HOW DO JUMPING SPIDERS CATCH UP ON THEIR PREY?: A MODEL FOR PURSUIT BEHAVIOUR. (ARANEAE; SALTICIDAE)
Lyn. M. Forster, McMasters Rd., RD 1, Saddle Hill, Dunedin. New Zealand.
Malcolm R. Forster, Philosophy Department, University of Wisconsin, Madison, USA.
Preliminary Draft, 06 Aug 1999
To catch a ball thrown into the air, we need to estimate its direction, speed and likely place of fall to earth, and to do this we have to keep our eyes on the ball. To catch their prey, jumping spiders are faced with similar tasks and must also keep their eyes on the target. But how does a small arachnid make the necessary decisions? We explore the possibilities.
|Fig. 1: Trite Planiceps: The jumping spider used in the study. Drawing © 1967 by R. R. Forster, scanned by N. K. Forster.|
Jumping spiders have good eyesight (Homann 1928, Land 1969 a b), making use of six of their eight eyes to turn towards, catch up on and jump at their prey. Briefly, either the posterior-lateral (PL) or anterior-lateral (AL) eyes induce turns towards nearby movement, and the anterior-median (AM) eyes, now directed at the target, identify it. If it is prey, the spider sets off in pursuit and finally jumps to capture it. These coordinated movements, described as Orientation, Pursuit and Capture (Forster 1977) are readily observed in the field or in captivity. For most of these spiders, pursuing the prey may be achieved by chasing (mediated by the AL eyes) or stalking (mediated by the AM eyes), distinctive locomotory movements which depend on the angular velocity of the target as well as spider-target distances (Forster 1979). Chasing can be as fast as 50 mm/s whereas stalking is recognized by the low crouching profile of the spider combined with stealthy creeping movements.
The visual determinants of their predatory behavior have been investigated several times in the laboratory using a variety of techniques such as attaching stimulus models to the interior of a revolving drum (Land 1969a,b, Duelli 1978, Forster 1985) or the frontal presentation of two-dimensional dummies within the anterior visual fields of view (Homann 1928, Drees 1952, Gardner 1965). However, in cases where spiders were tethered or where stimuli were stationary or quasi-stationary, rapid pursuits were not elicited, hence chasing behavior was not observed.
|Fig. 2a: Diagram of apparatus showing position of the light source and the stationary platform about which the cylindrical drum revolves. A curtain placed over the light and around the drum shields the area from variable light sources (such as sunlight) and minimizes perception of the observers movements of the spider.|
Studies using jumping spiders able to move freely and in which different pairs of eyes were occluded (Forster 1979) showed that chasing behavior is controlled by the anterior-lateral eyes if the target is moving at angular velocities of more than 4°/sec. However, during chasing, the principal eyes are still involved in tracking and evaluating the target in the manner described by Land (1969b). The present studies examined a series of pursuits by Trite planiceps (Araneae: Salticidae) in which spiders chased targets moving at more than 4° /s. A model and analyses of pursuit behaviors derived from records of fast target-oriented chases are presented here.
MATERIAL AND METHODS:
Subjects. Fifty adult female Trite planiceps (average body length 8 mm) were collected from the leaves of native flax (Phormium tenax) along Taieri Beach Road, Otago, New Zealand. They were provided with flax retreats and maintained in plastic containers (11 cm diam. 2 cm deep) and fed with 3-4 houseflies (Musca domestica) twice a week as previously described (Forster 1979). Spiders were stabilized in the laboratory for at least three weeks at nightly temperatures of 10°C to 12°C and daily temperatures of 16°C to 20°C, concurrently being exposed to normal circadian levels of illumination. Ten days before testing meal size was reduced to two Drosphila and testing commenced not less than four days later.
|Fig. 2b: Testing area inside the drum was halved by a strip of cardboard. x indicates place of target appearance, y indicates place of target disappearance, (st.) indicates target direction.|
Apparatus. The apparatus (Fig. 2a) used in these experiments was modeled on the one described by Land (1969a). It consisted of a revolving cylindrical drum (27cm in diam. and 3 cm deep) driven by a variable speed motor. Within the drum a stationary semi-circular platform was used as the test substrate upon which the spider was allowed to move freely. A clear plastic cover over the drum prevented the spiders escape.
Fifty percent of the drum arena was masked from the spider during tests (Fig 2b). Pilot studies showed that stimulus exposure under such conditions provided ample scope, both spatially and temporally, for measurable reaction levels. Since activation of the motor did not coincide with the appearance of the target this arrangement allowed the spider a short period of acclimation to its vibration. In practice, most spiders were not disturbed by the apparatus but any that showed adverse reactions were discarded. Illumination was provided by a 100 watt lamp centered above the arena which was shielded from daylight during tests by a dark curtain. Total luminance of substrate = 1300 lux ± 3% measured with a luxmaster photometer.
Stimulus target. Pilot studies showed that a black, homogeneous, elliptical shape (length = 5 mm, height 3 mm) against a white background (contrast = 80%), elicited maximal predatory reaction frequencies (90%) at a target speed of 12 mm/sec. The ellipsoid target was made from a RAPIDESIGN template and cut by hand from a photographic reduction; it was then mounted on a card and fastened to the inside of the drum 2 mm above the substrate.
Recording. The semi-circular platform on which the spider was tested was marked in a series of concentric, color-coded semi-circles, 4 cm apart. This area was further sub-divided into eight sectors with alternate sectors a darker hue (see Fig 1b), a visual aid to the localization of the spider and the mapping of its pursuit path by the observer. An identical board was mounted to the right of the drum and overlain with transparent folio paper, one sheet being allocated to each spider. On these sheets, records of reactions, pursuit paths and target positions were made (see Fig 2 for examples). Since it was impossible to trace the entire path during rapid pursuits, a series of meaningful reference co-ordinates was plotted and the complete routes filled in immediately afterwards. The distance traveled by the target and the duration of each pursuit was recorded. Experience with equipment, documentation techniques and habits of the spider greatly facilitated recording and improved the accuracy of the results.
Procedure. Spiders were light-adapted at test illumination levels for 20 minutes prior to testing. After being placed in the drum, spiders first surveyed their surroundings and then began to move about. Some spiders jumped to the side of the drum or the cover, but as these surfaces were smooth most of them returned to the substrate. Rotation of the drum did not begin unless the spider was on the substrate. In these tests, the drum revolved from left to right but supernumerary tests in which the drum was revolved manually from right to left showed that response levels were similar. Mapping of the spiders movements began as soon as the target came into view, although occasionally spiders ignored it. Pursuits were discounted if they were not completed, or if spiders were close enough to jump at the target when it appeared, or if they performed inappropriately.
|Fig 3 a-e. Five pursuit
paths sampled from record sheets, a - short path, target approaching, b - short path,
target receding, c - very long, gently curving path, target moving across field of view, d
almost straight path, e - medium length, target initially moving across field of view, then receding. Paths a, b and c closely fit the computer model, while d is faster than predicted and e is slower than predicted by the model.
Thirty spiders were tested three times, at 2-min intervals, at a target speed of 12 mm/s. For comparison, 20 spiders were similarly tested at a target speed of 50 mm/s. A pursuit was deemed to be successful if the spider oriented towards the target, chased and jumped at it. 57 completed pursuits at 12 mm/s and 21 at 50 mm/s were available for analysis.
RESULTS AND OBSERVATIONS
In these tests, the elliptical target was either treated as prey or ignored after the spider oriented but not once was it ever mistaken for an adult conspecific. We know this because potential mates and conspecifics reveal their recognition of each other by conspicuous and distinctive behavior (L. M. Forster 1985).
|Table 1: The total pursuit time and distance for the 5 pursuits shown in Fig. 3.|
Because spiders were able to move freely, they began pursuits from widely differing locations on the test substrate (Fig 3). To the spider, therefore, the target might appear to be receding, approaching, or crossing the field of view. To close the gap, spiders either had to chase the target faster than the target was moving or more slowly, at the same time maintaining a target-oriented pursuit path. The maximum distance from which spiders could begin to chase was 270 mm, and since jumps occurred from 60 mm or less, pursuit distances ranged from 30 mm to 250 mm. At 50 mm/s target speed, pursuits tended to be longer but fewer chases were completed. Jumps appeared to be relatively consistent in length but are probably linked with target speed since the faster speed generally elicited longer jumps.
Figure 3 samples five pursuit paths, a, b, c, d and e, which represent spiders' reactions to the target from different locations. In path a, the spider's pursuit takes » 3 seconds for a distance of 50 mm. In path b, the spider's pursuit takes 3.8 seconds for a distance of 80 mm. In path c, the spider's pursuit takes 4.6 seconds. For path d, the spider travels 120 mm in 2.4 seconds, which is unexpectedly fast. In path e, the spider takes almost 14 seconds for a 185 mm pursuit path, which is rather slow. A summary of the sampled data is presented in Table 1.
|Fig. 4: How the spider computes its direction of travel from perceptual cues (see text for details). This is the model used in the simulations to follow.|
A computer model was developed in order to account for the 5 sampled pursuits in Fig. 3. The idea is that the spider has certain perceptual information available to it at any time, including (i) the position and direction of the prey relative to the spider and (ii) the direction and speed at which the prey is travelling. From this, the spider can extrapolate the position of prey to a time d seconds from now on the assumption that the prey will continue to travels at its current velocity. The prediction is a very simple linear extrapolation. The perceptual and computed variables are then used to determine the distance and direction of travel of the spider.
The model is implemented as a discrete time model. Every tenth of a second the program computes a direction and distance to travel in the next tenth of a second. It then moves that distance in that direction. Then it repeats the computation after a tenth of a second using fresh perceptual data, and so on. In this way, the program is able to adjust to different target speeds, and even to an unpredictable prey motions, although in our case the motion of the target happens to be very uniform.
The direction of travel is somewhere between current position of the prey and the direction of its predicted position (at the tip of the red arrow in Fig. 4). The direction of the predicted position depends on how many seconds ahead the prey's motion is predicted. In the model, this number is labelled as d, which we call the predictivity parameter. If d = 0, then the two vectors coincide, and the spider will move directly towards the prey. This 'non-predictive' motion would be appropriate, for example, if the prey is pursuing a randomly moving target, since the current position would be the best prediction of future positions. If d = 1, then the spider linearly extrapolates the prey's motion from the previous tenth of a second to 1 second into the future. Then the spider aims at half-way between these vectors, which coincides with the prey's predicted position ½ second in the future. If d = 2, then the spider extrapolates the prey's motion 2 seconds into the future and aims at a point closer to the predicted position by a factor of 1 to d + 1. That is, it aims at where the spider is predicted to be in 2/3 of 2 seconds (see Fig. 4). If d = 3, then the spider extrapolates the prey's motion 3 seconds into the future and aims at a point closer to the predicted position; namely the direction in which the spider is predicted to be in 3/4 of 3 seconds.
So far, we have only discussed the algorithm for determining the direction of travel. The distance travelled in that direction is also determined by the predictivity parameter. Qualitatively, the distance moved will be less for larger values of d. These ideas are built into the following mathematical formula, where the quantities may be deciphered from Fig. 4.
Here e is the time interval between computations, equal to one tenth of a second, and f is given by the formula:
Spider c, d = 1
Spider b, d = 1
Spider a, d = 1
The effect of this factor is to slow the spider up when the prey moving at the spider, and is close enough, or moving fast enough, to "cut across the spider's bow". In fact, if the angle f is greater than 90º, then the spider actually moves backwards. In the simulations (Fig. 9) there were instances in which the spider backed off from the prey more than it went forward (and the capture was still successful). The inclusion of this factor made the shape of the simulated trajectories fit the real trajectories fit better when the spider was near the target, even though there was no reverse motion observed in any of the experimental instances.
Spider e, d = 1
Spider d, d = 1
The simulations: To reduce the computer time, and to make the results easier to decipher on the diagrams, we actually chose e to be .5 rather than .1 seconds. This meant that the spider recalculated its travel path less often, and in effect, reapplied its previous calculation 5 times before recomputation. Naturally, this does make a difference to the trajectory, but the effect was not large. The results for trajectories a, b, and c, are shown in figures above. The dots are ½ seconds apart, and the predictivity parameter is 1. The trajectory shapes and the times of pursuit match the observed cases fairly well. This was not true for pursuits d and e.
For d = 1, the simulated pursuits for d and e are shown on the right. For d, the simulated pursuit took almost 4 seconds, whereas the real pursuit was over in 2.4 seconds. The simulated pursuit was too slow. On the other hand, the simulated pursuit for e took about 3 seconds, far less than the real pursuit, which lasted almost 14 seconds. In this case, the simulated pursuit was too fast. Nor did the pursuit path look anything like the real trajectory.
Spider e, d = 3.85
Spider d, d = 0.3
To match the real trajectory shapes and pursuit times, we had to adjust the predictivity parameter. We sped up the simulation that was too slow by lowering the predictivity parameter to d = 0.3. This made the chase more direct and quicker. Then we slowed down the simulation that was too fast by raising the predictivity parameter to d = 3.85. We adjusted the predictivity parameter in order to get the time of the pursuit right. However, it was gratifying to see that the shape of the pursuit trajectory also looked very much like the real thing (far right).
At the present time, we do not know whether the same will be true of other sampled pursuits. However, the same kind of data sampled in Fig. 3 is available for all 78 pursuits recorded. We plan to run the simulations for these pursuits as well, using the actual starting positions of the spider and its target in each case.
In the meantime, we did notice that the model correctly predicts some features of the data for the faster target speed (50 mm/s). While the model was fitted to the 5 trajectories with a target speed of 12 mm/s, the model easily generalizes to other target speeds. In fact it generalizes to any kind of prey motion because makes it computations on the basis of the current prey position and velocity, without any consideration of previous prey positions and velocities (this "no memory" feature of the model will be discussed in the next section). The model takes the prey velocity into account by shifting the predicted position of the target at t + d seconds, which will in turn shift the direction of travel futher ahead of the prey's current position (see Fig. 4).
|Fig. 8: Possible spider starting positions used to investigate the range of possible trajectories predicted by the model.|
|Fig. 9: Total time of pursuit (x-axis) versus total distance of pursuit (y-axis). The green points are simulated runs, while the black dots are from experimentally recorded data (target speed 50 mm/s).|
With a target speed of 50 mm/s and a standard value of the predictivity parameter, d = 1, we ran simulated pursuits for the range of possible spider starting positions, as shown in the diagram to the left (Fig. 8). Each of these starting positions was run with each of 7 equally spaced target starting positions on the perimeter of the drum. The program then computed the total pursuit time and the total pursuit distance (the distance the spider travels from start to the jump point) for each of these 525 imaginary pursuits. These are shown in red in Fig. 9. Note that the predicted pursuit times are generally much faster than for the slower target speed of 12 mm/s.
The black dots on the same diagram are the experimentally observed values for the 21 successful pursuits recorded for the faster target speed. Not only do the observed values fall roughly within the range of the simulated pursuits, but it predicts that there is likely to be a slight correlation between the variables. (The best fitting linear regression curve is y = 105.51x - 20.768 and the associated R-Squared value is 0.6233). The few points that lie outside of this range might be explained as having a higher predictivity value, just as for pursuit e above. Whether this prediction bears out more exactly must await the more precise simulations that make use of the recorded starting positions.
SOME THEORETICAL PROPERTIES OF THE MODEL
|Fig. 10: Diagram of theoretical pursuit path illustrating the basic premise underlying the pursuit model.|
Consider two pursuit paths, Path 1 and Path 2, in a context in which the target speed is held fixed. If we imagine that video recordings of the pursuits are played backwards from the terminal of the pursuit path (the jump point), then the two motions will be identical up until the point X1. The only difference is that the pursuit along Path 1 will terminate at X1, whereas the second pursuit will continue backwards to point X2. This fundamental property of the model leads to some other important properties.
Error Feedback: An important feature of the model concerns the ready availability of error feedback. Any prey-catching organism must make decisions based on the sensory data it receives concerning the prey. The computations it makes are aimed at predicting the movement of the prey and the consequent actions are designed to move the spider into a strategically better position. The computations required for any such computational process are naturally subject to error, and it is especially important that the spider be able to minimize the effect of such errors without the loss of other utilities. From the viewpoint of the spider, the prey-catching strategy described by our model has the advantage of providing constant error correction.
Learnability: In light of known evidence that spiders do improve their hunting skills through experience (references? Le Guelte 1969? Manly and Forster?), the availability of error feedback explains how such learning is possible.
Generalizability: At corresponding points of different pursuits, a spiders predictive computation and motor response will be the same, or at least similar. Therefore, practice in one situation will generalize more readily to new pursuit situations.
...to be continued
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