Ecologists confirm Alan Turing’s theory for Australian fairy circles

Posted: September 23, 2020 by oldbrew in modelling, research

Image credit: Science News


We highlighted this in a 2016 blog post, and now new research provides this update.
– – –
Fairy circles are one of nature’s greatest enigmas and most visually stunning phenomena, says Phys.org.

An international research team led by the University of Göttingen has now, for the first time, collected detailed data to show that Alan Turing’s model explains the striking vegetation patterns of the Australian fairy circles.

In addition, the researchers showed that the grasses that make up these patterns act as “eco-engineers” to modify their own hostile and arid environment, thus keeping the ecosystem functioning. The results were published in the Journal of Ecology.

Researchers from Germany, Australia and Israel undertook an in-depth fieldwork study in the remote Outback of Western Australia. They used drone technology, spatial statistics, quadrat-based field mapping, and continuous data-recording from a field-weather station.

With the drone and a multispectral camera, the researchers mapped the “vitality status” of the Triodia grasses (how strong and how well they grew) in five one-hectare plots and classified them into high- and low-vitality.

The systematic and detailed fieldwork enabled, for the first time in such an ecosystem, a comprehensive test of the ‘Turing pattern‘ theory.

Turing’s concept was that in certain systems, due to random disturbances and a ‘reaction-diffusion’ mechanism, interaction between just two diffusible substances was enough to allow strongly patterned structures to spontaneously emerge.

Physicists have used this model to explain the striking skin patterns in zebrafish or leopards for instance.

Earlier modeling had suggested this theory might apply to these intriguing vegetation patterns and now there is robust data from multiple scales which confirms that Alan Turing’s model applies to Australian fairy circles.

Continued here.
. . .
The article concludes:
In 1952 when the British mathematician, Alan Turing, published his ground-breaking theoretical paper on pattern formation, he had most likely never heard of the fairy circles before. But with his theory he laid the foundation for generations of physicists to explain highly symmetrical patterns like sand ripples in dunes, cloud stripes in the sky or spots on an animal’s coat with the reaction-diffusion mechanism. Now, ecologists have provided an empirical study to extend this principle from physics to dryland ecosystems with fairy circles.

Comments
  1. oldbrew says:

    Turing’s paper says (start of section 12):
    The treatment of homogeneity breakdown on the surface of a sphere is not much more
    difficult than in the case of the ring. The theory of spherical harmonics, on which it is based,
    is not, however, known to many that are not mathematical specialists.

    – – –
    Spherical harmonics

    Spherical harmonics are important in many theoretical and practical applications, including the representation of multipole electrostatic and electromagnetic fields, electron configurations, gravitational fields, geoids, the magnetic fields of planetary bodies and stars, and the cosmic microwave background radiation. [bold added]

    https://en.wikipedia.org/wiki/Spherical_harmonics

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