Crossing the Functional Desert: Cascade-Driven Assembly and Feasibility Transitions in Early Life

TL;DR

This paper demonstrates that nonlinear cascade dynamics in networks can enable the emergence of functional organization in early life, crossing the 'functional desert' barrier by transitioning near a critical connectivity threshold.

Contribution

It introduces a minimal, substrate-agnostic mechanism based on cascade dynamics that facilitates the emergence of functional responses in networked systems, relevant to origins of life.

Findings

Near critical connectivity, system-spanning cascades emerge.

Cascades enable structured, discriminative functional responses.

Mechanism applies broadly to networked systems with nonlinear thresholds.

Abstract

The origin of life poses a problem of combinatorial feasibility: How can temporally supported functional organization arise in exponentially branching assembly spaces when unguided exploration behaves as a memoryless random walk? We show that nonlinear threshold-cascade dynamics in connected interaction networks provide a minimal, substrate-agnostic mechanism that can soften this obstruction. Below a critical connectivity threshold, cascades die out locally and structured input-output response mappings remain sparse and transient-a "functional desert" in which accumulation is dynamically unsupported. Near the critical percolation threshold, system-spanning cascades emerge, enabling discriminative functional responses. We illustrate this transition using a minimal toy model and generalize the argument to arbitrary networked systems. Also near criticality, cascades introduce finite-timescale structural and functional coherence, directional bias, and weak dynamical path-dependence into otherwise memoryless exploration, allowing biased accumulation. This connectivity-driven transition-functional percolation-requires only generic ingredients: interacting units, nonlinear thresholds, influence transmission, and non-zero coherence times. The mechanism does not explain specific biochemical pathways, but it identifies a necessary dynamical regime in which structured functional organization can emerge and be temporarily supported, providing a physical foundation for how combinatorial feasibility barriers can be crossed through network dynamics alone.