Table Of ContentReference: Bio/. Bull. 2(12: 296-305. (June 2002:
An
Self-Organized Fish Schools: Examination
of Emergent Properties
JULIA K. PARRISH1-2'*, STEVEN V. VISCIDO2. AND DANIEL GRUNBAUM1
' School ofAquatic and Fishery Sciences, Box 355020, University of Washington, Seattle. Washington
98195-5020; ~ Zoologv Department, University ofWashington; and ' School ofOceanography,
University of Washington
Abstract. Heterogeneous, "aggregated" patterns in the framework that synthesizes much ofthis previous work, and
spatial distributions of individuals are almost universal to identify relationships between behavioral parameters and
across living organisms, from bacteriato higher vertebrates. group-level statistics.
Whereas specific features ofaggregations are often visually
striking to human eyes, a heuristic analysis based on human Types of Aggregations
vision is usually not sufficient to answer fundamental ques-
tions about how and why organisms aggregate. What are the Aggregation occurs in the smallest organisms bacte-
individual-level behavioral traits that give rise to these ria and the largest whales and spans virtually the en-
features? When qualitatively similar spatial patterns arise tire extant diversity of taxon, habitat, trophic level, life-
from purely physical mechanisms, are these patterns in history strategy, degree of mobility, and many other
organisms biologically significant, or are they simply epi- biological characteristics (Fairish and Edelstein-Keshet,
phenomenu that are likely characteristics of any set of 1999; Camazine et ai, 2001). Physical aggregation can be
interacting autonomous individuals'* If specific features of regarded as part ofa continuum in group integration. At one
spatial aggregations do confer advantages or disadvantages end ofthis continuum are territorial animals with little need
in the fitness ofgroup members, how hasevolution operated to engage in information transfer and no need for group
to shape individual behavior in balancing costs and benefits structure. At the other end are highly integrated, long-term
at the individual and group levels? Mathematical models of associations between individuals that know and perhaps
social behaviors such as schooling in fishes provide a prom- are even related to other members of the group, and in
ising avenue to address some ofthese questions. However, which members can potentially have high rates ofdirect and
the literature on schooling models has lacked a common indirect information exchange. Honeybee hives, cetacean
framework to objectively and quantitatively characterize pods, and human communities are examples ofthese highly
relationships between individual-level behaviors and group- integrated groups (Wilson, 1975). In these systems, estab-
level patterns. In this paper, we briefly survey similarities lished pathways of long-term communication between
and differences in behavioral algorithms and aggregation known individuals (clones, siblings, reciprocating group
statistics among existing schooling models. We present members), or at predetermined locations (the hive, the calv-
preliminary results of our efforts to develop a modeling ing grounds, the dinner table), may supplement immediate
sensory contact. Thus, the members remain part of the
*To whom correspondence should be addressed. E-rmiil: |pnrnxh< "group" even while they range widely in space. In these
u.washington.edu dispersed groups, coordinated function can be maintainedas
This paper was originally presented at a workshop titled The Limit-, in long as the necessary information is transferred between
Self-OrganizationinBiuln^icnlSmemx.Theworkshop,whichwasheldat group members (<'.#., the sensory integration systems of
the J. Erik Jnnsson Center ofthe National Academy ofSciences, Woods Morris and Schilt. 1988; Schilt and Morris, 1997). though
tHoorleA.dvMaasnscaecdhuSsteutdtise,sfirnotmhe11S-p1a3ceMLaiyfe20S0c1ie,nwceassastpothnesoMraerdinhey tBhieolCoegnitcaelr distance between interacting components inevitably affects
Laboratory, and funded by the National Aeronautics and Space Adminis- the evolution and stability of emergent group properties
tration under Cooperative Agreement NCC 2-896. (Hillier and Hanson, 1990; Latane et al., 1995).
246
SELF-ORGANIZED FISH SCHOOLS 297
Between these extremes of group integration are what ena, and to more explicitly and mechanistically describe the
could he considered "prototypical" animal aggregations links between individual behaviors and group pattern.
herds, swarms, flocks, and schools. Within the fishes, over Dynamic patterns and movement are necessary charac-
50% of species school that is. display synchronous and teristics of many biological aggregations, and are perhaps
coordinated movement at some point in their life histories better criteria to distinguish adaptive responses from epi-
(Shaw, 1978), and an unknown additional numberaggregate phenomena. For example, tish schools display complex
more coarsely. Prototypical aggregations exhibit coordi- emergent properties such as coordinated motion and di-
nated motion, but group members are generally unrelated rected activity. Compression, hourglass, vacuole. fountain,
and never develop lasting relationships (in the game-theo- and flash expansion (Fig. 2; Pitcher and Parrish, 1993) are
retic, "tit-for-tat" sense) with other members. Many ofthese all maneuvers that minimize predatory risk only ifall mem-
groups are extremely large (e.g.. a school ot a billion bers perform them correctly (e.g.. Fairish, 1989). Parabolic
herring). Individuals in such groups interact with a neigh- formations in tuna schools may allow cooperative hunting
borhood ofother members, but those may represent a van- advantages (Partridge ct ai. 1983). These emergent group
ishingly small fraction of the group as a whole. This sug- properties appear to have readily apparent biological inter-
geststhat mechanisms which maximize information transfer pretations, and physical analogs may be harder to find.
among individuals could be evolutionarily beneficial. One However, these dynamic group properties clearly confer
example ofthis is a repeated arrangement within the group. more evolutionary advantages under some circumstances
reminiscent ofcrystal lattices, in which individuals assume than others (e.g.. evading small predators that target indi-
preferred positions and orientations relative to their neigh- viduals while becoming targets for large predators that
bors. Such arrangements could, forexample, maximize sen- target groups; Parrish. 1993). Furthermore, the key evolu-
sory contact between members in such as way as to reflect tionary question remains: do these behaviors involve trade-
ambient conditions, and the organisms' predominant sen- offs between short-term gain for the individual and long-
sory systems, morphology, etc. (Parrish. 1992; Parrish and term functioning of the group? If so, what is the
Edelstein-Keshet, 2000). evolutionary context in which selection for these behaviors
We can characterize possible behavioral adaptations in occurs?
members of these groups on at least two levels: ( 1 ) short-
term reactions to modify position with respect to immediate Traffic Rules
neighbors; and (2) behavioral responses that do not neces-
sarily improve position relative to immediate neighbors but Assuming structure is advantageous, how is it main-
that contribute to group-level characteristics that ultimately tained? Laboratory and field attempts to address this ques-
benefit the individual by benefiting the group. These group- tion in fish schools havebeen limited (Partridge and Pitcher.
level adaptations are among the most fascinating and the 1980; Aoki el ai. 1986; Parrish and Turchin, 1997). in part
most difficult to assess aspects of animal aggregations. because obtaining three-dimensional trajectories on specific
individuals for a relevant period of time is difficult. Data
Pattern versus Function that do exist are typically from highly artificial conditions
(e.g.. relatively small schools in highly lit still-water tanks;
Human perception tends to recognize attributes of the Parrish and Turchin, 1997). Three-dimensional tracking
whole: an even density profile, polarity, distinct edges, or techniques have not yet advanced to the stage where it is
specific shape. While it is tempting to assume that conspic- feasible to observe large schools (i.e., over 10), in three
uous features of biological aggregations are somehow ben- dimensions, over long times (i.e.. for more than seconds).
eficial, the existence of qualitatively similar patterns that Despite these difficulties, quantitatively accurate observa-
arise from physical phenomena shows that this need not be tions of fish behavior within schools will undoubtedly be-
the case. For example, some shapes found in three-dimen- come available in the next few years. However, while those
sional schools (e.g., torus and funnel) are echoed in two- datawill provideameans ofassessing short-termbehavioral
dimensional insect configurations (e.g.. wheel), suggesting responses by fish to neighbors within a group, they will not
that such shapes may be adaptive for group members (Fig. by themselves provide the strong linkage between individ-
1). However, these patterns could be evolutionarily neutral, ual and group characteristics that we require to understand
or even pathological. Virtually identical shapes can be the mechanics and evolution of schooling behaviors.
found in a wide range ofinanimate aggregations, from water Making this linkage requires an additional approach,
vapor to planets, in which these patterns arise from simple namely, mathematical or computational models of school-
abiotic interactions between individual components, in the ing behavior. These models posit a specific, quantitative set
absence ofevolutionary dynamics. Key steps in understand- of behavioral interactions essentially, they create a set of
ing biological aggregations in nature must be to distinguish traffic rules and quantitatively assess the emergent prop-
biologically relevant features from nonadaptive epiphenom- erties of the resulting schools. Ideally, both the inputs (i.e..
298 J. K. PARRISH ET AL
GettyImages/FPG/DougPerrine StScI,NASA NorbertWu
r o
OAR/ERL/NSSL NASA T.C.Schneirla
Figure 1. Three- and two-dimensional expressions ofemergent structure in animate and inanimate aggre-
gations whorl patterns. Left: tornadostructure in fish (top)and watervapor(bottom). Middleand right: whorl
andtoroid in planets, tish.ants,andwatervapor,clockwise fromtopleft. Top left reprinted with permission by
FPG; bottom left courtesy ofNational Severe Storm Laboratory; middle top and bottom courtesy of National
Aeronautic Space Administration; top right taken by Norbert Wu. www.norbertwu.com 1999; bottom right
taken by T. Schneirla and reprinted with permission by W. H. Freeman & Company.
individuals' responses to neighbors) and model output specifically address hydrodynamic interactions between
(group-level characteristics) can be compared to data from members of a school (e.g., Weihs, 1973).
real aggregations. Published modeling studies have for the most part ad-
A key puipose of modeling is to distinguish behavioral dressed a relatively restricted range of behavioral algo-
cause from organizational effect by studying the conse- rithms. Most analyses focus on variation in one of three
quences of various hypothetical social interaction rules. categories: behavioral matching, positional preference, and
Most simulation models of animal aggregations in the lit- numerical preference.
erature assign a set of forces that act on the speed and Behavioral matching (aka allelomimesis: Deneubourg
direction of each individual and are modulated in response and Goss, 1989) occurs when the individual agents try to
to other individuals or the local environment. Typical force match their behavior with other nearby agents. Most often,
components include locomotory (e.g., biomechanical forces behavioral matching is modeled by having each agent ex-
such as drag), aggregative (e.g.. long-range attraction, short- plicitly match its orientation with that of its nearby neigh-
range repulsion), arrayal (e.g., velocity matching), and ran- bors (e.g., a zone of parallel orientation: Aoki. 1982: Huth
dom (e.g., individual stochasticity; Griinbaum and Okubo. and Wissel, 1992: Dill ct <//., 1997; Table 1, Fig. 3). Less
1994). The detailed biomechanics of locomotory forces are often, fish match their speed, either to that oftheir compan-
usually not considered in fish schooling simulations. In- ions, or to some arbitrarily decided value (e.g., Romey,
stead, most simulations simply associate behavioral move- 1996; Vabo and N0ttestad, 1997).
ment "decisions" with the movements that result. However, Positional preference refers to each fish having a pre-
there are exceptions, notably a few modeling studies that ferred position relative to one or more of its companions.
SELF-ORGANIZED FISH SCHOOLS 299
Avoid
Herd
Flash expansion
\\fy>'
m^^ \\\\
\\^
4^
\W\\X
Cruise 1JI*N
-
SiST/"
^^z-w/%b&vty WJ??^'
r&tf?'
'"* /b
x^?'
b^^_ '%,/; Join
Vacuole
Confusion
zone
Hourglass
Figure 2. Examples of coordinated movement and directed activity, both emergent properties of fish
schools, which are also commonly cited defense tactics against predatory attack. Fig. 12.8. from Pitcher and
Fairish 1993. Reprinted with permission from the authorand Kluwer Academic Publishers.
Usually, positional preference is formulated as a preferred relatively small population (e.g., 8 to 20 fish; Table 1),
distance to one or more nearest neighbor(s). Variations on despite the fact that several studies point out that small
positional preference include assigned distance zones (e.g., numbers offish may produce artificial results (e.g., Romey,
repulsion, parallel orientation, attraction, searching) within 1996). Most models have operated in two dimensions. Al-
which neighbors are treated equally (Huth and Wissel, though this may be justified on the basis of computational
1992; Stocker, 1999) or continuous distance weighting resources, generalizing from two to three dimensions may
(Warburton and Lazarus, 1991: Reuterand Breckling, 1994; not be straightforward. Many models include some stochas-
Romey, 1996). In some models, otherpositional parameters ticorchaotic elements: however, thedegree ofreplication in
influence responses, such as bearing angle to neighbors, or modeling studies is generally lower than ideal to character-
estimated collision time (Dill el al., 1997). The biological ize the frequency distributions of possible outcomes.
underpinning is obvious: that individual group members do Most simulation studies also assume that all individuals
not collide, that groups do not dissolve, and that stragglers are identical. Romey (1996) has shown that the inclusion of
jporienf.erTeankceendetsocgreitbheer,whbaethaavifoirsahlshmoautlcdhidnog, ea.ngd., pmoosivteiontaol- (amseiansgulerefdishaswigtrhoudpiffsepreeendt tarnadffitcurrnuliensg wrialtle).altFeurrtshcehromoolrien,g
wfpmoeaurrrNccdnuheesmpietogcrirhoiobnancosawrifladsieye(lprdFrafietrg(fio.neomern3i;engneRihctibePgoshOrrhbeAoofsurecsldras,delipatneglogniidvgtrneehuenlwecai.nentu.TyhmaTbnbaneelbeierligehgo1bhf1)ob.r)o,nsrea,ingsidnhebahortorchwhse tcpehrmoeoeldruiugmncencenlssutsosipfoorrnoutpniegonrufgtliam(etusRelsot(.imep.eGgly.eu,,eahrgo1ore9nin9z6teo)sln,tawa/wi.lh.thib1ca4ohn9nd6ems)a.ovyfTerhttserwuasonpsoelrsxausttlieebeinlisdineetttdyos
to which a fish pays attention, which we generically refer to that variability within the group may not only affect emer-
as the rule size. Variations include an apriori value (e.g.. 4: gent properties such as coordinated movement and spatial
Warburton and Lazarus, 1991) or a conditional value (e.g.. pattern, but may also itselfbe an emergent property, clearly
choose up to 4 in the nearest zone: Aoki. 1982; choose up deserves further consideration in modeling studies.
to4,frontprioritized: Huth and Wissel. 1992). Many simply The parameter space explored by each model is typically
have each fish average over all other fish (e.g.. all visible: only a small subset of possible variations, which ideally
Reuter and Breckling, 1994; Vab0 and N0ttestad. 1997: all would include variations in (at least): initial position and
fish: Romey, 1996). velocity; the strength and type of stochastic components;
In general, modeling studies of schooling have been spatial distribution of repulsion, parallel orientation, and
limited in several important respects, which future studies attraction; and degree of variation between individuals in a
should aim to improve upon. Most models have used a group (Table 1 ). Because most studies are not consistent in
300 J. K PARRISH 7" AL.
Table 1
Siininiiiryoffish schoolsimulationparameters andoutput variables. R/PO/A-sequential zones ofrepulsion, parallelorientation (variablyused), and
attraction \\here "zone" implies equalforce within aproscribedarea (see Figure 3). Direction matching implies the use ofa zone ofparallel
orientation. Allotherdefinitions as in the text. Numbers inparentheses refertofootnotes.
Population R/PO/A Direction
Reference Size Starting Orientation Velocity Dependence Matching? Neighbor Scaling Rule Size
Aoki (1982. 1984) 8,32 Random position & Random Zone(I, 2) Yes Position, weighted by Upto4
orientation within front priority
bounded area
Warburton & Lazarus 2-9 Regular square lattice Notspecified Lineardistance No Constant 1-8
(1991)
Huth & Wissel 8 Random position & Random Zone(1) Yes Constant; Single Upto4,front
(1990. 1992. 1994) orientation in fixed choice (4) prioritized
area
Reuter & Breckling 10.20.30, Random position. Notclear Lineardistance Yes Distance-weighted All visible
119941 40,50 orientation & average (1/D; l/D')
speed within
bounded area
Romey (1996) 2-10 Random position & Constant Lineardistance No Constant All
orientation within
bounded area (5)
Vab0 & Nottestad 900 Random position & Constant Discretedistance No Single choice (7) All visible
(1997) orientation within
bounded & fixed
areas
Stocker (1999) 12.64 Random position & Constant Zone(1) Yes Constant Variable(8)
orientation within
bounded area
Reference
SELF-ORGANIZED FISH SCHOOLS 301
11 (a) 1
0.5 0.5
-0.5 -0.5
-1 -1
302 J. K. PARRISH KT AL.
Table 2
Aggregation indices at the individual, group, orpopulation level iiteilti> cva/iiute truffle rule-, in nur.\iniiilution
Index
SELF-ORGANIZED FISH SCHOOLS 303
RandomForce Drag A/Rfunction Neighbor RuleSize
Low High Convex Scaling 4
(High) (Low) (Piecewlse Logistic (16)
linear) (Constant)
Curvature
304 J. K. PARRISH ET AL
portance of this distinction is that emergent properties may Simulation studies like these hinge directly on two ques-
be closely tied to indirect behavioral adaptations, which tions (1) what is optimal, and (2) what is the relationship
benefit individuals by benefiting the group. To satisfy the between individual and group optimality? Such questions
definition of emergent properties, the larger system (the are certain not to have simple or universal answers. It is
group) must possess them, while its components (the indi- unlikely that we will soon attain complete, realistic models
vidual members) do not (Clark ft nl.. 1997). To a large of an aggregating organism's life history that would allow
extent, designating a group characteristic as "emergent" or us to truly represent "fitness" in a population with evolving
not is a matter of degree. For instance, models in which behaviors. However, we are optimistic about the role of
individuals actively align their directions to those of neigh- schooling simulations in addressing two central issues
bors typically produce polarized groups (Huth and Wissel, raised in this paper. First, we believe model studies will be
1992, 1994; Renter and Breckling. 1994; Stocker, 1999), successful in elucidating the mechanistic relationships be-
but this is probably too direct an outcome of the assump- tween individual-level behavior and the group-level spatial
tions to be considered an emergent property. Dill ft al. patterns they produce. Second, we expect that the combi-
( 1997) pose a model in which each fish estimates its time to nation of explicit observations of schooling fish, improved
impact with other fish. In such a system, agents implicitly simulations ofthe observed behaviors, and expanded use of
considertheir neighbors' orientation, velocity, and position, statistical indices of aggregation on real and model aggre-
rather than explicitly doing so. Collision avoidance would gations will prove sufficient to identify the true behavioral
therefore seem to be a direct outcome and not an emergent algorithms used by fish.
property of this model. However, what about the converse:
is polarization an emergent property ofcollision-avoidance Acknowledgments
behavior?
From a biological perspective, an operational distinction This paper is the result of fruitful interactions with the
might be to consider whether the group behavior benefits participants of the CASSLS workshop (The Limits to Self
the members because of their memhership. For example, Organization in Biological Systems) and the International
Grunbaum (1998) used model results to suggest that when Ethological Conference symposium (The Man\ Facets of
individuals simultaneously display gradient-climbing and Gregariousness), in particularJean-Louis Deneubourg, Guy
alignment behaviors in a noisy environment, groups to Theraulaz, Charlotte Hemelrijk, and Laurent Dagorn. Kate
which they belong more accurately climb environmental Litle and Jennifer Weitzman provided invaluable last-
gradients, whereas loners can not. Ifdisplaying both behav- minute help. The original manuscript was greatly improved
iors is costly to an individual, but it nonetheless benefits by by two anonymous reviewers. This research was supported
being part of a group in a better environment, this would in part by a National Science Foundation grant to JKP and
qualify as emergent under this criterion. DG, CCR-9980058.
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