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OPEN 3 ACCESS Freely available online
Quantifying the Interplay between Environmental and
Social Effects on Aggregated-Fish Dynamics
M anuela C ap ello1*, Mare Soria1, Pascal C otel1, Jean-Louis D en eu b ou rg2, Laurent D agorn3
1 UMR EME, Institut d e Recherche pour le D éveloppem ent (IRD), Saint Denis, La Réunion, France, 2 USE, Unit of Social Ecology, Université Libre d e Bruxelles (ULB),
Bruxelles, Belgium, 3 UMR EME, Institut d e Recherche pour le D éveloppem ent (IRD), Victoria, Seychelles
Abstract
Dem onstrating and quantifying the respective roles o f social interactions and external stim uli governing fish dynamics is key
to understanding fish spatial distribu tion. If seminal studies have con tribu te d to o u r understanding o f fish spatial
organization in schools, little experim ental inform ation is available on fish in the ir natural environm ent, where aggregations
often occur in the presence o f spatial heterogeneities. Here, we applied novel m odeling approaches coupled to accurate
acoustic tracking fo r studying the dynamics o f a gro up o f gregarious fish in a heterogeneous environm ent. To this purpose,
we acoustically tracked w ith subm eter resolution the positions o f tw elve small pelagic fish (Selar crum enophthalm us) in the
presence o f an anchored floating object, con stituting a p o in t o f attraction for several fish species. We constructed a fieldbased m odel for aggregated-fish dynamics, deriving effective interactions for both social and external stim uli from
experiments. We tuned the m odel parameters th a t best fit the experim ental data and quantified the im portance o f social
interactions in the aggregation, providing an explanation for the spatial structure o f fish aggregations found around
floating objects. Our results can be generalized to oth er gregarious species and contexts as long as it is possible to observe
the fine-scale m ovem ents o f a subset o f individuals.
C itation : Capello M, Soria M, Cotel P, D eneubourg J-L, Dagorn L (2011) Quantifying the Interplay betw een Environmental and Social Effects on Aggregated-Fish
Dynamics. PLoS ONE 6(12): e28109. doi:10.1371/journal.pone.0028109
Editor: Gonzalo G. d e Polavieja, Cajal Institute, Consejo Superior d e Investigaciones Científicas, Spain
Received Septem ber 6, 2011; A ccepted November 1, 2011; Published December 12, 2011
C opyrigh t: © 2011 Capello e t al. This is an open-access article distributed under th e terms of th e Creative Commons Attribution License, which permits
unrestricted use, distribution, and reproduction in any medium, provided th e original author and source are credited.
Funding: This work was supported by th e Regional Council o f Reunion Island, the French Ministry of Overseas, th e 'Run Sea Science' (Theme - Capacity Building,
contract 229968) and th e 'MADE: Mitigating adverse ecological impacts o f open ocean fisheries' (Theme 2 Food, Agriculture, Fisheries and Biotechnology, contract
210496) FP7 European projects. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of th e manuscript.
C om peting Interests: The authors have declared th a t no com peting interests exist.
* E-mail: manuela.capello@ird.fr
distributions. O n one h a n d , m icroscale m odels [9-1 4 ], w hich
consider individuals e m b ed d ed in a n hom ogeneous environm ent,
can explain the observed schooling a n d m illing p h e n o m e n a b u t
can n o t be used to m ake predictions on the spatial distribution o f
the different fish species due to the difficulty in estim ating m odel
p a ram ete rs experim entally. O n the o th er h a n d , m acroscoscale
m odels [15] capable o f in co rp o ra tin g the response o f fish
populations to e nvironm ental gradients for different species do
not take into account behavioral features th a t could play a crucial
role in the fish spatial distribution. In this study, w e w orked at an
interm ediate scale, deriving a field-based m odel for fish dynam ics
th a t could in co rp o rate a t the sam e tim e the basic ingredients for
fish response to social stim uli a n d e nvironm ental heterogeneities.
R em arkably, this m odeling a p p ro ac h can be applied to a large
variety o f p h e n o m e n a w henever the spatial distribution o f
individuals results from the m u tu al response to environm ental
a n d social interactions. W e used the case o f a group o f fish in the
presence o f a floating object, know n in the literature as a Fish
A ggregation D evice (FAD) [16,17]. FA Ds can be artificial or
na tu ra l floating structures, eith er drifting or a n ch o red . T h e y have
b e en m assively deployed by com m ercial fisheries since the eighties
because they constitute a po in t o f attrac tio n for m an y fish species.
H ow ever, the reason fish aggregate a ro u n d FA Ds is still unknow n.
U n d e rstan d in g aggregated-fish beh av io r is beco m in g m ore urgent,
due to the large a n d continually grow ing exploitation o f FADs.
R ecently, concerns th a t FA Ds m ay act as ecological traps for fish
have b e en voiced [18], suggesting th a t the retain in g ch ara cte r o f
Introduction
D espite the social a n d econom ic im p o rtan ce o f fisheries,
q u antitative tools capable o f pred ictin g fish distribution a n d its
variations w ith respect to e nvironm ental changes a n d h u m an
activities are still missing. T h e m ain a pproaches th a t are currently
used in fisheries m an ag em en t require going b e yond the study o f
isolated targ et fish species a n d d e m a n d taking into account intraa n d inter-specific interactions, b ehavioral factors as well as
responses to the e nvironm ent [1,2]. M o re generally, they raise
fu n d am en tal questions o n anim al o rganization in a n a tu ra l
environm ent. D e m o n stratin g a n d quantifying the respective roles
o f external factors a n d social influences is key to u n d e rstan d in g the
spatial distribution a n d organization o f anim als in their e n viron­
m ent. In the last decade, several studies have show n how social
interactions govern the dynam ics o f anim al groups, such as fish
schools, b ird flocks, sheep herds o r aggregations o f insects [3-9].
H ow ever, in a n a tu ra l environm ent, anim al aggregations often
occur in the presence o f e nvironm ental heterogeneities, constitut­
ing a p o in t o f a ttrac tio n for feeding, sheltering o r o th er behaviors.
T his d em ands the creation o f dedicated analytical a n d m odeling
tools capable o f taking into account interactions, b o th w ith the
o th er individuals a n d w ith a heterogeneous environm ent. T h e re is
substantial evidence th a t social beh av io r is im p o rta n t for m an y fish
species, yet w ithin the existing e x perim ental a n d m odeling
approaches, it is difficult to quantify the respective roles played
by fish social interactions a n d external stim uli in th eir spatial
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FA Ds m ay alter th e biological characteristics o f fish populations
associated w ith them , like m igration, grow th, condition factors,
p re d atio n a n d n a tu ra l m ortality. T h e validity o f these scenarios
strongly depends on the type o f m echanism s leading to
aggregation, a n d this requires furth er investigation. T o this end,
precise inform ation o n the range a n d structure o f fish aggregations
is needed. T o date, several acoustic surveys have b e en done in
o rd e r to ch aracterize fish aggregations a ro u n d FA D s [19-21].
H ow ever, no in form ation was available so far on aggregated-fish
dynam ics at subm eter scales, w here fish b e h av io r could be studied
in detail.
0.2
0.15
=>
0.1
o
c
cr
1—
U-
0.05
•3
-2
1
0
1
2
3
0 [radians]
In this p ap er, we in tro d u ced a new m odeling a p p ro ach , coupled
to accu rate acoustic tracking m easurem ents, capable o f quantify­
ing the driving forces leading to aggregation. W e considered an
obligate schooling small pelagic fish species, Selar crumenophthalmus,
in the p roxim ity o f a FA D located in Saint P aul’s Bay at R eu n io n
Island (W est In d ian O cean) [22]. T h e FA D was a 12-m b o a t fixed
at 17 m d e p th by five anchors to p rev en t any m ovem ent. Tw elve
fish w ere tagged w ith H T I ™ acoustic pingers (H ydroacoustic
T echnology Inc., Seattle, USA) a n d released next to the FA D,
along w ith o th er n on-tagged individuals. T h e 3D tracking o f each
tagged fish (one position every second w ith sub-m eter resolution)
was possible w ithin a radius o f a pproxim ately 50 m from the FA D
w ith the use o f a n H T I ™ acoustic detection system. E xperim ental
d a ta collected d u rin g one h o u r w ere used to construct a m odel for
aggregated-fish dynam ics, w hich took into acco u n t the possible
interactions w ith the FA D a n d the o th er tagged fish, w hile all o th er
factors (e.g., light, food a b u n d an c e, a n d currents) w ere considered
constant d u rin g this p erio d o f observation. M odel p a ram ete rs w ere
fine-tuned w ith experim ental data, w hich allow ed us to quantify
the interplay b etw een social interactions a n d attrac tio n to the FA D
a n d to gain insights o n the aggregation p h e n o m e n a.
0.1
0.05
0
0
0.5
1
1.5
V [m/s]
Figure 1 . Analysis o f individual-fish dynam ics. (A) T u rn in g a n g le
d is trib u tio n : e x p e rim e n ta l p o in ts (red) a n d fit (black) w ith th e W ra p p e d
C au c h y D istrib u tio n <D(0) = —
’
sin h (p )—
. ^ f¡t t ¡n g p a ra m e te r
2 k cosh(p) —cos(0)
a K
p — 0.16. (B) Individual s w im m in g s p e e d d is trib u tio n : e x p e rim e n ta l
p o in ts (b lu e ) a n d fit (black) w ith th e G a m m a d is trib u tio n f ( x )
= r.vexp( — x /s ) w ith sca le p a r a m e te r 5 = 0 .1 6 a n d n o rm a liz a tio n
c o n s ta n t c — 1.2.
d o i:1 0 .1 3 7 1 /jo u rn a l.p o n e .0 0 2 8 1 0 9 .g 0 0 1
Results
w here r is the radial distance am o n g fish pairs (Fig. 2B). T h e
depletion o f g ( r ) for distances sm aller th a n 0.3 m indicated a zone
o f repulsion. A t in term ed iate distances, the fish p air-correlation
was constant a n d m axim um , revealing a zone o f com fort. F or
distances larg er th a n 0.9 m , the pair-co rrelatio n decayed expo­
nentially, revealing th a t it was less p ro b a b le to find inter-individual
distances in this range. B oth the speed a n d tu rn in g angle
distribution, as well as the pair-co rrelatio n function, w ere
in d ep e n d en t o f the radial distance from the FA D , see Fig.S4 in
S upplem entary m aterial.
E x p e rim e n ta l d a t a an aly sis
T w o variables w ere considered to characterize the individual
fish dynam ics: tu rn in g angle a n d sw im m ing speed in the ,vy plane.
T h e turning-angle distribution was well described by a w ra p p ed
C auchy distribution, w ith a sharp p e ak cen tered at zero (Fig. 1A).
A t the tim e scale o f o u r observations, no evidence o f correlation
a m o n g subsequent tu rn in g angles was found [23]. T h e speed
distribution h a d a m ax im u m at approxim ately 0.16 + 0.03 m /s
(Fig. IB). Based on the observation th a t the average fork length o f
o u r tagged fish was 0.17 + 0.02 m , this finding was com patible
w ith the w idely accepted kinetic rule o f 1 b o d y -len g th /se co n d . At
h igher speeds, the distribution decayed exponentially. T h e
re co rd e d fish trajectories in the ,vy plan e (see Fig.S2 in
S upplem entary m aterial) d e m o n stra ted a radial sym m etry a ro u n d
the FA D . T herefore, in o rd e r to analyze the fish spatial
distribution, we calculated the tim e-averaged radial distribution
P i(R ) for each fish / w ith respect to the FA D position, w here R is
the radial distance from the FA D in the ,vv plan e (Fig. 2A). T his
qu an tity gave inform ation on the probability to find a fish at a
distance R from the FA D [24], R em arkably, all o f the tagged fish
show ed the sam e rad ial distribution. Close to the FA D , th ere was a
region (at a distance sm aller th a n 2 m) characterized by a high a n d
constant P i{R ). T h ere afte r, P¡{R ) decreased exponentially u p to a
distance o f a pproxim ately 10 m , w here the radial distribution was
o f the o rd e r o f the constant distribution associated to a fish
occupying hom ogeneously the detection area. T his scale sets the
b o u n d a ry o f the zone o f aggregation. T h e interactions betw een
tagged fish, as well as th eir variations in space, w ere investigated
th ro u g h the tim e-averaged fish pair-correlation function g (r) [24],
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M o d e l resu lts
In o rd e r to gain quantitative insights into the fish response to
b o th the FA D a n d the o th er fish, w e derived effective interactions
from the experim ental quantities discussed above. E xpressing the
average fish-radial distribution P (R ) a ro u n d the FA D as the
exponential o f a B oltzm ann w eight P ( i ? ) ~ e x p [ — F f,id(í?)] [25],
we o b tain e d the effective fish-FAD interaction V f a d ( R ) ~
log[P (R )]. F ro m the b ehavior o f the experim ental P (R ) this lead
to the follow ing expression for the fish-FA D interaction:
Vf ad ( R ) = \
f c o n st
for R < R s,
[ yR
for R > R st
f
“
(!)
w here R st is the stationarity radius, found a t 2 m , w hich
corresponds to the region w ith constant probability to find the
fish. B eyond this distance was the zone o f FA D attractio n , w here
fish resp o n d ed to the presence o f the FA D th ro u g h a constant
attractive force, w hose strength, a, was o b tain e d by com parison
2
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0.1
0.01
fe 0.001
0.0001
1e-05
R [m]
0.04
0.035
0.03
0.025
I
0.1
0.01
0.001
0.0001
1e-05
1e-06
0^02
0.015
0.01
0.005
0 5 10 15 20
B
0
0 2 4 6 8 10 12 14 16 1820
r[m ]
Figure 2. Analysis o f fish spatial d istrib ution around the FAD.
(A) Radial d is trib u tio n a ro u n d th e FAD fo r e a c h o f th e 12 ta g g e d fish
( r e p r e s e n te d b y d if f e r e n t c o lo rs ) in s e m ilo g a r ith m ic s c a le . T h e
h o riz o n ta l line in d ic a te s th e b e h a v io r o f P ( R ) fo r a fish h a v in g a
h o m o g e n e o u s d is trib u tio n in a circle o f ra d iu s e q u a l to 3 0 m . Inset:
m e a n v a lu e o v e r all fish. (B) Fish p a ir-c o rre la tio n fu n c tio n . Inset: th e
s a m e in s e m ilo g a rith m ic scale.
d o i:1 0 .1 3 7 1 /jo u rn a l.p o n e .0 0 2 8 1 0 9 .g 0 0 2
w ith experim ental d ata, as show n below . T his zone was assum ed
to be m u ch larger th a n the o th er spatial scales governing fish
dynam ics [26]. T h e definition o f its bo u n d aries w ent b eyond the
scope a n d experim ental lim its o f this study.
A nalogously, w e derived effective fish-fish interactions from the
pair-co rrelatio n function, defining F/¡¿/¡(r)~log[g(r)] [25]. A c­
c o rding to the b e h av io r o f g(r), w e identified th ree m ain zones for
the fish-fish interaction: a zone o f repulsion w ithin a radius
r rep = 0-3 m, a zone o f com fort u p to rcomf = 0.9 m a n d a zone o f
a ttrac tio n a t larg er distances. T his lead to the follow ing effective
fish-fish interaction:
P (R ) averaged over all fish (Fig. 3A). T h e pair-co rrelatio n function
(Fig. 3B) calculated for the optim ized non-social system was
different th a n the one found from the experim ental d ata, signaling
th a t the observed fish aggregation a ro u n d the FA D was n o t purely
a consequence o f the FA D attractio n . W e th e n adjusted the
p a ram ete rs a a n d ß in E q .l a n d E q.2 to find the m in im u m o f the
SS R for b o th the fish radial distribution a n d the p air-correlation
function (see T ab le 1). Indeed, ad d in g fish-fish interactions
resulted in agreem ent b etw een the m odel a n d experim ental d a ta
for all quantities a n d show ed th a t the fish dynam ics a ro u n d the
FA D was also the fingerprint o f a tru e fish-fish in teractio n (Fig. 3G
a n d 3D). M oreover, starting from the optim ized m odel th a t best fit
the experim ental d ata, we studied the system sensitivity to changes
o f one m odel p a ra m e te r a t a tim e. First, we calculated the radial
distribution a ro u n d the FA D for different values o f the individual
fish speed, v, keeping constant the fish-fish a n d fish-FAD
interactions. Sm all changes in v affected the zone o f aggregation
significantly, w ith a n aggregation radius increasing w ith speed
(Fig. 4A). N ext, we analyzed the role o f social interactions, keeping
constant the FA D attractio n . W e o b tain e d th a t non-social fish
should have a larger dispersion a ro u n d the FA D , w ith an
aggregation radius o f a b o u t 60 m ra th e r th a n 10 m for social fish
(Fig. 4B). Finally, we studied the fish-group dynam ics in the
absence o f a FA D . T h e fish-group b a ric en te r p erfo rm ed a ra n d o m
w alk a n d explored the env iro n m en t (Fig. 5A), w ith the group
staying com pact. T his is clear from the com parison o f the fish paircorrelation in the p re sen c e /a b se n ce o f a FA D (Fig. 5B).
D iscussion
E xperim ental d a ta revealed the existence o f a sharp zone o f
aggregation, w here Selar crumenophthalmus c o n cen trate a t small
distances from the FA D . All tagged fish exhibited the sam e
beh av io r a n d m ostly stayed w ithin 10 m from the FA D . W e could
distinguish a stationarity region very close to the FA D ( < 2 m),
w ith a constant a n d high p robability o f finding fish, as well as a
N on-social
0 .0 2 5
Social
0 .0 2 5
mode l
0 .0 1 5
~
m odel
exp
,\
0 .0 0 5
0 .0 0 5
V /M ir) = { c o n st
ßr
0
for r < rrep
for rrep < r <
5
10
15
2
R [m]
f com f
>
(2)
for r > r comf
w here the analytic form o f the short-range repulsion was assum ed
linear for simplicity, a n d v is the individual fish speed (v = 0.17 m /
s, following the rule o f 1 b o dy-length/second). T h e p a ram ete r, ß,
setting the degree o f attrac tio n b etw een fish, was o b tain ed by
com parison w ith experim ental d ata, as show n below . G iven these
effective interactions, we m odeled the system follow ing a
co rrelated ra n d o m walk dynam ics (CRW ) em b e d d ed in a force
field [27,28], In o rd e r to evaluate the role o f the fish-FAD
interaction in the m easu red quantities, we first c o m p a red results
from the non-social m odel (i.e., no fish-fish interaction) w ith
experim ents. T ak in g the expression o f the effective fish-FAD
interaction in E q .l, the only free p a ra m e te r was the FA D
a ttrac tio n strength, a. W e estim ated the value o f a th a t m inim ized
the sum o f squared residuals (SSR) for the rad ial fish distribution
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\
'
—r r
-
0 .0 1 5 k
0 .0 2 5
0 .0 4
3
0 .0 3 5
0 .0 3 ,*
0 .0 2 5 i 1
0 .0 1 5
0 .0 1 5
0 .0 0 5
0 .0 0 5
0 .0 3 5
mode l
model
e xp ™
.
*■ ^
■
V
D
,
10
15
20
r[m ]
Figure 3. Com parison am ong o p tim ize d m odel and experi­
m ental results for the fish radial d istrib ution P(R) around the
FAD and the p air correlation function g (r ). Left p a n e ls: n o n -so c ial
fish m o d e l (A) radial d is trib u tio n a n d (B) p a ir-c o rre la tio n fu n c tio n . R ight
p a n e ls: social fish m o d e l (C) radial d is trib u tio n a n d (D) p a ir-c o rre la tio n
fu n c tio n .
d o i:1 0 .1 3 7 1 /jo u rn a l.p o n e .0 0 2 8 1 0 9 .g 0 0 3
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T ab le 1 . Model parameters.
M o d el P aram eter
Sym bol
Number o f fish
N
12
12
Individual speed [m/s]
V
0.17
0.17
W rapped Cauchy distribution param eter
P
0.16
0.16
FAD Stationarity radius [m]
Rst
2
2
FAD attracting potential strength *
a
0.014
0.0015
Fish-fish repulsion radius [m]
rrep
-
0.3
Fish-fish comfort radius [m]
r conf
B
0.9
Fish-fish attracting potential strength *
ß
N on-social
-
60
Social
>
20
0
0
larg e r-ran g e d zone (2—10 m) w ith a n exponentially decaying
p robability. T h is level o f spatial accuracy, as well as in form ation
o n th e specific shape o f th e zone o f aggregation, c a n n o t b e re ac h ed
v=0.13
v=0.15
v=0.17
.19
0.01
0.001
40
60
I
m/s
m/s
m/s m
m/s
0.1
0.01
0.001
0.0001
16-05
1e-06
1e-07
1e-08
1e-09
0
5
w ith sta n d ard acoustic techniques [19-21], revealing th a t this
experim ental a p p ro ac h is ideally suited for u n d e rstan d in g the
beh av io r o f fish aggregated to FA Ds a t a fine scale. In o rd e r to
identify the factors th a t shaped the zone o f aggregation, we
constructed the sim plest m odel o f fish dynam ics th a t w ould take
the m ain ingredients into consideration, w here the fish-FAD a n d
the fish-fish interaction was d educed from the spatial distribution
o f the tagged fish. A lthough the attrac tio n o f the FA D alone
allow ed m odeling o f the fish aggregation to the object, the
m atch in g b etw een experim ental a n d m odeled d a ta was only
possible w hen taking into account the fish-fish interaction. T h e
optim ized value o f the FA D attractio n , a, was m u ch sm aller th an
the C R W individual speed p a ram ete r, v, indicating th a t the
stochastic term was playing a m ajo r role. In o th er w ords, w h en fish
stayed in the zone o f aggregation, th eir m ovem ents w ere
d o m in a ted by the c o rre late d -ra n d o m w alk com ponent. T h e
o ptim ized value o f the fish-fish attractio n , ß, was larger th a n a
a n d was necessary in o rd e r to rep ro d u ce the ex p erim ental paircorrelation function. In this way, the m odel highlighted the
im p o rta n t role o f social interactions in the distribution o f fish
a ro u n d a FA D . Indeed, alth o u g h we only tagged som e individuals
from a group, the tim e average o f o u r tagged-fish p air-correlation
offered insights into the entire fish aggregation n e a r the FA D . T h e
effective fish-fish interaction im plicitly took into account the
presence o f o th er n o n-tagged fish in the system. T his represents a
key im provem ent in the study o f social b eh av io r o f wild anim als in
their environm ent, as an exhaustive observation o f all m em bers o f
5 10 15 20 25 30 35 40
R[m]
NON SOCIAL
SOCIAL
0.001
0.0001
ST
le -0 5
20
m o d e l p re d ic tio n fo r th e (A) fis h -g ro u p b a ric e n te r (FAD re p re s e n te d
w ith a b lu e circle) a n d (B) p a ir-c o rre la tio n in th e p re s e n c e /a b s e n c e o f a
FAD.
do i:1 0 .1 3 7 1 /jo u rn a l.p o n e .0 0 2 8 1 0 9 .g 0 0 5
0
£■
15
Figure 5. Role o f FAD attraction on fish agg reg atio n. O p tim iz e d
1e-06
0.01
10
r[m]
le -0 5
0.1
100 120
NO FAD
FAD
0.0001
ST
80
X [m]
Model param eters used to fit th e experimental data in Fig. 3. Stars indicate the
free param eters estim ated through minimization o f th e SSR on the radial
distribution function and th e pair correlation function. Third column, non-social
fish model. Forth column, social fish model.
doi:10.1371 /journal.pone.0028109.t001
0.1
20
0.003
1e-06
1e-07
1e-08
0 10 20 30 40 50 60 70
R[m]
F igure 4. Role o f ind ividu al sw im m ing speed and social
interaction on fish agg reg atio n. Radial d is trib u tio n a ro u n d th e
FAD o b ta in e d fro m th e o p tim iz e d m o d e l (w ith fish-fish in te ra c tio n s)
w h e n v a ry in g (A) th e in d iv id u al fish s w im m in g s p e e d v, (B) th e social
in te ra c tio n p a r a m e te r ß (NON-SOCIAL c o rre s p o n d s to ß — 0 a n d SOCIAL
in d ic a te s th e o p tim iz e d m o d e l).
d o i:1 0 .1 3 7 1 /jo u rn a l.p o n e .0 0 2 8 1 0 9 .g 0 0 4
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M o d e lin g A g g re g a te d -F is h D yn a m ics
a g roup is alm ost never possible. M oreover, o u r optim ized m odel
shows th a t the fish-fish in teractio n alone, estim ated th ro u g h our
field-based a p p ro ac h n e ar the FA D , c an ensure a stable group
dynam ic, even in the absence o f a FA D . T his pred ictio n signals
th a t the observed aggregation is a stable entity a n d could be the
precu rso r o f schooling [17,22].
Finally, o u r m odel allow ed us to m ake predictions for different
values o f the param eters controlling the aggregated-fish dynam ics.
W ithin o u r schem e, the boundaries o f the zone o f aggregation
a p p ea r to be very sensitive to b o th changes in the fish speed a n d
social interaction. Indeed, social individuals w ould b e closer to the
FA D th an non-social fish, im plying a n am plification o f the
individual response to the FA D attractio n in a social group [29].
M oreover, fish characterized by a high speed w ould have a w ider
zone o f aggregation, signaling possible correlations am o n g the fish
sw im m ing speed (or size) a n d their spatial distribution a ro u n d
FADs. T his provides a unique explanation for the structure o f fish
aggregations a ro u n d floating objects, w here sm aller species (or
sm aller individuals), characterized by a sm aller sw im m ing speed, are
found closer to FA Ds th an larger fish [19-21]. T his ap p ro ac h can
be used to study the fish dynam ics o f o th er species a n d pred ict the
occurrence o f different shells o f fish concentrations a ro u n d the FA D.
A fine-tuned analysis o f the strength o f interactions w ould be
req u ired to b e tte r assess the aggregation radius o f each species.
Flowever, by fixing the sam e ratio am o n g all quantities a n d simply
scaling all the param eters governing the dynam ics o f a factor, F, our
m odel predicts low er a n d u p p e r b ou n d s for the zone o f aggregation
o f social a n d non-social fish a t lO x F m a n d 60 x F m , respectively.
By using a value o f 5 for F, a scale th a t could correspond to the
individual sw im m ing speed a n d size o f a tuna, w ould result in an
aggregation radius betw een 50 m a n d 300 m . T his low er b o u n d is
close to the center o f mass for tu n a aggregations found in recent
acoustic experim ents [20,21], suggesting a potentially strong social
effect for tu n a aggregated to FADs.
transm issions p e r second) was prog ram m ed to be different for each
tagged fish a n d ranged betw een 1.43 a n d 1.16 i _ 1. T hese settings
w ere optim al for the duratio n o f o u r experience, w ith a theoretical
period o f life tags o f six days. D a ta processing involved two steps.
First, the acoustic record o f each tag on each o f the five hydrophones
was m anually p roofed using H T I ™ M ark T ags Software to exclude
acoustic noise. Second, files w ere processed in H T I ™ Acoustic T a g
pro g ram to track acoustic echoes. T his p rocedure used a hyperbolic
algorithm to solve for the transm itter 3D position. In addition, a
tim e-stam p was calculated so th a t the transm itter was referenced in
b o th space a n d tim e. T h e accuracy o f the position in the horizontal
plane ranged from 0.1 to 0.3 m in the m onitoring netw ork. In the
vertical direction, the accuracy was low er (around 1.0 m). W e
m easured c u rre n t through the A an d eraa R M C 9 Self R ecording
C u rre n t M eter, w hich was fixed u n d e r the b o a t (at 5 m eters depth)
in order to record the horizontal cu rren t speed a n d direction. T h e
m inim um -current p eriod recorded by the cu rren t m eter occurred
w hen the direction o f the tidal cu rre n t reversed (Fig. S3 in
Supplem entary Inform ation), betw een 13:00 a n d 14:00.
Fish S p e c ie s a n d T a g g i n g p r o c e d u r e
T h e fish species we studied was the big-eye scad (Selar
crumenophthalmus). It is a small coastal pelagic fish com m on in the
circum tropical area [31] a n d is a n obligate schooler (i.e., unable to
survive outside a fish school [32,33]), w hich is know n to associate
aro u n d FADs [34]. In R eunion Island, Saint Paul’s bay is the m ain
a rea w here this species is caught. H ere, traditional beach seiners
target shoals o f bigeye scads aggregated aro u n d anchored FADs near
the shore. Forty fish w ere caught using h a n d lines in Saint P aul’s bay,
transported in baskets a n d m aintained in tanks a t the A quarium of
R eunion Island during ten days for acclim ation. T hey w ere fed and
treated w ith a solution o f m ethylene blue (from the first day) and
copper sulfate to kill bacteria a n d to prevent the proliferation o f fungi.
M ost fish showed only superficial wounds, w hich w ere caused by
fishing (hook) or handling. T h e tagging operation was carried out on
the 1st o f M ay 2003. Twelve fish w ere anesthetized w ith a solution of
clove off [35]. T h e acoustic tags w ere im planted gastrically by
ingurgitation, a tagging technique well suited for short-term
experim ents [36]. T h e fish were held for two subsequent days in
tanks to ensure fish survival a n d tag retention. N o further m ortality
was observed in either tagged or untagged fish during this period. All
fish (tagged a n d non-tagged) w ere released on the 3rd o f M ay 2003 at
12:00 in the proxim ity o f the boat, anchored in the nearby o f the
fishing location. Based on visual observation, we could estim ate that
fish im m ediately form ed a small school. All fish stayed w ithin the zone
o f detection until 19:00, w ith very few excursions outside the range of
detection. T hree fish stayed a t night, leaving the zone the subsequent
m orning, while the others left aro u n d 19:00. F our fish m ade short
visits during the second a n d third day o f the experim ent.
M aterials and M ethods
Ethic S t a t e m e n t
T h e fish e x perim ental protocols w ere p e rm itte d u n d e r the
A q u ariu m o f R e u n io n Island anim al care certificates delivered by
the F ren ch V eterin ary M edicine D irectorate. Protocols w ere
carried o u t w ith the au th o rity o f the N atio n al V e terin ary School o f
N antes (France) validating a certificate o f train in g in anim al
experim entation a n d a degree in experim ental surgery o n fish.
E x p e rim e n ta l s e t t i n g
T h e experim ent was conducted in open field o f a shallow-water
region (17 m depth in average) in the center o f S aint P aul’s Bay in
R eu n io n Island (South W estern In d ian O cean). T h e H T I ™
Acoustic T a g T racking System (M odel 290) was com posed o f five
hydrophones connected b y cables to the Acoustic T a g Receivers
system em bedded on the boat. T hese hydrophones surrounded the
b o a t in a square o f approxim ately 100 m eters p e r side (see F ig.S l in
Supplem entary Inform ation). T h e hydrophones w ere arran g ed a t
the surface a n d n ear the sea b e d to allow for optim al reception. T h e
cables connecting the hydrophones to the b o a t reached the sea
bo tto m straight below the boat, constituting a vertical subm erged
structure w hose position was taken as o u r FA D position (Fig.S2 in
Supplem entary Inform ation). T h e H T I ™ acoustic tags (M odel 795)
w ere 7 m m diam eter, 17 m m length a n d 1.5 g w eight in the w ater.
T his w eight was less th an 0.1% o f the m ean fish weight. W e were
therefore confident th a t the tags did n o t affect the buoyancy o f the
fish [30]. T h e in situ test led us to choose a pulse duratio n o f 4 msec.
In order to discrim inate fish, the repetition rate (num ber of
PLoS ONE I w w w .p lo s o n e .o rg
M e t h o d s for d a t a an alysis
E xperim ental d a ta analysis co n ce n tra ted on one h o u r, betw een
13:00 a n d 14:00 o f the first day, w hen the c u rre n t was negligible
a n d all o f the tagged fish w ere present. T his allow ed us to collect
good statistics, w ith a b o u t 3600 positions for each o f the twelve
tagged fish. D u rin g the rest o f the day, o u r results still held, b u t we
observed a shift in the position o f the fish baricen ter, due to nonnegligible c u rre n t effects. D u e to the system geom etry, w here the
floating object was associated to a subm erged vertical structure
reach in g the sea-bottom (see Fig.Sl), d a ta analysis focused on the
x y plane, integrating over the vertical direction. T h is ap p ro ac h
was supported b y previous acoustic survey m easurem ents [19-21]
w ere the fish spatial distribution along z was n o t affected by the
presence o f the FA D b u t ra th e r d e p en d e d on the fish species. T h e
5
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M o d e lin g A g g re g a te d -F is h D yn a m ics
presence o f each fish i a ro u n d the FA D was analyzed th ro u g h the
tim e-averaged radial distribution function:
S ( R - R ,( t) )
P ,(R ) =
2nR dR
w here the delta function selects the fish positions R ¡(t) a t tim e t with
radial distance from the FA D w ithin the interval [R — d R ,R \ [37],
a n d brackets denote the tim e average. T h e d en o m in ato r co rre­
sponds to the a rea o f the rin g o f radius R a n d w idth d R a ro u n d a
FA D . W ith this d enom inator, the q uantity P ¡(R ) was norm alized:
d V ( { x j,y j } )
J P i(R ) 2 n R d R = 1
Fy =
T herefore, P ¡(R ) could be interpreted as the probability o f the
presence o f fish i a t distance R from the FA D , p e r un it a rea .T h e
strength o f o u r ap p ro ac h resided in the high n u m b e r o f sam pled
points, w hich clearly allow ed us to speak in term s o f probabilities.
W e chose d R = 0.3 m , w hich was com patible w ith the experim ental
precision for fish detection in the x y plane. Because we h a d d etailed
spatial inform ation concerning several fish, w e calculated the fish
pair-correlation function (or pair-distribution function) g(r) am ong
synchronous fish [24], T his gave us a n understan d in g o f fish
interactions a n d their variations in space. W e took synchronicity
intervals o f 1 second because this tim e fram e was sufficient to obtain
a large n u m b e r o f synchronous fish. W e calculated the tim eaveraged fish pair-correlation function g(r), w hich in two
dim ensions can be w ritten as:
^ ¿ ( r - r ÿ(0)
g(r)=
N (t)
right h a n d side constituted the sta n d ard C R W dynam ics, w ith v
b ein g a c o n stan t defining the individual sw im m ing speed.
C o n cern in g the a n g u lar com ponent, a>t co rresp o n d ed to the fish
o rien tatio n angle in o u r reference fram e a t tim e Í a n d 6 was a
ra n d o m n u m b e r taken from a probability distribution ® (0) th a t
sets the tu rn in g angle. T his p robability distribution, as well as the
co n stan t for the individual sw im m ing speed, was taken from
experim ents. In particular, v c o rresponded to the sta n d ard rule o f
1 body length p e r second a n d ® (0) follow ed a w ra p p ed C auchy
distribution. T h e last term s in E q.3 constituted the determ inistic
dV^Xuyd}
p a rt o f the fish dynam ics, w here F x ( t ) = ---------- —-—-—
2 nrdr
the
X
(y)
co m p o n e n t
of
the
determ inistic force associated w ith a poten tial V { { x j,y j} ) a t tim e
i, d ep en d in g o n fish positions. W e considered additivity in the
forces. O u r poten tial h a d the form:
V(xi,yi) = Vfad (R í) + J 2 vM rv)
v
w here the first term was the FA D potential, a n d the
second
term
set the
fish-fish interaction,
w ith
R¡ =
\ J ( x fad — Xi)2 + (yFAD — y i)1 bein g the radial distance am o n g
the FA D a n d fish i a n d ry = \ J (xj — x¡)2 + (jy —y i f bein g the
distance am o n g fish i a n d fish j . T h e analytic form s o f these
potentials w ere derived from the experim ental radial distribution
P (R ) a n d the p a ir correlation function g(r) [39]. T h e optim ized
m odel p a ram ete rs are show n in T ab le 1.
Supporting Information
w here N ( t ) is the n u m b e r o f co p lan ar pairs detected in the tem poral
interval [ í , í + l í ] a n d A /(0 is the p lan a r distance am ong
synchronous fish i a n d j . C o planarity was established w hen two
fish w ere w ithin 1 m in the z-direction, w hich was com patible with
o u r experim ental accuracy in the vertical direction. T h e delta
function selects fish pairs a t p lan a r distance in the range [r — d r,r\,
w ith dr = 0.3 m , a n d brackets d enote the tim e average.
F ig u re S I T h e H T I ™ e x perim ental setting. T h e boat, w ith the
cables u n d e rn ea th , represents the floating object or ‘F A D ’.
(TIF)
M o d e l d efin itio n
F ig u re S3 C u rre n t speed (red line) in c m / s a n d c u rre n t angle
(blue line), w ith respect to the N o rth (East = 90; W est = 270)
re co rd e d d u rin g the experim ent.
(TIF)
L ag ran g ian dynam ics [37,38] are c h aracterized by the use o f
stochastic differential equations th a t describe the evolution o f the
positions o f each individual in tim e. T h e system evolves u n d e r the
effect o f b o th determ inistic forces a n d a ra n d o m com ponent. Flere,
we used a v a ria n t o f the L ag ran g ian dynam ics, the co rrelated
ra n d o m w alk (CRW ) [27,28], in the presence o f a force field. In
the C R W m odel, a n anim al m akes discrete steps, w ith tu rn in g
angles sam pled from a given p robability distribution. A t each step,
the tu rn in g angle is in d ep e n d en t o f the previous one. Flere, in
ad dition to isolated-fish C R W dynam ics, fish m ovem ent was
influenced determ inistically. T h e tim e evolution o f the position o f
fish i in the plane follow ed the equations:
X i(t + A í) = x,-(i) + v e o s(cot + 0 )A t + A tFx (t)
y¡(t + A í) = y¡(t) + v sinfuy + 0)A í + A tFy (t)
(3)
w here x,-(i) a n d y ¡(i) are the x a n d y co m p o n e n t o f the position o f
fish i a t tim e Í, a n d A í was the tim e step. T h e first term s on the
PLoS ONE I w w w .p lo s o n e .o rg
F ig u re S2 T rajectories o f the tracked fish in the x y plane a ro u n d
the FA D from 13:00 to 14:00 D ifferent colors indicate different
fish a n d black p o in t indicates the FA D position.
(TIF)
F ig u re S4 Sw im m ing speed distribution (A), tu rn in g angle
distribution (B) a n d pair-co rrelatio n function (C), calculated at
different radial distances from the FA D .
(TIF)
A ck n ow led gm en ts
W e thank G. Potin, M . T aquet, L. Bigot, P. Durville, M . Tim ko, G. Fritsh
for their help in fishing an d tagging operations an d P. Fréon, F. Becca, O.
Zagordi and G. Nicolis for interesting discussions.
Author C ontributions
C o n c eiv ed a n d d esig n ed the ex p erim en ts: M S . P e rfo rm e d the
experim ents: M S PC LD. A nalyzed the data: M C M S. C o n trib u ted
reag en ts/m aterials/an a ly sis tools: J-L D LD . W rote the paper: LD M C
MS J-L D .
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| V o lu m e 6 | Issue 12 | e 2 8 1 0 9
M o d e lin g A g g re g a te d -F is h D yn a m ics
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D e c e m b e r 2011
| V o lu m e 6 | Issue 12 | e 2 8 1 0 9