Towards of a firmer explanation of large shoal formation, maintenance and collective reactions in marine fish

Abstract

Avoiding predation is generally seen as the most common explanation for why animals aggregate. However, it remains questionable whether the existing theory provides a complete explanation of the functions of large shoals formation in marine fishes. Here, we consider how well the mechanisms commonly proposed to explain enhanced safety of group living prey explain fish shoals reaching very large sizes. By conceptually re-examining these mechanisms for large marine shoals, we find little support from either empirical studies or classical models. We address first the importance of reassessing the functional theory with predator-dependent models and the need to consider factors other than predation to explain massive fish shoals. Second, we argue that taking into account the interplay between ultimate benefits and proximate perspectives is a key step in understanding large fish shoals in marine ecosystems. Third, we present the growing body of evidence from field studies that identify shoal internal structure as an important feature for how large shoals can form, maintain and react as a coordinated unit to external stimuli. In particular, we consider a mechanistic basis of local rules of interaction for group formation and collective dynamic properties that can account for groups reaching very large sizes. Recent research in collective animal behaviour has shifted focus from the importance of global properties (group size) to local properties (local density and information transfer). In contrast to studies of fish shoals in the laboratory, the difficulty in measuring behaviour in large shoals in marine systems remains a major constraint to further work. Advances in acoustical observation have shown the greatest potential to provide data that can link proximate mechanisms in, and ultimate functions of, large marine fish shoals.

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REVIEWS
Towards of a firmer explanation of large shoal formation,
maintenance and collective reactions in marine fish
Guillaume Rieucau •Anders Ferno
¨•
Christos C. Ioannou •Nils Olav Handegard
Received: 6 September 2013 / Accepted: 8 August 2014 / Published online: 13 August 2014
Springer International Publishing Switzerland 2014
Abstract Avoiding predation is generally seen as
the most common explanation for why animals
aggregate. However, it remains questionable whether
the existing theory provides a complete explanation of
the functions of large shoals formation in marine
fishes. Here, we consider how well the mechanisms
commonly proposed to explain enhanced safety of
group living prey explain fish shoals reaching very
large sizes. By conceptually re-examining these
mechanisms for large marine shoals, we find little
support from either empirical studies or classical
models. We address first the importance of reassessing
the functional theory with predator-dependent models
and the need to consider factors other than predation to
explain massive fish shoals. Second, we argue that
taking into account the interplay between ultimate
benefits and proximate perspectives is a key step in
understanding large fish shoals in marine ecosystems.
Third, we present the growing body of evidence from
field studies that identify shoal internal structure as an
important feature for how large shoals can form,
maintain and react as a coordinated unit to external
stimuli. In particular, we consider a mechanistic basis
of local rules of interaction for group formation and
collective dynamic properties that can account for
groups reaching very large sizes. Recent research in
collective animal behaviour has shifted focus from the
importance of global properties (group size) to local
properties (local density and information transfer). In
contrast to studies of fish shoals in the laboratory, the
difficulty in measuring behaviour in large shoals in
marine systems remains a major constraint to further
work. Advances in acoustical observation have shown
the greatest potential to provide data that can link
proximate mechanisms in, and ultimate functions of,
large marine fish shoals.
Keywords Large marine fish aggregations 
Shoaling behaviour Collective behaviour functional
explanations Local properties Shoal internal
structure
Introduction
Aquatic ecosystems can host spectacular massive
aggregations of micro- and macro-organisms where,
for instance, some pelagic fish species are able to reach
shoal sizes up to several million individuals (Misund
1993; Makris et al. 2006). By its complexity and
G. Rieucau (&)N. O. Handegard
Institute of Marine Research, P.O. Box 1870,
5817 Nordnes, Bergen, Norway
e-mail: guillaume.rieucau@imr.no
A. Ferno
¨
Department of Biology, University of Bergen,
P.O. Box 7800, 5020 Bergen, Norway
C. C. Ioannou
School of Biological Sciences, University of Bristol,
Woodland Road, Bristol BS8 1UG, UK
123
Rev Fish Biol Fisheries (2015) 25:21–37
DOI 10.1007/s11160-014-9367-5

taxonomically widespread nature, animal aggrega-
tions have fascinated and challenged scientists for
decades. Unraveling the mechanisms and functions of
aggregations has been one of the main foci of the study
of animal behaviour (Krause and Ruxton 2002). In
general, reducing predation risk is presented as the
most widely-applicable explanation for why animals
aggregate (Hamilton 1971; Pulliam 1973; McNamara
and Houston 1992; Lima 1995b; Krause and Ruxton
2002; Caro 2005) and is regularly used to explain the
formation of large aggregations observed in marine
fishes (Pitcher and Parrish 1993). However, one
important limitation to a better understanding of why
and how some fish species form large aggregations
remains the challenging task of obtaining accurate
behavioural data in natural conditions. It thus remains
questionable whether the existing ultimate explana-
tions are suitable to ascertain the functions of large
marine fish shoals.
The main objective of our article is not to review the
literature related to group-living behaviour in fishes.
Instead we aim to build a better understanding of how
large shoals form, are maintained, and behave. Firstly,
we revisit the classical ultimate explanations of large
marine shoals; secondly, we integrate results from
in situ research on large shoals of pelagic fish with
recent considerations from research in collective
behaviour. Before starting this exercise, it is necessary
to define the terminology employed throughout our
article such as shoals, schools and, especially what we
mean by ‘massive shoals’. The term ‘aggregation’ will
be used to define any collection of fish that is clumped
in space; this could be due to either active attraction
between individuals or aggregation around a resource.
In contrast, we employ the term ‘shoal’ to refer
specifically to an aggregation of fish presenting a level
of social cohesion (Pitcher 1983). The term ‘school’
will be employed as a specific subset of a fish shoal
where fish present polarized, synchronous swimming
patterns and are equally spaced with between-individ-
ual distances typically not greater than one body size
(Pitcher et al. 1976; Pitcher 1983; Pitcher and Parrish
1993). Yet, it is noteworthy that these well-accepted
heuristic definitions have received recent critics as
they ‘‘…lack precision in terms of quantification’’
(Delcourt and Poncin 2012). If the minimal shoal size
is obviously 2 fish, attempting to clearly define the
concept of ‘‘massive shoal’’ remains a difficult task
and, to date, we are not aware of any published
definition in the scientific literature. Here and there-
after, we will use the expression ‘massive shoals’ or
‘massive schools’ to refer to large-scale shoals or
schools of such a size that any given individual cannot
interact directly with all shoal/school members simul-
taneously due to sensory limitations.
By re-examining the classical mechanisms explain-
ing prey group security and challenging them beyond
the group sizes that they were originally designed to
apply to, we consider how well the ultimate benefits
explain very large marine fish shoals. In particular, we
highlight the current knowledge gap between the
conclusions made by experiments on relative small
fish groups in controlled environments (e.g., tanks)
and information from field studies on large-scale
aggregations of marine fishes. We address the impor-
tance of reassessing the functional theory with pred-
ator-dependent models as well as taking into account
factors other than predation such as foraging or abiotic
factors. A better understanding of massive fish shoals
requires considering the interplay between proximate
mechanisms and ultimate benefits. In particular, we
argue that by combining knowledge from in situ
studies on large pelagic schools that identify the
importance of structural and morphological school
features (Fre
´on et al. 1992,1996; Gerlotto and Paramo
2003; Gerlotto et al. 2004,2006; Paramo et al. 2007)
and developments in the field of collective behaviour
will help identify the whys and hows of massive shoal
formation in marine fishes. There is now a wealth of
evidence from field studies on pelagic fishes that
aspects of shoal structure, such as inter-individual
distance, packing density, internal density heteroge-
neity (e.g., vacuoles and nuclei) and fish polarization
and alignment, are more important in the functioning
of large shoals than simple group size, for example in
how fish collectively and synchronously respond to
external stimuli (e.g., environmental factors and
predation). Recent research in collective animal
behaviour focuses on local inter-individual interac-
tions to give a mechanistic basis for how animals
groups are formed, maintained and move. This
framework can account for groups reaching sizes far
beyond the perceptual limit of any group member, i.e.,
a ‘massive school’. As group size increases over
orders of magnitude, a conceptual shift from the
importance of global properties (e.g., group size) to
local properties (e.g., local density or information
transfer) in explaining both the behaviour of
22 Rev Fish Biol Fisheries (2015) 25:21–37
123

individuals within groups and their risk of predation
can be identified.
Risk protection in group-living prey: is
the traditional view applicable to massive shoals?
Many authors have identified shoaling behaviour as an
adaptation to avoid predation (Magurran 1986;
Pitcher and Parrish 1993). Over the years, various
theoretical models have been developed to formulate
predictions on the security advantages of animal
grouping (Hamilton 1971; Pulliam 1973; Bertram
1978; Turner and Pitcher 1986; Dehn 1990; Bednek-
off and Lima 1998). It has been often argued that
grouping offers a combination of several anti-preda-
tory mechanisms to social prey such as a greater
power of predator detection through collective vigi-
lance (Lima and Dill 1990; Magurran 1990; Lima
1995a,b), a numerical dilution of risk (Foster and
Treherne 1981; Ioannou et al. 2011a) and reduced
predator’s efficiency due to a confusion effect (Miller
1922; Landeau and Terborgh 1986; Krakauer 1995;
Ioannou et al. 2008) and/or coordinated evasion
(Magurran and Pitcher 1987). An increase in an
individual prey’s safety as group size increases is
commonly reported in various taxa; the classical
group size effect (Lima 1995a; Krause and Ruxton
2002; Caro 2005). As group size increases, prey
benefit from an enhanced safety allowing them to
reduce their individual effort in anti-predator behav-
iour (e.g., individual level of vigilance) without
increasing their vulnerability. As they experience a
reduced predation risk, group-living prey can reinvest
time and effort saved in anti-predator behaviour into
other fitness enhancing activities as foraging, parental
caring or searching for reproductive partners.
Despite this research, there are still important gaps
in our basic knowledge of the functions of massive
groups. This shortcoming mostly arises because the
predictions of the classical theoretical models have
only been empirically validated for small to medium
prey group sizes, mainly in controlled laboratory
settings. As a consequence, when applying these
theoretical frameworks to massive marine fish aggre-
gations only extrapolation is possible. In this section,
we examine how well the different mechanisms
proposed to explain enhanced safety of group-living
prey are likely to apply to large-scale fish shoals.
The dilution of risk
Once a prey group has been detected by a predator,
prey benefit from a reduced risk of predation from the
direct presence of their congeners. This numerical
dilution of risk (Bertram 1978) is generally considered
an important anti-predator mechanism that provides
safety benefits to group-living prey. The concept
(Cresswell 1994; Bednekoff and Lima 1998) is based
on the simple assumption that, at a given time, only
one group member is preyed upon during a solitary
predator’s attack. In this specific situation, an individ-
ual’s probability to survive an attack can be numer-
ically expressed by (N -1)/N where N represents the
size of the group threatened. However, we see some
issues with arguing unswervingly that risk dilution
confers security improvement to prey when transposed
to large size aggregations.
When parameterized for large group sizes, the risk
dilution model predicts that an individual’s survival
probability would rapidly pass 95 % (corresponding to
a group of 97 individuals) but any further increases of
group size would not provide supplemental advanta-
ges in the absolute level of security. It is important to
note that the maximal group size parameterized,
10,000, is still several orders of magnitude lower
than, for example, aggregations size of Atlantic
herring (Clupea harengus) during winter periods
(Misund 1993). Therefore, above a certain shoal size
the dilution effect is unlikely to solely explain these
observed large shoals.
When shoaling, fish may not only face predation
pressure from solitary predators killing only one
individual per attack, but may also be preyed upon
by predators in social groups employing cooperative
hunting strategies or large predators able to catch
several prey during a strike. For instance, some whale
species are able to engulf a large number of prey at
once and sometimes even the entire prey shoal
(Goldbogen et al. 2006,2008). When parameterized
for large group sizes and accounting for different
predators’ hunting strategies (number of prey caught
per attack), the risk dilution model predicts that the
survival probability of an individual attacked by a
predator taking several prey during an attack would
not pass 95 % until a higher number of individuals
were caught. In addition, it appears that a very large
group size would still not provide supplemental
benefits in security (Fig. 1).
Rev Fish Biol Fisheries (2015) 25:21–37 23
123

Furthermore, many marine predators use hunting
strategies that take advantage of the aggregative
behaviour of their prey (Pitcher and Parrish 1993)by
forcing shoals to become denser to ensure a better
catch efficiency during a single attack (Jonsga
˚rd 1966;
Nøttestad et al. 2002) or multiple successive attacks.
In this case, large shoals become great foraging
opportunities for these predators where the high
density of prey located in a particular place reduces
the search effort or time required to locate the next
foraging item. Whilst aggregating in large groups is a
successful anti-predator strategy to relax prey from the
predation pressure exerted by solitary predators, it
may also be a deadly trap for high density fish
aggregations when facing large predators that can
capture a part (e.g., killer whales) of or the entire shoal
during an attack (e.g., baleen whales and human
fishing fleets using trawls and purse seine technology).
Surprisingly, general knowledge about the survival
patterns of aggregated prey when the predator(s) can
consume more than one individual is very limited.
Connell (2000) experimentally varied group size in
juvenile Acanthochromis polyacanthus (Pomacentri-
dae) while manipulating predator exposure in a lagoon
environment using a two-treatment design: in one
treatment prey were threatened by large predatory fish
able to eat several prey during a single attack, and in a
second treatment those predators were removed using
exclusion cages. This tested the hypothesis that
predation pressure from large fish predators on
A.polyacanthus increases with shoal size inducing a
decline in survival in larger shoals. Connell (2000)
found a greater per capita mortality in large prey
groups compared to small ones, challenging the
traditional ‘‘safety in number’’ principle. Shoaling
may not enhance safety at all times, particularly when
more than one prey are killed during a single strike.
When facing large predators able to consume prey
in large numbers, a safer strategy could be to disperse
rather than to aggregate, but to date empirical evidence
supporting this idea is lacking. In marine ecosystems,
shoaling fish may experience predation pressure from
a large spectrum of predator species using different
hunting modes, and shoaling could enhance security in
most cases. It has been proposed that benefits of group
size depend both on predator types and hunting modes
(Cresswell and Quinn 2010). The development of a
predator-dependent theoretical framework that incor-
porates predators’ attack efficiency (e.g., number of
prey killed during a strike), hunting strategy (e.g.,
solitary or in cooperating groups) (Lima 2002; Cres-
swell and Quinn 2010) and is informed by the results
of direct experiments on large fish aggregations in
natural conditions is therefore warranted.
Risk abatement and predator avoidance
Safety of aggregated prey may be related to the
interplay of predator avoidance and the numerical
dilution of risk (Turner and Pitcher 1986; Inman and
Krebs 1987). Massive fish shoals generally occupy an
important volume in the environment making them
more conspicuous for predators against the open
marine background (Pitcher and Parrish 1993), espe-
cially for predators detecting prey items visually or by
echo-location. The absence of sensory barriers in the
Fig. 1 The Norwegian Spring Spawning herring (C. harengus) example: the ‘‘predator-dependent risk dilution model’’ parameterized
for large size aggregations (up to 100,000 fish) and accounting for different predators’ hunting strategies
24 Rev Fish Biol Fisheries (2015) 25:21–37
123

oceanic pelagic zone (as well as refuge for prey) can
make it easier to localize prey aggregations than
solitary prey. Turner and Pitcher (1986) presented the
attack abatement model that shows that despite an
animal group being more likely to be detected by a
predator than a solitary prey individual (Pitcher and
Parrish 1993), aggregated individuals may neverthe-
less reach the security benefits of grouping from a
decrease in the individual risk of being captured,
assuming a fixed number of prey is taken per detection
(Ioannou and Krause 2008).
To date, most studies addressing this question have
focused on solitary foragers, and the general pattern
emerges that prey evolve towards clumped distribu-
tions, a response that reduces the overall efficiency of
predator searching (Ioannou et al. 2011a). However,
predators in large groups have been reported to locate
food patches more quickly than fish in smaller groups
(Pitcher et al. 1982). Cooperative social hunters are
expected to be more efficient locating prey as they can
combine their search efforts. However, social foraging
may not always improve search efficiency (Giraldeau
and Beauchamp 1999; Giraldeau and Caraco 2000).
This is especially true if some individuals use the
search effort of their companions at their advantage; a
situation akin to the game theoretic producer/scroun-
ger scenario (Barnard and Sibly 1981; Parker 1984;
Barta et al. 1997; Giraldeau and Caraco 2000). Using
simulations based on genetic algorithms, Hamblin
et al. (2010) explored the evolution of a prey clumping
strategy when preyed upon by non-social or social
predators (which include producers searching for prey
by themselves and scroungers joining the discoveries
of others). The study demonstrated a strong selection
for high ‘‘clumpiness’’ (sensus Hamblin et al. 2010)
for prey under the pressure of non-social predators and
conversely low ‘‘clumpiness’’ for individuals preyed
upon by social predators. In both cases, prey survival
was improved by inducing higher rates of scrounging
and reducing predator search efficiency. Conse-
quently, these results call for a firmer re-examination
of the predator avoidance effect while accounting for
the various hunting strategies employed by social
predators.
Position within a shoal and the selfish herd
An individual’s position within a group affects its risk
of predation. A great deal of work on differential
predation risk within prey aggregations in various taxa
shows that individuals at the periphery of a group
suffer greater predation risk compared to individuals
at the group center (Rayor and Uetz 1990; Colagross
and Cockburn 1993; Krause 1994; Krause and Tege-
der 1994; Barber and Huntingford 1996; Bumann et al.
1997; Stankowich 2003; Morrell and Romey 2008).
However, even though the majority of empirical
studies exploring differential predation risk within
prey groups reported a positive gradient of risk from
the group center to its edge, several studies on fish
aggregations nevertheless challenged this result (Par-
rish 1989; Parrish et al. 1989). Parrish (1989) found an
opposite gradient of risk in shoals of Atlantic silver-
sides (Menidia menidia), with fish that occupied more
central positions suffering greater predation risk from
predatory black sea bass (Centropristis striata)
whereas silversides located at the periphery of the
shoal were targeted less often by predators. Therefore,
it seems important to consider predator hunting
strategies (e.g., original position of the attack, prey
preference) during predator–prey interactions (Lima
2002) for a better understanding of the centre-edge
effect within animal aggregations.
Within an aggregation, prey should attempt to seek
positions that minimize their chance of being the
victims of an attack. Gregarious animals can enjoy a
reduced predation risk by minimizing the space
around them that is closer to them than any other
prey, their ‘‘domain of danger’’, assuming that preda-
tors can appear anywhere and attack the nearest prey.
This ‘‘selfish herd’’ model, formulated by Hamilton
(1971), allows individuals to reduce their risk of being
killed by a predator by simply moving toward their
neighbours, selfishly interposing neighbours between
the predator and themselves. This results in group
formation and a compaction of groups (Hamilton
1971; Vine 1971; Viscido et al. 2002). Although the
movement rules leading to the group compaction
predicted by Hamilton (1971)’s model have been
theoretically challenged over the years (Viscido et al.
2002; Reluga and Viscido 2005; Morrell et al. 2011),
in nature animal groups becoming denser once
alarmed is a widespread observed phenomenon across
many animal species including fish (Parrish 1989),
supporting the predictions of the selfish herd model
(Hamilton 1971).
However, this common view of differential safety
related to the spatial distribution of individuals within
Rev Fish Biol Fisheries (2015) 25:21–37 25
123

an aggregation can be undermined when transposed to
large fish shoal systems. In the wild, a common
response to increased predation risk exhibited by
schooling pelagic fish is a reduction of inter-fish
distances and greater fish polarization levels (Fre
´on
et al. 1992; Gerlotto et al. 2006). This particular anti-
predatory strategy, increasing school cohesion and
density, nevertheless favours the foraging success of
large marine mammal predators (Jonsga
˚rd 1966;
Nøttestad et al. 2002). Again, predator foraging
strategies can alter the relationship between social
behaviour and risk. A recent study on the manipulation
of the aggregative behaviour of hosts (Artemia sp.) by
parasites (Flamingolepis liguloides,Anostracospora
rigaudi and Enterocytospora artemia) showed that the
parasites induce host swarms to become denser,
increasing the catch efficiency of filter-feeding avian
predators (Greater Flamingos, Phoenicopterus ro-
seus), and therefore their transmission to their final
hosts (Rode et al. 2013). It appears then that in some
cases an increase in group size may not necessarily
translate to an increase in security for aggregated
individuals. This suggests that a reduction of the
‘‘domain of danger’’ through group compaction may
not always enhance prey safety but on the contrary
favor predators foraging success.
Collective detection and information transfer
Sharing information about approaching predators among
group members is a critical component of safety in fish
shoals. Individuals may reduce the risk of predation as
group size increases through a greater detection power of
the group provided by the increased number of individ-
uals available to detect approaching predators: the
‘‘many-eyes hypothesis’’ (Elgar 1989; Lima and Dill
1990;Lima1995b). The collective vigilance models
generally assume that a whole group will be unambig-
uously risk aware as soon as one individual detects a
threat (Pulliam 1973;Dehn1990; Lima and Dill 1990;
McNamara and Houston 1992). Even if supported by
empirical evidence from small animal aggregations, the
‘‘one aware, all aware’’ principle behind collective
detection remains to be explored empirically for large-
scale animal aggregations.
Dehn (1990) developed a series of models predicting
survival probability of group-living prey with the aim of
investigating the specific contribution of risk dilution
and collective detection with an increase of the animals’
group sizes. Amongst these models, the ‘‘security
model’’ predicts that animals gain security benefits with
increasing group size through the combination of risk
dilution and collective detection. Later, several studies
employed the security model to explore vigilance
behaviour of free-ranging gregarious species showing
its ability to adequately explain the observed vigilance
patterns (Rieucau and Martin 2008; Rieucau et al. 2012).
However, the size of the groupsunder investigation was
relatively low (never exceeding 50 individuals). When
challenged by large group sizes, the ‘‘security model’’,
when considering one predator catching only one prey,
predicts that above a moderate group size, approxi-
mately 95 individuals, prey survival probability passes
over 95 % with only limited security enhancement for
groups beyond this size.
It is becoming increasingly clear that rapid infor-
mation transfer is vital for many group-living animals.
The process of information transmission in shoals is
thought to affect the dynamics and behaviour of shoals
in natural conditions (Gerlotto et al. 2006; Handegard
et al. 2012). For instance, Handegard et al. (2012)
demonstrated that coordinated predatory sea trouts
(Cynoscion nebulosus) use an attack strategy that
forces prey shoals (juvenile Gulf menhaden, Brevoor-
tia patronus) to split, reducing the shoals’ cohesion
and thus disrupting information transfer within the
shoal and thereby increasing predators’ catch success.
The principal requirement for an efficient transmission
of information is that the information is conveyed
rapidly among all group members before the attack
regardless of their positions in the group. The speed of
transmission through the group can exceed the speed
of an approaching predator: the ‘‘Trafalgar effect’’ as
demonstrated by Treherne and Foster (1981). Sudden
changes in swimming speed or direction from risk-
aware fish can inform other individuals of the threat.
Then, the speed at which information spreads through
the shoal can outpace the swimming speed of fish
ensuring a rapid propagation of predator cues improv-
ing the safety of all group members (e.g. ‘‘waves of
agitation’’ Radakov 1973, Treherne and Foster 1981).
The transmission of detection information through a
group can be affected by the structure of the aggre-
gation (Lima and Zollner 1996; Proctor et al. 2003),
warning signals specificities (Beauchamp and Ruxton
2007), or characteristics of the environment such as
water turbidity (Abrahams and Kattenfeld 1997)or
water flow (Chicoli et al. 2014). For instance, water
26 Rev Fish Biol Fisheries (2015) 25:21–37
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turbidity can alter the transmission of visual informa-
tion in fish shoals (Abrahams and Kattenfeld 1997),
with fish not directly responding to the threat being
less likely to observe the anti-predatory behaviours of
risk-aware companions, reducing their probability to
survive an attack.
Although there is evidence that anti-predator reac-
tions of fish can propagate rapidly across large shoals,
understanding how information spreads in shoals
remains a central challenge. Numerous studies have
examined the mechanisms of long-range information
transfer in animal groups (Radakov 1973; Gerlotto
et al. 2006; Ballerini et al. 2008; Makris et al. 2009;
Cavagna et al. 2010; Bialek et al. 2012; Strandburg-
Peshkin et al. 2013). Waves of agitation have been
proposed as a possible mechanism for how massive
shoals can react collectively to external stimuli
(Radakov 1973). Radakov (1973) first experimentally
demonstrated the process of waves of agitation in
laboratory settings on relatively small shoals (300
individuals), and recent field studies have observed
and quantified such waves of agitation directly in free-
ranging shoals (Axelsen et al. 2001; Gerlotto et al.
2006; Makris et al. 2009). For instance, Gerlotto et al.
(2006) found, using multibeam sonar, that the average
speed at which waves of agitation crossed schools of
anchovies (Engraulis ringens) was 24 times faster than
the average schools speed. A key result from these
in situ studies is that information can be conveyed
rapidly and effectively, with no loss of informative
content (Axelsen et al. 2001), over great distance size,
and importantly regardless of the shoal size.
Several field studies have highlighted the impor-
tance of shoal internal organization on the transmis-
sion of information among fish (Fre
´on et al. 1992;
Freon et al. 1993; Fre
´on et al. 1996; Axelsen et al.
2001; Gerlotto and Paramo 2003; Soria et al. 2003;
Gerlotto et al. 2004; Makris et al. 2009; Paramo et al.
2010). Variations in shoal internal structure (e.g.,
inter-fish distances, polarization and alignment levels
between neighbouring fish) are common in pelagic fish
exposed to the risk of predation or changes in
environmental factors (Fre
´on et al. 1992; Misund
1993; Ferno
¨et al. 1998; Axelsen et al. 2000). Shoal
structural flexibility is considered as an adaptation
improving information transfer among school mem-
bers (Axelsen et al. 2001; Gerlotto and Paramo 2003;
Gerlotto et al. 2006; Makris et al. 2009). The internal
structure of massive Peruvian anchovy schools
changed after the passage of a first wave of agitation
in response to an attack from sea lions (Arctocephalus
australis and Otaria byronia), with fish becoming
more homogenously distributed (Gerlotto et al. 2006).
This indicates that anchovies adopted spatial organi-
zation that would enhance the propagation of infor-
mation during subsequent waves of agitation, and
ultimately the efficiency of their collective evasive
reactions towards predators. In particular, high
degrees of polarization and alignment between neigh-
bours fish are thought to enhance shoal cohesive
structure and facilitate an effective information prop-
agation (Viscido et al. 2005,2007; Herbert-Read et al.
2011; Ioannou et al. 2011b). Atlantic herring can
regain their pre-exposure level of alignment extremely
rapidly (\1 s) after being exposed to an artificial
stimulus, demonstrating the importance of aligned
swimming in schooling fish (Marras et al. 2012). Shoal
internal structure appears to be a key component that
needs to be considered to better understand the
reactions of shoals’ to external stimuli and predators,
as the security benefits from collective detection
cannot be fully explained by simply looking at the
number of individuals shoaling together.
Confusion effect, coordinated escapes and shoal
maneuvers
Cognitive constraints on information processing can
reduce the targeting efficiency of predators as they
attack multiple prey, reducing risk for prey in groups
(Tosh et al. 2006; Ioannou et al. 2008). To overcome
the increased difficulty of selecting and successfully
targeting an individual prey item from many, predators
can reduce vigilance for their own predators (Milinski
1984), increase the time taken to make an attack
(Milinski 1977a), and/or shift attacks to prey in smaller
groups or on the edge of the group (Milinski 1977b).
The result is an increased safety for prey that join and
stay with large groups. However, as was discussed
previously with regards to the dilution effect, predators
that do not rely on targeting single individuals, such as
Great Flamingos which filter feed (Rode et al. 2013)or
baleen whales, are unlikely to suffer from a confusion
effect and instead increase their feeding efficiency
when prey aggregate. A predators’ experience with
large prey groups can reduce the strength of the
confusion effect (Tosh 2011), suggesting a frequency-
dependent effect. Prey movement is generally thought
Rev Fish Biol Fisheries (2015) 25:21–37 27
123

to be required for the confusion effect, but the
coordinated movements seen in fish aggregations and
other prey groups such as European starlings (Sturnus
vulgaris) (Cavagna et al. 2010) are not necessary to
induce the effect (Ruxton et al. 2007; Ioannou et al.
2012). Thus, the confusion effect is likely to apply to
most fish shoals irrespective of the degree of coordi-
nated motion. It is likely, however, that the coordinated
responses seen in fish shoals as directed responses to
predators’ attacks, e.g., splitting and joining behind the
predator or the ‘‘fountain effect’’ (Major 1978; Ma-
gurran and Pitcher 1987; Handegard et al. 2012),
increases predatory confusion as well as social infor-
mation transfer and a selfish herd effect. There will of
course be a minimum number of fish in a school
required to perform these coordinated responses,
suggesting that the relationship between group size
and the degree of confusion will not be simple (e.g.,
increasingly sharply at a threshold number of prey
before saturating at large group sizes).
The confusion effect is produced by a cognitive
overload of the predator’s sensory system (Tosh et al.
2006). As prey group size increases, it becomes
increasingly likely that only a subset of the group is
visible to the predator, especially when the predator is
close to prey (Ioannou et al. 2009). In aquatic systems
where water turbidity can substantially reduce visual
range, this could occur at relatively small group sizes.
The degree of confusion would thus be related to the
number of prey visible in the predator’s visual field
(i.e., the local density of prey), and not the total group
size. In support of this hypothesis, Ioannou et al.
(2009) demonstrated that targeting accuracy of three-
spined sticklebacks (Gasterosteus aculeatus) was
related to the density of other prey close to the target
individual, rather than a larger-scale measure of
density that included all prey individuals in the group.
To date, no study has explicitly tested whether the
confusion effect is affected more by local density than
overall group size in large groups of prey, and it is
highly unlikely that individual predators can see all
prey in groups that can exceed many kilometers in size
(Makris et al. 2006).
The need to consider factors other than predation
Apart from anti-predatory behaviour, fish are also
engaged in other fitness enhancing activities where
group size may influence performance. Within the
same species, variability in both shoal size and
external shape are regularly observed in marine
systems and generally explained by the actions of
several abiotic and biotic factors. For example, in the
North Sea, a great variability in intra-specific shoal
size of herring, saithe (Pollachius virens), and sprat
(Sprattus sprattus) has been reported (Misund 1993).
Although predation is seen as the main driver for the
evolution of group behaviour, factors other than
predation can be identified to explain the formation
of massive shoals in marine fishes (Parrish 1991;
Pitcher and Parrish 1993), and the intra-specific
differences in shoal shape and structure (e.g., diffuse
layers or dense schools). Among these factors, the
most commonly cited are geographic differences
(Misund 1993), vertical distribution and migration in
the water column (Axelsen et al. 2000), seasonality
(Nøttestad et al. 1996), diel cycle and light intensity
(Skaret et al. 2003), reproduction (synchronous
spawning) (Axelsen et al. 2000), reduced oxygen
levels inside dense shoals (Dommasnes et al. 1994;
Brierley and Cox 2010), and energetic requirements or
motivational state (Langa
˚rd et al. 2014).
Locating resources is critical for fish undertaking
long distance migrations (Makris et al. 2009) where
navigating to a suitable habitat in an energetically
efficient way is crucial. There is evidence that
schooling fish and other migrating animals can orient
more accurately in larger groups (Quinn and Fresh
1984) because different individual migration tenden-
cies or errors in gradient following are averaged
resulting in a more accurate estimate of the correct
destination (the ‘‘many wrongs’’ principle: Simons
2004, see also Gru
¨nbaum 1998; Torney et al. 2009).
Such a positive effect of collective behaviour would,
however, be expected to saturate above a certain
number of individuals. In a recent laboratory study
using golden shiners (Notemigonus crysoleucas),
Berdahl et al. (2013) demonstrated that shoals were
increasingly able to track gradients of darkness as
group size increased within a range of 1–256 fish and
that individuals have only a poor ability to track the
gradient when solitary. Both of these results suggest
that the advantage of grouping is more robust and
general than the ‘‘many wrongs’’ principle as this is
expected to saturate at relatively small group sizes.
Fish also seem to rely on experienced group members
during group movements (Corten 1999), and in a large
28 Rev Fish Biol Fisheries (2015) 25:21–37
123

group there is a greater probability that at least some
individuals know the way. A certain number (Couzin
et al. 2005) or proportion (Huse et al. 2002)of
experienced fish seem to be required to navigate or
maintain traditional migration routes.
Foraging is a particularly important activity to be
considered in a thorough examination of large shoal
sizes. Empirical evidence suggests that a group of fish
(up to 20 individuals) locates food faster than solitary
foragers, and a larger group is more effective than a
small group (Pitcher et al. 1982). However, the benefit
of reduced search time is expected to reach an
asymptote fairly quickly as group size increases
(Pulliam and Caraco 1984). Competition for food
appears as the major cost of shoal membership
(Pitcher and Parrish 1993), and for large groups the
ratio between the benefit and cost is rapidly reduced by
increasing group size since the benefit stays the same
while competition is assumed to increase continually.
Smaller, less cohesive shoals have a reduced overlap
of perceptive field resulting in less competition and
less interference of individual feeding acts (Blaxter
1985).
Fish also have to overcome the hydrodynamic drag
from the water. Schooling may offer hydrodynamic
advantages as it may reduce energy costs as the fish
can stay in the slipstream of another (Weihs 1973;
Sfakiotakis et al. 1999; Hemelrijk et al. 2014). For
instance, rainbow trout utilize vortices when swim-
ming in strong water currents (Liao et al. 2003).
However, the hydrodynamic advantages of schooling
are debated with some species not swimming in the
optimal spatial positions to minimize drag (Partridge
and Pitcher 1979). While testing empirically the
hydrodynamic effects in schooling fish remains a
difficult task, the recent development of computer
models considering complex hydrodynamic effects of
fish swimming, such as viscosity or interactions
among wakes and individuals (Hemelrijk et al.
2014), allows researchers to better grasp the energetic
benefits of swimming in schools. Additionally,
although the fish can divide the costs by changing
position in the school over time, it remains untested
whether potential positive hydrodynamic effects will
increase above a moderate shoal size.
Parasites are believed to constitute a very serious
threat for group-living fish (Barber and Rushbrook
2008). An increased group size gives, under some
conditions, protection from parasites by a dilution of
risk and by an increased chance of the parasites being
eaten by the predatory fish (Poulin and FitzGerald
1989). However, here again this has only been clearly
demonstrated for small to moderate group sizes (up to
20 fish).
In conclusion, with regard to factors other than
predation it is unlikely than fish benefit significantly
by staying in shoals above a certain size. The positive
effects of an increase in group size has generally been
demonstrated for a relatively small number of fish in
captivity and strong evidence suggesting that an
increase above a moderate shoal size would provide
any benefits is still lacking.
Constraints in available information
and mechanisms
Traditionally, it has been questioned if an optimal
group size exists under realistic conditions (Sibly
1983; Pulliam and Caraco 1984). However, even if we
assume that there is an optimal shoal size, it is still a
formidable task for fish to stay in a shoal of that size
(Ferno
¨et al. 1998). Due to variations in abundance and
type of predators and resources, the theoretically
optimal shoal size would be expected to show large
fluctuations, often over short time intervals. A
dynamic interplay between the threat constituted by
different predators with various hunting strategies
together with variations in abundance and patchiness
of resources at different scales should make it
practically impossible for an individual fish to be, at
all times, in a shoal with the optimal number of
conspecifics. To be in a shoal of the optimal size
averaged over longer time periods is a challenge that
would demand advanced perceptive and cognitive
skills. Nevertheless, we can attempt to depict the set of
decisions that fish in shoals would take to accomplish
such adjustments. First, fish would have to monitor the
average situation they experience to determine their
mean preferred shoal size. Further, to adjust to this set
value, fish would need to estimate their present shoal
size. In theory, it would be possible that fish could get a
rough estimate of current shoal size based on, for
instance, the number of times they are in contact with
the edge of the aggregation. Finally, between-individ-
ual differences must be accounted for. What consti-
tutes the optimal shoal size for one individual is not
necessary the right one for another individual in a
Rev Fish Biol Fisheries (2015) 25:21–37 29
123

different state, for example, an individual with higher
energetic demands.
Given these constraints in the perceptive, cognitive
and group size-adjusting mechanisms, it is not realistic
to expect fish to stay in groups of the theoretically
optimal size. It becomes conceptually difficult to
identify mechanisms that would permit shoal size to be
reasonably well adjusted to the prevailing conditions.
However, this does not rule out that some variations in
shoal size seem clearly adaptive. Several studies with
small numbers of fish have shown that hungrier fish
spend less time with larger groups of conspecifics than
do well-fed individuals (Barber and Huntingford
1995; Reebs and Saulnier 1997), and non-feeding
pelagic fish shoals have been observed to be larger
than feeding shoals (Nøttestad et al. 1996). We will
now consider how fish could accomplish such struc-
tural adjustments in shoals.
Local rules explaining the existence and behaviour
of massive fish shoals
In contrast to the functional discussion above on the
reasons why fish form shoals of a particular size,
research on collective behaviour has shifted focus to
the individual local rules of interaction that generate
groups and collective properties (Aoki 1982; Giardina
2008). In this section we advocate that by combining
the results from collective behaviour research and
acoustic observations of oceanic shoals, a more
accurate explanation for the formation, maintenance
and structural and morphological variations of mas-
sive shoals in marine fishes can be provided.
An individual fish does not need an overview of the
composition and behaviour of the shoal it is within at a
particular moment; information that may be costly or
impossible to acquire when shoals are large. Instead
the properties of a shoal are the product of local rules
between neighbouring fish that, via self-organization,
generate behaviour at the group level as an emergent
consequence of individuals’ interactions (Parrish et al.
2002; Vabø and Skaret 2008). Models of collective
behaviour generally make the assumption that indi-
viduals repel one another when they get too close and
otherwise are attracted toward, and/or align their
direction of travel with their neighbours. Despite
seeming over-simplified, these models have been
successful in recreating both distributions of local
properties such as inter-individual spacing (Lukeman
et al. 2010) and global properties (Hemelrijk and
Hildenbrandt 2012). For example, by simply changing
the distance over which individuals align with their
neighbours, Couzin et al. (2002) simulated disordered
swarms, groups milling around an empty core (as often
observed in several pelagic fish species), and highly
aligned, mobile groups (see also Nøttestad et al.
(2004)). Increasingly realistic models based on
attraction-alignment-repulsion in shoals of fish are
also able to recreate empirical observations of shoal
shape and internal structure (Hemelrijk and Hilden-
brandt 2012).
In the past few years, detailed examination of
shoaling behaviour based on large datasets collected in
controlled settings has been possible with advances in
computer tracking and analysis (Katz et al. 2011;
Gautrais et al. 2012). This has been facilitated greatly
by the extensive modeling that has established a
conceptual framework for interactions in groups,
allowing empirical tests of both the models’ assump-
tions and predictions. One important finding from these
studies is that the rules fish use to interact with one
another appear to be qualitatively similar across group
sizes (Katz et al. 2011; Gautrais et al. 2012). In the
study of Tunstrøm et al. (2013), local and global group
properties were examined across a range of group sizes
from 30 to 300 fish in a shallow tank. Although global
properties such as the degree of rotation and time spent
in a disorganized, swarm-like state changed with
increasing group size, local properties (fish speed and
local density) were constant across group sizes and
only affected by the type of shoal formation (swarm,
polarized and milling). This suggests that grouping
behaviour is not directly affected by the total group size
and instead fish regulate local properties that are within
their immediate perceptual range.
Variations in shoal size can thus be explained by
simple individual behavioural rules based on attrac-
tion and repulsion towards near-by fish (Katz et al.
2011) in combination with attraction to external
stimuli like food (Nøttestad et al. 2004). In particular,
Katz et al. (2011) found attraction between individuals
until they have reached a certain inter-fish distance
after which they repel each other. In non-feeding fish
with no other force influencing them, this could result
in larger and larger shoals, as shoals that encounter
each other would have a certain probability to join
because of attraction between near-by fish in different
30 Rev Fish Biol Fisheries (2015) 25:21–37
123

shoals that come into contact. If, however, the fish are
engaged in feeding activities or are strongly motivated
to feed, the relative attraction to conspecifics will then
decrease, resulting in more individualistic behaviour
with increasing inter-fish distances as food level
decreases (Robinson and Pitcher 1989; Sogard and
Olla 1997; Hensor et al. 2003). This should increase
the probability for individuals and groups to come
apart, and the resulting splitting of shoals will reduce
the shoal size. Banded killifish (Fundulus diaphanous)
freely form shoals where size is adjusted in a context-
dependent fashion, forming smaller shoals when
presented with food odour and aggregating in larger
shoals when exposed to chemical alarm cues (Hoare
et al. 2004). Modeling work has demonstrated that a
range of shoal sizes and characteristics can occur by
changing the strength and range of the attraction and
repelling forces between the individual fish (Vabø and
Nøttestad 1997). Hence, by assuming interplay
between these tendencies, it is then possible to develop
a better understanding of how shoal size can be
roughly adjusted to the relative importance of preda-
tion and food.
Individualfish not only have the option to join, stayor
leave a shoal based on the prevailing conditions but may
also influence the shoal density by changing their inter-
fish distances. Variations in shoals density, which are
often observed in pelagic fish (Nøttestad et al. 1996), are
usually explained by changes in the parameter values of
the forces between nearby fish influencing the local
interactions. Such changes in density would enable
individuals within a shoal to rapidly adjust to various
situations without adjusting the number of fish in the
shoal. For instance, although increasing prey density
may increase conspicuousness to a predator (Ioannou
et al. 2009), a more compact shoal should decrease risk
via a stronger confusion effect and more effective
escape maneuvers. Likewise, a shoal can decrease
competition for food or avoid oxygen depletion that
arises at the center of dense aggregations (Dommasnes
et al. 1994; Brierley and Cox 2010) by spreading out
without splitting into smaller groups or by distributing at
depth with more dissolved oxygen. Such behavioural
and structural changes would reduce possible negative
effects associated with massive shoals.
Acoustics surveys, conducted in oceanic systems,
showed that large shoals of sardines, herrings and
anchovies can display a great range of shape and
internal organizations, for example shoal density, fish
positioning or intra-shoal density distribution (Fre
´on
et al. 1992; Gerlotto and Paramo 2003; Gerlotto et al.
2006; Paramo et al. 2007,2010). Several mechanisms
have been identified, such as the ‘‘moving mass
dynamic’’ (Misund 1990) or ‘‘compressing-stretch-
ing-tearing’’ (Fre
´on et al. 1992), to explain variations
in internal organization of a shoal, and in particular its
internal density distribution (Fre
´on et al. 1992; Misund
1993). The compressing-stretching-tearing (CST)
hypothesis (Fre
´on et al. 1992) predicts that inter-fish
distances and polarization level depend on the state of
the environment (e.g., stressed vs. unstressed situa-
tions). Under low stress, shoaling fish should exhibit
more individualist/exploratory behaviour resulting in
greater inter-fish distances and lower polarization until
the shoal would reach its lowest cohesive limit; the
‘‘maximal stretching distance’’ (Fre
´on et al. 1992).
This ‘‘stretching’’ mechanism is used to explain how
vacuoles, i.e., zone with few or no fish, can form in a
shoal as the results of a set of decisions made by each
fish to join or leave their closest neighbours. Con-
versely, when exposed to higher risk, schools should
become denser, with fish getting closer to each other,
exhibiting greater polarization, and closing the vacu-
oles until reaching a ‘‘minimal compressing distance’’
(Fre
´on et al. 1992). An expected result of the
compressing mechanism is the formation of zones of
high fish density inside a shoal, i.e., nuclei (Gerlotto
and Paramo 2003). Nuclei are presented as the
maximal self-organized units of interaction responsi-
ble of shoal cohesion, efficient information flow and
emergence of collective reactions (Gerlotto and Para-
mo 2003; Viscido et al. 2005; Gerlotto et al. 2006). In
wild sardines (Sardinella aurita), shoals are comprised
of several nuclei of which the diameter can reach 10 m
(Gerlotto et al. 2006).
In conclusion, there are obvious parallels between
the attraction–repulsion rule of interaction and the
proposed mechanisms of variation in pelagic shoal
internal organization, reinforcing the idea that forma-
tion of massive shoals in natural conditions can be
mechanistically understood without referring to the
specific shoal size.
Does shoal size still matter?
Evidence accumulating from in situ observations and
experimentation in controlled settings allow us to now
Rev Fish Biol Fisheries (2015) 25:21–37 31
123

tease apart the mechanisms directly involved in large-
scale collective behaviours and formation of massive
shoals. The joint achievements of these two axes of
research have demonstrated the importance of con-
sidering internal organization in the formation of very
large marine shoals and their reactions to external
stimuli such as predators, vessels or other environ-
mental factors.
Strengthening the idea that a shoal’s internal
structure is critically important compared to shoal
size in the case of massive shoals will require the
development of experiments in which internal orga-
nization could be manipulated and collective
responses quantified. Recently, Rieucau et al. (2014)
and (Rieucau et al. in press) explored the collective
evasive reactions of wild caught Norwegian herring by
conducting a series of simulated-predator encounter
experiments in sea cages on schools which matched
the sizes of natural aggregations (*60,000 fish). In
particular, school density, perception of risk and
predator characteristics were manipulated. Using
echosounders and high-resolution imaging sonar, they
demonstrated that the strength of herring collective
avoidance depends on the sensory signature of the
simulated predator and on the school density. For
instance, weaker collective avoidance reactions were
observed in a low density school compared to a denser
school, suggesting that the magnitude of collective
reactions and how efficiently predator-related infor-
mation spreads across a school strongly depend on a
shoal’s internal organisation.
Finally, fish can combine the advantages of being in
a small and large group. As mentioned earlier, shoal
clustering could provide shoals with the option of
rapid size adjustments through splitting and joining
and thus permit flexibility of responses to a dynamic
environment (Mackinson et al. 1999). This may enable
shoals to have effective predator defense whilst
simultaneously receiving foraging benefits associated
with smaller schools. Hence, both changes in density
and keeping close distance to neighbouring shoals
could be alternative mechanisms that in a given
situation could reduce the negative fitness conse-
quences of deviations from the theoretically optimal
shoal size. However, can these simple mechanisms
really explain the existence of massive aggregations of
several millions of fish? In non-feeding shoals there is,
with increasing shoal size, initially an increasing ratio
between benefits and costs resulting in an increased
individual fitness up to a certain shoal size. If the
fitness to stay in shoals above that size remains
relatively constant, then very large shoals will not be
more beneficial than shoals of a moderate size but
neither do they incur any significant disadvantages.
The availability of other shoals in the vicinity may be
restricted. Hence, it could be an advantage to stay in a
somewhat larger shoal that provides a buffer against
such unforeseen events. In addition, splitting can take
place relatively easily when the presence of resources
decreases the cohesion between the fish.
Conclusion
By re-examining the classical functional theory and
the commonly proposed mechanisms that underlie
improved safety of group-living prey (dilution of risk,
predator avoidance, enhanced predator detection,
confusion effect, coordinated evasive maneuvers) for
large group sizes, we advocate that the functional
framework, in its current state, does not adequately
account for the formation of fish shoals reaching very
large sizes. Reassessing the functional theory requires
the development of predator-dependent theoretical
models combined with direct observations and exper-
imentations on large fish shoals to better understand
the ultimate benefits and costs of massive fish
aggregations. In particular, more explicit attention
should be devoted to integrating the large range of
predator types, hunting strategies (e.g., solitary vs.
social, prey preference, original position of the attack)
and attack efficiency (e.g., number of prey catch per
strike) that aggregated prey may encounter.
The collective behaviour framework provides a
mechanistic basis focusing on local rules of interaction
for group formation and collective dynamic properties
that can explain how marine fish form massive
aggregations. Recent research in collective animal
behaviour suggests that the rules of individuals’
interactions are constant across group sizes, explaining
the occurrence of very large aggregations beyond the
perceptual limit of any group member (Kunz and
Hemelrijk 2012). Thus, the further development of a
framework that integrates ultimate and proximate
perspectives would allow the generation of precise
functional and mechanistic predictions to build a firmer
explanation of large shoals in marine fish. In addition,
field studies on pelagic social fishes have accumulated
32 Rev Fish Biol Fisheries (2015) 25:21–37
123

supporting evidence that identify the important role of
internal organization (e.g., packing density, density
heterogeneity, fish position and polarization) to
explain why marine fishes aggregate in massive shoals
and how they collectively react to environmental (e.g.,
abiotic factors and predation) and anthropogenic (e.g.,
fishery gear, vessels) perturbations.
Advances in acoustical and optical observation
technology provide efficient means to precisely quan-
tify large-scale collective behaviours in shoaling fish
in situ. These techniques can be used to address
several of the challenges we face when validating and
refining the behavioural models and to link proximate
mechanisms and ultimate benefits. In particular,
simulation frameworks where different behavioural
patterns are simulated and the corresponding acoustic
signals are predicted (Holmin et al. 2012) provide a
powerful tool to aid the interpretation of the observa-
tions. Fine-scaled prey-predator interactions can be
observed, and changes in anti-predator behaviours as a
function of predator strategy and shoal size could be
assessed. To our knowledge, no other biological
system can be observed across these scales, and the
marine systems are thus well suited to challenge the
existing theoretical models.
We believe that collectively we possess most of the
puzzle’s pieces to explain the evolutionary basis of the
formation of massive shoals. The missing pieces of
knowledge will certainly be found in experimental
studies conducted on wild massive shoals directly in
the open ocean.
Acknowledgments This work was financed by the Norwegian
Research Council (Grant 204229/F20). CCI was supported by a
Leverhulme Trust Early Career Fellowship and a NERC
Independent Research Fellowship. We thank Lise Doksæter,
Olav Rune Godø, Egil Ona, Espen Johnsen for providing us with
helpful comments on this manuscript. We are also grateful to
Graeme Ruxton and Iain Couzin for comments while we were
developing the original idea of this paper.
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