Alan Turing's Math Equations Used to Understand Bird Behavior

Alan Turing's mathematical equations, developed over six decades ago, have helped researchers understand why birds segregate themselves across a landscape.

A research team from the University of Sheffield tracked flocks of long-tailed tits across the local Rivelin Valley. They later found patterns on how these birds separate themselves. Their findings are reported in the Journal of Animal Ecology.

The Long-Tailed Tit: A Round, Quirky Bird

A long-tailed tit, or Aegithalos caudatus, is also known as the silver-throated tit or dasher. This species is generally characterized as a small bird with a round body and short, stubby bill and a long, narrow tail - thus the name, long-tailed tit.

The bird is commonly found across Europe and the Palearctic region.

Although classified as a non-territorial species, the long-tailed tit have puzzled scientists by segregation themselves into various areas in a landscape. They conduct this patterned segregation even when it is observed that there is enough food to provide for multiple flocks.

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The Sheffield research team used mechanistic home range analysis (MHRA) to try and characterize the segregation strategies of long-tailed tit flocks. Aside from their tendency to avoid relatives and larger flocks, the long-tailed tit has also shown a preference for central parts of woodland areas.

"Long-tailed tits are too small to be fitted with GPS trackers like larger animals, so researchers follow these tiny birds on foot, listening for bird calls and identifying birds with binoculars," said Natasha Ellison, lead author of the study and a Ph.D. student at the University of Sheffield. She added: "The fieldwork is extremely time consuming and without the help of these mathematical models these behaviors wouldn't have been discovered."

Aside from visualizing the distribution tendencies of long-tailed tits over a woodland area, their study has also successfully extended the use of the MHRA to non-breeding, non-territorial passerines. Through this study, space use patterns like the MHRA can be used even without territorial scent-marking.

As for the tits' preference toward central areas of the woodland, the researchers propose a variety of hypotheses supported by previous studies. One of which proposes that core areas are better than edge parts for the avoidance of predators.

The Role of the Mathematics Developed by Alan Turing

"Mathematical models help us understand nature in an extraordinary amount of ways and our study is a fantastic example of this," Ellison said.

The news article from the University of Sheffield mentioned that the equations used to generate the mathematical models in the study are similar to those previously developed by Alan Turing, English mathematician, and computing genius, to describe the animals' probability of developing striped or spotted patterns.

Back in August 1952, Alan Turing introduced the concept later known as the Turing pattern in his paper titled "The Chemical Basis of Morphogenesis." In his paper, Turing suggested that a system of chemical substances reacting together and diffusing through tissue can offer sufficient information for the main phenomenon of morphogenesis. Its application is found in nature, most famously in developing animals in the womb.

In the University of Sheffield study, they used a similar mathematical approach, only applied to patterns made by the long-tailed tits in the landscape.

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