Modeling an electrosensory landscape : behavioral and morphological optimization in elasmobranch prey capture
Department of Physics, University of San Francisco, San Francisco, CA 94117, USA
* e-mail: brownb{at}usfca.edu
Accepted 19 January 2002
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Summary |
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Key words: electroreception, elasmobranch, prey capture, bioelectric field, hammerhead, evolution, computational neuroethology, modelling
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Introduction |
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A predator must use sensory input to determine its prey's distance and heading as precisely as possible. The geometry of sensor location can greatly affect this task. Research into the auditory system of predators such as the barn owl, for example, has revealed that bilateral asymmetry in the auditory system one ear is higher than the other facilitates prey capture (Volman and Konishi, 1990).
Elasmobranchs can use an electrical sense to locate prey, even in the
absence of other cues (Kalmijn,
1966,
1982
). Although detailed
observations have been made (Kalmijn,
1971
,
1982
,
1997
), a quantitative model
for the way in which elasmobranchs `see' their local electrical landscape has
yet to emerge. Here, a mathematical model is used to link quantitatively the
physical geometry and movement of an elasmobranch to its resulting neural
input.
Some marine elasmobranchs are sensitive to electric fields of less than 5
nV cm-1, and they possess hundreds of electrically sensitive organs
known as the ampullae of Lorenzini
(Kalmijn, 1971;
Bennett, 1971
). The ampullae
are small, innervated bulbs, and these are connected to the aqueous
environment by narrow canals terminated by pores. Both the ampullae and the
canals are filled with an ion-rich jelly with electrical properties
approximating those of sea water (Waltman,
1966
). A single canal/ampulla system shows a maximum sensory
response when an electric field (voltage gradient) is applied parallel to the
canal (Murray, 1962
). The
ampullae are not sensitive to absolutely static electric fields. Instead, they
are sensitive to changes in the electric field that occur in the range 0.1-10
Hz, relevant biological frequencies for prey swimming movements or even gill
movements (Montgomery, 1984
;
Tricas et al., 1995
). Since
the strength of even a static field emanating from stationary prey will
necessarily drop off quickly with distance, a predator approaching the prey
will perceive a changing electric field. The relative motion between the
observer and the source is the key aspect for the underlying
electrodynamics.
Voltages within an ampulla are amplified by ion-channel-mediated
interactions between the apical and basal membranes of the ampullary sensing
cells (Lu and Fishman, 1994).
Sudden voltage changes in the ampullae have been shown to modify firing
patterns in the afferent nerves (Murray,
1962
; Montgomery,
1984
; Wissing et al.,
1988
; Lu and Fishman,
1994
). A sudden drop in voltage within the jelly leads to an
increase in the apparent firing rate (excitatory response), while a sudden
increase in the jelly voltage leads to a decrease in the measured firing rate
(inhibitory response). However, the mapping of voltage to firing rate is not
linear, and it can vary from organ to organ
(Tricas and New, 1998
).
Moreover, refined work has shown that the firing rate per se does not
change, but rather the probability of neuron firing changes
(Wissing et al., 1988
;
Braun et al., 1994
).
While the single-organ studies noted above have been very illuminating, an
elasmobranch's use of multiple ampullae in mapping its electrical environment
remains somewhat mysterious. Some have suggested that the relatively long
canals in marine elasmobranchs dampen high-frequency electrical signals
(Waltman, 1966). Others have
noted that the location of the ampullae and the orientation of their
associated canals should be critical to their electric field sensitivity
(Bennett and Clusin, 1978
). But
how does the ensemble of electrosensitive ampullae collaborate to recognize
the electric field of nearby organisms? What kind of information do the organs
collectively pass to the nervous system?
To link behavior and morphology to actual signals in an elasmobranch's nervous system, I have used electrodynamics to calculate the voltage changes arising at the ampullary ends of the associated canals as a predatory elasmobranch moves near prey. In this way, an approximate picture of body-wide electrosensory input the electrosensed landscape for the predator emerges. Since the location and orientation of the canals exhibit great variation both within a single species and among species, and since these geometrical factors influence the results of the calculations, the calculations lend themselves to comparisons of elasmobranch morphology.
After describing the model calculations, the present work uses the technique to address two separate issues. First, certain field observations of elasmobranch feeding patterns are quantitatively evaluated. Second, the modeling technique is used to explore evolutionary optimization by contrasting two elasmobranch morphologies.
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Materials and methods |
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The calculation for one canal is described first. Full simulations then
calculate the evolving voltages for 36 such canals. The coordinate system of
the calculation is centered on the prey fish (see
Fig. 1A). The dipole field
emanates from the prey, and a position vector
locates any relevant point in the
model elasmobranch. A dipole vector
represents the electric dipole of the prey fish. The canal, modeled as a
vector running from a pore to the corresponding ampulla, is labeled by the
angle this vector makes with respect to the forward direction of the predator
(upwards on the page). The fact that the label corresponds to canal
orientation and not to canal location must be emphasized because a canal's
orientation label will often be markedly different from a universal notion of
its location. (For instance, in Fig.
1A, the central canal would typically correspond to 0° as a
location in the horizontal plane, but the canal vector, running towards the
center of the body, would have an orientation of 180° with respect to the
forward direction.)
|
A useful representation of the dipole field for the present task is one
that assumes a spatial origin in the center of the dipole and describes the
resulting electric field at a distant point
in terms of the
dipole vector
and the separation
vector
:
![]() | (1) |
The canals leading to the ampullae are long (5-20 cm) and narrow (roughly 1
mm across). While the jelly inside conducts reasonably well (the reported
electrical resistivity of 24 cm places it within the realm of
semiconductors), the walls of the canals are highly resistive
(Waltman, 1966
). For this
reason, the canals can be treated as one-dimensional insulated electrical
antennae. For the model, the potential difference (V) between the
ampulla and the surrounding sea water is calculated using:
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The importance of vector geometry in this simulation contrasts with that
required for Polydon spathula, the paddlefish, a freshwater
electrosensitive predator that has been the subject of recent experiments and
modeling efforts (Russell et al.,
1999; Greenwood et al.,
2000
). In the paddlefish, the ampullae are located so close to the
skin that only the intensity of the prey's electric dipole field is relevant
(Greenwood et al., 2000
).
Vector geometry also distinguishes our modeling effort from those modeling the
sensory input of Apteronotus albifrons, a small, weakly electric
predatory fish with sense organs on its surface
(Nelson and MacIver, 1999
).
Furthermore, Apteronotus albifrons uses active electrolocation,
whereas the elasmobranchs use passive electrolocation. This is roughly
analogous to the difference between the active echolocation system of a bat
and the passive auditory system of the barn owl. Most elasmobranchs must
detect the weak electric field of the prey as opposed to an electric response
to their own electric field, and the vector nature of the field comes into
play as a result of the detailed variation of canal location and
orientation.
Since the elasmobranchs appear most sensitive to voltage changes within the
range 0.01-10Hz (Murray, 1962;
Montgomery, 1984
), the change
in the instantaneous voltage (
V) is computed between two
nearby time points as the ampulla moves with respect to the prey dipole:
![]() | (3) |
To calculate the relative differences in potential at the ampullary ends of
the canals, a reference potential must be set at the pore end when computing
the line integral in equation 2. In keeping with the assumptions of Kalmijn in
his treatment of geomagnetic orientation in sharks, the model assumes a
potential of zero at the pore (Kalmijn,
1973). This assumes that the sea water electrically `shorts' the
circuit of any two points on an elasmobranch's surface. In fact, the
functional model assumption here is much less restrictive. Since this model
seeks the change in potential at an ampulla, it assumes only that the
potential at an individual pore stays relatively constant over a fraction of a
second.
For simplicity, the sea water is assumed to be unmoving. Moving, ion-rich
sea water constitutes electric current, and other efforts have convincingly
described the way in which an elasmobranch might detect the fields resulting
from sea currents (Kalmijn,
1973).
The voltage changes are computed for 36 ampullae simultaneously. Results
from two simple predator geometries are presented below. The models (see
Fig. 2) are bilaterally
symmetrical and purely two-dimensional, and they are intended to explore the
utility of the technique more than to reflect exact elasmobranch anatomy. Each
model includes an array of 36 straight canals, oriented at intervals of
10° in the horizontal plane. The angles are defined for the vector
originating at the pore and terminating at the ampulla, with an angle of zero
corresponding to a vector pointing `north' on the page. Ampullary voltage
changes are denoted Vn, where n is the
angle index.
|
Model , a `roundhead' elasmobranch, is depicted in
Fig. 2A. This can be considered
a top view of a predator moving up the page (north). The canal vectors all
point inwards and terminate in a cluster of ampullae. All canals in model
have the same length of 10cm. Admittedly, this model is more
symmetrical and uniform than real elasmobranchs. However, actual elasmobranch
canal orientations do show nearly 360° of variation, and canals typically
have a horizontal component directed away from the skin
(Tricas, 2001
). In this sense,
model
is a useful, generic model. It is a sensible starting place for
a marine shark or marine ray.
Model ß, a `hammerhead', is shown in
Fig. 2B. The hammer geometry is
especially well suited for the simulation because it is two-dimensional and it
highlights the extreme morphological variation of elasmobranchs. Although
still simple and symmetrical, this model is not an unrealistic version of
hammerhead canal geometries, particularly for Sphyrna lewini
(Gilbert, 1967). The model
canals vary in length and terminate in three distinct clusters of ampullae.
The canal orientations mark out 10° intervals exactly like those in model
. The width of the rostrum is 50 cm, and the hammer measures 20 cm from
front to back. The sizes of the models are realistic for the heads of
sub-adult reef sharks and hammerheads of the same approximate length tip to
tail.
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Results |
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The voltage changes in the ampullae are plotted in Fig. 4 on the ordinate for the 36 canals, with canals designated by their vector orientation, ranging from 0 to 360° on the abscissa. In this picture, 90° corresponds to the left side of the predator, 180° corresponds to the tip of the rostrum and 270° corresponds to the right side. Again, note that the location of the sense organs is typically shifted by 180° from the corresponding canal orientation.
|
Fig. 4A shows the organ-by-organ voltages that develop over 0.2s when the model moves at 0.5 ms-1 through a point located 80 cm to the south of the prey dipole. Similarly, Fig. 4B depicts a later point, when the separation is 50 cm, and Fig. 4C depicts the results when the separation is only 20 cm. Please note that the scale of the ordinate increases by roughly two orders of magnitude from Fig. 4A,B to Fig. 4C (0.1-10µV scale). In fact, many figures will vary the voltage scale to display the results best.
The basic patterns in Fig. 4
are typical of all such trials for various dipole and elasmobranch
orientations. A range of adjacent organs experience positive
Vn values, while the others experience negative
Vn values.
To reiterate, voltage decreases have been linked to excited firing rates
and firing probabilities in the primary afferent nerves of elasmobranchs,
while voltage increases have similarly been linked to inhibited firing rates
and probabilities (Murray,
1962; Montgomery,
1984
; Lu and Fishman,
1994
; Braun et al.,
1994
; Tricas and New,
1998
). The modeled
Vn in
Fig. 4B, for instance, show a
maximum change of approximately 75 nV. According to experiments on ampullae
excised from skates, a 75 nV voltage rise within the ampulla would lead to an
approximately 0.3% decrease in the firing rate of the primary afferent nerve
(Lu and Fishman, 1994
). In
situ measurements show much greater sensitivity of the firing rate to
electric field variations. In anesthetized thornback rays, a 75 nV increase
would correspond to an almost 2% change in the firing rate of the primary
afferent nerve and, notably, a modification of more than 18 % in the firing
rate of the secondary neurons (Montgomery,
1984
). More recent measurements on live round stingrays have shown
organs with different tiers of sensitivity
(Tricas and New, 1998
). In the
most sensitive organs, a 75 nV increase would correspond to an almost 10 %
change in the primary afferent firing rate. The sensitivity of the organs in
that study showed dependence on stimulus amplitude. Given the range of results
and the apparent non-linearity of rate coding in these organs, the results
here will present voltages without a translation to firing rates.
A more complicated and more likely scenario of prey capture is taken up next. Here, the elasmobranch's initial path will not take it directly to the prey. In this case, as shown in Fig. 5, the elasmobranch begins reacting to electrosensory input at point A, when it is directly southeast of the prey, 40 cm south and 40 cm east, and moving at 0.5 m s-1 to the north. For variety, the dipole is oriented north in this example, parallel to the elasmobranch's heading. The development of ampullary voltages is computed first at point A and then for three predator options: maintaining the original course (path A to B); moving along a path similar to those recorded in certain behavioral studies, where the elasmobranch maintains a somewhat constant orientation to the dipole field (path A to C); or turning sharply to take a direct path to the dipole source (path A to D).
|
Observationally, Kalmijn collected data for sharks approaching a man-made
dipole, so that other senses could presumably be ruled out. He found that
Mustelus canis, the dogfish, turned and snapped at the dipole source
at short range (Kalmijn,
1982). However, he also observed non-direct approaches for both
the dogfish and Prionace glauca, the blue shark, in which a predator
moved along a precise curved path and did not face the prey until just before
capture. Both approaches have been observed more recently in Sphyrna
lewini, the scalloped hammerhead, and Carcharhinus plumbeus, the
sandbar shark (S. M. Kajiura and T. Fitzgerald, personal communication).
Kalmijn (1982
) described the
non-direct behavior by proposing an `approach algorithm' in which the predator
seeks to maintain a roughly constant angle between its central axis and the
local electric field.
Values of Vn in the ampullae of model
were calculated for point A and for three options that could possibly
follow. Fig. 6A depicts the
initial voltage signals to which the elasmobranch model reacts as it moves
directly northward. The results for an unaltered course are shown in
Fig. 6B; here, the elasmobranch
ignores the prey dipole. Results for a path like those observed in
Mustelus canis are shown in Fig.
6C. (It is actually impossible to maintain the relationship of
each canal to the electric field because of the unique gradient of the dipole
field; here, at point C in Fig.
5, the model has rotated 47 ° counterclockwise, maintaining
the relationship of most canals to the electric field vector to within 5
°.) Results for a quick turn followed by a direct approach are shown in
Fig. 6D.
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Comparison of morphology
The two models, and ß, were compared and contrasted in two
simple predatorprey scenarios.
Fig. 7A,B displays the
results of models and ß passing a prey fish to the side. The
elasmobranch position in each case is 50 cm west and 15 cm south of the prey
dipole. The dipole is oriented at 10 ° east of north, and the elasmobranch
moves directly north.
|
Fig. 7C,D also gives the
Vn values that develop in models
and ß
as they directly approach a prey dipole oriented at 45 ° with respect to
north, from a distance of 20 cm. This corresponds to the scenario of
Fig. 4C, and the data for model
are replotted for purposes of comparison.
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Discussion |
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The resulting Vn data sketch the sensory input
for a creature detecting a vector field. This is novel in that most sensory
systems detect scalar information. Olfactory, auditory, thermal and mechanical
sensors are all based on the pure intensity of input, whereas the electrical
sense attempts to divine both the intensity and the direction of the stimulus.
Note the counterintuitive nature of some results. While canals closer to the
prey typically give larger signals than the canals on the opposite side of the
model rostrum, the data presented in Fig.
7A,B, for example, show relatively small voltages for the organ on
the right side (270 °) of the rostrum for both models, even though this
organ is one of the closest to the prey fish. The signal is limited because
the canal is nearly perpendicular to the dipole field in this case. For a
purely intensity-based sense, this organ would register one of the highest
voltages.
The basic patterns shown in Figs 4, 6 and 7, an inhibitory electrosensory response from one segment of the rostrum mixed with an excitatory sensory response from another, could be the fingerprint that an elasmobranch learns for nearby organisms.
Prey-capture approach strategies
The modeling results summarized in Figs
5 and
6 offer a sensible explanation
for the proposed approach algorithm of Kalmijn
(1982, 1987) in which an
elasmobranch approaches prey in such a way to maintain a constant orientation
to the electric field vector. Note that the forms of
Fig. 6A and
Fig. 6C are very similar. An
animal moving along path A to C would, after first reacting
to the prey electric field at point A, simply reinforce the initial
firing rate alterations. By loose analogy, an organism can approach a
particular sound's source by moving in such a way as to increase the perceived
intensity of that sound. Here, the elasmobranch appears to move in such a way
as to increase the intensity of a telltale firing pattern from its
ampullae.
However, by maintaining its course (path A to B) or
turning to directly approach the prey (path A to D), the
elasmobranch substantially changes the pattern of
Vn. Many organs change their polarity for choices
B and D, so that initially inhibitory responses would become
excitatory and vice versa. In fact, for the results in
Fig. 6B, the organ at 100°
(almost the left-most organ on the head) has gone from having the maximum
positive voltage change (Fig.
6A) to a negative voltage change.
The previous comments offer a qualitative first impression of the data
presented in Fig. 6. Ideally,
to offer a more quantitative analysis of the results, one would accumulate the
firing rate changes from the array of organs, perhaps using a population
vector. Such an analysis has been carried out successfully for the sand
scorpion Paruroctonus mesaensis, a predator that passively collects
vibrational data from an array of sensors to locate prey
(Sturzl et al., 2000).
However, as noted above, rate coding in the elasmobranch's electrosensor is
not fully understood, and the population vector is beyond the scope of the
initial step presented here.
Instead, behavioral options can be roughly evaluated in a picture of signal
reinforcement. A dimensionless measure, R, is defined here as a
reinforcement factor. It averages the perorgan ratio of initial
Vn (
Vn,init) to final
Vn (
Vn,final), and it
weights the importance of each organ by the size of its original voltage
signal compared with the average (
Vavg,init):
![]() | (4) |
Computing this quantity for the data shown in Fig. 6 gives the following. For the unaltered path A to B, R=-1.3; for the direct path A to D, R=-1.1; and for the algorithm path A to C, R=+9.1. These results, together with the numbers of organs maintaining polarity out of 36, are presented in Fig. 8A. Path A to C gives strong reinforcement of the detected electrosensory signal, with the average organ maintaining its original polarity and increasing the related signal. However, both paths A to B and A to D give negative reinforcement values, so that the strong signals typically change polarity. It is somewhat surprising that the turn to a direct approach (which has been observed) is apparently no more beneficial than a path that ignores the signal. Note, however, that the ordinate scales in Fig. 6 show that an animal pursuing path A to D would receive the largest voltage signals of any option.
|
To further compare approach strategies depicted by paths A to
C and A to D, the reinforcement factor is also
computed for the simple direct approach shown in Figs
3 and
4. This approach does not
involve the quick turn, but otherwise it serves as a sort of intersection of
the two observed strategies. When an elasmobranch's initial velocity leads to
the prey dipole along a direct radial path (presumably rare if all
possibilities are considered), the predator automatically maintains its
orientation to the dipole electric field, and this is consistent with the
approach algorithm of Kalmijn
(1982, 1987). R is
calculated for the change from 80 to 50 cm and for the change from 50 to 20
cm. The results are shown, again with the number of organs maintaining
polarity, in Fig. 8B.
Apparently, this path shows dramatic reinforcement of the initial
Vn pattern. However, the polarity fraction numbers
decrease. As the predator draws close to the prey, some of its organs change
polarity, even as the
Vn values themselves increase
dramatically.
Perhaps the approach algorithm serves as a guide for the predator until, at closer range, it can more precisely determine the prey's exact location. At this point, the algorithm and maintenance of organ polarity are abandoned, and the predator moves as quickly and as directly as possible to the dipole source. Such a detection strategy could help explain the fact that both forms of approach are observed in behavioral experiments. These comments are highly speculative for such a skeletal calculation. In addition to adding computational and morphological complexity, future models of feeding behavior should also consider observed non-linear, pre-detection motions of the predator (e.g. side-to-side movement of the rostrum at a regular frequency).
Comparison of morphology
Although the results for two morphologies display many differences, the
qualitative similarity of voltage trends is important in evaluating the
modeling technique itself. The induced polarities (positive or negative) of
the values of Vn of model ß typically match
those in the simple rounded model. This is true despite significantly
different canal lengths, canal locations and ampullae locations. Since the
canal orientations are the only shared characteristic of the two models, the
qualitative similarity of the results underscores the importance of canal
orientation. Moreover, the similarity increases the confidence with which one
can view the results of the behavioral trials discussed above. In short,
models more sophisticated than model
give qualitatively similar
results. Therefore, the behavioral results above are significant even though
model
is more simple and symmetrical than an actual elasmobranch.
Despite the qualitative similarity of Vn
patterns for the two models, they also show striking quantitative differences.
In the case of Fig. 7B, model
ß shows substantially greater voltage signals. In fact, the maximum
amplitude of voltage change in model ß (-185 nV) is approximately six
times that found in model
(-30 nV). Referencing data in the thornback
ray again, such voltages could correspond to a 0.75% change in primary
afferent nerve firing rates in model
versus a 4.5% change in
model ß (Montgomery,
1984
). This result is not surprising since the hammerhead model
places the canals, and some of the ampullae themselves, closer to electric
field sources that lie at some distance from the central axis of the
elasmobranch. However, model ß would also afford an elasmobranch finer
angular resolution of the prey location than model
. Note that the
largest signal in model ß (-186 nV at 240°) is more than double the
signal found in organs only 20° away. In addition, the peak stimulus is
proportionally much greater than the background for model ß. Taking the
absolute value of all ampullary signals, the maximum signal in model ß is
4.8 times its average ampullary signal (39 nV). Meanwhile, model
has a
maximum signal (32 nV) only 2.1 times greater than its average ampullary
signal (15 nV).
The results in Fig. 7D also
show fine angular resolution in the hammer-shaped model. Although the canals
are no closer to the prey source in model ß, and the magnitudes of the
resulting Vn are no larger, the model again offers
better angular resolution than model
. An elasmobranch with sensory
organs arrayed along a hammer would evidently have a more precise knowledge of
the prey's bearing.
To summarize, the results show a strong quantitative evolutionary advantage
for model ß over model . Although many have proposed that the
curious hammer shape evolved to aid electroreception, this may be the first
detailed, quantitative support for that hypothesis.
The computational technique advocated here shows promise for further
morphological comparison. It should be able to illuminate which elasmobranch
morphologies are better suited for which electromagnetic task. Future plans
for the technique include incorporating greater computing power and digitizing
the canal systems of several different elasmobranchs. Such goals appear to be
especially well suited for a `neuroecological' analysis of elasmobranch
morphology, and detailed morphological data for the electrosensors of several
species have recently appeared in the literature
(Tricas, 2001;
Kajiura, 2001
).
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Acknowledgments |
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References |
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