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First published online December 14, 2005
Journal of Experimental Biology 209, 141-151 (2006)
Published by The Company of Biologists 2006
doi: 10.1242/jeb.01981

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Hunting archer fish match their take-off speed to distance from the future point of catch

Saskia Wöhl and Stefan Schuster^*

Universität Erlangen-Nürnberg, Institut für Zoologie II, Staudtstrasse 5, 91058 Erlangen, Germany

View larger version (9K): [in a new window]   Fig. 1. Geometry of prey catching in archer fish. (A) Immediately as their dislodged prey starts falling (arrow), archer fish can dart right towards the later point of impact P. To do so the fish must correctly predict the bearing of this point. In principle, however, the fish's `internal estimate' of this point could be anywhere within the green area defined by the bearing error the fish makes: erroneous estimates P' or P'' would still lead to a correct bearing. The present study excludes this view and shows that the fish can also predict their distance from the point of impact reasonably well. (B,C) Predicting the bearing requires three independent pieces of information to be taken into account. The prey insect is shown at start of falling after being dislodged by a successful shot, and the turn a bystander fish (initially oriented along the dotted black line) must make is illustrated. (B) At a given position and orientation of the responding fish, turn size must be matched to the initial height (H) and speed (s) of the falling prey. For small values of H or s (H<, s<, later point of impact marked blue) the fish must make a smaller turn than for large values of H or s (H>, s>, later point of impact marked red). (C) At given H and s values the responding bystander fish must also take the initial direction of the prey's motion into account in selecting which bearing to choose. This direction is not cued by the shot itself because it scatters widely around the shot's direction.

View larger version (29K): [in a new window]   Fig. 2. Suitability of the responses analyzed in this paper. (A-C) Evidence that the responses were directed at the predicted later point of impact but were not based on an approximate mechanism. (A) Illustration of the errors analyzed. A shooter has dislodged a fly, which falls towards its later point of impact P. At the instant shown, a bystander has just finished its initial turn and starts to head off with a bearing indicated by the solid line. The actual position of the fly is at P'. The solid line crosses line of prey movement (from P' to P) at point S. Errors and ' denote the angular deviations of the bystander's bearing with respect to either the later point of impact P or the actual position P' of the fly (broken lines). Error (') is positive when the respective reference point P (P') is before S, otherwise the error is negative: in the situation shown ' is positive and is negative. (B) Bearing errors made with respect to the later point of impact are symmetrically distributed around zero. (C) In contrast, the distribution of errors ' with respect to the fly's actual position, is systematically offset towards positive values (P<0.001, t-test). Errors and ' are sampled in intervals of 2°. (D) Distribution of distances the responding fish had to cover from their initial position towards the later point of impact. Bin width 50 mm. (E) The time that remained till prey impact when the fish had sampled the necessary information about target motion, had finished their turn and were ready to take off. The histogram shows how remaining times , binned in 0.02 s intervals, were distributed in the set of responses. (F) The fish responded over a remarkably wide range of target-flight directions with respect to their initial orientation. The histogram shows the correspondingly wide distribution of turn sizes the responding fish made. Bin width is 20°. All histograms are based on the same N=90 responses and are normalized so that their total frequency equals 1, ticks on ordinate indicate 10% frequency.

View larger version (14K): [in a new window]   Fig. 3. Take-off speed is rapidly gained at the end of the turning phase and is changed only very slightly in the immediately subsequent translatory phase. For each of the N=90 responses, speed measurements v1, v2, v3 were derived from changes in position during the first, second and third 20 ms interval, respectively, of the fish's initial translatory motion. The histograms show the distribution of speed differences between subsequent intervals. Distribution of (A) speed changes v2-v1, (B) v3-v2. Both distributions are systematically shifted towards positive values, but the shifts (0.05 m s-1 and 0.07 m s-1, respectively, both P<0.01; t-test) are small compared to the basis speed level of about 1 m s-1 acquired during the final phase of the turn. Speed differences in A and B are sampled in intervals of 0.1 m s-1 and accumulated into histograms normalized so that total frequency is 1, ticks on ordinate indicate 10% frequency.

View larger version (15K): [in a new window]   Fig. 4. Take-off speed correlates with distance from the later point of prey impact. (A-C) The speed values determined within the first (A), second (B) and third (C) 20 ms interval after the fish has executed its initial rapid turn and starts moving in the direction of the predicted later point of impact while the fly is still falling. In each case the correlation is highly significant (P<0.0001; r2=0.20, 0.33 and 0.21 in A-C, respectively).

View larger version (26K): [in a new window]   Fig. 5. How take-off speed appears to be determined by distance plus remaining time of falling. (A-D) Plots of take-off speed vs `virtual speed', i.e. distance (d) of responding fish from the predicted catching point divided by the time () the prey has still to fall when the fish has finished its turn and is ready to take off. Virtual speed is the speed the fish would have to choose in order to arrive simultaneously with the prey after a course with constant velocity. (A) Plot that includes responses (within the grey area) in which virtual speed was above the actual speed limit of the fish (arrow), corresponding to 15-25 fish lengths s-1. Take-off speed was determined from the first 20 ms of translation. (B-D) Plots of take-off speed vs virtual speed within the accessible range of speed values that the fish can potentially realize (N=60 responses). (B) Speed in the first 20 ms interval after take-off; (C,D) speed in the subsequent two intervals of 20 ms duration. In each case correlation coefficients are highly significant (P<0.0001; r2=0.45, 0.35 and 0.54 in B-D, respectively) and higher than the corresponding correlation coefficients in the plots of take-off speed against distance (Fig. 4A-C).

View larger version (17K): [in a new window]   Fig. 6. With no immediate competition at the point of catch fish arrive very slightly after the prey has landed. (A) Actual arrival times at the point of catch. The histogram shows the distribution of actual arrival times with respect to prey impact (which occurs at time t=0). In this diagram t>0 means that the fish arrives after the prey has landed, t<0 means that fish arrives before prey. (B) Histograms of arrival times expected on the basis of the respective take-off speed and supposing that the fish would simply continue to move with this speed. This distribution corresponds well to that of actual arrival; however, systematically larger expected than actual arrival times show that take-off speed was chosen slightly too slow and that later speed corrections were made. Expected and actual times were sampled at intervals of 0.02 s and accumulated in histograms that were normalized so that the total frequency equalled 1. All N=90 responses, ticks on ordinate indicate 10% frequency.

View larger version (21K): [in a new window]   Fig. 7. Prey is taken on the move. Plot of speed at capture vs speed at take-off shows that fish had no tendency to reduce their speed at the catching point but rather to increase it, making the catch at full speed. The line marks where speed at capture equals speed at take-off. All N=90 responses.

View larger version (10K): [in a new window]   Fig. 8. Scrutiny of a constant-speed approach path towards the predicted point of impact. (A) Path of falling fly (open circles, calculated projection onto the plane of the water surface) and of responding fish (filled dot indicates the head) sampled every 20 ms. For the fish, only every second sample is shown. (B,C) The corresponding time course of (B) speed and (C) angle. The phase of rapid turning is shown by grey shading. Three filled dots indicate the speed determined in the first, second and third interval of 20 ms duration after take-off. The impact of the fly is indicated by an arrow. Sequence ends with the catch. In B, speed values report translational speed except for the phase of turning (grey shading) in which values report only the change of head position that was due to turning. During translation the speed is approximately constant. Note that speed could not be estimated better than about 0.05 m s-1. (C) After an initial turn of about 30°, the bearing is maintained. A bearing of 0° denotes a course in the orientation of the scale bar in A (0.1 m).

View larger version (9K): [in a new window]   Fig. 9. Example of an approach path in which the fish did not hold a constant speed, but rather accelerated till the point of catch. (A) Path of falling fly (open circles, calculated projection onto the plane of the water surface) and of responding fish (filled dot indicates the head) sampled every 20 ms. Each sample is shown. Arrangement of panels A-C and the ordinate scale in B and C are as in Fig. 8. In contrast to speed (B), the bearing of the fish's movement (C) is kept rather constant.

View larger version (10K): [in a new window]   Fig. 10. Approach path with irregular velocity changes before the fly's impact at the water surface. Path of falling fly (open circles, calculated projection onto the plane of the water surface) and of responding fish (filled dot indicates the head) sampled every 20 ms. Each sample is shown. Arrangements of panels A-C and the ordinate scale in B and C are as in Fig. 8. Despite speed changes (B), the bearing (C) of the fish's movement is held throughout the approach.

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