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6 August, 2025

They twist and turn across the sky in dense, whirling formations—murmurations of birds that seem to move as one, captivating watchers and puzzling scientists for decades. Now, a new analysis suggests that one of the most mysterious features of these aerial displays—the behaviour of birds at the edges—may stem from accident rather than intent.

A study examining the flocking patterns of jackdaws has found that the sharp borders of murmurations, and the way certain birds linger at the edges, can be explained by the mathematical rules that govern how individuals interact with their neighbours.

Scientists have long noted two peculiar features of flocking birds: those on the outer edges tend to remain there longer than expected, and the border of the flock appears remarkably well-defined, almost as if deliberately maintained. Previously, it was thought that these edge behaviours might have evolved as adaptive traits—perhaps allowing certain birds to spot predators more easily or respond faster to threats.

But according to the new study using stochastic (random) models of animal movement, these patterns emerge naturally when birds follow what are known as topological rules—coordinating their movement with a fixed number of nearby neighbours, regardless of the actual distance.

In contrast, the same striking edge behaviours did not emerge when birds interacted using metric rules, where coordination depends on who is physically closest. The findings were further supported by existing GPS tracking data from jackdaw flocks, which revealed patterns consistent with the topological model.

“What’s fascinating is that these highly structured, seemingly purposeful formations might actually be the result of very simple interaction rules,” said Rothamsted’s Andy Reynolds who conducted the analysis. “The sharpness of the border and the persistence of edge birds aren’t necessarily deliberate strategies. They’re just what happens when the system runs on topological interactions.”

The study adds to a growing body of evidence that complex group behaviours—from fish schools to insect swarms—can arise from surprisingly minimalist rules. It also raises questions about how much of animal group behaviour is shaped by evolution, and how much simply falls out of physics and geometry.

Murmurations, often seen in starlings but also performed by other species such as jackdaws, have long drawn both artistic and scientific fascination. While their precise function is still debated, they are believed to offer protection from predators and help in roosting.

This new research doesn’t rule out the idea that edge behaviours might be beneficial—but it suggests they may not have evolved for that purpose. Instead, they might be a fortunate accident of nature’s algorithm.

Why is Rothamsted studying murmurations?

A better understanding of swarming behaviours in nature provides scientists with important information on how various pest species that affect our crops might behave.  By mathematically modelling what holds a swarm together, strategies can be developed that improve our ability to predict, monitor and control the movements of insect pests.   

(Image: Shutterstock)

Publication
Contacts

Andy Reynolds

Physicist

ABOUT ROTHAMSTED RESEARCH

Rothamsted Research is the longest-running agricultural research institute in the world. We work from gene to field with a proud history of ground-breaking discoveries in areas as diverse as crop management, statistical interpretation and soil health. Our founders, in 1843, were the pioneers of modern agriculture, and we are known for our imaginative science and our collaborative approach to developing innovative farm practice.
Through independent research, we make significant contributions to improving agri-food systems in the UK and internationally, with economic impact estimated to exceed £3 bn in annual contribution to the UK economy. Our strength lies in our systems approach, which combines strategic research, interdisciplinary teams and multiple partnerships.
Rothamsted is home to three unique National Bioscience Research Infrastructures which are open to researchers from all over the world: The Long-Term Experiments, Rothamsted Insect Survey and the North Wyke Farm Platform.
We are strategically funded by the Biotechnology and Biological Sciences Research Council (BBSRC), with additional support from other national and international funding streams, and from industry. We are also supported by the Lawes Agricultural Trust (LAT).

ABOUT BBSRC

The Biotechnology and Biological Sciences Research Council is part of UK Research and Innovation, a non-departmental public body funded by a grant-in-aid from the UK government.
BBSRC invests to push back the frontiers of biology and deliver a healthy, prosperous and sustainable future. Through our investments, we build and support a vibrant, dynamic and inclusive community which delivers ground-breaking discoveries and develops bio-based solutions that contribute to tackling global challenges, such as sustainable food production, climate change, and healthy ageing.
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BBSRC proudly forges interdisciplinary collaborations where excellent bioscience has a fundamental role. We pioneer approaches that enhance the equality, diversity, and inclusion of talent by investing in people, infrastructure, technologies, and partnerships on a global scale.

ABOUT LAT

The Lawes Agricultural Trust, established in 1889 by Sir John Bennet Lawes, supports Rothamsted Research’s national and international agricultural science through the provision of land, facilities and funding. LAT, a charitable trust, owns the estates at Harpenden and Broom's Barn, including many of the buildings used by Rothamsted Research. LAT provides an annual research grant to the Director, accommodation for nearly 200 people, and support for fellowships for young scientists from developing countries. LAT also makes capital grants to help modernise facilities at Rothamsted, or invests in new buildings.