Component systems: do null models explain everything?

TL;DR

This paper introduces a unifying mathematical framework for component systems across various domains, explaining common patterns as sampling constraints and proposing methods to identify system-specific mechanisms beyond these null models.

Contribution

The paper develops a general framework to compare modular systems, revealing null trends and system-specific features, and applies statistical and machine learning tools to distinguish generative processes.

Findings

Null models explain many observed regularities in component systems.

The framework highlights the distinction between universal patterns and system-specific features.

Methods are proposed to isolate informative features for understanding underlying mechanisms.

Abstract

Component systems - ensembles of realizations built from a shared repertoire of modular parts - are ubiquitous in biological, ecological, technological, and socio-cultural domains. From genomes to texts, cities, and software, these systems exhibit statistical regularities that often meet the "bona fide" requirements of laws in the physical sciences. Here, we argue that the generality and simplicity of those laws are often due to basic combinatorial or sampling constraints, raising the question of whether such patterns are actually revealing system-specific mechanisms and how we might move beyond them. To this end, we first present a unifying mathematical framework, which allows us to compare modular systems in different fields and highlights the common "null" trends as well as the system-specific uniqueness, which, arguably, are signatures of the underlying generative dynamics. Next, we can exploit the framework with statistical mechanics and modern machine-learning tools for a twofold objective. (i) Explaining why the general regularities emerge, highlighting the constraints between them and the general principles at their origins, and (ii) "subtracting" them from data, which will isolate the informative features for inferring hidden system-specific generative processes, mechanistic and causal aspects.