Known Evolutionary Forces Reproduce Theoretical Order-Increase in NK Fitness Landscapes: A Sufficiency Test of Hatcher's Empirical Premise

**Ozone Archive Research Program**

**Paper ID:** O0-PAPER-004

**Underlying study:** O0-CRP-023

**Date:** 2026-07-29

**Version:** 1.0.0

**Record class:** SCIENTIFIC PAPER · single-study IMRAD wrapper

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Abstract

Hatcher (1994) advances an abductive argument that observed evolutionary order-increase requires an unobservable ordering force beyond the mutation-plus-selection consensus. This paper tests one empirical premise of that argument in an NK-model fitness landscape: given known mutation and tournament selection, does a population reliably produce theoretically predicted order-increase, or does it systematically fall short? We ran 480 genetic algorithm evolutions across 4 K-values (K ∈ {2, 5, 10, 15}), 4 configurations (tournament, high-mutation, random-search, no-selection), and 30 seeds each. Result: known evolutionary forces reliably produce order-increase matching theoretical prediction within a mean absolute delta of 0.089. Selection is required (random-search produces zero gain). Hatcher's empirical sufficiency premise is not supported *in silico* at N=20, G=500.

**Verdict:** SUFFICIENCY SUPPORTED (the sufficiency of known forces, not Hatcher's metaphysical claim).

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1. Introduction

Hatcher's 1994 paper argues that observable evolutionary forces are insufficient to produce observed order-increase in living systems, therefore an unobservable ordering principle should be abductively inferred. The argument rests on a specific empirical premise: that mutation + selection cannot, in principle, produce the observed magnitude of adaptive gain in bounded time.

This paper tests the empirical premise *in silico* using the NK model — a well-established rugged fitness landscape (Kauffman, 1993). We do not test the abductive move itself (which is a philosophical claim outside the archive's scope) but only the specific empirical premise about the sufficiency of known forces.

2. Methods

**Model.** NK-model fitness landscape with genome length N=20 and ruggedness parameter K ∈ {2, 5, 10, 15}.

**Configurations.**

• **Tournament** — standard tournament selection (size 3), single-point mutation rate 1/N.
• **High-mutation** — mutation rate 5/N (increased mutation, same selection).
• **Random-search** — random sampling of same number of genomes as tournament tested.
• **No-selection** — mutation only, no selection pressure.

**Parameters.** Population size P=100, generations G=500, 30 seeds per (config, K) cell = 480 runs.

**Analysis.**

• Preregistered sufficiency criteria: (1) tournament produces gain > 0.05 at all K, (2) selection required (tournament > random-search + no-selection), (3) observed matches Kauffman-style theoretical adaptive-walk prediction within 20%.
• Effect sizes with 95% bootstrap CIs.

3. Results

**Sufficiency criteria all pass:**

1. Tournament produces fitness gain of +0.06 to +0.13 across K values (all p < 1e-10 vs baseline).

2. Random-search produces mean gain ≈ 0.00; no-selection ≈ 0.005; tournament strictly larger in 4 of 4 K values.

3. Mean absolute delta between observed and theoretical: 0.089 (< 20% preregistered threshold).

**Selection is required.** No-selection and random-search do not produce order-increase.

**High-mutation regresses at high K.** As K→15 (rugged landscape), high-mutation begins to lose ground — consistent with the mutation-drift tradeoff in NK theory.

4. Discussion

The specific empirical premise in Hatcher's argument — that observable evolutionary forces are insufficient to produce observed order-increase — is not supported within our computational sandbox. Known forces (mutation + tournament selection) reliably produce order-increase matching Kauffman's theoretical predictions.

**What this establishes:** In an NK-model sandbox at N=20, G=500, mutation + selection are sufficient to produce the theoretically predicted rate of order-increase.

**What this does not establish:**

• That Hatcher's abductive methodology is wrong. The abductive move (inferring unobservable causes from observed effects) is not tested here.
• That biological evolution follows the NK model exactly.
• That real-world evolutionary rates are consistent with known forces at biological scale. See O0-CRP-028 for a scale-up test.

5. Limitations

• N=20 is far below biological genome scale.
• The NK model is a mathematical abstraction; real fitness landscapes may differ.
• Only tournament selection tested; alternative selection schemes not compared.

6. Related studies

• **O0-CRP-028** — scales to N=50, G=2000. Sufficiency criteria still pass.
• **O0-SCOPE-002** — claim registry entries C005, C006.

7. Data and code availability

• Full record: `research/studies/O0-CRP-023/scientific_record.md`
• Source: `research/studies/O0-CRP-023/src/`

8. References

• Hatcher, W. S. (1994). *Logic and Logos: Essays on Science, Religion and Philosophy.* Oxford: George Ronald.
• Kauffman, S. A. (1993). *The Origins of Order.* Oxford University Press.
• Mitchell, M. (1996). *An Introduction to Genetic Algorithms.* MIT Press.