### Animal Stripes for Camouflage

February 18, 2016

Mathematician, Alan Turing (1912-1954), who was born a little more than a hundred years ago, is known for his work on many early computer science problems. One of the easiest to understand is the Turing test, which is a test of a computer's ability to mimic intelligence. "Intelligence" in this case is human intelligence, so a computer program must mimic human ignorance as well as human intelligence to pass the test.

In 1936, Turing developed a model of an ideal computer that's now called the Turing machine. This computer functions by just reading and manipulating symbols on a tape according to a table of rules. Turing used his machine to solve the problem of whether an arbitrary computer program will finish its computation, a problem known as the "Halting problem."

Such a problem is one of a type called an
Entscheidungsproblem in deference to David Hilbert, the German mathematician who introduced it. Turing showed that it can't be decided by a general algorithm whether a computer program will ever complete.

David Hilbert (1862-1943)

While Hilbert did some important mathematics, he's best known for his twenty-three problems in mathematics published in 1900.

These problems are of a fundamental nature, and some of them, such as the Riemann hypothesis (the 8th problem), are still unsolved.[1]

(Via Wikimedia Commons.)

The portion of Turing work that most people would associate with computers was done during World War II, when he built electromechanical computers to do cryptanalysis of secret messages at the British Bletchley Park facility. He also collaborated on a method, called Good–Turing frequency estimation, to estimate the probability of finding a unique species based on observations of other species. I wrote about a problem of this type in an earlier article (Earth's Mineral Wealth, October 19, 2015).

Turing was also interested in problems outside the field of computer science. One of these was the problem of how animals, such as the tiger, gets their stripes. In his 1951 paper, "The Chemical Basis of Morphogenesis," Turing explicated the pattern-forming process as a competition between two chemical species having different reaction and diffusion rates.

Turing assumed that an activator chemical can produce more of itself, but also an inhibitor, the function of the inhibitor being to destroy or stop the activity of the activator. The activator chemical, for example, can be responsible for a
color change. If the inhibitor diffuses faster than the activator, a pattern will form as the chemicals diffuse through a medium (see figure).

Development of a Turing reaction-diffusion pattern. This shows the formation of a hexagonal pattern from a noisy initial condition in a two-component reaction-diffusion system of the Fitzhugh-Nagumo type. (Images from Wikipedia.)

When nature develops such a unique mechanism, it generally has some evolutionary advantage. Most determinants of appearance, such as the peacock's feathers, affect sexual selection, but it's always been thought that stripes on an animal aid in camouflage. It's supposedly harder to see a zebra against a stand of small trees, since it has stripes.

A recent paper in Scientific Reports by scientists at the University of Exeter (Cornwall, UK), the University of Cambridge (Cambridge, UK), and the University of Cape Town (Rondebosch, South Africa) provides evidence that this is true for some nesting birds.[3-4] For two bird species that flee in the face of threat, the research team found that their eggs were more likely to survive when the contrast of the eggs matched the surroundings. Another species, the nightjar, remains motionless when approached by a threat, and the survival of their eggs depended on how well the birds matched their surroundings.[3-4]

Avian camouflage. Left, the eggs of the Bronze-Wing Courser. Right, a Fiery-Necked Nightjar.Left image by Claire Spottiswoode, right image by Jolyon Troscianko.)

To make accurate conclusions as to what's really visible to animals, the research team used calibrated digital cameras and computer models of animal vision. Birds have color vision that extends into ultraviolet wavelengths, but a mongoose only sees blues and yellows.[4] Says the University of Exeter's Jolyon Troscianko, lead author of the paper,
"We know that animal camouflage has evolved over millions of years to help prey evade being seen by predators – it is a classic example of natural selection. Yet although it may seem obvious that blending into your background makes you less likely to be seen, it is surprisingly difficult to test this in a natural setting. This is partly because very well camouflaged animals are of course difficult to find in the wild, and also because they tend to keep moving around, meaning the match between their own appearance and their background is constantly changing. In addition we had determine which predators were eating the nests so that we could take into account their different visual systems."[4]

The hypothesis that a zebra's stripes are there to offer camouflage and thus confer an evolutionary advantage has been debated since the time of Charles Darwin. Among other hypotheses is that the pattern confuses parasitic flies.[5] Darwin, citing observations of herd behavior, thought that they were designed merely for sexual selection.

Darwin's evolutionary shadow, Alfred Russel Wallace, believed that the stripe pattern was especially effective at twilight, so it would offer camouflage during that hunting period. Wrote Wallace, "Mr. Francis Galton, who has studied these animals in their native haunts, assures me, that in twilight they are not at all conspicuous, the stripes of white and black so merging together into a gray tint that it is very difficult to see them at a little distance."[6]

A zebra grazing on a grassy plain

(University of California Davis image by Tim Caro.)

Recent research by scientists at Washington University (St. Louis, Missouri), the University of Calgary (Calgary, Alberta, Canada), Kyushu University (Fukuoka, Japan), and the University of California Davis (Davis, California) indicates that a zebra's stripe pattern actually doesn't offer camouflage against predation.[6-8] They examined the ability of lions (Panthera leo), and the principal predator of zebras, the spotted hyaena (Crocuta crocuta), to resolve zebra stripes at various distances. To do this, they filtered digital images of zebras to simulate their appearance to each species.[6]

Humans can resolve zebra stripes at distances 4.5 and 7.5 times the distances of lions and spotted hyaenas, respectively, but in open treeless areas in which zebras are more likely to be found, lions can spot zebras as easily as they can spot similar-sized ungulates, so stripes don't disrupt the zebra's outline.[6-7] Stripes are also not a very effective camouflage in woodlands.

A zebra as it may appear to a human, lion and hyaena at 6.4 meters. All these species can see the stripes. (Fig. 2 of ref. 6, licensed under a Creative Commons Attribution License.[6]

The study authors conclude that It's highly unlikely that stripes are a form of anti-predator camouflage, since at long distance the stripes would not be visible against a treed background. Stripes would only help at close distance to a predator, but at these distances the predators would smell or hear the zebras moving.[6] Avoidance of biting flies might be the most parsimonious explanation for zebra stripes.[6]

### References:

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