MachineSex/results/figS13_mating_breadth/README.md

E14 — Mating systems: monogamy vs promiscuity (mate-pool breadth)

Claim tested. The society experiments (E8–E11) assumed panmixia — every offspring recombined from parents sampled across the whole population. Biology's mating systems instead span a continuum from monogamy (mating within a narrow, local circle) to promiscuity (mates drawn freely from everyone), and population genetics says the choice matters: wide gene flow spreads a good allele fast but homogenises the population, while restricted gene flow (population structure / isolation by distance) keeps demes distinct so several fitness peaks can be explored in parallel (Wright's shifting balance). E14 asks how the best mating system depends on how entangled the skills are.

Setup. A finite population of N=48 genotypes (L=12 biallelic loci) evolves on a Kauffman NK landscape (ruggedness K). Agents sit on a ring; an offspring's second parent is drawn from a window of half-width ≈ breadth·N/2 around the focal parent, so mate-pool breadth b is a single scalar: b→0 = monogamous / structured (local mating), b=1 = promiscuous / panmictic. Selection is local — an offspring replaces the incumbent at its own ring position only if strictly fitter — so restricted mating can actually sustain distinct demes instead of being washed out. Sweep b ∈ {0.03, 0.08, 0.17, 0.35, 0.6, 1.0} × K ∈ {0, 3, 6, 10}, 60 generations, 20 replicates, μ=0.003, crossover rate 0.5. Bitwise-reproducible from the master seed.

Results — the best breadth shrinks as the landscape gets more rugged

best_fitness / global_opt (the champion), mean over 20 reps; bold = best breadth at that K:

K \ breadth	0.03	0.08	0.17	0.35	0.60	1.00
0 (additive)	1.000	1.000	1.000	1.000	1.000	1.000
3 (mild)	0.995	0.993	0.997	0.993	0.9997	0.993
6 (rugged)	0.986	0.972	0.983	0.989	0.984	0.982
10 (very rugged)	0.961	0.968	0.967	0.980	0.964	0.965

• K=0 saturates: an additive (single-peak) landscape is solved by everyone regardless of mating, so the champion metric can't discriminate (it only shows up in diversity, below).
• K=3: the optimum is at wide breadth (b=0.6) — near-promiscuous mating maximises the champion when the landscape is mild.
• K=6, K=10: the optimum moves to an intermediate breadth (b=0.35), and full promiscuity falls below it. Wide mating prematurely converges on rugged landscapes; pure monogamy over-fragments (too little gene flow to combine complementary basins). The best of both is intermediate structure — the mating-system image of E9's "optimal recombination rate shrinks with ruggedness."

Results — the diversity/mean tension that drives it

Two monotone effects, opposite in sign, at every K (mean over reps at K=10):

breadth	0.03	0.08	0.17	0.35	0.60	1.00
mean fitness / opt	0.890	0.914	0.926	0.941	0.941	0.943
diversity (pairwise Hamming)	0.441	0.413	0.384	0.346	0.265	0.282
distinct local optima occupied	11.0	8.6	7.4	7.3	7.2	6.9

• Mean fitness rises monotonically with breadth: panmixia lifts the typical individual toward a good consensus fastest.
• Diversity and occupied peaks fall monotonically with breadth: promiscuity homogenises; monogamy preserves the standing variation (and the parallel exploration of distinct basins) — most strongly on rugged landscapes.

So promiscuity maximises the typical model and destroys diversity; on a rugged landscape the best model needs that preserved diversity, so an intermediate breadth wins the champion even though the wide breadth still wins the mean. (Panel A = champion, Panel B = mean, Panel C = diversity.)

Positioning

This is the population-structure axis the model-merging literature does not have. Merging/soup work implicitly assumes panmixia (fuse everything, or route among a flat pool); E14 says the breadth of who merges with whom is itself a design knob, and its optimum is set by the entanglement of the skills: merge widely when skills are additive; keep sub-populations (structured / island merging) when skills are rugged and diversity must be preserved to explore and later combine basins. It complements E9 (recombination rate) and E11 (diversity is load-bearing) on a new, orthogonal axis. Falsifier (not triggered): the best breadth independent of K (no crossover), or promiscuity best at every ruggedness — instead the optimal breadth shifts from 0.6 (K=3) to 0.35 (K≥6), and diversity is monotonically lost to breadth throughout.