快猫短视频

Zebrafish are exceptionally good synchronised swimmers, forming tight schools that contain hundreds of individuals. Physicists have shown how the fish stay together even as they swim faster to avoid a predator 鈥� and they do so by subconsciously performing the kind of weighted averages calculation familiar to high-school mathematics students.

Small fishes tend to swim in schools. Sticking together decreases the risk of any individual fish being killed by predators, and biologists say a school of fish can have more foraging success because many eyes are better than two when it comes to searching for food.

快猫短视频s have built mathematical models to understand how fish manage to swim so closely to dozens of others without colliding. They found that in order to maintain the schools鈥� structure, every fish keeps tabs on what many of its peers are doing 鈥� their speed, orientation, and any changes in either of these.

Gonzalo de Polavieja at the Champalimaud Centre for the Unknown in Portugal wanted to know if these rules still applied when the school comes under attack from a predator and the fish must swim faster.

Predator attack

With his colleagues, de Polavieja tracked the movement and speed of over 200 zebrafish swimming in groups in fishtanks in their lab. Through modelling, they found the earlier mathematical models no longer apply when the fish move quickly 鈥� at more than three body lengths per second. At these higher speeds, the fish collect the bare minimum information they need to avoid collisions and synchronise their swimming with others.

The model shows each fish considers the position, speed and direction of just five neighbours on average. Even then, not all of them matter equally. The movement and speed of neighbours that swim faster or are closer have the biggest impact on the direction and speed of any individual fish.

鈥淚t鈥檚 like doing a weighted average calculation in mathematics,鈥� de Polavieja. 鈥淭hese fish are particularly clever when they aggregate information.鈥�

Of course, says Shaun Killen at the University of Glasgow in the UK, this doesn鈥檛 mean the fish are consciously making the calculations in their head. 鈥淭hese behaviours are intuitive to fish,鈥� he says. 鈥淸But] it is amazing how apparently complex behaviours can often be explained by relatively simple mathematical models.鈥�