Estimating transmission noise on networks from stationary local order

TL;DR

This paper demonstrates that the noisiness of trait transmission in networks can be ranked using stationary state measures, independent of network topology, enabling inference from spatial data in various domains.

Contribution

It introduces a method to rank trait transmission noisiness solely from stationary state measures, applicable across different network topologies.

Findings

Traits can be ranked by transmission noisiness using stationary measures.

The ranking is independent of network topology.

Application to language traits suggests broader applicability.

Abstract

In this paper we study networks of nodes characterised by binary traits that change both endogenously and through nearest-neighbour interaction. Our analytical results show that those traits can be ranked according to the noisiness of their transmission using only measures of order in the stationary state. Crucially, this ranking is independent of network topology. As an example, we explain why, in line with a long-standing hypothesis, the relative stability of the structural traits of languages can be estimated from their geospatial distribution. We conjecture that similar inferences may be possible in a more general class of Markovian systems. Consequently, in many empirical domains where longitudinal information is not easily available the propensities of traits to change could be estimated from spatial data alone.