Reef fish on a Curaçao coral patch never bolted from a black disk expanding on an iPad below two metres a second, and that threshold sits just under the speeds at which bar jacks on the same reef were filmed attacking

Looming is the word for what an approaching object does to an eye. The image of the thing grows, and it grows at an accelerating rate, and that rate carries information: how fast the object is coming, and roughly when it will arrive. Animals right across the tree of life respond to it, from insects to birds to us. In fish the response is a whole-body flick called a C-start, a bend into the shape of the letter followed by a burst of speed away.

What has been unclear is where the line sits. A reef fish sees predators constantly, most of them not hunting, and every false alarm costs feeding time. Working on shallow reef flats off the west coast of Curaçao, three researchers put a number on it. No fish in their recordings performed an escape response until the stimulus was expanding like an object closing at more than two metres a second. Most of the escapes came at three metres a second or above.

The comparison that makes the number interesting came from the same reef. In a separate filming effort the team tracked 61 attacks by bar jacks, filmed hunting typically brown chromis, one of the study’s two dominant species, and found their fast-approach speeds spanning 2.7 to 9.0 metres a second. In effect no escape response was recorded to anything as slow as a cruising predator.

The rig on the coral patch

The experiment ran at Cas Abou and Kokomo Beach, at five sites around three metres deep, in twelve trial sessions across the two locations. At each one the team set up a 12.9-inch iPad Pro beside an isolated coral patch that the local fish use as a refuge. Every ninety seconds for about an hour the screen played a black disk expanding on a white background.

Three GoPros recorded at 240 frames a second, two looking down and one from the side. That let the team reconstruct each fish in three dimensions and measure how far it sat from the coral and at what angle it viewed the screen. Fish that were invisible to one of the stereo cameras or left the field of view were dropped, and a whole video was thrown out when more than a third of its tracked fish were unusable. After filtering, 247 videos survived, 67 of them containing at least one fish that bolted and 180 containing none.

The expansion rate of the disk was calibrated to reproduce what a predator approaching at one of nine speeds would do to a fish’s retina: 0.5, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0 or 8.0 metres a second, presented in random order. No animals were handled, and the work ran under a Curaçaoan government permit held by the CARMABI research station.

A flat screen showing a two-dimensional expanding disk is a long way from a predator. It strips out shape, body motion, water displacement, chemical cues, and the fact of being an object instead of an image. Isolating approach speed is what the design is for, and it is also the boundary of what the result can say about a real attack, which the paper acknowledges in its discussion.

Escape probability jumps above two metres a second

Across every analysis, stimulus speed dominated. Response probability did not climb steadily with speed. It stayed flat and near zero through the slow presentations and then rose sharply above about two metres a second, and formal comparisons confirmed that curved fits describe the data better than a straight line.

That shape is what a threshold looks like in data. It is also consistent with the circuitry involved: the Mauthner cell, the giant neuron that fires the C-start in fish, sits on a pathway tuned to approach speed, so slow growth in the visual field can pass through the system without triggering anything.

The authors read the near-absence of response to slow stimuli as consistent with threat-sensitive predator avoidance, in which prey grade their escape to the level of threat and respond weakly to slow-moving or non-attacking predators. Damselfish of the genus Stegastes, which is the genus of one of this study’s two dominant species, are already known to behave that way. The Curaçao work adds a measured speed at which the response switches on.

Two variables in the setup mattered as well, and both are about visibility. Fish closer to the screen and viewing it at a smaller angle responded more often, which the authors attribute to the flat display becoming reflective and the disk becoming harder to make out from oblique positions.

A second set of cameras timed the jacks

Attack speeds came from a different deployment: stereo cameras at 120 frames a second on the same reef, at other times, recording bar jacks instead of damselfish. The team tracked head positions through 61 attacks, each followed from the moment the jack entered frame or began its run until the prey, typically a brown chromis, escaped or was caught.

Instantaneous speed is noisy when it is measured by hand from video, so the team used the 90th percentile of the predator’s speed as a stand-in for its top attack speed, which captures the fast-approach phase while damping tracking noise. Those values ran from 2.7 to 9.0 metres a second, and the authors call the correspondence between those speeds and the response threshold a close one.

Two different kinds of speed are being set beside each other there, and the piece the comparison rests on is thinner than it looks. One is a programmed number, the approach speed a disk on a screen was calibrated to imitate. The other is a tracked speed of a real animal in water, summarised at a percentile rather than at its maximum. They are close, and the closeness is the finding, but the overlap is not a calibration and should not be read as one.

No comparable figure has been published for how fast a bar jack swims when it is not hunting, and the authors say so. The closest available number is for a relative, the green jack, which cruises at around a metre a second or less at similar body sizes. That speed sits below the threshold, in the band where the fish in this study never responded at all. Broader work on reef fishes reports attack movements running several times faster than routine swimming, so the difference these fish are exploiting is a wide one.

The species gap survives the model

The two dominant species behaved differently. Bicolor damselfish, which are territorial and hold small patches of coral, responded less often than brown chromis, which form site-attached aggregations and feed on plankton in the open water above the reef.

That difference tracks where they were when the disk appeared. Chromis were found significantly further from the coral than damselfish, and distance from shelter on its own predicted a higher chance of fleeing. Put both variables into one model and distance stops being statistically significant, which is what happens when two predictors carry overlapping information.

The species difference does not dissolve the same way. Adding log-transformed distance to a species model shrank the species coefficient by more than a third and improved the fit. The species effect stayed statistically significant, which the authors read as an intrinsic difference between the two fishes and not a matter of exposure alone.

Social context did nothing, which the authors flag as contrary to their expectations. Whether a fish had company nearby, and how close that company was, had no measurable bearing on whether it fled.

Sixty-seven of 247 videos contain any escape at all, and the escapes cluster at the top of the speed range, so the threshold is estimated from the thin end of the data. No natural predator attack occurred during any of the presentations that were analysed, which means the alignment between the two datasets is an alignment between separate recordings and not a case of the same fish responding to both. A threshold measured on one reef, in two species, at three metres of depth, in daylight clear enough for a screen to work, is a number for these fish here.

The rule the fish carry

What the study describes is not vigilance so much as a setting. The fish are not weighing each approaching shape on its merits. They are running a rule that ignores everything below a speed and reacts to everything above it, and the rule sits just under the speeds at which the local predator was filmed attacking.

That is a cheap way to be right most of the time. It is also blind in one direction, at least in principle, and the study did not test that direction: a rule of this kind would miss something that closed slowly and never accelerated. The paper narrows that gap itself. Pursuit, ambush and stalking alike, it notes, end in a rapid terminal approach, which is why approach speed works as a cue at all.

The study cannot say how the setting got there, whether it is learned on a particular reef or built in and inherited. Either way it is a number a fish carries around with it, and it was measured on an animal watching a screen that no predator has ever resembled.