Giorgio Gilestro
62c68d6c8c
Enter the Lamarckian society with a robust theoretical frame. The single-
locus, fixed-p* model can only express recovery toward a ceiling; the
society's load-bearing claim is vertical -- capability that EXCEEDS any
component. Generalize knowledge to a distribution over genotypes (L
biallelic loci, K=2^L, additive fitness = # correct loci), reusing all the
K-mode machinery. The one new operator is recombination: free recombination
sends p -> product of per-locus marginals (linkage equilibrium).
E8 (star, kind: society) -- the vertical claim / Fisher-Muller: decorrelated
PARENTS (specialists, expert on their loci, agnostic elsewhere) are
recombined; sexual merge assembles a genotype fitter than any parent,
climbing to the optimum (12/12, a genotype no parent had) as parent count
grows and rho->0, while the best single parent (~8.7) and the mean-mixture
"model soup" (~11.6) plateau below. Reuses make_retention_matrix (locus
mastery replaces tail-item retention).
E7 (kind: genotype_lineage) -- the advantage of sex: a single population
adapts toward the optimum; the sexual lineage adapts faster than asexual
(clonal interference) by keeping loci in linkage equilibrium (LD->0 vs LD
spike). Honest scope: a speed advantage, not a permanent Muller's-ratchet
gap (subtle to force); E8 carries the headline.
Metaphor shift (per GG): the society is sexual reproduction with UNBOUNDED
parents, not teacher->pupil. Teacher->pupil caps at the ceiling; n-parent
recombination is combinatorial and generative, and unlike biology there is
no two-parent limit. Collapse = asexual degradation; the cure = sex. This
unifies E4 (merge != average) + E6 (irreversibility) under evolution-of-sex
theory and reaches ground Riis's single-locus n-grams cannot.
New: knowledge/{genotype,genotype_lineage,society}.py, configs/layer1/{E7,
E8}.yaml, figures/plot_{E7,E8}.py, READMEs, tests/test_genotype.py (+7).
experiment.py dispatch (kind in {genotype_lineage, society}); make layer1
wired. 112 tests green.
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
31 lines
2.3 KiB
Markdown
31 lines
2.3 KiB
Markdown
# E7 — the advantage of sex: recombination adapts faster than clonal reproduction
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**Claim tested.** The dynamic mechanism behind E8: *why* can a recombining society reach capability a
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lone lineage cannot? Because recombination reassorts beneficial variants that arise in different
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sub-lineages, while an asexual (clonal) lineage suffers **clonal interference** — the variants compete
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and cannot combine.
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**Setup.** A single population (distribution over `2^L` genotypes, `L=12`) adapts from **all-wrong**
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toward the multi-locus optimum under the composed step: selection (fitness-proportional) + drift
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(resample `n=150`) + mutation (per-locus flips, `μ=0.02`) + recombination. Two arms — **asexual**
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(`recomb_rate=0`) vs **sexual** (`recomb_rate=1`). 20 replicates.
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### Symbols
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- **asexual/clonal** = offspring are whole-genotype copies (Layer-1's regime) · **sexual** = loci reassorted across the population each generation.
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- **fitness** = number of correct loci (optimum = `L`) · **linkage disequilibrium |D|** = how far the loci are from statistical independence (correct alleles scattered across different genotypes).
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### The two panels
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1. **Advantage of sex.** Mean fitness over generations: the **sexual lineage (red) climbs faster**
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than the asexual one (grey) through the adaptation phase (gen ~10–35). *Honest scope:* both plateau
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near the optimum by gen ~40 in this tractable regime — this is a **speed** advantage, not a
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permanent gap (the single-population Muller's ratchet is subtle to force; E8 carries the headline).
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2. **Mechanism.** Linkage disequilibrium over generations: the asexual lineage spikes to `|D|≈0.04`
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during adaptation (beneficial alleles held apart, scattered across genotypes), while the sexual
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lineage stays at `|D|≈0` — it *assembles* them. The LD gap is exactly why sexual adapts faster.
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### Takeaway
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Recombination's advantage is real and classical: it combines good ideas that arose independently,
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which clonal reproduction cannot. This is the population-level reason a single evolving model lineage
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degrades or stalls where a recombining **society** climbs — and it grounds the E8 vertical result in
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the evolution-of-sex theory. **Falsifier (not triggered):** if the sexual lineage adapted no faster
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than the asexual one (and kept the same LD), recombination would do no work.
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