Here are some tricks worth applauding in the never-ending parade of dazzling performances in the animal world.

Oh, Rats!

For the Year of the Rat, here is some design evidence in vermin. It’s not rats’ fault that plague-carrying fleas sometimes hitch a ride on their fur, and that some medieval folks didn’t remember that cleanliness is next to godliness. These days, clean rats are mainstays of the science labs, generating knowledge that enhances our health. One enterprising rat even overcame rattist bias by opening a gourmet restaurant.

A rat deserves a little more respect just for its facial hair. Physiologist Robyn Grant of Manchester Metropolitan University, writing for The Conversation, discusses how she and her colleagues “found a special maths equation hidden in rat whiskers.” The team first counted about 70 whiskers per rat, “varying hugely in size and shape.” All mammals (including human males) have whiskers, but the whiskers of rats are super-sensitive and movable. They enable these “whisker specialists” to explore and sense their surroundings, even in the dark. Investigating the whiskers more closely, the team discovered that the arrangement of whiskers fits a mathematical equation called the Euler Spiral, elucidated by the prolific 18th-century math genius Leonhard Euler (1707-1783). 

We found that rat whiskers can be accurately described by a simple mathematical equation known as the Euler spiral. It’s an example of how special spiral patterns are found throughout the natural world. And spotting them can help us not only understand nature better, but also improve our own engineering.

The Euler spiral — also called the Cornu spiral, Spiros or Clothoid — is a shape whose curvature changes linearly with its length. It looks quite like an s-shape, where the tips of the “s” carry on curving in to spirals that get rapidly tighter. As a result, aspects of the curve can fit a wide variety of shapes including those that are straight or s-shaped, those that increase in curvature and those that decrease in curvature. [Emphasis added.]

This kind of spiral, different from the logarithmic spiral, follows a transition from flat to curved, from one curl to the opposite curl. In their paper “The Euler spiral of rat whiskers” in Science Advances, Starostin et al. say that consideration of a “form-to-function relation must be the key to our understanding of the rat’s tactile processing system.” On that point, they reference D’Arcy Thompson’s pivotal book on structuralism, a key idea Michael Denton discussed in his book Evolution: Still a Theory in Crisis. Structuralism stands in opposition to Darwin’s adaptationist view. The authors have little to say about evolution other than speculation: e.g., 

While we observe the uniformity of this particular angle value, we cannot offer an explanation, but we speculate that it relates to sensory function of vibrissae [whiskers], i.e., it may be an evolutionary phenomenon. One can, nevertheless, assume that the positions of the whisker tips on the shroud together with their relative orientations are key factors in the functioning of the rat’s vibrissal system.

In short, it was form and function — not evolution — that led to their identification of the Euler spiral in rat whiskers. Presumably, the precise mathematical form optimizes the sensory function in the whiskers by distributing the tips in an organized way. Stiff hairs alone, however, accomplish nothing unless they are linked to sensors which can communicate with the brain. 

Whiskers are actually made up of dead hair cells but they sit within a specialised sensitive follicle. The follicle is what extracts information about the force and direction of the whisker as it touches objects, and transfers that information to the brain. This information is what the rat uses to perceive objects and judge their shape, size and texture.

The brain, in turn, must continuously activate follicle muscles in response to those signals. That’s why they call it a “vibrissal system.” Grant concludes with thoughts that might stimulate celebrations for the Year of the Rat.

Nature is full of mathematical patterns. Given how rat whiskers follow the Euler spiral, and that spirals are so common in nature, we think there’s a good chance the whiskers of other mammals probably follow similar rules and may also be described by Euler spirals. In this way, maths can give us a special insight into how biological structures and systems work.

Giant Squid

The next performer is the giant squid. The genome of this “legendary, mysterious” sea monster has been sequenced, reports the Marine Biology Laboratory of the University of Chicago. Giant squid have the largest brains among invertebrates. All squid are extremely agile creatures. They amaze scientists with their camouflage, the ability to change color almost instantaneously. “How did the monstrous giant squid – reaching school-bus size, with eyes as big as dinner plates and tentacles that can snatch prey 10 yards away — get so scarily big?”

There were no unique aspects in the genome. “In terms of their genes, we found the giant squid look a lot like other animals,” the geneticists found. The genome is about 90 percent the size of the human genome — a surprising discovery, considering how far apart humans and squid are on Darwin’s tree diagram. In fact, scientists at the University of Queensland say that “Squid brains approach those of dogs.” (To explain this, they fall back on the old Darwinian trick of “convergent evolution.”)

Several features in the giant squid genome seem downright un-Darwinian. The team expected to find evidence that the genome grew through whole-genome duplication, but they didn’t. And they found more than 100 genes in the protocadherin family, “typically not found in abundance in invertebrates — in the giant squid genome.” Caroline Albertin was surprised by this:

“Protocadherins are thought to be important in wiring up a complicated brain correctly,” she says. “They were thought to be a vertebrate innovation, so we were really surprised when we found more than 100 of them in the octopus genome (in 2015). That seemed like a smoking gun to how you make a complicated brain. And we have found a similar expansion of protocadherins in the giant squid, as well.”

Albertin speculates that the new genetic data “can help us understand how new and novel genes arise in evolution and development.” It can (with a lot of imagination), but it didn’t. They expected to see whole-genome duplication, but evidently the giant squid “did NOT get so big through whole-genome duplication, a strategy that evolution took long ago to increase the size of vertebrates.” The last retreat of an evolutionist is the promissory note: “So, knowing how this squid species got so giant awaits further probing of its genome.”

Moon Jellies

The graceful, pulsating moon jellyfish move in “a very efficient way,” say biologists at the University of Bonn. They perform an elegant dance in the cirque de la mer.

Scientists at the University of Bonn have now used a mathematical model to investigate how these cnidarians manage to use their neural networks to control their locomotion even when they are injured. The results may also contribute to the optimization of underwater robots.  

Moon jellies use circular muscles at the base of the bell to contract and force water out, thus swimming by jet propulsion. Since the bell is elastic, it passively returns to its original shape for the next pulse. Other design features give it exquisite control:

The jellyfish can perceive their position with light stimuli and with a balance organ. If a moon jellyfish is turned by the ocean current, the animal compensates for this and moves further to the water surface, for example. With their model, the researchers were able to confirm the assumption that the jellyfish uses one neural network for swimming straight ahead and two for rotational movements.

That’s pretty astonishing for a “primitive” animal. Because the activity of nerve cells spread in a wave-like pattern, the jelly can continue functioning even when part of the bell is injured. “The scientists hope that further research will shed light on the early evolution of the neural networks,” they conclude. Good luck, because the underwater robots under development to mimic the moon jelly’s “swimming principle” are being designed by intelligent minds.

Photo credit: © Volker Lannert via University of Bonn (press release).