Without the help of these mathematical models these behaviours wouldn't have been discovered.
Scientists have used mathematical modelling developed by Alan Turing to learn more about the behaviour of birds.
Researchers used the method to study why flocks of long-tailed tits segregate themselves into different parts of the landscape.
The team tracked the birds around Sheffield's Rivelin Valley which eventually produced a pattern across the landscape, and using maths helped the researchers to reveal the behaviours causing these patterns.
Natasha Ellison, PhD student at the University of Sheffield who led the study, said: "Mathematical models help us understand nature in an extraordinary amount of ways and our study is a fantastic example of this.
"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.
"The field work is extremely time consuming and without the help of these mathematical models these behaviours wouldn't have been discovered."
Flocks of long-tailed tits are less likely to avoid places where they have interacted with relatives and more likely to avoid larger flocks, whilst preferring the centre of woodland, according to the findings published in the Journal of Animal Ecology.
It was previously unknown why the birds live in separate parts of the same area, despite there being plenty of food to sustain multiple flocks and the birds not showing territorial behaviour.
The equations used to understand the birds are similar to those developed by Mr Turing to describe how animals get their spotted and striped patterns.
The maths indicates if patterns will appear as an animal grows in the womb, while in the study it was used to find behaviours that lead to the patterns across the landscape.
Territorial animals often live in segregated areas that they aggressively defend and stay close to their den, the researchers say.
Before the current study, these mathematical ideas had been used to understand the patterns made by territorial animals such as coyotes, meerkats and even human gangs.
However, this study was the first to use the ideas on non-territorial animals with no den pinning them in place.
Nina Massey is the PA science correspondent.