Swarming and reaction time
What reaction times are needed for swarming? Do insects encode any special reaction times to enable swarming flight?
Visual reaction time
Go ahead, you'll be able to compare your reaction time to an insect below!
Reaction time is the amount of time it takes your neural system (vision through motor neurons) to see a visual target and begin motion relative to it. Most human reaction times are between 180 and 320ms (milliseconds). The average (according to human benchmark) is 284 ms, but about 30ms is probably due to delays in your mouse and computer, so let's call that 250ms, or 1/4 of a second.
To measure insect reaction times while they are inflight, we set up an experiment in which a visual target moves and the insect attempts to follow that target. We used a three camera automated realtime tracking system called VISIONS to track the animals as they chased the target.
In some cases, only one insect was tracking the target,
while in other cases, multiple insects followed the target.
We measured a total of 425 insects tracking the stimulus.
Then we used a technique called system identification to measure both the dynamic equations of motion (representing physics) for the animal and the neural processing delay (representing reaction time).
When the insects were on their own (ie, they were the only animal tracking the target), they showed reaction times anywhere from 7 to 120 ms. To the left, you'll see a distribution--this is the likelihood that an insect will have a given reaction time. If you know what a histogram is, this is the same concept but with a y-axis scaled from 0 (meaning never) to 1 (meaning always).
So, reaction times were much faster than humans, and over a very wide range. The average reaction time was 30 ms, or almost 10 times faster than a human reaction time. But the solo insects were remarkably diverse. Some insects were only about twice as fast as the human average, and some were almost 40 times as fast. One way to quantify how wide a histogram is with a standard deviation, in this solo case, the standard deviation is 40ms.
That picture changed a lot when other neighbors were trying to track the target as well.
In that case, the animals adjusted their reaction time, and they had a much narrower range of measured reaction times. Some insects were slowing down their reactions (those around 7ms), and some insects were speeding up (those around 100ms). The average reaction time was 15ms, and the standard deviation was now just 7ms.
In other words, the group insects had found a way to synchronize their reaction times.
Why might insects in group settings want to synchronize their reaction times? One possible reason is to coordinate their motions in swarms. Theoretical analysis says if reaction times get too large, you won't be able to coordinate your swarm. To examine if that was a reason, we built a mathematical model of insects visually reacting to eachother's motion (including a reaction time delay), and applied two mathematical techniques called mean field analysis and bifurcation analysis to find something called a Hopf bifurcation.
Mean field analysis is a way to consider the effects of your neighbors in a swarm as an amorphous blob, rather than individual agents. A bifurcation occurs when a mathematical equation has a sudden change in behavior. In the case of a Hopf bifurcation, that is a sudden change between behaviors that tend to return to a condition vs tend to diverge from that condition. So we looked at when the swarm center tended to remain fixed or drift.
We used a curve fit--a gamma distribution to be technical--to the measured delay distributions for theoretical analysis (dashed green line). This choice allows us to consider what happens because of the shape of the distribution without being tied to the specific number of agents we measured. We also used a map of how strongly an animal remembers the direction it was going (alpha) versus how much it adjusts to neighbors (beta). This generalization allows us to say something about the problem without being tied to a specific choice of weight. The results were interesting.
The analysis showed that the reaction times seen in group flight maintained stability for a larger region of ego-weight alpha and neighbor weight beta than the reaction time in solo flight. In other words, the reaction times allowed more diverse preferences to still support coordinated behavior.
But, of course, this was for a curve fitted set of delays, not for the measured delays. Would the behavior persist for the measured delays? To answer this, we implemented a simulation of the visually-interconnected swarm, and this time, we gave each member of the swarm one of the measured delays.
Solo delay swarm
As predicted, the insects that were assigned the reaction times measured in solo flight had a swarm center that drifted. Perhaps worse, there was no observable order to the resulting motion.
Group delay swarm
The insects that used reaction times measured in group flight, however, showed a stable center of mass and also achieved a formation.
From the experimental, theoretical, and simulated results, we concluded that these insects synchronize their reaction times when in group flight, and one reason that the insects may adjust their reaction times like this is to improve visually-guided swarming behaviors.
What was your reaction time? How did it compare to the honeybees we studied? Do you think it would be sufficient to participate in a swarm? Tell us what you thought at the Contact page.
This page is an adaptation of a finding under peer review, find the technical version here.
The work received support from an ONR Young Investigator Award N00014-19-1-2216, and any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the Office of Naval Research.