Scientists at the University of Sheffield have used mathematical modelling to understand long-tailed tit behaviour. The research, published in the Journal of Animal Ecology, was carried out in Rivelin Valley, Sheffield, and aimed to understand why flocks of long-tailed tits live in different parts of the valley, despite having no nest or roost and rarely displaying territorial behaviour.

Natasha Ellison, the PhD student who led the study, said: “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.”

Field ecologists recorded the birds’ locations over several months, allowing the team to identify their home range patterns. Each flock of long-tailed tits used an area of the valley exclusively, so the team hypothesised that flocks could be avoiding each other after interacting. However, this was too difficult to test experimentally because every flock would have to be observed all the time.

Instead, Ellison and her team created a mathematical model of each flock’s memory of past interactions. The model revealed that flocks of long-tailed tits do avoid each other, and that they are more likely to avoid places with less related flocks. They also found that the birds prefer the centre of woodland.

The equations used to model the probability density of the interacting long-tailed tit flocks were similar to Alan Turing’s equations which he used to model the density of reacting chemicals, which determine patterning (spots and stripes) in animals. Here, the team used Turing’s theory to understand when home range patterns form in long-tailed tits.

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

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