[Paper Review] From Entropy to Information: Biased Typewriters and the Origin of Life

Christoph Adami, Thomas LaBar|arXiv (Cornell University)|Jun 23, 2015

Origins and Evolution of Life4 citations

TL;DR

This paper investigates the spontaneous emergence of self-replicating information systems using a computational model of digital life (Avida), showing that biased instruction distributions—shaped by prior self-replicators—dramatically increase the likelihood of discovering functional replicators. The key finding is that information-rich, non-uniform sequence distributions significantly enhance the probability of evolving self-replication, suggesting that early life may have emerged not from random chance, but from entropy-reducing, information-accumulating processes in prebiotic chemistry.

ABSTRACT

The origin of life can be understood mathematically to be the origin of information that can replicate. The likelihood that entropy spontaneously becomes information can be calculated from first principles, and depends exponentially on the amount of information that is necessary for replication. We do not know what the minimum amount of information for self-replication is because it must depend on the local chemistry, but we can study how this likelihood behaves in different known chemistries, and we can study ways in which this likelihood can be enhanced. Here we present evidence from numerical simulations (using the digital life chemistry "Avida") that using a biased probability distribution for the creation of monomers (the "biased typewriter") can exponentially increase the likelihood of spontaneous emergence of information from entropy. We show that this likelihood may depend on the length of the sequence that the information is embedded in, but in a non-trivial manner: there may be an optimum sequence length that maximizes the likelihood. We conclude that the likelihood of spontaneous emergence of self-replication is much more malleable than previously thought, and that the biased probability distributions of monomers that are the norm in biochemistry may significantly enhance these likelihoods

Motivation & Objective

• To investigate whether self-replicating systems can emerge spontaneously from random sequences in a computational model of digital evolution.
• To determine how instruction distribution bias—shaped by prior self-replicators—affects the likelihood of discovering new self-replicators.
• To test whether information content, rather than sequence length, is the critical factor in the spontaneous emergence of self-replication.
• To explore the role of entropy reduction and non-uniform probability distributions in the origin of life-like information systems.

Proposed method

• Generated random genomes of lengths L = 8, 15, 30, and 100 using uniform (unbiased) instruction distributions (1/26 per instruction) in Avida.
• Defined self-replicators as organisms that successfully divide and produce viable, self-replicating offspring (colony-forming), using Avida’s default lifespan and replication rules.
• Introduced a biased instruction distribution using the formula $ p(i,b) = (1-b)(1/26) + b p_\star(i) $, where $ p_\star(i) $ is the frequency of instruction i in previously discovered self-replicators.
• Performed iterative biasing: used self-replicators from one search to define the next bias (1st, 2nd, 3rd bias), progressively shaping the instruction distribution toward functional sequences.
• Conducted large-scale searches: $10^9$ sequences for L=8,15,30 and $3\times10^8$ for L=100 under unbiased conditions; $10^8$ sequences per bias level for L=15 and L=8,30 under biased conditions.
• Measured the frequency of self-replicators across different bias levels to assess how instruction distribution entropy influences replicator discovery probability.

Experimental results

Research questions

• RQ1 What is the likelihood of spontaneous emergence of self-replicating sequences in a random, unbiased search across different genome lengths?
• RQ2 How does biasing the instruction distribution toward sequences found in previously discovered self-replicators affect the probability of discovering new self-replicators?
• RQ3 To what extent does information content—measured via entropy reduction—determine the success of self-replicator emergence, rather than sequence length?
• RQ4 Can iterative biasing of instruction distributions lead to a cumulative increase in the discovery rate of self-replicators, simulating a prebiotic information-accumulating process?

Key findings

• The probability of discovering self-replicators increased significantly with instruction distribution bias, especially at higher bias levels (b=1), indicating that non-uniform distributions enhance replicator emergence.
• For L=15, the number of self-replicators discovered under full bias (b=1) was substantially higher than under uniform distribution, demonstrating that functional sequences are not randomly distributed in sequence space.
• Iterative biasing (1st, 2nd, 3rd bias) led to a progressive increase in the frequency of self-replicators, suggesting a self-reinforcing process of information accumulation.
• The study found that information content, not sequence length, is the key determinant of self-replicator discovery, as longer sequences under uniform distribution did not yield higher success rates.
• The results support the hypothesis that life-like information systems could emerge not by pure chance, but through entropy-reducing, information-accumulating processes in prebiotic systems.
• The model demonstrates that biased typewriters—where certain instructions are favored—can simulate the emergence of functional complexity, offering a plausible mechanism for the origin of life.