The Effect of Different Communication Mechanisms on the Movement and Structure of Self-Organised Aggregations

Abstract

The formation, persistence and movement of self-organised biological aggregations are mediated by signals (e.g., visual, acoustic or chemical) that organisms use to communicate with each other. To investigate the effect that communication has on the movement of biological aggregations, we use a class of nonlocal hyperbolic models that incorporate social interactions and different communication mechanisms between group members. We approximate the maximum speed for left-moving and right-moving groups, and show numerically that the travelling pulses exhibited by the nonlocal hyperbolic models actually travel at this maximum speed. Next, we use the formula for the speed of a travelling pulse to calculate the reversal time for the zigzagging behaviour, and show that the communication mechanisms have an effect on these reversal times. Moreover, we show that how animals communicate with each other affects also the density structure of the zigzags. These findings offer a new perspective on the complexity of the biological factors behind the formation and movement of various aggregations.

The Role of Avoidance and Learning Behaviours on the Formation and Movement of Biological Aggregations

“…Despite the fact that such studies have started to be performed in [7,8,14,17], we are still far from understanding pattern formation in these types of nonlocal hyperbolic models.…”

Mathematical Modelling in Theoretical Ecology: Introduction to the Special Issue

“…It has been convincingly demonstrated that heterogeneity in the distribution of organisms across the environment can play a key role in shaping ecosystem dynamics and enhancing persistence of populations [6,8,9,15]. In the current issue, four contributions [4,12,20,23] directly focus on the role of space in population dynamics.…”

“…Understanding the mechanisms of biological aggregation and patchiness is a hot topic in theoretical ecology with various models suggested [6,18,21]. In her work, R. Eftimie [20] investigates the movement of aggregations of organisms mediated by various signals as a result of communication and social interactions. The mathematical framework used in [20] is based on nonlocal hyperbolic equations with integral kernels.…”

“…In her work, R. Eftimie [20] investigates the movement of aggregations of organisms mediated by various signals as a result of communication and social interactions. The mathematical framework used in [20] is based on nonlocal hyperbolic equations with integral kernels. It is demonstrated that animal groups using communication can travel in a zigzagging manner and the maximal speed of group movement is estimated using analytical techniques.…”