This marine eeltail catfish has almost no predators, given its viciously venomous spines, which can lock erect even in death. It feeds on the bottom in large moving shoals, with a well defined leading edge like a weather front. As a fish feeding on the bottom finds itself being left behind by the crowd, it swims up and over its companions to restart at the front.
An MSc thesis from 1967 describes similar ‘roller feeding’ in the Cattle Egret: “The birds all advance in the same direction, with birds at the back continually flying over the heads of the others to feed in the front rank.” Also termed ‘leapfrog foraging’, it has been modelled for locust swarms, “and includes a takeoff zone, a landing zone, and a stationary zone where grounded locusts can rest and feed.” (Accessible pdf here.)
Amazingly (to me), the model drops the third dimension for the swarm (width) and yet makes invaluable predictions. The article refers to a prior one which dealt with modelling the transition from random to ordered ground level, carpeting ‘marching’ by pre-flight locust nymphs. (It offers vital help for authorities trying to prevent such transitions so they don’t lead to swarms.) Their two dimensional activity was also modelled by dropping one dimension and, “consists of a set of pointwise particles moving synchronously and interacting locally by trying to align with their neighbors,” along a line.
This got me wondering about whether any zero dimension biological models of one dimensional behaviour exist. When researching one of my observations from Papua New Guinea, I found an article about, “where gobies are often seen lined up in single file when two or more individuals share the same whip coral.” From there I discovered that researchers into processionary behaviour among caterpillars had found that for thigmotactic (touch-based) single file formations, they could effectively distill a whole procession’s behaviour into a single head-to-tail (prompting) or tail-to-head (inducing) contact point. (Accessible pdf here.)
Have you come across any observations of behaviour involving group rolling? Or an accessible paper modelling a one dimensional group behaviour? Or maybe even a three dimensional model of a four dimensional behaviour (involving time)?