[Paper Review] Assembly Theory Explains and Quantifies the Emergence of Selection and Evolution

A. S. Sharma, Dániel Czégel+4 more|arXiv (Cornell University)|Jun 5, 2022

Origins and Evolution of LifePhysics and Astronomy17 citations

TL;DR

This paper introduces Assembly Theory (AT) as a framework to quantify the emergence of selection and evolution in physical systems by measuring the minimal steps (Assembly Index, a) needed to construct an object from basic components. By combining this with copy number to define 'Assembly,' the theory quantifies selection pressure and identifies a formal transition from undirected exploration to directed evolutionary processes, offering a measurable criterion for life and explaining complexity emergence in a law-governed universe.

ABSTRACT

Since the time of Darwin, scientists have struggled to reconcile the evolution of biological forms in a universe determined by fixed laws. These laws underpin the origin of life, evolution, human culture and technology, as set by the boundary conditions of the universe, however these laws cannot predict the emergence of these things. By contrast evolutionary theory works in the opposite direction, indicating how selection can explain why some things exist and not others. To understand how open-ended forms can emerge in a forward-process from physics that does not include their design, a new approach to understand the non-biological to biological transition is necessary. Herein, we present a new theory, Assembly Theory (AT), which explains and quantifies the emergence of selection and evolution. In AT, the complexity of an individual observable object is measured by its Assembly Index (a), defined as the minimal number of steps needed to construct the object from basic building blocks. Combining a with the copy number defines a new quantity called Assembly which quantifies the amount of selection required to produce a given ensemble of objects. We investigate the internal structure and properties of assembly space and quantify the dynamics of undirected exploratory processes as compared to the directed processes that emerge from selection. The implementation of assembly theory allows the emergence of selection in physical systems to be quantified at any scale as the transition from undirected-discovery dynamics to a selected process within the assembly space. This yields a mechanism for the onset of selection and evolution and a formal approach to defining life. Because the assembly of an object is easily calculable and measurable it is possible to quantify a lower limit on the amount of selection and memory required to produce complexity uniquely linked to biology in the universe.

Motivation & Objective

• To address the longstanding challenge of how complex, selected systems like life can emerge from fixed physical laws without pre-existing design.
• To develop a formal framework that quantifies the emergence of selection and evolutionary dynamics in physical systems.
• To provide a measurable, physics-based criterion for distinguishing non-living from living or evolved systems.
• To formalize the transition from undirected, exploratory processes to directed, selection-driven processes in assembly space.
• To establish a lower bound on selection and memory required to produce complex, biologically relevant structures.

Proposed method

• Defining the Assembly Index (a) as the minimal number of steps required to construct an object from basic building blocks.
• Introducing the concept of 'Assembly' as the product of the Assembly Index (a) and the copy number of the object.
• Mapping physical systems into 'assembly space' to analyze the dynamics of undirected discovery versus directed selection.
• Using computational modeling to compare undirected exploration processes with those driven by selection within assembly space.
• Applying the theory to trace the emergence of complexity and selection in systems ranging from prebiotic chemistry to technological artifacts.
• Deriving a formal criterion for the onset of selection based on the transition from random exploration to non-random, cumulative selection in assembly space.

Experimental results

Research questions

• RQ1 How can selection and evolutionary processes be formally quantified in physical systems governed by fixed laws?
• RQ2 What measurable property distinguishes undirected, exploratory processes from directed, selection-driven processes in assembly space?
• RQ3 Can a universal metric be defined to quantify the amount of selection and memory required to produce complex, biologically relevant structures?
• RQ4 At what point in assembly space does the transition from random discovery to cumulative selection occur?
• RQ5 How does the combination of Assembly Index and copy number provide a formal definition of evolutionary emergence?

Key findings

• The Assembly Index (a) provides a measurable, physics-based metric for the complexity of any observable object, defined as the minimal number of steps to construct it from basic components.
• The product of the Assembly Index and copy number—defined as 'Assembly'—quantifies the cumulative selection pressure required to produce a given object or ensemble.
• The theory identifies a formal transition point in assembly space where undirected exploration gives way to directed, selection-driven processes, marking the onset of evolution.
• The framework allows for the quantification of a lower bound on selection and memory required to produce complex, biologically relevant structures, independent of biological context.
• Assembly Theory provides a formal, measurable criterion for distinguishing non-living from living or evolved systems based on their selection history.
• The model successfully explains the emergence of complexity in systems ranging from prebiotic chemistry to human-made technology, all within a unified physical framework.