Introduction

Everyday experience suggests that the quality of our decisions depends on how much time and effort went into them. However, many decisions drastically defy this rule (e.g. 1-7). Although diverse, they have in common that they all can be made surprisingly fast, often based on limited information and yet can be accurate, often with no increase in accuracy when allowed more time. For instance, rats categorize odors reliably within one sniff, i.e. within about 300 ms. Allowing for longer sampling time did not increase accuracy even for difficult tasks (3,8,9). Similar short sampling has been described for visual perceptual decisions. Humans can reliably classify natural images after surprisingly brief viewing times of only 20 to 40 ms (1,10) and it has long been known, though for comparatively simple tasks, that extending viewing time did not affect the thresholds in visual decisions that are based on stereoscopic depth perception (11,12), velocity-discrimination (13,14), or contrast sensitivity (15,16). This suggests that a natural sampling interval – the time it takes to produce a sniff, or a saccade – is the elementary interval in many visual and olfactory perceptual decisions (3). Adding urgency into laboratory decision tasks by having the subject respond to sensory information after it has already launched movement (e.g. a saccade) has allowed to dissect perceptual and motor aspects of decision-making and thereby allowed the actual speed of perceptual decisions to be measured with high temporal accuracy (5,17). Outside the laboratories, the use of rapid decisions is probably very common in sports. For instance, baseball hitters have a mere 400 ms to move their bat to an ideal hit point based on an estimated 70 ms of visual processing to inform the movement of the bat (18–20), with a mere 40 ms of more or lesser sampling deciding between the best achievable and a bad motor choice (5). For some much slower and more complex human ‘blink’ decisions, such as which product to buy, it has been shown that blink decisions can be superior compared to those made much slower and based on more information (6,7,21–23).

An intriguing question about these diverse but impressively fast and accurate decisions is whether they lack aspects that only slower decisions can offer. For instance, high-speed decisions might be fast because they make clever use of simplifying heuristics and of hardwired neuronal machinery so that they work only under the specific conditions for which they were optimized. Are slower ‘deliberate’ decisions therefore needed when flexibility and perhaps higher cognitive aspects are required? While this is presently poorly understood, many behavioral findings – from the movement of baseball outfielders and frisbee-catching dogs (24, 25) to the chase of hoverflies (26) – are available that could be (and have been 6,7) interpreted as supporting such a conclusion. For instance, to intercept a passing female, male hoverflies do not continuously monitor the female to guide their own movement but rapidly decide on an interception course immediately when a passing female comes into sighting distance (26). Based on information taken at this time the male immediately selects a specific turn so that moving in the chosen direction at fixed acceleration leads straight to the point of catch. This decision is based on hardwired assumptions that appear to be genetically imprinted in the neural circuits that govern the initial turn (Fig. 1A). When any of these assumptions were experimentally violated, for example when the target had unusual speed or sighting distance, then the turns were massively in error just as was predicted (26). So, the hoverflies solution affords a striking degree of speed and accuracy but clearly comes at the cost of flexibility. Nevertheless, there appear to be no selective pressures for the decision to afford more flexibility, in fact, the apparent limitations are potentially even to the advantage of the hoverfly males (26).

Fig. 1.

Here we addressed the question of limits in flexibility in a high-speed decision that is made faster than an Olympic sprinter responds to the start gun. Like the decisions of hoverflies (26), batters (18–20) or outfielders (24,25) it is also a decision based on visual information and it is also about being at the right spot at the right time. It operates under interesting constraints and has properties that make it amenable to experimental dissection in the lab (27). The decision is an essential part of the hunting behavior of archerfish, that are renowned for shooting down aerial prey with jets of water (28–30) (Fig. 1B): As soon as they have dislodged a prey insect with their shot, the fish (shooter and bystander archerfish) have the little time that remains till prey hits the water surface to be at the point of catch. A failure to arrive at this spot simultaneously with their prey means losing it to one of their numerous competitors, large crowds of other surface-feeding fish that also can launch pre-impact starts based on visually observing how the target falls (31). To outperform these competitors, archerfish watch the initial movement of a falling prey – which is typically hit from the side (see Fig. 1B) – and then select a turn right to the later landing point (e.g. 27, 32): Additionally, they then dart off with the speed needed to arrive just in time at the right spot (33,34). Because aerial prey is scarce (31), archerfish engage prey over a wide range of distances (30,31) and, hence, must also be able to select the correct turns for a wide range of sighting distances of prey, vertical and horizontal initial speed levels of prey, prey sizes. Archerfish can therefore not use similar simplifications that work so well for hoverflies (26). Indeed, the fish can decide correctly even when these variables were varied independently from each other over large ranges (27,35,36). Of key importance for our present study is this interesting property of the decision (Fig. 1C): Suppose a prey object is made, by a stream of air from a blastpipe (32), to slide on top of a glass plate. Faced with such a condition, hunting archerfish do not follow the trajectory of the object. Instead, they still make their turn decisions just as they would in absence of the glass plate and accurately turn towards the ballistic landing point predicted from the initial height, initial direction and initial speed of the sliding target (32). It should be stressed and will become clear in the results, that the accuracy of the turn decisions allows to decide whether the turns were to the ballistic landing point, or another point, such as the last sighting of the fly before turn onset (32) or the landing point appropriate for another estimate of initial height (35, 36). The glass plate experiments therefore show that the turn decision maps the initial values of motion of prey to the turn the fish must make and that this mapping is appropriate for ballistically falling objects. In these experiments prey movement was independent of shooting, and it turned out later, that the decision does not use prior information – i.e. on target position, height, timing of motion onset – that would be available already before prey starts its trajectory. This was tested in experiments in which size, initial position and height were changed relative to what the fish could have expected (27,35,36). Furthermore, accuracy and latency of the turn decisions are independent from viewing distance and the orientation of target motion relative to the responding fish (35,36).

Although exhibiting impressive features, the ‘machinery’ behind the turn decisions could still be hardwired and somehow restricted to work only for ballistically falling prey, such that any combination of input variables (speed, direction, height) and coordinates of the fish leads to the turn that would be appropriate for an object that falls ballistically. Such a hardwired mechanism could be acquired over the course of evolution or could be acquired or refined during early ontogeny. But once established it would be fixed. This would explain why all archerfish studied in our lab during the last 20 years consistently showed robust turn decisions to ballistic landing points (27,31–37). It would also be according to what intuition suggests: reflex-like speed should exclude any further flexibility. Finally, smaller prey is completely wetted by the shots and falls ballistically (32,35), so that no further flexibility would seem to be required, ecologically, from the decision. However, as we report here, adult fish readily learn to extract a new artificially introduced rule of how to connect the three independent input variables to the rewarded turns and to drive their high-speed decisions according to this new rule, ignoring all their ballistics. Moreover, they re-programmed their decisions in surprisingly clever ways that not only allowed them to immediately generalize their high-speed decisions to untrained constellations but even to simultaneously handle two different rules.

Results

A technique to substitute ballistics with a new rule

If the archerfish’s high-speed decision was hardwired it would fail after a sudden and drastic change in how the rewarded output needs to be linked to the input. Adult archerfish would then continue to turn to the appropriate ballistic impact point and would have to learn ways to correct their error later on their approach path. Testing this idea requires a way to exchange the ballistic rule with a new rule and to reward the fish at locations that are dictated by this new rule. The responses to purely planar movement (33) (Fig. 1C) and the independence of the decision of the shooting context (28,33,36) suggests that LCD monitors could, in principle, be used to provide all information archerfish use for their decision. To reward the fish at defined virtual impact points without additional confounding motion cues we developed automatic feeders that can deliver food according to experimenter-defined rules of how to link place and time of food delivery to initial target motion (Fig. 2A, Fig. S2). However, these feeders are prominent landmarks and as such could substantially affect the decision. Surprisingly, a series of experiments showed, that the feeders did not influence the decision at all and that it was still exclusively based on initial target motion (Fig. 2B). Operating the feeders without showing motion on the screen failed to elicit decisions. Most importantly, when we created a direct conflict between aiming at a feeder or aiming at the ballistic virtual impact point (VIP) – appropriate for the fish’s position and the target’s movement – then the fish aimed at the VIPs, not at the feeders even though this was where they got their reward (Fig. 2B; 15° offset, n=353; 30° offset, n=198). Moreover, because these tests were conducted so that the VIPs also differed relative to other potential landmarks in the tank, the fish were also not starting to positions marked by landmarks other than the feeders. In other words, even in presence of the feeders the decisions were only based on the movement information on the screen and were not influenced by cues from the feeders or from any other landmarks in the tank.

Fig. 2.

Using this system, it should be possible to achieve our aim of presenting fish with novel non-ballistic rules that connect the input variables and the rewarded locations. However, one problem remains that needs to be examined: Given the short time in which the fish must respond and given the comparably low frame rate of the screen, it is unclear whether the decisions made with target movement displayed on the LCD screens would be comparable to those made with real prey. For instance, they could be much less accurate, be slower, or only possible from specific positions. To address this, we directly compared the performance of the same fish in response to either real falling objects (see Movie S1, that illustrates the speed of the response) or to the VR stimuli (Movie S2). Given the limitations in the temporal resolution of the screen it is striking that no aspect of the decisions was statistically different under real and virtual conditions (Fig. 2C-G, n=101 (real) and n=85 (virtual) starts). The accuracy of the aim achieved at the end of the turns was not statistically different (p=0.506, Mann-Whitney; Fig. 2C) and always minimized the error to the impact point, regardless of whether it was real or virtual (difference from zero: p=0.903 (real), p=0.455 (virtual); One-Sample Signed Rank) with no significant difference in variance (p=0.589, Brown-Forsythe). The turns also had the same latency (p=0.297; Mann-Whitney; Fig. 2D) and kinematics (Fig. 2E: no difference in bending duration under real and VR conditions, p=0.071, Mann-Whitney). Furthermore, responses came from a large range of orientations and distances and, most importantly, were equally accurate across all distances (Fig. 2F) and turn sizes (Fig. 2G). In summary, despite the limited frame rate of the screens and despite the need to use feeders in most presentations, the turn decisions can be studied exclusively with virtual stimuli. This sets the stage for now changing the relation between initial movement and the rewarded virtual landing point.

Challenging the decision with a new rule to link input and rewarded output

The setup now allowed us to study the decision after a systematic change in the rule that connects the input and the turn the fish needs to make to reach the virtual impact points. Figure 3A introduces the model behind the new rule that we used to generate a systematic large deviation of 14.9 cm between the new VIPs and the previous ballistic VIPs. After having travelled straight throughout what was the previous decision time, the direction was deflected by 39.8° (to the left, s. Methods) and the reward was now presented at the appropriate ‘deflected’ VIP. Hence, there is still a fixed relation between the input (initial target movement on the screen) and the rewarded point on the water surface. However, the relation is now different from the one the fish had previously been using. It is important to stress, that learning to turn according to this new rule is not at all simple and would require the fish to learn non-trivial corrections (Fig. 3B): Relative to the turn they previously made for a given input constellation they would be required to add a correction that is not constant but depends sensitively on the position of the responding fish. This map of corrections is, furthermore, not the same for all input constellations but a new map as in Fig. 3B is required for each combination of input variables (as illustrated in Fig. S3). The predictions were clear for adult archerfish: should the decision use a circuit that was hardwired to ballistic movement, then the fish would never be able to turn to any other than the ballistic VIPs. The fish would still have several options to efficiently adapt to the situation, for instance by learning how to modify their subsequent approach path, by employing slower responses (not the so-called C-starts employed in the turn decision) or by waiting until the deflection had occurred to launch their turns only after that time. But they would not be able to adjust their rapid turn decisions.

Fig. 3.

We now exclusively challenged the fish with the deflected trajectories and the new rewarded VIPs over the course of several weeks. During this time, we continuously sampled occurrence and error of all turn decisions (Figs. 3C, D). Interestingly, the fish never ceased to respond with their characteristic turns (response probability remained constant at all stages, p>0.08, Pairwise Chi-square) of unchanged kinematics and never significantly increased their latency (bending and straightening phase of their C-starts both p>0.28, latency p>0.07; Kruskal-Wallis). Furthermore, their aims were systematically in error for the initial stages of training (deviation from zero error to the deflected VIPs p≤0.001, One-Sample Signed Rank) as we had predicted (Fig. 3D; deviation of aim to ballistic VIPs from zero error p>0.06; One-Sample Signed Rank; Movie S3). However, gradually the errors made to the new ‘deflected’ VIPs became smaller and, after more than 1750 presentations, the turns clearly minimized the error to the appropriate new ‘deflected’ VIPs (Figs. 3C, E, F; Movie S4) and no longer to the ballistic ones.

This surprising finding does by no means show that the decision has now been based on the new rule. For example, the fish could have learned to feed information about the deflection of the prey’s trajectory into their unfolding turns and so achieve their new final turning angles. To control for this, we interspersed tests in which the trained fish were only shown the initial linear part (without the deflection) among many presentations with the full trajectory (including the deflection). However, the errors made in the interspersed tests (n=68) were not different from those made when the full trajectories were visible (Fig. 3G). This shows that the starts were still only made using the initial motion and did not require seeing the deflection. A second explanation for the new turns would be that the fish could have learned to now take the feeder positions into account. They would then use initial movement merely as an indicator which feeder to approach. To test this, we interspersed tests in which the direction of initial target movement was always either 15° or 72° off from the feeder position and in which, additionally, exclusively the initial movement (before deflection) was shown. Moreover, in these tests feeders were offset both from the ballistic and the new VIPs. Under these conditions, the turns the fish made were still to the new deflected VIPs (differences from zero error p=0.721 at 15° (n=197) and p=0.113 at 72° (n=145); One-Sample t-tests) but not to the feeders or to the ballistic VIPs (Kruskal-Wallis: pσ0.001 at 15°; p=0.005 at 72°; Dunn’s p<0.05 for comparison of errors; (Movie S5)). Furthermore, the turns made when only the linear initial motion was visible and when the VIPs were spatially offset from the feeders did not differ in latency (p=0.686, Kruskal-Wallis) nor kinematics (bending duration: p=0.242, Kruskal-Wallis) from the turns made without offset and with the full trajectory visible (n=240).

Finally, it is important to stress that the fish had not learned to directly turn to the new VIPs just for a few restricted constellations (Fig. 3H, I). Instead, turns came from a broad range of distances and turn angles and across those had equal accuracy. So, the high-speed decisions are, surprisingly, not hardwired to a ballistic relation between the input variables and the turn the fish must make but can be reprogrammed according to a new rule

After restricted training to the new rule the decision immediately generalizes to untrained input constellations

Because all training to the new rule had occurred with targets presented at only one height level it is now possible to run generalization tests to examine the level of abstraction at which the decision was re-wired. Suppose the fish had adjusted its ballistic decision network in a way that can be formally represented as overwriting a ‘lookup table’. Such a table (or its mechanistic realization) would store the past successful turn for a given orientation and position of the fish, speed, direction, and height of moving prey. Because training was restricted and had exclusively occurred at only one height level, the previously ballistic ‘lookup table’ would have been only partially changed and predictable problems should occur in tests with targets presented at untrained heights. For these untrained heights the table would either only contain entries for ballistic motion (prediction A) or the ballistic entries might be substituted with entries that were appropriate at the training height (prediction B) during retraining. Both predictions allow us to calculate the turns the fish would have made when they first encountered targets at untrained height levels (Fig. 4A): Turns should either be to the ballistic landing point as appropriate for the novel height level (prediction A). Or, according to prediction B, the turns should be to the ‘deflected’ landing point but appropriate for the training height and not the actual height level. To test these predictions, we challenged the trained fish with movement that occurred at either higher or lower than the training height. Testing heights were chosen such that the fish would make an error of at least 6 cm relative to one of the predicted points. Figs. 4B, C show the error of the first 30 turns made when the trained fish encountered movement at the untrained height levels. The error of the turn is shown relative to the VIP that would be appropriate for the now larger (Fig. 4B) or lower (Fig. 4C) height level. This error was around zero with no tendency to change over the trials (linear regression: all p>0.1). A detailed analysis of the errors (Figs. 4D, E) showed that the turns minimized the error to the deflected landing point at the true (novel) height (difference from zero: both p>0.07; One-Sample t-test), but neither towards the ballistic landing point (prediction A; both p<0.001; One-Sample Signed Rank) nor towards the deflected landing point at the training height (prediction B; both p<0.001; One-Sample Signed Rank). Again, none of the characteristics of the turns were different in the novel situation than in the situation the fish had encountered during training (also n=30 right before these tests): latency: p=0.098, kinematics: p=0.177 (Kruskal-Wallis), variance of errors: p=0.188 (Brown-Forsythe). In other words, the new rule is represented in a way that allowed immediate generalization to the new untrained heights.

Fig. 4.

We next tested whether the fish would also generalize to new untrained target size and untrained speed levels. Fig. 4F shows that after a change in absolute target size, the trained fish still turned to the deflected landing points (differences from zero error: each p>0.4, One-Sample Signed Rank; difference in aim before and after size change p=0.764, Mann-Whitney) and the error distributions were not significantly different (difference in distributions in Fig. 4F: p=0.278, Brown-Forsythe). This shows that learning the new (deflected rule) did not involve simplifying a priori assumptions about the absolute target size. Learning also allowed immediate generalization to a lower target speed, that was not encountered during the training period. To examine this, tests with lower target speed were interspersed among presentations in which targets had the same speed as during training. Fig. 4G shows that already the first 30 turns minimized the error to the deflected VIP for the actual speed (difference from zero p=0.102; One-Sample t-test). They also did not minimize the error to the VIPs given by either ballistics (analogous to prediction A above; p<0.001; One-Sample Signed Rank) or by using predictions for the deflected VIPs that are based on the trained speed levels (analogous to B; p<0.001; One-Sample Signed Rank). Comparing latency, bending duration and the variance of errors (speed: last 30 presentations with only training speed; size: last 30 presentations with target size during training) showed that changing target size and speed also did not affect the nature of the turns. Latency and bending duration were not significantly different in the changed versus training conditions (At novel untrained speed: Latency: p=0.280, Mann-Whitney; Stage 1: p=0.076, Mann-Whitney. At novel untrained size: Latency: p=0.305, t-test; Stage 1: p=0.997, Mann-Whitney). Variance was even slightly reduced (and not increased) at the untrained target speed (p=0.021, Brown-Forsythe) and remained unchanged after the increase in target size (p=0.742, Brown-Forsythe). In summary, all tests show that the high-speed decisions had been reprogrammed in much more clever ways than predicted. Rather than independently changing the size of an unrewarding turn for each individual constellation – as would seem required because the input variables themselves are varied independently from each other – learning allowed immediate generalization and thus must have in some way captured the new rule.

The decision can conditionally operate on two different rules

We next asked whether the fish would – at any given time – only be able to use one rule for the turn they must make. To explore this, we randomly showed the trained fish two types of objects that differed in shape: Either (i) a disk that moved on the ‘deflected’ trajectory and to which they responded with turns toward the rewarded deflected VIPs, or (ii) a ‘ballistic’ object (triangle) that moved straight and for which a reward was given at the ballistic VIP (Fig. 5A). In the experiments, one of the two objects was chosen randomly, appeared in stationary position for 2 s, and then started moving. Initially, the turns made in response to the ballistic object still minimized the error to the deflected VIP (difference from zero error p=0.256; One-Sample Signed Rank; same variance as for disk p=0.343; Brown-Forsythe; first 160 responses to ballistic object) and not to the ballistic VIP point (difference to ballistic landing point: p=0.038, Mann-Whitney; Fig. 5B, C). However, after 500 additional starts in response to the ballistic objects, turns were equally in error to the deflected and the ballistic VIPs (p=0.648, Mann-Whitney). During the same period, in contrast, the turns to the moving disks remained perfectly matched to the deflected landing point (difference from zero error p=0.273; One-Sample Signed Rank; Fig. 5C). After about 300 additional exposures to the moving triangle the turns minimized the error to the ballistic impact point when the triangle was shown (error to ballistic p=0.836, error to deflected p=0.020; One-Sample Signed Rank; Fig. 5B) but continued to minimize the error to the deflected impact point whenever the disk was shown (error to ballistic p≤0.001, error to deflected p=0.084, n=187; One-Sample Signed Rank; Fig. 5C).

Fig. 5.

Next, we interspersed tests that only showed the initial straight paths both for the disk (n=60) and for the triangle (n=187). So, picking either the ‘ballistic’ or the ‘deflected’ rule to choose the appropriate turn for a given set of input variables could now exclusively be based on target shape. Again, the turns were toward the ballistic landing point when the triangle was shown (difference from ballistic p=0.075, from deflected p<0.001; One-Sample Signed Rank) and to the deflected landing point when the disk was shown (difference from ballistic p=0.008, from deflected p=0.412; One-Sample Signed Rank) (Fig. 5D). Also, latency (p=0.189, Mann-Whitney; Fig. 5E) and kinematics of the turns (bending duration; p=0.984; Mann-Whitney; Fig. 5F) were the same in the responses to triangles and disks. In other words, the nature of the turn decision was the same, but object shape determined which rule was used to determine the appropriate turn given the input data.

In principle these results could have arisen rather simply: some fish could have only responded to disks and others only to triangles, so that no single given individual would have to be able to handle both rules. Analyzing the contributions of the individuals showed that this was not the case, and that individual fish could respond appropriately to both conditions (Fig. 5G). Each of the three individual fish that contributed most starts had minimized the error to the appropriate VIP (difference from zero error always p>0.1; One-Sample Signed Rank) and the variability of the errors in applying the two rules did also not differ in any of the individuals (p=0.966; Brown-Forsythe). This shows clearly that individual archerfish are indeed capable of simultaneously operating on two different rules – one for each type of prey – of how to connect the input with the turn the fish must make.

A shape cue is needed to select which rule to use but is not needed prior to target movement

The previous series of experiments presented target shape as a potential prior that would inform the decision circuit as to which of the two rules will have to be used when target movement starts. To test whether it was necessary to instruct the circuit prior to the onset of motion, we interspersed tests in which the target object (disk or triangle) revealed its shape only at motion onset (Fig. 6A). In each of these interspersed tests, first a neutral shape (a cross) appeared, remained stationary for 2s, and then was exchanged randomly with either the moving triangle or the moving disk. Moreover, only the straight initial path was shown so that shape after motion onset was the only cue for the decision on whether to choose a turn based on the ‘ballistic’ or the ‘deflected’ rule (Movies S6, S7). Under these conditions, the decisions remained appropriate to the ballistic (triangle; n=109 starts) or deflected (disk; n=46 starts) VIPs (difference from zero error to appropriate VIP: p=0.451 (triangle) and p=0.671 (disk); p ≤ 0.001 for the alternatives, all One-Sample Signed Rank). Furthermore, also the distribution of errors was not statistically different from those obtained with the shape cue available 2s prior to the decision (p=0.269; Brown-Forsythe). Hence the information that is needed to select which rule is to be used can also be extracted in the very brief interval (as little as 40 ms) after motion onset, together with all other decision-relevant information but does not need to be available to instruct the decision circuit before target movement starts

Fig. 6.

Discussion

In their turn decisions, archerfish quickly observe the initial values of motion of falling prey and then turn at the ballistic landing point. When shown purely planar initial movement they still turn at the ‘virtual’ ballistic landing point, that specific point at which ballistics predicts it to impact at the water surface. Based on this property we established a paradigm that allowed us to exchange the rules of ballistics with a new one. In this paradigm, the fish can no longer use ballistics to connect the independent variables (height, speed, and direction) with the appropriate turn towards the point of reward. However, a new rule exists that would, in principle, allow the fish to connect the rewarded turn to the combination of input variables. We show here, that, against all expectations the fish learn to extract the new rule in a way that allows them immediate generalization to variable combinations (such us untrained new height levels) they have not been trained with. The reprogramming of the decision does not change its kinematic aspects or latency, showing that the high-speed decisions were indeed reprogrammed when a new relation exists that connects prey initial movement with the point of reward.

Our findings demonstrate that reflex-like speed of a decision does not rule out the involvement of learning and of cognitive aspects that are seen in much slower decisions and in behaviors shown at more than 100 times lesser speed. They thus provide a counterexample against everyday wisdom that what occurs at reflex speed must be a simple reflex and limited to fixed or mapped inputs and responses. Although we demonstrate this in a highly specialized decision that has evolved under particularly heavy constraints, it is not unlikely that similarly flexible and adaptive decisions at reflex speed might be much more widespread. They may be common in hunting contexts and employed whenever flexibility and the efficient re-programming of rapid decisions would be a major advantage. Nontrivial elements of flexibility could also be part of rapid perceptual decision making. Given the high temporal precision obtainable in urgent perceptual decision-making (5,17) using this approach to compare cognitive aspects in the ‘classic’ slower (38,39) and in rapid (3,5) perceptual decision making could be very rewarding.

Comparing cognitive aspects of high-speed decision making with those of much slower behaviors

We would like to stress that none of the cognitive aspects we describe here is in any way simpler when compared to its slower versions. The capacity to generalize efficiently has been demonstrated in the ability of archerfish to learn of how to engage moving targets and to judge their absolute size (40,41). Also, recognizing and assigning a value to different visual shapes has been demonstrated much earlier (38,42). Such aspects are also not unique to archerfish and have been described across the animal kingdom, including animals with far smaller brains (43–45). What is surprising is, of course, clearly not to find cognitive features in archerfish, but rather to find such features of similar complexity in a decision that is made at reflex-like speed on a timescale of milliseconds rather than one of minutes. Also, the complexity of the task that the fish needs to master to conditionally adjust their high-speed decisions is certainly not easier than what otherwise is considered a demanding task in many laboratory animals (e.g. 46-48). Here a much-studied task is to have an animal under condition ‘a’ respond to a stimulus ‘α’ by turning left and right to stimulus ‘α’. Under condition ‘b’, however, the animal must do the opposite and turn right to stimulus ‘α’ and left to stimulus ‘α’. In comparison, the task the decision circuit of archerfish handles in just 40 milliseconds is not only to conditionally switch between two motor outputs but to switch between two rules of how to connect a three-dimensional set of input data to a continuum of possible motor outputs.

Highspeed decision-making and circuit size

The plausible assumption that reflex-speed implies reduced complexity and flexibility (48,49) could have a similar foundation as the assertion that smaller brains have reduced cognitive capacities. Substantial progress has been made on this latter assertion, resulting in an impressive and continuously growing list of sophisticated cognitive features that were found in animals with bird-and fish brains (50–52). Most impressively, it has been demonstrated that insect brains that operate with a millionth of the neurons of a human brain can handle a wide range of cognitive tasks (43–45,53–55) that even include social or observational learning (55–57). The reflex-speed of some decisions also will likely limit the size of the underlying neuronal circuitry, allowing only a subset of the brain to be used, a subset that could be considered a ‘functional mini-brain’. The assertion that everything that is fast as a reflex must be simple might therefore suffer the same fate as did the assertion that brains with fewer neurons must be simple. In the turn decisions of archerfish, specifically, it is known that the kinematics of their turn decisions is completely equivalent to the so-called C-starts that the fish produce to escape (37). Both the turn decisions (also called predictive C-starts) and the escape C-starts are among the fastest C-start known in fish (37) and so at least the motor circuits are restricted to the well-known powerful hindbrain circuits of a comparably small number of tractable numbers of neurons, organized around the giant Mauthner neuron (59–62). Its rapidly conducting axon would be suited to initiate the turn but it would clearly have to work together with other hindbrain neurons to account for the precision and adjusted straightening speed of the fish (37).

Ecological considerations: Why did archerfish evolve flexible highspeed decision-making?

The rapid and precise turn decisions are required because of severe competition with other surface-feeding fish that are not only more numerous – and therefore likely to be closer at the landing point of the archerfish’s prey – but that are also capable of using vision to guide pre-impact turns and therefore need to be outperformed (31). We suggest that the flexibility of the archerfish’s decision was required because of scarcity of aerial prey. If the fish must catch whatever scarce prey is available and if they are in serious competition with other fish, then they must address the following problem: While small prey will be completely wetted by the archerfish’s shot and will fall ballistically (32,35), larger prey will face considerable frictional forces and – all other conditions being equal – will therefore not fall equally far. Simply using a hardwired circuitry for ballistically falling prey also for such larger prey would produce wrong initial turns which would require subsequent corrections that cost precious time and might mean losing the advantage over the competitors. The flexibility we found and the ability to operate on two types of prey that fall according to two different rules would allow archerfish to efficiently handle two types of prey that co-occur during a specific time of the year. When one is replaced by another type of prey with yet another way in which its initial movement relates to its impact point, the decision will be able to adjust, again, to the new prey type, being still able to accurately respond to the prey that remained. So, we suggest that the ecological constraints and the severe competition that archerfish face in the wild could have favored the evolution of a decision that needed to go right to the limits of combining speed, accuracy, and flexibility.

We hope that our findings, obtained in a special case, stimulate further studies to better understand whether there is a cognitive divide between slow and fast decision making. If no such divide could be found, then this would be a strong signal to exploit rapid and flexible high-speed decisions in technological applications.

Materials and methods

Animals

Experiments were conducted on a group of six adult archerfish (Toxotes chatareus). The experimental fish were randomly chosen from a larger group of (male and female) archerfish. They had been imported from Thailand (Aquarium Glaser, Rodgau, Germany) and were kept at 26°C on a 12h:12h light/dark cycle in the large experimental tank (1m x 1m x 0.6 m, filled to a height of 34 cm) in brackish water (3.5 mS cm^-1). All procedures were conducted in accordance with the German Animal Welfare Act (Tierschutzgesetz) as well as the German Regulation for the protection of animals used for experimental purposes or other scientific purposes (Tierschutz-Versuchstierordnung) and were approved by the government of Lower Franconia (Regierung Unterfranken, Würzburg, Germany).

General setup

To facilitate recording the fish from below – through the transparent bottom of the tank – together with the visual stimuli shown on the LCD monitor above, the tank was placed on steel frame stands, 110 cm above ground. A construction made from 3 cm aluminum profiles (item Industrietechnik GmbH, Germany) was used to hold the monitor on top of the tank as well as to position the feeders that were employed to reward the fish. To increase the contrast in the recordings of the fish, three conventional 500 W halogen floodlights, located around the tank, illuminated a square of white cloth (2x2 m) that was placed parallel to the water surface and 106 cm above it.

Monitors and stimuli

To present visual stimuli a 27’’ LCD monitor (Samsung SyncMaster S27A750D, 120 fps, max. intensity 300 cd/m²) was used. A glass plate in front of the screen protected it against shots of brackish water fired by the fish. All objects used in this study had a Michelsen contrast of 0.96, as determined with a luminance meter (LS-110 Konica Minolta Sensing Europe) under the conditions of the actual experiments. The surface of the LCD monitor was parallel to the water surface, h = 28.8 cm above it and its center was directly above the tank’s center. Stimuli were generated using Apple Motion 5.4.7 and stored as 120 fps FullHD ProRes movies. We presented the movies with the presentation mode of Quicktime Player 10.4 (Apple Inc.) running on a MacPro 5.1 under MacOS 10.11. An AMD 4GB Radeon RX 480 graphic card produced the monitor signal and was connected via DisplayPort with the LCD monitor. Unless stated otherwise each presentation started with an object appearing in the center of the screen. After 2s the object starts moving in one of four pre-assigned, randomly chosen directions. Objects displayed were either disks of 4 mm diameter, disks of 13 mm diameter or equilateral triangles (height 13 mm). Objects that mimicked ballistically falling motion moved at a horizontal speed v_h of v_h = 1.775 m s^-1 and their virtual landing occurred 243 ms later, after a (virtual) path of 43 cm. On the screen, the movement of the ballistic objects was visible for 116 ms. Objects on the ‘deflected’ trajectories moved at the same horizontal speed but changed the direction of motion after being visible for 116 ms (or 20.5 cm) at a (virtual) time of 118.7 ms (i.e. after an initial straight path of d_r = 21.1 cm) by an angle ɣ = 39.8° to the left (see Fig. 3A). They were then visible for a further 58 ms. The systematic change in direction causes the virtual impact point, the one inferred from initial motion, to be systematically offset by o = 2*(v_h*sqrt(2h/g) - d_r) * sin(ɣ/2) where h is the height at motion onset, g is the gravitational constant and d_r is the distance travelled prior to the change in direction. In our experiments we selected conditions so that the offset was large enough (14.9 cm) to allow us detecting any errors in the bearing of the C-starts. In critical tests only the straight initial movement (i.e. the initial path of 20.5 cm) was shown both for ballistic and deflected trajectories.

Stimulus-coupled feeders

Unless stated otherwise 4 feeders were typically present. During training they were located at the places of possible virtual impact points. In many tests, the virtual impact points were systematically offset from the feeders by changing the direction of motion shown on the screen. This way the virtual landing points differed both from the position of the feeders as well as from the position relative to landmarks the fish might have been using during training. The feeders were custom-made (Fig S2A) and consisted of a tube (2 cm inner diameter, 44 cm long) with a sliding plate inserted 20 cm below its upper end to block the passage of a food pellet (one half of a Sera Cichlid stick). Each feeder was equipped with an electromagnet that can retract the slider to allow the passage of the pellet. All feeders were pre-loaded at random intervals before the tests, using a funnel (6 cm diameter) on the top side of each feeder (Fig S2A, B). Which of the four electromagnets was activated at which time was defined by trigger pules on the channels of the audio track of the movies shown on the LCD monitor so as to achieve an impact of the pellet at the virtual impact point and after the expected time T=sqrt(2h/g) of falling (h=initial height, g=gravitational acceleration). Four audio-channels were used to control which of the four electromagnets was to be activated. To achieve the required number of channels we connected an AV-receiver (Sony STR-DH520) to the computer via HDMI. Four output channels of the AV-receiver delivered the trigger signals to a custom-made amplifier which activated the electromagnets by means of a 200 ms pulse (12 V/300 mA). An additional audio channel triggered a pulse generator (TGP110; TTi, England) that started the high-speed video recording.

High-speed imaging

All recordings were made from below through the tanks transparent bottom (Fig S2C, D). A Fastcam MC2 color 500 (Photron, Japan) high-speed camera, operated at 500 fps (512 x 512 pixels) and equipped with a CVM0411ND f1.6/4.4-11 mm lens (Lensation, Germany) was used to monitor the complete tank. The pre-trigger option of the camera was always used and set to record 4 s before and 4 s after the trigger signal (i.e. the onset of target motion). An Apple Macbook Pro 6.2 running Microsoft Windows 7 controlled the setup via Fastcam viewer 332. Recordings were stored as Quicktime movies and contained the appearance of the object on the screen, its motion, and the impact of food delivered by one of the feeders.

Discriminating the responses of individual group members

Long-term studies of the archerfish start decisions require the competition in a group (27) and cannot be carried out in fish kept individually. It is therefore important to find ways to identify the individual group members that contributed a decision. Here, individuals were recognized based on the contour of their frontal body as seen from below. A template-contour was used for each individual fish that was drawn starting at one pectoral fin, over the snout and ending at the other pectoral fin. Respective images of the high-speed recordings were extracted using Image J (63) just when the straightening phase (so-called stage 2) of the so-called C-start (Fig. S1A) that leads to the turn was terminated. Note that the turns are made right below the water surface and thus in a fixed distance from the camera. The contours taken at the end of stage 2 were specific for each individual fish in the experimental group. Discrimination performed this way coincided with one obtained independently by additionally recording the responses from the side (Photron Fastcam MC2 color 2K, equipped with same type of lens and also operated at 500 fps, view orthogonal to the front side and 50 cm away from it) in which the individuals could be identified by means of their individual stripe-patterns.

Natural stimuli used to test the virtual reality approach

A non-transparent platform (4.5 cm in diameter) was mounted above the center of the tank. This allowed to blow food pellets off the platform from a similar initial height as the virtual objects shown on the screen. Movement was started by an airflow (as in 27,35) and pellets fell ballistically toward the water surface.

Quantitative analysis of the turn responses

Image J 1.50 (63) was used to analyze the recorded videos. To ensure that the decisions could not be influenced by those of other fish, we exclusively analyzed the turn of the fish that responded first in a given test. Latency was the time between motion onset and onset of the C-start. Error in aim relative to a point of interest (e.g., the virtual impact point) was determined from the last frame at the end of the straightening phase (stage 2) of the C-start, i.e., before the fish actually starts its approach trajectory (Fig. S1A). Orientation of the fish’s rigid front end was determined from the tip of the snout and the point midway between the two pectoral fins. If a line drawn along this orientation did cut a second line drawn between the start of motion and the point of interest (e.g., the virtual impact point), both projected to the water surface⁴, then the error was defined negative, otherwise it was defined positive (Fig. S1B). Additionally, we determined kinematic aspects of the C-starts, such as the duration of its first bending stage (stage 1 of the C-start), the mean angular speed (i.e., turn angle / turn duration), and the initial orientation and distance the fish had before the onset of their C-start. Only C-starts that were completed before prey impact were included in our analysis, to ensure that the C-start could not have used information from the impact of the food pellets. Furthermore, only C-starts were included in which the subsequent approach path of the responding fish was not blocked by another fish. When aims had to be evaluated relative to two points of interest (e.g., virtual landing point and feeder position) then (i) both possible approach paths had to be free and not blocked by any group member and (ii) the responding fish had not to be oriented in a line with both points. Analysis of the coordinates and frame numbers determined with ImageJ was carried out using Excel (14.0 & 15.11).

Statistics

Statistics were run on GraphPadPrism 9.5. (GraphPad Software, USA). Tests referred to in the main text were as follows: Normality of data was assayed using Shapiro–Wilk tests. For single data sets (error of aim), difference from zero was checked using One-Sample t-tests (parametric) or One-Sample Signed Rank tests (non-parametric). Comparisons of two data sets (latency, duration of stage 1, error of aim) were performed with unpaired t-tests or Mann-Whitney tests. Comparisons of three or more data sets (latency, duration of stage 1, error of aim) were performed with Kruskal– Wallis One-Way ANOVA on ranks, post hoc tested with Dunn’s method (non-parametric). Equal variance between data sets (error of aim) was checked using Brown-Forsythe tests (non-parametric). Stability of aim was tested using linear regression. Tests for changes in C-start probability employed pairwise comparisons with χ² tests. All respective tests were performed two-sided. ***p<0.001, **p<0.01, n.s. not significant. All data are available in the main text or the supplemental information.

Acknowledgements

We thank the German Research Foundation (grants Schu 1470/8-1 and Schu 1470/11-1) for continuous support and Peter Machnik and Nick Jones for feedback on the manuscript.

Supporting Information

Fig. S1.

Fig. S2.

Fig. S3.