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Predicting three-dimensional target motion: how archer fish determine where to catch their dislodged prey

Samuel Rossel, Julia Corlija and Stefan Schuster^*

Institut für Biologie I, Hauptstrasse 1, Albert-Ludwigs-Universität Freiburg, D-79104 Freiburg, Germany

View larger version (13K): [in a new window]   Fig. 1. Experimental situation and variables used. (A) A dead fly is attached to the lower side of a disk at height h above the water surface. When dislodged by the powerful water jet of an archer fish, it takes off passively at a horizontal speed hor and will hit the water surface at point P in a horizontal distance d. (B) The same situation as in A viewed from above, showing another archer fish nearby. After a quick initial turn the second fish has aligned itself in the direction indicated by the dotted line, on which it will then rapidly accelerate. At this time the fly is still on its ballistic path above the water surface. Two errors e and e' were analyzed in order to determine whether the fish rushes in the direction of either the later point of impact P or of point P', the horizontal projection of the target's position at the end of the turn. e(e')<0 if distance O—S<O—P(P'), where O is the initial target position and S is the point of intersection between the path of the fish and the fly (horizontal projection).

View larger version (14K): [in a new window]   Fig. 2. Evidence that the path of the dislodged prey followed the rules of simple ballistics, with negligible air resistance and initial vertical velocity. For each of the two initial prey heights h used in this study, h=20 cm (left; N=43 shots) and h=40 cm (right; N=50 shots), the horizontal distance d travelled by the prey is plotted as a function of its initial horizontal velocity hor. Dotted lines show the distance d=hor(2h/g)1/2 (g=9.81 ms-2) predicted, assuming that there were no frictional effects and no initial vertical velocity.

View larger version (20K): [in a new window]   Fig. 3. Archer fish respond over a large range of angles between their initial orientation and the take-off direction of the dislodged prey. Distribution of the absolute values of angles (inset) between take-off direction of the prey and the initial orientation of the responding fish. Angles were sampled at 20° intervals (starting at 10°; see Materials and methods) and accumulated in histograms normalized so that the total frequency equalled 1. (A) h=20 cm, N=60 responses; (B) h=40 cm, N=64 responses. Histograms are based on the responses analyzed in Figs 4,5,6.

View larger version (19K): [in a new window]   Fig. 4. Evidence that fish initiate their rapid turn within approximately 100 ms and are aligned while the prey is still on its ballistic path. The time intervals from when the prey was dislodged until the initiation of a turning maneuver (open columns) and until turning was completed (filled columns) were sampled at 20 ms intervals and accumulated in histograms normalized so that the total frequency equalled 1. The results obtained at both prey heights h are shown and the time to prey hitting the water surface (i.e. (2h/g)1/2, where g=9.81 m s-2) is indicated by the dotted lines. (A) h=20 cm, N=60 responses; (B) h=40 cm, N=64 responses.

View larger version (17K): [in a new window]   Fig. 5. Archer fish turn so as to minimize the error e with respect to the later point of incidence of prey (see Fig. 1). Evaluation of turning maneuvers in response to prey naturally dislodged by a shot from an initial height h=20 cm (A) or 40 cm (B), which was at the upper boundary of the natural shooting range of the fish. The responses are the same as in Fig 4. For each response the error is plotted against the horizontal take-off velocity hor of the prey. The mean of the errors e made with respect to the later point of incidence was not significantly different from zero (t-test).

View larger version (19K): [in a new window]   Fig. 6. Evidence that archer fish do not use an approximate strategy in which they minimize the error é with respect to the prey's position at the end of their turning maneuver. Plot of the error é (see Fig. 1) against the horizontal take-off velocity hor of the prey, as derived from the same responses as in Fig. 4, in which the times until initiation and completion of the turning maneuver are shown. In contrast to the error e made with respect to the true point of incidence (Fig. 5), the mean of the error é was significantly larger than zero (P<0.01; t-test) at both heights h=20 cm (A) and 40 cm (B).

View larger version (19K): [in a new window]   Fig. 7. Demonstration that archer fish base their prediction on an extraction of the horizontal speed and direction of dislodged prey and not on an extrapolation of the spatial trajectory. Fish were confronted with prey that moved only in a horizontal plane. Yet the fish turned towards the virtual point of incidence at which a natural prey of the same take-off speed and direction would have hit the water surface. This is shown for both heights, h=20 cm (N=83 responses) (A) and 40 cm (N=58 responses) (B) by displaying the errors e made with respect to the virtual point of incidence. At both heights the means did not deviate significantly from zero (t-tests). Prey velocity was adjusted to be within the naturally occurring range at the two heights (see Figs 4 and 5).