Drake scripts with evolvability simulation

This release adds simulation script for evolvability.

1.0

Below is a clean Markdown file suitable for inclusion in the repository and for direct upload to Zenodo as RELEASE_NOTES.md.

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Release Notes

Simulation Results for

Why Evolution Operates Near One Mutation per Genome per Generation

Version: v1.0
Author: Ishanu Chattopadhyay

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Overview

This release archives the simulation code and generated figures supporting the manuscript:

Why Evolution Operates Near One Mutation per Genome per Generation.

The simulations numerically validate the central theoretical result of the manuscript: that the expected rate of information-theoretic structure discovery under blind mutation is maximized when the expected number of mutations per genome per generation satisfies

[
U = n\mu \approx 1.
]

This corresponds to the inverse-length scaling

[
\mu^* \approx \frac{1}{n},
]

consistent with Drake’s empirical rule.

These results arise from purely combinatorial and information-theoretic considerations and do not rely on biological fitness landscapes or biochemical constraints.

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Contents

The repository contains:

• Numerical evaluation of the exact finite-(n) discovery expression derived in the manuscript.

• Evaluation of its asymptotic approximation.

• Monte Carlo validation of rarity scaling for exceptional mutants.

• Parameter sweeps over:

  • Genome length (n)
  • Alphabet size (q)
  • Novelty threshold (\Delta)
  • Mutation rate (\mu)

The simulations illustrate that the discovery rate function exhibits a single interior maximum at (n\mu \approx 1), and that this optimum remains stable across a broad range of parameters.

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Simulation Model

All simulations are based on:

• Sequence space ([q]^n)
• Mutation defined by Hamming distance
• Mutation count (M \sim \text{Binomial}(n, \mu))
• Novelty defined as positive randomness deficiency relative to the mutation-induced Hamming sphere

The expected discovery rate is computed as

[
\Phi(\mu) \propto (1-\mu)^n \sum_{m=1}^{n} \left(\frac{\mu}{q-1}\right)^m,
]

with asymptotic approximation

[
\Phi(\mu) \propto \mu e^{-n\mu}.
]

Both analytic and Monte Carlo experiments confirm maximization at (n\mu = 1).

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Reproducibility

All figures in the manuscript that involve simulations are reproducible using the scripts provided in the code/ directory.

Each script specifies:

• Random seed
• Genome length (n)
• Alphabet size (q)
• Novelty threshold (\Delta)
• Number of Monte Carlo replicates

Unless otherwise stated, genomes are generated as incompressible random sequences.

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Scope and Interpretation

These simulations are not empirical biological analyses. They are numerical demonstrations of the information-theoretic mechanism derived in the manuscript.

The purpose of this release is to:

1. Provide computational confirmation of the analytic scaling.
2. Ensure full reproducibility of simulation-based figures.
3. Document the parameter regimes under which the optimal mutation scaling emerges.

The inverse-length scaling of mutation rate arises here as a structural property of local stochastic exploration in high-dimensional discrete spaces.

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License

Released under the GNU General Public License v3.0 (GPL-3.0).

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