and Methods
Field Sites. In the study, we observedtwo colonies in FrenchGuiana, one local-
ized along the Route de Kaw (N4°33.370' W52°10.842') (colony A) and one
close to the dam of Petit-Saut (N5°17.887' W53°03.015') (colony B) between
September 27 and October 3, 2019.
Vibratory Lure. The lure performed oscillations around a position by means
of alternating and controlled rotations of a stepper motor. A return cycle
of the stepper motor generates one vibration. A set of potentiometers was
used to modify the duration of the step (adjustable from 64 μsto4.2s),the
latency (adjustable from 32 μs to 2.1 s), the number of steps (adjustable
from 1 to 33), and the vibration duration (i.e., the number of return cycles
is adjustable from 1 to 33). It was also possible to add noise to each parame-
ter. A freshly captured dead horsefly or a leaf fragment was placed at the
end of a piece of light and flexible wire that was attached to the axis of
rotation of the motor. The vibrator was then activated, and the lure was
put in contact with the web. We found by trial and error a combination of
parameters that seemed optimal to trigger a high number of hunting
sequences. Our multiple observations give us confidence that the collective
movements during the approach to the epicenter of the vibrations were
equivalent when spiders were presented with the lure or with a live prey.
Once an appropriate set of parameters was found, it was possible to gener-
ate relatively reproducible vibrations. Upon contact with the web, the
vibrator triggered the movement of the spiders in the direction of the
source of vibrations. In the experiments, the lure was alternately placed in
contact with the web or away from the web for short periods of time to
determine the influence of spider interactions on synchronization. We
stimulated different parts of the nest one after the other to recruit differ-
ent groups of spiders. It was also possible to stimulate the same part of the
web several times (up to five) before the spiders lost their motivation to
hunt, which is clearly detectable by their lack of reaction to lure vibrations
and their retreat under the leaves of the nest. After a few hours, the spiders
resumed their hunting activities and reacted again to the lure.
Video Recordings. We recorded hunts with a high-definition camcorder JVC
EverioR (GZ-RX645AE) at a rate of 50 frames per second (noninterlaced). The
camera was mounted on a stand and placed in front of a part of the web.
Each video began by recording a scale (graduated ruler or checkered paper)
placed on the web to allow us to estimate the distance between the spiders
during the subsequent analysis of hunting sequences. For the analysis, we
selected portions of the hunting web where the spiders could be considered
to be moving in two dimensions (see Movie S1 for a representative example).
Although we could not guarantee that a spider moving outside the camera's
fieldofviewdidnotinfluence the behavior of the spiders, we were confident
that this effect was minimal, as we took particular care to record the majority
of spiders and distant spiders have little influence on the behavior.
We analyzed four hunts to determine precisely the position of each indi-
vidual involved in the hunt in order to finely quantify the rules of spider
behavior (1 image/0.08 s). Three of these four hunting sequences (Sequences
1to3inSI Appendix,Fig.S1) were obtained on three different days with col-
ony B, and one sequence (Sequen ce 4 in SI Appendix,Fig.S1) was obtained
on colony A. We assessed the individual spider response to the lure using 4
sequences obtained on colony A for 2 d and 14 hunting sequences obtained
on colony B for 3 consecutive d (1 image/0.08 s). In addition, we analyzed
another 20 hunting sequences (obtained using colony B on three different
days) at a rate of one image every 0.16 s to quantify the intensity of synchro-
nization in the presence and absenceof the lure and to compare these values
with those obtained in the numerical simulations. All hunting sequences
were analyzed with eye.
Measure of Synchronization. We estimated the degree of synchronization in
experiments and simulations using the Fleiss’Kappa coefficients (37) using the
R package “irr”(38). Kappa coefficients vary between 1 and 1, with 1
indicating that the stops and moves of all individuals would be perfectly syn-
chronizedand0thattherewouldbenosynchronization.Ineachobservedand
simulated sequence, we calculated a score of synchronization when the lure
was active and a score when the lure was inactive (i.e., two scores for each
sequence). Spiders in experimental sequences whose spatial coordinates could
not be determined during the entire sequence because they were temporarily
hidden by a leaf, or entered or left the field of view during the sequence, were
not included in the calculation of the score. In the corresponding simulated
sequences (Simulations), these individuals were also not included in calculating
the level of synchronization (so that the score of synchronization was based on
the same number of individuals in both experiments and simulations). The
scores of synchronization obtained in experimental sequences in the presence
and absence of the lure were compared by a paired Student’sttest.
Peaks Detection. We aimed at determining the time intervals (i.e., periods)
between successive peaks of spider activity during hunting sequences. We
used the function fpeaks from the R package “seewave”which detect peaks
in time series (39). We checked by eye on a subset of sequences the accuracy
of peak detection. We used a LMM (lmer function of the lme4 package in R)
to compare the time intervals between consecutive peaks of activity where
the lure was active or not active in experimental sequences with sequence ID
asarandomfactor(toaccountforthecollectionofmultiplevaluesoftime
intervals in each sequence).
Simulations. In a first series of simulations, we used the same initial spatial
configuration of spiders and timing of lure activation than in the 20 observed
hunting sequences to compare the collective patterns in the experiments and
simulations. Spiders that were observed in less than one-half the duration of
the experimental sequence were not included in the simulations. For each set
of simulations (n=20) for each sequence (n=20), we determined the median
score of synchronization. The simulations were performed with a timestep of
0.08 s but analyzed at a timestep of 0.16 s to match the sampling rate of the
experimental sequences used to calculate the intensity of synchronization
and the periods between peaks. First, we performed simulations implement-
ing only the parameter values of behavioral rules obtained empirically to
compare the level of synchronization between experiments and simulations
in order to validate our model. We compared the scores of synchronization
and the periods between peaks of activity obtained in the presence and
absence of the lure in simulations with LMMs using sequence ID as ran-
dom factor.
Then, we used the model to explore the respective contribution of the
refractory state and social amplification on activity patterns. Thus, we ran
simulations (n=20 for each of the 20 hunting sequences) where the refrac-
tory state was implemented or not and where the probability of moving var-
ied or not as a function of the number of active spiders (SI Appendix, Fig. S5).
In the absence of the implementation of the refractory state, a stopped spi-
der could resume movement without the requirement that all spiders be sta-
tionary when the lure was inactive or that the signal from the lure be greater
than or equal to one-half the signal of spiders. In the absence of the imple-
mentation of social interactions, a stopped spider could begin to move either
spontaneously or in response to the vibrations of the lure but was not influ-
enced by the activity of other spiders. Next, we aimed to examine the
sensitivity of the values conditioning the exit of the refractory state on the
production of synchronized activity patterns. Therefore, we ran simulations
where we varied either the intensities of spider signal below which an indi-
vidual can leave the refractory state in absence of the lure or the ratios of
the lure signal over the spider signal beyond which the spider can leave the
refractory state. These simulations allowed determining the sensitivity of the
values associated to behavioral refractory state to the production of synchro-
nized activity patterns. Finally, we tested whether the implementation of a
refractory state of fixed, rather than variable, duration allowed the produc-
tion of synchronized activity patterns. In this condition, a spider was in a
refractory state for a fixed amount of time (range tested from 0.08 to 1.04 s)
and could then become active without requiring the other spiders to be
immobile or the ratio of the lure signal over the spider signal to exceed a
particular threshold.
In a second series of simulations, we aimed to explore how synchronized
alternations of mobility and stop phases is beneficial to groups of hunting
spiders in the presence of vibrational noise and prey of different size. We sim-
ulated prey of different size by varying the value of V0lure (i.e., the signal inten-
sity at epicenter of the prey’s vibrations) but using the same attenuation as
found in our field experiments. We ran simulations where the spider obeyed
or not a refractory state and where the noise produced by the moving spiders
was detrimental or not detrimental to the spider’s orientation toward the
prey (SI Appendix,Fig.S8). We also examined the impact of a fixed refractory
8of9 jPNAS Chiara et al.
https://doi.org/10.1073/pnas.2115103119 A variable refractory period increases collective performance in noisy environments
period (using a value of 0.16 s that corresponds to the median stopping time
of spiders in the presence of the lure) on hunt efficiency. For each simulation,
we determined the time required for 50% of the group to reach the prey (dis-
tance <1 cm). We simulated groups of spiders of different sizes (10 to 100 spi-
ders) that were randomly distributed in a circle whose radius varied with
group size (initial density for all conditions: one spider per 4 cm
2
) at a distance
D=40 cm from the lure (SI Appendix,Fig.S9). The lure was permanently
active. We varied the value of V0lure between 1.25 and 20.75 to simulate the
production of more intense vibrations by the prey.
We used R 3.3.3 to analyze data and to implement the agent-based
simulations.
Data Availability. R scripts and datasets to reproduce our analyses have been
deposited at Zenodo and can be accessed at https://doi.org/10.5281/zenodo.
5841117 (40).
ACKNOWLEDGMENTS. We thank Pierre Lacoste, Jean-Louis Deneubourg,
Alfonso Perez-Escudero, and the team Interindividual Variability and Emer-
gent Plasticity for their insights. We are also grateful to the anonymous
reviewers for their useful comments and suggestions. Logistical assistance was
provided by the Laboratoire HYDRECO in French Guiana. V.C. was supported
by a PhD grant from the French Ministry of Higher Education and Research.
Funding was provided by the National Center for Scientific Research (France)
and Universit
e Toulouse III to R.J.
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ECOLOGY
Chiara et al.
A variable refractory period increases collective performance in noisy environments
PNAS j9of9
https://doi.org/10.1073/pnas.2115103119
