Swarm dynamics may give rise to Lévy flights

Area of Science:

• Mathematical biology
• Animal movement ecology

Background:

• Continuous-time correlated random walks (CTRWs) are advanced models for animal movement, surpassing limitations of discrete models.
• CTRWs are based on the Langevin equation, typically driven by additive noise.
• Multiplicative noise fundamentally alters the Langevin equation, leading to Lévy flights, a model for scale-free movement.

Purpose of the Study:

• To investigate the role of multiplicative noise in biological movement models.
• To demonstrate how Langevin equations with multiplicative noise and Lévy flights naturally emerge in swarm dynamics.
• To connect theoretical models of movement to empirical observations in insect swarms.

Main Methods:

• Theoretical modeling using Langevin equations with multiplicative noise.
• Analysis of Lévy flight characteristics in swarm behavior.
• Empirical data collection of insect positions in laboratory swarms.

Main Results:

• Langevin equations driven by multiplicative noise naturally generate Lévy flight patterns.
• Model predictions show support from 3D, time-resolved movement data of Chironomus riparius midges.
• Multiplicative noise is identified as a key factor in generating scale-free movement patterns in swarms.

Conclusions:

• Multiplicative noise provides a natural generative process for Lévy flights in biological systems.
• This study offers a new perspective on Lévy flights as models for animal movement data.
• The findings link observed movement patterns to underlying generative mechanisms in insect swarms.