Innovation-exnovation dynamics on trees and trusses

TL;DR

This paper models innovation and exnovation dynamics on different graph structures, revealing how connectivity influences innovation speed, diversity, and system stability in complex networks.

Contribution

It introduces a phase diagram for innovation-exnovation dynamics on random graphs, linking structural connectivity to innovation outcomes and system resilience.

Findings

Higher connectivity accelerates innovation.

Increased connectivity raises collapse risk.

Structural connectivity influences diversity and extinction.

Abstract

Innovation and its complement exnovation describe the progression of realized possibilities from the past to the future, and the process depends on the structure of the underlying graph. For example, the phylogenetic tree represents the unique path of mutations to a single species. To a technology, paths are manifold, like a "truss." We solve for the phase diagram of a model, where a population innovates while outrunning exnovation. The dynamics progress on random graphs that capture the degree of historical contingency. Higher connectivity speeds innovation but also increases the risk of system collapse. We show how dynamics and structural connectivity conspire to unleash innovative diversity or to drive it extinct.