# Density distributions and depth in flocks

## TL;DR

This paper introduces a metric-free model for bird flocking that accounts for inhomogeneous density distributions and motional biases, successfully fitting real starling flock data and exploring how birds perceive their position within the flock.

## Contribution

The paper presents a novel, metric-free collective behavior model incorporating distributed motional bias, explaining density variations and depth perception in bird flocks.

## Key findings

- Inward bias at flock edges and outward bias inside the flock are necessary.
- The model fits observed starling flock density data.
- Simple visual analysis could enable birds to determine their depth.

## Abstract

Recent experimental evidence suggests that interactions in flocks of birds do not involve a characteristic length scale. Bird flocks have also been revealed to have an inhomogeneous density distribution, with the density of birds near the border greater than near the centre. We introduce a strictly metric-free model for collective behaviour that incorporates a distributed motional bias, providing control of the density distribution. A simple version of this model is then able to provide a good fit to published data for the density variation across flocks of Starlings. We find that it is necessary for individuals on the edge of the flock to have an inward motional bias but that birds in the interior of the flock instead must have an outward bias. We discuss the ability of individuals to determine their depth within a flock and show how this might be achieved by relatively simple analysis of their visual environment.