Ecological Modelling 134 (2000) 325 – 341
www.elsevier.com/locate/ecolmodel
Co-evolution of movement behaviours by tropical pelagic
predatory fishes in response to prey environment: a
simulation model
Laurent Dagorn a,*, Filippo Menczer b, Pascal Bach a, Robert J. Olson c
a
IRD-Laboratoire HEA, BP 5045, 34032 Montpellier Cedex 1, France
Management Sciences Department, Uni6ersity of Iowa, Iowa City, IA 52242, USA
c
Inter-American Tropical Tuna Commission, Scripps Institution of Oceanography, La Jolla, CA 92037, USA
b
Received 8 November 1999; received in revised form 4 July 2000; accepted 31 July 2000
Abstract
Predatory fishes, such as tunas, billfishes, and sharks, coexist in pelagic regions of the tropical oceans. In situ
experiments have revealed horizontal and vertical movement patterns for different pelagic species, but the influence
of the biotic environment on movement behaviour has not been studied. In this paper, we propose a simple model
in which the movement behaviour of these fishes is driven entirely by the biotic environment, without implementing
physiological constraints. We explore this concept via computer simulations based on the Latent Energy Environments model [Menczer, F., Belew, R.K., 1996a. From complex environments to complex behaviors. Adapt. Behav.
4(3/4), 317 – 63]. In our model, multiple behaviours for artificial fishes evolve in a three-dimensional environment
where spatial and temporal distributions of prey are patterned after hydroacoustic data taken during ultrasonic
telemetry experiments on tunas in the open ocean in French Polynesia. Interactions among individuals are modeled
through their shared prey resources. Movement patterns of the adapted individuals are analyzed to: (i) compare
artificial individuals with real fishes (three species of tuna, three species of billfishes, and one species of shark)
observed by ultrasonic telemetry; and (ii) examine how the artificial fishes exploit their environment. Most of the
individuals evolved vertical patterns virtually identical to those exhibited by fishes in the wild. The agreement between
our simple model and the ethological data validates the use of computational models for studies of the characteristics
of multiple species inhabiting a common ecosystem. © 2000 Elsevier Science B.V. All rights reserved.
Keywords: Pelagic oceanic environment; Multi-species behaviour; Tropical predator fish; Neural networks; Evolutionary algorithms;
Artificial life
1. Introduction
* Corresponding author. Tel.: + 33-4-67419400; fax: + 334-67419430.
E-mail addresses: dagorn@ird.fr (L. Dagorn), filippomenczer@uiowa.edu (F. Menczer), bach@ird.fr (P. Bach), rolson@iattc.org (R.J. Olson).
Large predatory fishes, such as tunas, billfishes,
and sharks, dwell in the open sea, and their habits
are a challenge to observe. Because of their eco-
0304-3800/00/$ - see front matter © 2000 Elsevier Science B.V. All rights reserved.
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L. Dagorn et al. / Ecological Modelling 134 (2000) 325–341
nomic importance, there is a great body of knowledge about them from fishery activities. However,
before the development of ultrasonic telemetry
techniques, little was known of their fine-scale
movements. By attaching sonic transmitters to the
animals and listening to the echoes produced by
these devices, it became possible to describe the
vertical and horizontal movement patterns of
these fishes in their natural habitats (see Yuen,
1970 for one of the first experiments). In most
cases, these studies showed diverse movement patterns for different species (Carey and Olson, 1982;
Carey and Robison, 1981; Cayré and Chabanne,
1986; Carey, 1990; Carey and Scharold, 1990;
Holland et al., 1990a,b; Cayré, 1991; Brill et al.,
1993; Block et al., 1997; Bach et al., 1998; Josse et
al., 1998; Brill et al., 1999; Dagorn et al., 2000).
The next challenge is to understand why these
species evolved such different movement
behaviours.
There are large temperature differences between
the warm upper layers of the ocean and the cold
deep waters. By moving a few hundred meters
vertically, an animal may encounter a greater
temperature change than it experiences seasonally
or while moving thousands of miles horizontally
(Carey, 1992). Most fish species are stenotherms,
but large fishes like billfishes are able to partially
control their body temperatures because thermal
diffusion through a large mass is a slow process,
and convective heat transfer is reduced in parts of
the body by a modified circulatory system
(Stevens and Neill, 1978). Moreover, tunas and
lamnid sharks are able to maintain their body
temperatures warmer than the ambient water temperature by means of countercurrent heat exchangers in the circulatory system between the
gills and muscle tissues. The vertical movements
of some oceanic fishes, observed by ultrasonic
telemetry, have been interpreted in relation to the
vertical structure of the abiotic environment,
mainly water temperature and dissolved oxygen
concentration (Holland et al., 1990a, 1992; Cayré
and Marsac, 1993; Block et al., 1997; Brill et al.,
1999).
Tunas, billfishes, and sharks require large
amounts of energy (Olson and Boggs, 1986; Boggs
and Kitchell, 1991; Brill, 1996; Cortés, 1997), and
they must be efficient predators to survive. Prey
distribution may, therefore, have an important
influence on the movement patterns of these species. Due to the difficulties in observing these
predators and their prey in their habitat, little
effort has been devoted until recently to study the
role of the biotic environment in explaining their
movements. During the ECOTAP1 program in
French Polynesia, experiments were developed to
collect simultaneously ultrasonic telemetry data
for yellowfin (Thunnus albacares) and bigeye (T.
obesus) tunas and acoustic data on their prey
(Josse et al., 1998; Dagorn et al., 2000). These
data show that the three-dimensional distribution
of the prey can account for an important part of
the small-scale movement patterns of the tunas,
but more studies are clearly needed.
Tunas, billfishes, and sharks have evolved different strategies to exploit the same environment.
Are different movement behaviours the result of
different physiological mechanisms in these animals, or is it possible to explain the movement
patterns by the dynamics of the prey, without
considering their physiological limits? Menczer
and Belew (1994), Sims (1994), Terzopoulos et al.
(1994) have addressed the evolution of morphology in artificial life organisms. Menczer and
Belew (1996a) showed theoretically that both abiotic and biotic environmental structure can play a
key role in shaping the evolution of behaviours.
In this study, we explore the structure of the prey
environment in shaping the evolution of behaviour patterns, without considering physiology.
Such studies can help us understand the role of
the biotic environment in behavioural adaptations
and how multiple behaviours can emerge in a
common ecosystem.
The purpose of this study is to develop a computational model of the movements observed in
multiple predator species sharing the pelagic
oceanic environment. Our approach is to abstract
1
ECOTAP (studies of tuna behaviour using acoustic and
fishing experiments) is a joint program between EVAAM (now
Service des Ressources Marines, SRM), Institut Français de
Recherche pour l’Exploitation de la Mer (IFREMER) and
Institut de Recherches pour le Développement en Coopération
(IRD).
L. Dagorn et al. / Ecological Modelling 134 (2000) 325–341
away from the physiological details of the different species and focus on an individual based
model with minimal assumptions about prey distribution and dynamics. The objective is to simulate a co-evolutionary process and analyze the
different behaviours emerging in a realistic prey
environment. We assess the predictive power of
the model in accounting for the heterogeneous set
of behaviours displayed by several tropical predatory fishes. We are not interested in modelling a
specific behaviour, but rather in studying the
range of behaviours that can result from co-adaptation in a shared biotic environment with given
characteristics. Such a model can be applied to
different environments where the same species
occur (e.g. the eastern Pacific Ocean), which
would be impossible if it were encumbered with
area-specific details.
In Section 2, we outline the three components
of the model: the shared prey environment, the
artificial fishes, and the evolutionary algorithm
used to adapt their behaviours. In Section 3, the
behaviours that evolved from the model are compared against our knowledge of actual species
from ultrasonic telemetry experiments. We also
analyze the emergent patterns in relation to the
artificial environment, and consider the sensitivity
of our model with respect to its assumptions. In
Section 4, we discuss our main findings, and
Section 5 concludes with a look at future work.
2. Model
We employ an agent-based model to simulate
the evolutionary process of a population of fish
situated in a dynamic environment, and analyze
the diverse set of adaptive behaviours that are
generated by the model.
Our model is based on the latent energy environments (LEE) framework (Menczer and Belew,
1996a,b). The agents share a three-dimensional
biotic environment, gathering resources to survive. The resources are replenished independently
of the behaviours of the agents, determining the
carrying capacity of the artificial ocean. Selection
for survival is based on a localized and endogenous form of density-dependent fitness, because
327
competition is limited to the spatially-distributed
resources. Individuals with behaviours that allow
them to make good use of the resources, survive
and reproduce. Individuals that exploit independent resources do not interact.
Artificial life models based on individuals (Judson, 1994), such as LEE, are appropriate to test
hypotheses like the one suggested in this paper
because they allow modelers to easily generate
heterogeneous populations and to explore the relationships between co-evolving species and environmental resources. For example Echo, a
computational framework that shares many features with LEE, was used by Hraber and Milne
(1997) to study how environmental and biotic
factors regulate species abundance and the composition of ecological communities. The absence
of centralized control and global selection in LEE
allows for many efficient behaviours to coexist,
without the bias of an optimization process that
would push toward a single solution. This approach is similar to the ‘animats’ model of Krebs
and Bossel (1997), while it differs from models
such as dynamic programming, where the objective is to find optimal solutions (e.g. Baker, 1996).
Other modeling efforts have focused on the
responses of population and community structure
and behaviour governed by species interactions
and prey environments (Dodds and Henebry,
1995; Matsumoto and Seno, 1995; Kawata, 1997;
Spencer, 1997). Because our objective is to generate behaviours based on assumptions about the
biotic environment, as opposed to testing different
models of animal decisions, the proposed approach also differs from ecological models in
which the rules governing the behaviour of individuals are pre-programmed (e.g. Downing and
Reed, 1996; Letcher and Rice, 1997; Beecham and
Farnsworth, 1998; Lorek and Sonnenschein, 1998;
Ziv, 1998). We follow the suggestion of Beecham
and Farnsworth (1998), that individual-based
models that refer to pre-programmed rules should
be extended to use evolutionary methods, where
each individual would evolve an individual-specific algorithm, in order to gain insight into the
evolutionary origins of alternative behaviours.
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L. Dagorn et al. / Ecological Modelling 134 (2000) 325–341
2.1. Biotic en6ironment
To model the biotic environment, we use general knowledge about the prey fauna of the open
ocean in French Polynesia and specific acoustic
observations made in French Polynesia during the
ECOTAP program. These data have not yet been
fully analyzed. In the absence of precise details on
prey characteristics, we model only two types of
prey. Type 1 prey are low in energy, typical of
those inhabiting the deep scattering layer (DSL),
and composed mainly of crustaceans, small fishes,
and jellies. It is well-known that, during the nighttime, the organisms of the DSL ascend to the
surface layer (Longhurst, 1976). At sunrise, the
community descends to deep waters, where it
spends the daytime. The DSL structure might be
characterized as very large and dispersed patches.
Prey of type 2 are more energetic and are found in
smaller, denser patches composed mostly of small
pelagic fishes and squids. They do not migrate as
deep as type 1 prey; they usually live in an intermediate layer during the day, and also occupy
surface waters at night.
The vertical distributions of the two types of
prey during day and night are used to define the
vertical environment of the model. The artificial
ocean of our predatory fishes is modeled vertically
by three depth layers: a surface layer, an intermediate layer, and a deep layer, corresponding to the
waters occupied by the two types of prey at night
and day. In French Polynesia, for example, the
lower boundaries of these layers are found at
approximately 150, 350 and 500 meters (the latter
Fig. 1. Model of the vertical dynamics of the biotic pelagic
environment. All the prey (types 1 and 2) are in the surface
layer during nighttime and in the intermediate layer during
dawn and dusk. At daytime, prey of type 1 are in the deep
layer while prey of type 2 are in the intermediate layer. Prey
types are described in the text.
depth is the vertical limit of the acoustic observations in the ECOTAP program). Horizontally,
each of these layers is modeled by a grid of 400 by
400 cells, representing an area of 40 by 40 n.mi.
( 75 by 75 km), and opposite sides are joined to
avoid edge effects and to form a torus.
A schematic representation of the biotic environment assumed for this model is presented in
Fig. 1. This is admittedly a very simplified model
of a prey community. For example, it disregards
the amount of time that it takes for different prey
taxa to move between depth layers. More importantly, it assumes that no prey are present in the
surface layer during the daytime, although it is
known that predatory fishes feed in the surface
layer of the ocean, especially in areas where the
surface layer is thin. However, during 2000 h of
acoustic surveys between 0 and 500 m in the
exclusive economic zone (EEZ) of French Polynesia, we did not find abundant prey in the surface
layer during the daytime. Therefore, our simplified model is generally consistent with those
field observations.
The energy density of type-2 prey is set at five
times that of type-1 prey in our simulations. We
set the number of prey to 150 items within a circle
of 8 n.mi. ( 15 km) radius for patches of type-1
prey and 50 items within a circle of 1 n.mi. ( 2
km) radius for patches of type-2 prey. One prey
item in our model does not represent one prey
item in the wild, but rather a combination of
several prey items. A more realistic representation
of the numbers of real prey (which is not known)
would have forced the model to consider millions
of prey items. To simplify the computation of
prey items in our model, we used the concept of
‘super-individuals’ proposed by Scheffer et al.
(1995). The prey population is then represented
by a smaller number of units. The super-individuals are classes of individuals for which parameters
are identical in the model (e.g. same energy content). Because we do not know the exact spatial
dimensions of these patches in the ocean, the radii
and spatial distributions of the patches are somewhat arbitrary, but consistent with our observations in French Polynesia.
Following the LEE approach, we adopt a constant prey replenishment rate: four patches of
L. Dagorn et al. / Ecological Modelling 134 (2000) 325–341
Fig. 2. Architecture of the neural networks used to model fish
behaviours.
type-1 and two patches of type-2 prey regularly
appear at random positions every half day. This
replenishment rate is independent of prey consumption. As in actual environments, competition
occurs only among individuals who share prey
resources. Other features that discriminate between prey types, such as size, palatability, and
ease of capture (i.e. swim speed), are either neglected in the model or accounted for indirectly
through the energy content.
One time step is defined as 15 min. Therefore,
the duration of the 11-h day and night periods is
44 time steps each, while the 1-h dawn and dusk
periods correspond to four steps each (Fig. 1). A
24-h cycle is represented by 96 time steps. Each
type of prey has a vertical distribution pattern
that depends on the period of the day (day, night,
dawn, and dusk), as observed in the wild (Fig. 1).
We simplify the computation of the model by
ignoring horizontal movements of prey, which is
reasonable when comparing the relative sizes
(100:1) and relative mobility of pelagic predators
and prey.
2.2. Fish beha6iour
The behaviour of the artificial predatory fishes
that we consider in this model is three-dimensional movement. Movements by an organism
causes its view of the surrounding habitat and its
spatial relationships with respect to the habitat to
329
change. In our experiment, we represent the mapping from sensory states to motor actions using
the well-known computational model of feed-forward neural networks (Rumelhart and McClelland, 1986). Generally speaking, these networks
are collections of simple units connected by
weighted links, which can compute arbitrary nonlinear functions. The organization of the individual networks used to model each artificial oceanic
predator is described in Fig. 2.
The artificial neural network is comprised of
two layers of units and connections. The behaviour of an artificial fish is characterized by the
weights of the connections. In our case, each
connection weight is represented by a floatingpoint number. Because feed-forward networks
have no recursive connections, the behaviours of
the simulated fishes are strictly reactive. Although
interactions between different forms of learning
and evolution have been explored in the artificial
life community, and even in the LEE framework
(Menczer and Belew, 1994; Cecconi et al., 1996),
our present model neglects any effect of individual
learning for the sake of simplicity; we first want to
focus our attention on the behaviours that can
emerge by way of evolution.
The neural network inputs represent internal
and external information provided by five sensors
(Fig. 2). The presence of a prey item can be
detected when (i) the prey item and the fish are
located in the same depth layer, and (ii) the prey
item is within a circle of a specified radius around
the predator. The distance at which a tuna or
billfish responds to a prey, by odor or vision, is
not known. Studies on Atlantic cod (Gadus
morhua) have shown that fish positioned as far as
700 m upstream of fishing gear can sense baited
hooks (Bjordal and Løkkeborg, 1996). Although
baited hooks are not the same as free-swimming
prey, and Atlantic cods are not the same as
tropical tunas or billfishes, we adopt this order of
magnitude and set the detection distance to five
cells ( 900 m).
The ‘prey – distance’ sensor indicates the Euclidean distance between the predator and the
closest prey item, and has continuous values between 0 and 1. The value is 1 for distances greater
than the detection distance. The ‘prey – angle’ sen-
330
L. Dagorn et al. / Ecological Modelling 134 (2000) 325–341
sor indicates the angle between the direction the
predator is facing and that of the closest prey
item. It also has continuous values between 0 and
1, corresponding to the range [−p, +p] (the
discontinuity occurs behind the predator). If no
prey item is detected, the value is random. The
‘wait-time’ sensor counts the number of time steps
(up to 20, or 5 h) since the last prey item was
eaten. The actual value is normalized to the interval [0, 1].
The two ‘period-of-day’ sensors have boolean
values that are combined to indicate the period of
the 24-h cycle, night, dawn, day, or dusk. Day
and night are not necessarily synonymous with
light and dark in aquatic environments, as light
depends on depth, brightness at the surface, turbidity, and other factors. (Helfman, 1993). Therefore, our time sensors could be viewed as sensory
perceptions combining information about light
intensity, depth, and internal-clock mechanisms.
Finally, because real sensory systems are noisy,
we include a random noise source as an additional
input. By omitting sensors that provide information such as prey size or speed, we make the
simplifying assumption that predators do not select for specific prey in the model. All predators
exploit the same prey fauna. Considering that
Fig. 3. Pseudo-code of the LEE evolutionary algorithm at the
basis of the proposed model. Note that energy is always
conserved; it enters the system through the replenishment of
prey resources and leaves the system in the form of work costs
for performed actions. Also note that the reproduction constant, THETA, is independent of population size. Therefore
the size of the population quickly converges to the carrying
capacity of the environment, determined by the prey replenishment rate.
tunas and other pelagic fishes are widely believed
to be opportunistic predators (Alverson, 1963;
Roger, 1994), this seems a reasonable assumption.
The network has one hidden layer with six units
and an output layer of three units. The first
output unit produces a change in direction of the
horizontal movement relative to the current heading. The second output unit indicates the swimming speed, between 2 and 10 cells per time step,
or between 0.4 and 2.2 m/s, consistent with ranges
of swimming speeds measured during field observations (Olson and Boggs, 1986; Brill et al., 1993).
The third output unit determines the depth layer
where the fishes swims: surface, intermediate, or
deep. The fact that the network outputs of all
artificial fishes correspond to identical ranges in
movement behaviours, mirrors our simplifying assumption of identical physiological abilities across
the modeled population of predators.
2.3. E6olution
As stated above, our use of the LEE model is
justified, in part, by our goal to study the evolution of a heterogeneous range of behaviours,
rather than the convergence to a single optimal
behaviour. While the latter would be appropriate
in a single-species model, we want to account for
the realistic situation whereby several species of
predators co-evolve different behaviours while
sharing a common habitat. LEE models allow
co-adaptation by an evolutionary algorithm based
on an endogenous fitness measure (Menczer and
Belew, 1996a,b). The model does not select directly on the behaviour evolved by a predator, but
on its resulting efficiency (net energy intake rate)
in the shared environment. To illustrate these
aspects of our model, our LEE evolutionary algorithm is outlined in Fig. 3. The evolved set of
behaviours resulting from this co-adaptive process
represents the model’s prediction of movement
behaviours, which we compare with real data.
We now illustrate, in further detail, the evolutionary algorithm of Fig. 3. To begin a simulation, we created 200 fishes, each with different
random weights uniformly distributed between
−0.5 and +0.5. All fishes are initialized with
2000 units of energy. The internal energy state of
L. Dagorn et al. / Ecological Modelling 134 (2000) 325–341
Table 1
Categories used to characterize vertical movement patterns
Category
Vertical pattern
A
More than 90% of the time in the surface
layer
More than 90% of the time in the
intermediate layer
More than 90% of the time in the deep
layer
Movements between the deep and
intermediate layers
Movements between the surface and
intermediate layers
Movements between all three layers
Movements between the surface and deep
layers
B
C
D
E
F
G
a fish can vary between 0 and 4000 units. The
fishes gain energy when they eat a prey item: 30
units for type 1 prey, and 150 units for type 2
prey. The fishes lose 1 unit of energy per cell
moved; i.e. the energy cost of swimming is proportional to the distance.
When a fish depletes its energy stores, it is
eliminated from the population. When a fish’s
internal energy reaches 4000 units, it reproduces
one offspring asexually. The parent divides its
energy with its progeny; i.e. each offspring starts
with 2000 units of energy. At birth, offspring and
parent are located at the same location. The evolution of behaviours depends only on random
mutations because there is no sexual recombination or cross-over. The offspring inherits its parent’s weights. Then, 2% of the weights are
randomly selected and mutated by adding random
noise drawn from a uniform distribution between
−1 and + 1. All weights are bounded to the
interval [−5, + 5].
3. Results
Ten runs of 150 000 time steps each resulted in
a total of 2489 artificial fishes. Each individual
was analyzed to characterize its vertical and horizontal movements. Next, we report on the movements exhibited during nighttime and daytime to
classify general movement patterns and to com-
331
pare them to behaviours of real predatory fishes
in the wild. Then, we evaluate the evolved artificial individuals in relation to the way they exploit
their environment. Finally, we analyze the sensitivity of the results.
3.1. Artificial 6ersus natural mo6ement patterns
To analyze movement behaviours, we fed the
sensors of the evolved individuals with a randomly generated input sequence. The sequence
corresponds to a succession of 30 model night
periods and 30 model day periods (2640 steps),
and it models a situation in which individuals do
not detect prey and have not eaten for a long
period of time (i.e. the ‘prey-distance’ and ‘waittime’ sensors are set to 1). Then, we analyzed their
searching behaviours while the fishes looked for
prey.
3.1.1. Vertical mo6ements
Our objective was to classify the vertical behaviours emergent from the ten runs into groups
which exhibited similar vertical patterns during
the various periods of the day. Each individual
was classified according to its swimming depth,
i.e. by its output when submitted to the pre-determined inputs outlined above. Seven categories of
vertical behaviours were considered, each category corresponding to the ocean layers where the
fishes swam most of the time (Table 1). Layers in
which a fish spent less than 10% of the time were
disregarded. The 10% threshold is arbitrary, but
helpful in visually classifying real species. We
considered different criteria (thresholds between 0
and 10%), and the classification was effectively the
same. Each individual was classified by one letter
corresponding to a vertical pattern category for
the daytime and another letter for the nighttime.
We first focus on nighttime and daytime patterns.
For each run, we computed the frequencies of
the 49 possible combinations (7×7 categories) of
vertical patterns during nighttime and daytime.
Because there was large variability across runs (cf.
Section 3.3), we ranked the behaviours by frequency of occurrence in each run, and used the
median of the rank distributions to classify the
results of the ten runs (Table 2). Only 19 of the 49
L. Dagorn et al. / Ecological Modelling 134 (2000) 325–341
332
classes of possible patterns were represented in the
ten final artificial populations. The five most frequent classes are highlighted in Table 2, and the
typical vertical movements in these five classes are
shown in Fig. 4. All five top classes include the A
pattern during the nighttime, which corresponds
to movements within the surface layer. The five
possible vertical patterns during the daytime,
combined with the surface nighttime pattern, correspond to the most frequent classes. The emergence of behaviours D and E (alternative
movements between different layers) is interesting
because it suggests a precise adjustment of the
weights of a neural network, and is discussed
further in Section 4.
We compared the behaviours that evolved in
these simulations with ultrasonic telemetry data
on movements of real fishes from experiments
conducted in French Polynesia or Hawaii. These
experiments provide us with accurate depth data.
In cases where ultrasonic telemetry data from the
tropical Pacific Ocean were not available, we used
data from other areas. We considered seven difTable 2
Vertical movement behaviours of the artificial individuals during nighttime and daytime, respectively, ranked by frequency
across ten simulationsa
Class
AB
AA
AE
AD
AC
ED
EB
CC
EC
AF
BB
EA
EE
BC
BD
EF
BE
DC
FF
a
Rank distribution median
2
2.5
2.5
3.25
6
7
7.25
9.5
13
18
27.75
28.75
28.75
29.5
29.5
29.5
30
30
30
The five most frequent classes are bold.
Table 3
Classification of seven oceanic predator species according to
their vertical movement patterns during the daytime and nighttime, respectivelya
Species
Class
Reference
Skipjack tuna
AA
Yellowfin tuna
AE
Bigeye tuna
AC
Swordfish
AC
Striped marlin
AA
Pacific blue
marlin
Blue shark
AA
French Polynesia, Pacific Ocean
(Cayŕ and Chabanne, 1986)
French Polynesia, Pacific Ocean
(Bach et al., 1998)
Hawaii, Pacific Ocean (Holland
et al., 1990a)
Eastern Pacific Ocean (Carey
and Olson, 1982)
French Polynesia, Pacific Ocean
(Dagorn et al., 2000)
Hawaii, Pacific Ocean (Holland
et al., 1990a)
Off Cape Hatteras, Atlantic
Ocean (Carey and Robison,
1981)
Hawaii, Pacific Ocean (Brill et
al., 1993)
Hawaii, Pacific Ocean (Holland
et al., 1990b)
Between George’s Bank and
Cape Hattera, Atlantic Ocean
(Carey and Scharold, 1990)
AD
a
Behaviour categories are as defined in Table 1. The classification criteria are the same used for the artificial fishes (cf.
Table 2), and are based on data from the references shown.
ferent species known to be predators in this environment. They include three tuna species:
skipjack (Katsuwonus pelamis), yellowfin (T. albacares) and bigeye tunas (T. obesus); three
billfish species: swordfish (Xiphias gladius), striped
marlin (Tetrapturus audax) and pacific blue marlin (Makaira nigricans); and one shark species,
blue shark (Prionace glauca).
It is difficult to generalize a regular vertical
pattern for individuals of any particular species
because individual behaviour is not rigid, but
rather composed of adaptive actions. Nevertheless, we used published data to classify the vertical
patterns of the above species according to the
criteria used for our artificial fishes (Table 3). The
behaviours that emerged in our simulations are
consistent with the behaviours exhibited in nature;
the seven species considered were categorized in
the top five classes of the artificial population.
L. Dagorn et al. / Ecological Modelling 134 (2000) 325–341
333
Fig. 4. Typical vertical movements of artificial individuals in the five most represented classes (from top to bottom: AB, AA, AE,
AD and AC). The horizontal axis corresponds to time (the 24-h period, from 18:00 to 18:00 h), with the four periods of the day
marked by the background levels of gray. The vertical axis corresponds to the depth layer.
334
L. Dagorn et al. / Ecological Modelling 134 (2000) 325–341
The only behaviour predicted by our model but
not observed in the real fishes by ultrasonic
telemetry is AB. However, longline catch data
suggest that albacore tuna utilize the AB pattern
(see Section 4).
3.1.2. Horizontal mo6ements
To perform quantitative analysis of horizontal
movement patterns, we measured two statistics
for each individual and for each 11-h period (day
or night):
path length L, the linear distance covered along
the horizontal trajectory (proportional to the
average swimming speed);
diffusion distance D, the Euclidean distance
between the two extreme points of the horizontal trajectory.
The distributions of these measures, obtained
by combining all 2489 individuals from the final
populations of the ten runs, are shown Fig. 5. The
respective distributions of daytime and nighttime
individual path lengths have the same mode (88
cells), which corresponds to an average swimming
speed of two cells per time step (the lowest swimming speed in our simulations). Nevertheless, nocturnal movements were usually more extensive
than diurnal ones. During the daytime, individuals did not cover long distances (maximum value
of L is 180 cells) and 76% of the individuals had
a path length L of 88 cells. During the nighttime,
this path length value (88 cells) is only observed in
15% of the individuals and L values range up to
320 cells.
From this data we conclude that the model
selected for animals with low horizontal speeds.
Several tracking studies found that, in general,
fishes do not adopt high speeds for their movements (Carey and Robison, 1981; Carey and Olson, 1982; Cayré and Chabanne, 1986; Carey,
1990; Carey and Scharold, 1990; Holland et al.,
1990a,b, 1992; Cayré, 1991; Brill et al., 1993,
1999; Block et al., 1997; Bach et al., 1998; Josse et
al., 1998; Dagorn et al., 2000). Although it is
known that fishes can move rapidly when attacking prey or avoiding danger (Walters and Fierstine, 1964), there is probably little routine use for
high speeds, as suggested by Carey (1992). This
suggests that the convergence toward low speed is
consistent with reality.
The diffusion distance D was longer during the
nighttime than during the daytime (Fig. 5). During the daytime, 75% of the individuals have a
diffusion distance less than or equal to 10 cells.
During the nighttime, however, 80% of the individuals have a diffusion distance greater than 10
cells. This suggests high sinuosity and exploitative
behaviours (Benhamou, 1992) during the daytime,
as opposed to more extended, exploratory behaviours during the nighttime.
No conclusive data about the horizontal movement patterns of actual oceanic predatory species
are yet available to assess the validity of the
predictions of diffusion distance. While some
sonic tagging experiments with yellowfin and
bigeye tunas in Hawaii (Holland et al., 1990a) and
with yellowfin tuna in the Indian Ocean (Cayré,
1991) seem consistent with our model, these data
are for coastal areas. A few tracking experiments
with large bigeye tuna in the open ocean (Dagorn
et al., 2000) suggest the need for further experiments on predators in the open ocean.
3.2. Analysis of e6ol6ed strategies
To examine the vertical behaviours exhibited by
the artificial individuals during a complete 24-h
cycle, we consider the depth of predators during
night, day, dawn, and dusk. Individuals were
subjected to an input sequence representing 30
24-h cycles. We used the codes in Table 1 for the
vertical patterns during all four periods. For the
analysis, one individual is characterized by four
letters, one for each period of the day in the
above order. The classification of the final populations in the ten runs includes 70 out of 2401
possible classes. These are ranked by frequency of
occurrence, and the median of the rank distributions for the ten runs is shown in Table 4 for the
top ten classes.
The most frequently observed 24-h movement
class is AAAA, which corresponds to individuals
swimming in the surface layer most of the time.
The artificial fishes exhibiting this behaviour forage efficiently only during the night period, because in our artificial ocean no prey are present in
the surface layer during the day, dawn, or dusk.
We conclude that, while this strategy is the sim-
L. Dagorn et al. / Ecological Modelling 134 (2000) 325–341
335
Fig. 5. Distributions of path length L (top) and diffusion distance D (bottom), characterizing the population’s horizontal
movements.
plest possible with respect to vertical movements,
it provides individuals with sufficient energy for
survival from prey caught during the nighttime
alone. This exclusively nocturnal activity pattern
might correspond to primitive predator species
(Helfman, 1993).
The top eight classes include the A pattern at
night, indicating that the fishes are active during
L. Dagorn et al. / Ecological Modelling 134 (2000) 325–341
336
the nighttime. All patterns except AAAA indicate
that the predators forage during the daytime as
well. Such diurnal foraging capabilities correspond to more advanced species (Helfman, 1993).
The dawn and dusk patterns are the same for
each of the top ten classes, reflecting the same
environmental conditions in spite of different inputs from the time-of-day sensors. Six of the top
ten patterns indicate that the fishes are active
during the twilight periods as well as during night
and day. Helfman (1993) points out that such
activity patterns represent opportunistic behaviours, which characterize many fishes, particularly predatory ones. Our model agrees with
Helfman’s conclusion that the activity patterns of
fishes in the wild may be strongly determined by
the activity patterns of their prey.
Table 4
Classified vertical movement behaviours of the artificial individuals during the four periods of the day (night–day–dawn–
dusk), ranked by frequency across ten simulationsa
Class
AAAA
ABAA
AEAA
ABEE
AEEE
ADBB
ADEE
ABBB
EBBB
CCCC
Rank distribution median
1.5
3
4
5.75
6.25
8.25
8.75
11
12.5
20.75
a
Only the ten most frequent classes are shown. The median
of the frequency rank distribution drops below 610 from the
11th class.
Table 5
Values of the prey distribution parameters held constant during the original simulations, as well as the four sensitivity
analysis runs
Prey type
Npatches
Etot
1
2
8/day
4/day
36 000/day
30 000/day
3.3. Sensiti6ity analysis
Using an individual based model, such as LEE,
to represent a population of artificial individuals
and their environment entails a number of assumptions. The purpose of some of the assumptions is to keep the model simple, while others are
required by several aspects of the model. Therefore, it is critical to determine how sensitive the
model predictions are to the assumptions.
Ideally, one would repeat the simulations several times while varying each parameter by some
amount, and assess the variability of the results
with respect to the assumption denoted by that
parameter. Because such a full-scale sensitivity
analysis is computationally prohibitive2, we decided to focus our analysis in a couple of ways.
First, we looked at the population dynamics from
the original runs to determine the number of time
steps necessary for the population size to stabilize
around the carrying capacity of the environment.
We concluded that after 10 000 time steps the
fluctuations in population size were essentially
reduced to noise. Second, we focused on the two
critical parameters whose initial values were assigned with less confidence than the others in the
original runs: (i) the relative amounts of energy in
the two prey types, and (ii) the detection distance.
In the original simulations, the ratio of energy
between the two types of prey was E2/E1 =5. The
formula that correlates the energy of an item of a
given prey type with the total replenishment energy per unit time, the number of patches, and the
number of prey items per patch of the same prey
type is given by:
X
N prey/patch
=
EX
tot
EXN X
patches
where X {1, 2} is the prey type. The number of
patches (Npatches) and total energy (Etot) were fixed
at their original values (Table 5). Thus, we used
the energy values of the prey (EX ) as independent
variables, which determined the ratio, and derived
the numbers of prey items per patch (Nprey/patch) as
dependent variables. We ran four additional simu2
A single 150 000-step run of our C + + simulation code
required 40 CPU h on a 400 MHz P2 Linux workstation.
L. Dagorn et al. / Ecological Modelling 134 (2000) 325–341
337
effect that we call ‘ancestor bottleneck.’ Consequently, genetic drift causes a large variability in
the behaviours evolved by the populations across
different runs (Menczer and Belew, 1994). This is
why we focused on rank when analyzing vertical
movement behaviours (cf. Section 3.1.1). For the
same reason, we used the Spearman correlation
coefficient, Rs, to see whether the results of the
four additional runs were consistent with those of
the ten original runs. The rank correlation was
calculated between (i) the vertical movement behaviours emerged at the end of the seven sensitivity runs (percentages), and (ii) the medians of
rank distributions across the original ten runs.
Table 6 shows that all rank correlation values are
highly significant. Therefore, our model is not
sensitive to variations in the energy ratio of the
prey types nor to the distance at which a fish
responds to a prey item.
4. Discussion
Fig. 6. Size of the artificial population in the four sensitivityanalysis runs for various ratios of energy between the two prey
types (upper graph), and the three sensitivity-analysis runs for
various detection distances of prey (lower graph).
lations with energy ratios E2/E1 {1, 3, 5, 7}. In
the original runs, the prey detection distance was
5 cells, i.e. 900 m. We also ran three additional
simulations with prey detection distance at 4, 5
and 6 cells, i.e. 720, 900 and 1080 m. All the seven
sensitivity runs were stopped after 10 000 steps
(see Fig. 6).
An important observation from our simulations
is that few of the individuals in a starting population happen to be initialized with a random behaviour that is efficient enough to allow them to
survive (Fig. 6). All the individuals at the end of a
run are descendants of these few ancestors, an
Most large oceanic predators live in all of the
oceans, in different oceanographic conditions.
Usually, habitats of these species are defined in
relation to the physical and chemical structure of
the ocean, rarely as a function of the biotic environment (see Longhurst, 1998 for large-scale
oceanic provinces defined from hydrology and
phytoplankton distribution). Acoustic data have
Table 6
Spearman rank correlation coefficients, Rs, between the rank
of the median of the ranks of the behaviour frequencies in the
original ten runs, and the rank of the behaviour frequencies in
each of the seven sensitivity analysis runsa
Run
Rs
Probability
E2 = E1
E2 = 3E1
E2 = 5E1
E2 = 7E1
Prey detection distance = 4 cells
Prey detection distance = 5 cells
Prey detection distance = 6 cells
0.67
0.55
0.69
0.78
0.64
0.52
0.49
\0.9999
0.9999
\0.9999
\0.9999
\0.9999
0.9998
0.9997
a
The control runs with E2 = 5E1 and prey detection distance =5 cells have identical conditions to the ten original
runs (except for the seed of the random number generator).
338
L. Dagorn et al. / Ecological Modelling 134 (2000) 325–341
traditionally been used for stock assessment or
direct observations of animal behaviour, but have
largely been ignored in ecological modelling
(Brandt and Mason, 1994). The biotic environment of the present model was inspired by the
results of acoustic experiments conducted in
French Polynesia under the ECOTAP program,
which was designed specifically to study the ecology and behaviour of tropical tunas. The aim of
the present study was not to represent exclusively
the ocean in French Polynesia, but to draw from
real observations a realistic model of the environment in which different pelagic predatory fishes
live. The various tropical oceanic zones have different abiotic factors, such as temperature and
dissolved oxygen, which influence the depths
reached by different types of prey. Our model can
be applied to different biotic environments that
have similar prey macro-structure even if the micro-scale details (e.g. the depths of the layers) vary
between environments. This explains our preference for general terms (‘surface’, ‘intermediate’,
and ‘deep’) to model the depth layers rather than
specific values in meters.
We used tracking results for only few individuals per species to define one pattern per species,
but these data clearly indicate the existence of
behavioural variability across individuals of the
same species, as well as within a single individual
depending upon the variability of the environment. We focus our discussion only on the interspecific variability observed in the wild, but our
modelling approach also provides a means to
study
intra-specific
and
intra-individual
variability.
Physiology is generally considered the key determinant of the vertical movement patterns of
fishes. For example, skipjack and yellowfin tunas
occupy shallower depths than bigeye tuna during
the daytime (Cayré and Chabanne, 1986; Holland
et al., 1990a; Cayré, 1991; Dagorn et al., 2000).
Bigeye tuna have the ability to physiologically
and behaviourally thermoregulate (Holland et al.,
1992), allowing them to expand their niche into
deep, cold water below the thermocline (Dagorn
et al., 2000). During the daytime, bigeye tuna
make frequent, regular upward excursions to
warm up, as indicated by the ultrasonic telemetry
experiments of Holland et al. (1992). Because of
different physiological capabilities, different species are not able to exploit the same vertical
habitats.
The modelling work presented here, on the
other hand, indicates that predator adaptations to
prey dynamics can also lead to the same vertical
movement dynamics, without any physiological
constraints. Our simulations suggest that diverse
behaviours can emerge due to adaptation to the
prey environment alone. All the artificial fishes
had the opportunity to develop movements in
deep and cold waters (the intermediate and deep
layers). The structure and the dynamics of the
biotic environment alone were responsible for the
simultaneous differentiation of several strategies
for survival in the artificial ocean. The model
suggests the possibility that behaviours evolved
first, creating progressive selective pressure for
changes in physiological capabilities, or, at least,
that behaviours and physiology might have coevolved simultaneously.
The absence of tracking data corresponding to
the most frequently observed vertical behaviour
pattern predicted by our model may seem discouraging. However, there is evidence that the albacore tuna (T. alalunga) fits this category. Albacore
is the most abundant tuna species in French Polynesia. However, no published tracking data for
this species in a tropical area yet exist. Therefore,
we examined experimental longline fishing data,
with quasi-uniform vertical distribution of hooks,
to assess the vertical movement behaviour of albacore tuna. Based on this data, albacore tuna in
tropical waters utilize mostly the intermediate
layer during the daytime, i.e. the AB pattern (Fig.
7). Thus, all five behaviours most frequently predicted by our model are found in nature.
Behaviours D and E (rapid changes between
depth layers) deserve special attention. The emergence of these behaviours requires a very precise
adjustment of the synaptic weights, which suggests that these behaviours are especially adaptive
to the structure of the environment. The ability to
make rapid, frequent changes in depth is a special
adaptation in some pelagic fishes. Special sonictracking experiments were developed to study why
these animals exhibit these striking vertical move-
L. Dagorn et al. / Ecological Modelling 134 (2000) 325–341
Fig. 7. Depth distribution of albacore tuna catches (black
bars) and fishing effort (shaded bars) based on 53 daytime
fishing experiments (281 individuals captured). The experiments used an instrumented longline, with a total of 27 750
hooks set between 9 and 14° south in the French Polynesian
EEZ.
ments. Thermoregulation was demonstrated for
bigeye tuna, for example (Holland et al., 1992).
Carey and Scharold (1990) proposed that sharks
moved vertically to search for food using olfaction. A combination of factors may be involved in
explaining frequent, rapid vertical movements,
and these factors may differ from species to species. Our model indicates that this particular vertical behaviour could have evolved to efficiently
exploit the biotic environment.
5. Conclusions
We presented a minimal computational model
to explore the hypothesis that the biotic environment may have played a major role in the evolution of movement behaviours of tropical oceanic
predatory fishes. The model illustrated that realistic vertical movement patterns can evolve based
on simple, yet robust assumptions about prey
distributions. The success of this approach confirms the promise of individual-based artificial life
models for this kind of study (Judson, 1994), and
particularly the use of approaches like LEE to
study co-evolution of animals living in a same
environment (Menczer and Belew, 1996b).
339
A second objective of this work was to determine whether the biotic environment could induce
the emergence of several co-adapted behaviours.
Our results suggest that the variety of behaviours
exhibited by individuals or species corresponds to
different solutions for exploiting the same environment. While it remains important to study the
physiological limits of predatory species, our
modelling suggests the need for more research to
characterize the biotic environment of tropical
oceanic fishes and its relationship with behaviour.
This minimal model lends itself to numerous
refinements and extensions. Incorporating additional data about the French Polynesia EEZ
would benefit the model. For example, data on
the depth distributions of additional predatory
species is becoming available from fishing experiments. Predator diet data will also be available
soon from stomach content analyses. The model
of the prey environment could be made more
precise using information on horizontal and vertical prey distributions and dynamics, which is currently being analyzed from underwater acoustics
surveys combined with trawl sampling. This kind
of data will allow a more accurate, continuous
three-dimensional model of the environment, and
consequently a more refined model of fish movement behaviour.
Another direction for future work is to apply
this modelling approach to different environments. This would not be possible if the model
was specific to a particular area. Our assumptions
about the biotic environment could easily be adjusted to reflect conditions more realistic in other
areas. For example, in this paper we assumed that
no prey are found in the surface layer during the
daytime while the opposite is true in the eastern
Pacific Ocean. Yellowfin tuna feed on epipelagic
prey throughout the daylight hours in the eastern
Pacific (Olson and Boggs, 1986). By simulating
biotic environments corresponding to alternative
areas and comparing the emergent behaviours
with the known movement patterns of actual
fishes in those areas, we can test the generalization
power of the model.
Finally, the model could be extended to include
factors such as predator size, prey selection, and
physiological constraints corresponding to differ-
340
L. Dagorn et al. / Ecological Modelling 134 (2000) 325–341
ent individuals and species. We chose to disregard
predator size and prey selection in our model as a
simplifying assumption, albeit somewhat unrealistic. One way to address these problems would be
to include some adaptive physiological capabilities into the genotypic model, and study the relationship between the evolutions of behaviour and
physiology in heterogeneous populations. This
modelling approach might also be appropriate to
tease apart the variability observed in diet data
for different predatory species and different individuals of the same species in different environments. In this sense, our approach would be a
precursor for models that assume given trophic
relationships to study ecosystem dynamics (Pauly
et al., 1998).
Acknowledgements
The authors wish to sincerely thank the officers
and crew of the research vessel ‘Alis’ for providing valuable help during all of the ECOTAP
cruises. LD and PB would like to thank all the
scientists from SRM, IFREMER and IRD, who
worked with them during this program in French
Polynesia. FM acknowledges support from a University of Iowa travel grant.
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