A Behavior-Based Model of the Hydra, Phylum
Cnidaria
Malin Aktius1 , Mats Nordahl2 , and Tom Ziemke1
1
University of Skövde
School of Humanities and Informatics
SE-541 28 Skövde, Sweden
{malin.aktius,tom.ziemke}@his.se
2
Department of Applied Information Technology
Göteborg University and Chalmers University of Technology
SE-417 56 Göteborg, Sweden
[email protected]
Abstract. Behavior-based artificial systems, e.g. mobile robots, are frequently designed using (various degrees and levels of) biology as inspiration, but rarely modeled based on actual quantitative empirical data.
This paper presents a data-driven behavior-based model of a simple biological organism, the hydra. Four constituent behaviors were implemented in a simulated animal, and the overall behavior organization was
accomplished using a colony-style architecture (CSA). The results indicate that the CSA, using a priority-based behavioral hierarchy suggested
in the literature, can be used to model behavioral properties like latency,
activation threshold, habituation, and duration of the individual behaviors of the hydra. Limitations of this behavior-based approach are also
discussed.
Key words: behavior-based modeling, data-driven modeling, hydra,
colony-style architecture
1
Introduction
Drawing upon theories from, for example, neuroscience, ethology, cognitive sciences, and evolutionary game theory, the use of biology in robotics has been
influenced by several types of mechanisms underlying behavior [1]. The degree
of biological inspiration for artificial agents is, however, quite diverse: ranging
from classical control systems using only vague arguments founded in biology
to actual replication of biological behavior [2]. In this work, we are concerned
with the ethological3 perspective on behavior, which explains behavior from a
functional aspect, in terms of e.g. reflexes, fixed action patterns, and orientation of movement (e.g. [3]), and we investigate the possibility for a data-driven
approach to behavior-based modeling of a lower animal.
3
The study of animal behavior under natural conditions.
2
Malin Aktius, Mats Nordahl, and Tom Ziemke
A behavior-based model at the ethological level is proposed in [4], in terms of
decision upon straight-line swimming vs. tumbling behavior in bacteria. Turning
to a more complex animal, another example can be found in [5], where parts of
the visuo-motor behavior of the praying mantis4 are modeled using the framework of schema theory, and implemented in a hexapod robot.
In this work, we aim at developing a data-driven behavior-based model of
the constituent behaviors and the behavioral organization of a simple biological
organism. For this approach, the following criteria are proposed for a model organism: (1) Sufficient availability of literature on quantitative behavioral studies
– for input-output modeling of sensorimotor actions. (2) Sufficient availability
of literature on studies of interaction of behaviors – for implementing a relevant
behavior selection system. (3) The organism should have a simple nervous system – for ease of modeling internal processes. Based on these criteria, the hydra
(Hydra) was selected model organism for this work. The next section provides
some background information on the hydra. Section 3 then states the models
and methods used, whereas the experiments and results are provided in Section
4. Finally, Section 5 discusses the outcome, recommendations for future work,
and limitations of the model.
2
Background: The Hydra and its Behavior
The selected model organism, the hydra, is shown in Fig. 1. Hydra belongs to the
phylum Cnidaria, the first evolved animals (that still exist) to possess nerve cells
and sense organs. It lives in ponds, lakes, and streams, where it is most often
found attached, by its foot, to some vegetation. The hydra feeds on small aquatic
invertebrates, can reproduce sexually or asexually, in the latter case by means
of budding. It remains in its tube-shaped polyp form throughout its lifetime [6].
Fig. 1. Three hydras. Image courtesy of BioMedia Associates [7].
4
A large, carnivorous insect.
A Behavior-Based Model of the Hydra, Phylum Cnidaria
3
Turning now to the behavior of hydra, the distinct movement patterns of the
animal, resulting from alternating activity of its motor cells, consist of: (1) contraction and extension of body and tentacles, (2) feeding, involving a sequence of
actions, and (3) locomotion, accomplished either by gliding (by means of cilia5
on the foot.), or by somersaulting [8, 9]. In the literature, the behaviors of hydra
are described in terms of responses to specific stimuli rather than in terms of
the actual movement patterns of the animal. Mainly, four distinct constituent
behaviors are identified: spontaneous actions, response to mechanical and light
stimuli, respectively, and feeding [8, 9]. A priority-based organization of the behaviors has been suggested in e.g. [10], with feeding inhibiting responses to light
and mechanical stimuli, and response to light inhibiting response to mechanical
stimuli.
Spontaneous actions: Without changes in hydra’s external environment, it
shows spontaneous, periodic, contractions and locomotion. There is an adaption to background illumination in the sense that the contraction frequency
varies with ambient light conditions. The actions also depend on the nutritional state of the animal: contraction frequency decreases with starvation, while locomotion is more common in starved hydras. After one week of
starvation, practically any overt behavior ceases, and the animal eventually
perishes [11].
Response to mechanical stimuli: Response to mechanical stimuli, such as
shaking or physical contact, occurs by means of contraction or locomotion.
The way in which the hydra responds depends on stimuli interaction history
as well as on the nutritional state of animal: starved animals are more likely
to respond by locomotion, whereas a contraction response is more common
in well fed animals. The response shows habituation to repeated stimuli [12].
Response to light stimuli: On exposure to strong light there is an immediate inhibition of any ongoing contraction. Following a latency, a response
consisting of either contraction or locomotion is evoked. Also in this case,
locomotion is more common in starved animals. The latency is inversely
related to light intensity [13], and there is no habituation [12].
Feeding: Hydra’s feeding behavior consists of a sequence of actions, and the
behavior is evoked by mechanical stimulation of hydra’s tentacles or by the
presence of glutathione (GSH), a peptide released by prey stung by hydra’s
nematocysts6 . The activation threshold for feeding is regulated by hydra’s
nutritional state, with starved animals having a lower threshold than recently
fed ones. There is also a refractory period following a feeding response, during
which the capacity of responding is gradually regained e.g. [10].
In summary, hydra’s response to a given stimulus depends on: (1) stimulus
configuration, such as intensity or concentration, (2) state of internal variables,
such as its nutritional level, and (3) stimulus interaction history, such as habituation to a mechanical stimulus.
5
6
Small, hairlike extensions.
Stinging organelles located on hydra’s tentacles.
4
3
Malin Aktius, Mats Nordahl, and Tom Ziemke
Models and Methods
This section starts by presenting the simulated hydra and its environment, and
continues by briefly describing the colony style architecture (CSA) for behavior
selection, as well as presenting the implemented CSA behavioral organizer. Due
to lack of space, some details are omitted, but can be found in [14].
3.1
The Simulated System
The hydra was modeled here ignoring the dynamical properties of its body. In
this simplified model, the animal’s body is represented in 2D, by a circle with
radius r and maximum extension length lmax . The movement of the animal is
controlled by setting the physical state variables in a simplified manner. The
environment of hydra consists of a square-shaped arena with periodic boundary
conditions. The implemented physical state variables are shown in Table 1.
In [15], the concept of motivational state is explained as the combined perceptual and physiological state of an animal, i.e. the state of its external and
internal environment. Table 1 shows the five motivational state variables that
were implemented in the simulated hydra.
Table 1. Top panel: Physical state variables for the simulated hydra in a 2D environment. For the extension rate, rext , 0 denotes maximal contraction, and 1 maximal
extension. S denotes the side-length of the arena. Bottom panel: Motivational state
variables for the simulated hydra. The upper limit imposed on hunger, hmax , corresponds to one week of starvation, see Section 2.
Variable
Range
Ml
[0, 1]
Mm
[0, 1]
Mc
[0, 1]
Mh
[0, hmax ]
Mbeh B1,B2,B3,B4
Variable
xf
yf
θext
θloc
rext
Range
[0, S]
[0, S]
[0, 2π]
[0, 2π]
[0, 1]
Description
Reading of light sensor
Reading of touch sensor
Reading of GSH sensor
Nutritional state
Current active behavior
Description
Position of foot
Position of foot
Direction of body extension
Direction of animal locomotion
Extension rate
Four main constituent behaviors were implemented in hydra’s behavior repertoire: spontaneous actions, response to mechanical stimuli, response to light stimuli, and feeding. The first three behaviors all generate movement of the animal in
terms of either contraction or locomotion, and these movement patterns were implemented as sub-behaviors of the corresponding main behaviors. Table 2 shows
the implemented behaviors in the model of hydra.
A Behavior-Based Model of the Hydra, Phylum Cnidaria
5
Table 2. Behaviors and sub-behaviors in the simulated hydra. Priority 1 denotes the
highest priority.
Sub-behaviors of B1-B3
Label Priority Description
Label
Description
B1
4
Spontaneous actions
B2
3
Response to mechanical stimuli B11, B21, B31 Contraction/
B3
2
Response to light stimuli
Extension
B4
1
Feeding
B12, B22, B32 Locomotion
3.2
The Control Architecture
For coordination of hydra’s constituent behaviors, the CSA [16] was used. Developed by Connell, it descends from the subsumption architecture presented by
Brooks [17], and operates according to the following principles [16, 18]:
– It uses an arbitration method, i.e. only one behavior is active a time.
– Behaviors are arranged in layers, in a priority-based manner.
– Each behavior is associated with an applicability clause (AC), and a transfer
function (TF). The AC determines whether the behavioral output should be
active or not, while the TF determines what action the agent would take
(typically the motor output), assuming that the behavior is active.
– Switches on the behavioral interconnections perform the actual behavior
selection (see Fig. 2). The following switch types exist: (1) Suppression, where
an active output from a a higher-priority behavior replaces any lower-priority
behavioral output. (2) Inhibition, where a higher-priority behavior (whenever
active) prevents a lower-priority one to generate any output. (3) Release
type, where a higher-priority behavior enables the output of a lower-priority
behavior to pass through the switch.
In a CSA, an AC can be either situation-driven or event-driven. A situationdriven AC is related to a goal state, and only the present motivational state of
the agent determines whether the AC should be true or false. An event-driven
AC, on the other hand, is of set/reset type where a certain event7 triggers the
AC, and another event resets it.
For the priority-based interaction of the behaviors in the hydra, suggested in
e.g. [10], behavioral organization using a CSA can be accomplished by organizing
the behaviors in layers with respect to priorities, using switches of suppression
type for the behavioral inter-connections. Fig. 2 shows the implemented behavioral model.
In [8, 9], a random-walk movement was observed in undisturbed hydras. To
implement this property in the simulated animal, the locomotion direction, θloc ,
was set to a new, random value for each locomotion response. Also, in the abovementioned works, it is suggested that the animals extend in a new, random direction following a contraction. Thus, also the extension direction, θext , of the
7
According to Connell, an event is characterized by a very brief (point-like) occurrence, whereas situations typically are extended intervals of time [16].
6
Malin Aktius, Mats Nordahl, and Tom Ziemke
simulated hydra was set to a new, random value for each contraction. To simulate the nutritional state of the hydra, Mh , was set to decrease during feeding,
and increase while any other behavior is active.
Fig. 2. Implemented overall organization (in the CSA) of the constituent behaviors
B1-B4 in the simulated hydra. Here, S represents switches of suppression-type.
4
Experiments and Results
Using a CSA, generation of the constituent behaviors amounts to defining an
AC and a TF for each behavior. Experimental data from the literature was used
to validate the properties of ACs and TFs. As described in Section 3, the actual
movement patterns of the animal were implemented as sub-behaviors of the
main behaviors. The biologically plausible concepts of contraction pulses (CPs)
and locomotion pulses (LPs) [10, 11] were adopted. In this way, contraction and
locomotion are accomplished by corresponding pulse signals, extended in time,
which cause animal movement. Note that an active AC only states a potential
activeness of its corresponding behavior, the actual behavior selection is carried
out by the way in which the behaviors are interconnected (i.e. how they are
arranged in layers and what switch types are used).
4.1
Spontaneous Actions (B1)
By default, a spontaneous action is an applicable behavior, and hence the AC
for this behavior is always true. The TF consists of CPs and LPs at certain
times, which were implemented as inhomogeneous Poisson spike trains to agree
with the behavior suggested in [11], as briefly described in Section 2. The results,
shown in Fig. 3, are an expected value of CP rate that is linearly decreasing with
Mh (i.e. with the time of starvation), and an expected value of LP rate that is
normally distributed with mean at Mh = hmax /2.
A Behavior-Based Model of the Hydra, Phylum Cnidaria
4.2
7
Response to Mechanical Stimuli (B2)
As previously described, B2 shows habituation to repeated stimuli, and the
evoked response is either contraction or locomotion. Following the suggestion
in [4], a habituation model based on cascaded leaky integrators was used, where
the model output denotes the response probability, pB2 , in the presence of a
stimulus. An event-driven AC was used, with activation criteria Mc > 0 and
pB2 > X, where X ∼ U (0, 1). Completion of an evoked response, i.e. the end
of a CP or an LP, resets the AC. A constant latency was used, and an example
of a TF during B2 (in the case of contraction) is shown in Fig. 3. Following
observations made, e.g. in [8], that starved animals are more likely to respond
by locomotion, the probability of LP was set to increase with Mh . With Y1 as
the stimulus input, the equations for unit j in a cascade of n leaky integrators
become:
Vj (k + 1) = aj Vj (k) + bj Yj (k),
Yj+1 (k) =
Yj (k) − Vj (k), Yj+1 (k) > Tj
0,
otherwise.
(1)
(2)
Yn+1 , the output from the n:th unit, was taken as pB2 . An evolutionary algorithm
(EA) was used to optimize the size and parameters of the habituation model,
with respect to training data from experiments carried out in [12]. The final,
evolved, model consists of 10 units, and its response to various inter-stimulus
intervals (ISIs) is shown in Fig. 3.
4.3
Response to Light Stimuli (B3)
Since the evoked response to light stimuli, to a great extent resembles, the one to
mechanical stimuli, the behavior generation is similar to the one of B2. For B3,
however, no habituation occurs, whereas the latency is invesely related to the
intensity of a stimulus, see Fig. 3. Activation of the (event-driven) AC occurs if
Ml > Tl , where Tl is the activation threshold, set here to be constant. The same
CP/LP relation as in B2 was used.
4.4
Feeding (B4)
B4 was modeled to be activated by the presence of GSH, where the activation
threshold depends on hydra’s nutritional state and where there is gradual recovery of feeding ability, as discussed in Section 2. An event-driven AC was used,
where activation of the AC occurs if Mc > Tf , and the AC is reset if tB4 > Df ,
or if Mc = 0. Here, tB4 denotes the time for which B4 has been active, and Df
denotes the ability of the feeding response, in terms of duration, at the time of
activation of B4. Thus, feeding occurs until repletion or until the presence of
food is no longer detected by the sensory system.
8
Malin Aktius, Mats Nordahl, and Tom Ziemke
Expected pulse rates
-3
3.5
x 10
3
Output from model at ISI = 16
Output from model at ISI = 8
Output from model at ISI = 4
Training data, ISI = 8
1
0.8
2.5
Response strength
Expected rate [1/s]
Response from 10 unit leaky integrator model
Expected CP rate
Expected LP rate
2
1.5
1
0.6
0.4
0.2
0.5
0
0
0
1
2
3
4
5
6
0
7
Nutritional state, Mh
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
Time [s]
x 10
Latency vs. stimulus intensity
2
4
x 10
Effects of starvation on feeding threshold
-3
450
10
Measured threshold
Approximated threshold
Measured data
Function approximation
Glutathione concentration [M]
400
350
Reaction time [s]
0.2
5
300
250
200
150
100
-4
10
-5
10
-6
10
50
0
-7
0
10
20
30
40
50
60
70
80
90
100
10
0
1
10
Relative light intensity [%]
2
10
10
Starvation time [h]
Example of contraction response to mechanical stimulus
Time for recovery of feeding response
1800
1
Transfer function during B2
Duration of feeding reflex [s]
1600
1400
1200
1000
800
600
400
200
0
Contraction pulse
0.8
0.6
0.4
Set of AC
0.2
Reset of AC
Latency
0
0
5
10
15
20
25
30
Starvation time [h]
35
40
45
50
0
2
4
6
8
10
Time [s]
12
14
16
18
20
Fig. 3. Top left: Expected values of CPs and LPs, respectively, for B1 as functions
of the simulated hydra’s nutritional state. Top right: Decrease in response strength,
pB2 , for B2 as a result of the habituation effect. Output generated by the best evolved
leaky integrator model, consisting of 10 units. Middle left: The latency of B3 as a
function of stimuli intensity. Middle right: The activation threshold of B4 as a function
of the simulated hydra’s nutritional state. Bottom left: The effect of starvation on the
(possible) duration of B4. Bottom right: Example of behavioral output from the model,
showing the transfer function for a contraction response, B21, to a mechanical stimulus.
A Behavior-Based Model of the Hydra, Phylum Cnidaria
5
9
Discussion and Conclusions
The general conclusion of this work is that it is possible to model several of the
behavioral properties of the hydra using the CSA as a framework. The modeled
latency of the animal’s response to light stimuli, the habituation effect of its
response to mechanical stimuli, the duration of the feeding response, and the
feeding activation threshold are consistent with experimental data obtained in
experiments with the real hydra. Specifically, it was found that a habituation
model based on cascaded leaky integrators can represent the habituation properties of the animal. In order to obtain conclusive results concerning the overall
behavior of hydra, however, some improvements remain. Currently, only little
experimental data on the integration of behaviors in the real animal is available,
which of course constrains this data-driven model. Generation of more test data
from experiments with the real hydra is recommended to inform improvement
of the current model. For example, a recording not only of the spatial patterns
of movement of the real hydra (as in [8, 9]), but also of the time of occurrence
for each movement, could be used as validation data for simulation results of the
animal’s spontaneous movement. Also of interest for further work is an investigation of the extent to which the suggested priority-based behavior organization
holds. For this purpose, experiments on how the real animal reacts to light and
mechanical stimuli during feeding are recommended.
Finally, while the data-driven behavior-based modeling approach taken here
has the advantage that it matches very well typical ethological descriptions of
behavior as consisting of a discrete set of constituent behaviors, fixed action
patterns, identified by a human observer, it should of course also be noted that
this approach has its limitations. Several authors have argued and demonstrated
that relying on an observer’s distal description of behavior in breaking down
behavior-generating mechanisms into sub-behaviors is problematic, and should
ideally be replaced by self-organization of behavior-generating mechanisms (e.g.
[19]). Biró and Ziemke [20], for example, analyzed the case of simple recurrent
neural networks evolved for the control of visually guided search behavior, and
showed that the networks, through feedback and self-modulation over time, exhibited what to an observer could very well appear to be a number of distinctly
different behaviors organized in a subsumption architecture. Hence, the fact that
we have shown in this paper that ethological descriptions of the hydra’s overall
behavior as consisting of four distinct constituent behaviors can be modeled in
a corresponding CSA, should not be taken as conclusive evidence that the real
hydra’s behavior is actually organized this way. An alternative approach to modeling the hydra’s behavior would be, for example, an evolutionary-robotics based
model in which the empirical data available for the real hydra could inform the
formulation of an appropriate fitness function for the evolution of its artificial
counterpart without breaking down the control architecture in a modular fashion
a priori.
Acknowledgments. This work was supported by a European Commission
grant to the project “Integrating Cognition, Emotion and Autonomy” (ICEA,
10
Malin Aktius, Mats Nordahl, and Tom Ziemke
IST-027819, www.iceaproject.eu) as part of the European Cognitive Systems
initiative. The experimental part was carried out while the first author was at
Chalmers University of Technology [14]. The writing of this paper has benefited
from discussions with Robert Lowe.
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