Limits for Rumor Spreading in stochastic populations

TL;DR

This paper investigates how communication noise impacts rumor spreading in biological-like populations, revealing that noise severely limits efficiency unless the system has structural stability or noise-resistant communication features.

Contribution

It provides a theoretical lower bound showing noise prevents efficient rumor spreading in amorphous systems, and demonstrates an exponential separation between PUSH and PULL models under noise.

Findings

No significant improvement over trivial spreading under moderate noise.

Exponential separation between PUSH and PULL models with noise.

Empirical analysis of desert ant recruitment supports theoretical results.

Abstract

Biological systems can share and collectively process information to yield emergent effects, despite inherent noise in communication. While man-made systems often employ intricate structural solutions to overcome noise, the structure of many biological systems is more amorphous. It is not well understood how communication noise may affect the computational repertoire of such groups. To approach this question we consider the basic collective task of rumor spreading, in which information from few knowledgeable sources must reliably flow into the rest of the population. In order to study the effect of communication noise on the ability of groups that lack stable structures to efficiently solve this task, we consider a noisy version of the uniform PULL model. We prove a lower bound which implies that, in the presence of even moderate levels of noise that affect all facets of the communication, no scheme can significantly outperform the trivial one in which agents have to wait until directly interacting with the sources. Our results thus show an exponential separation between the uniform PUSH and PULL communication models in the presence of noise. Such separation may be interpreted as suggesting that, in order to achieve efficient rumor spreading, a system must exhibit either some degree of structural stability or, alternatively, some facet of the communication which is immune to noise. We corroborate our theoretical findings with a new analysis of experimental data regarding recruitment in Cataglyphis niger desert ants.