# E9 — landscape robustness: when recombination helps, and the outbreeding-depression risk

**Claim tested.** E8 showed sexual recombination assembling super-parent offspring — but on an
*additive* landscape, where recombination trivially helps. The honest, credibility-critical question
(the classic "why sex?" problem): does the benefit survive **epistasis**, or does merging entangled
models break them?

**Setup.** Parents are **local optima** ("trained models") of a **Kauffman NK landscape** (`L=12`),
whose ruggedness `K` (epistatic interactions per locus) is swept together with the **recombination
rate**. `K=0` is additive/smooth; larger `K` is rugged (co-adapted allele blocks, many local optima).
Fitness ∈ [0,1]. 24 replicate landscapes; 200 offspring per point.

### Symbols
- **NK landscape** — tunable-ruggedness fitness landscape; `K` = epistasis (0 = additive, high = rugged).
- **recombination rate** — per-gap crossover probability (0 = clonal / copy a parent; 0.5 = free recombination, loci independent).
- **outbreeding depression** — offspring *less* fit than parents because recombination broke co-adapted allele blocks.

### The two panels
1. **The risk.** Mean offspring fitness *minus* best parent, vs recombination rate, one curve per
   ruggedness `K`. On the additive landscape (`K=0`) it's flat at 0; as `K` grows the curves plunge
   **negative**, and deeper the higher the recombination rate — **outbreeding depression, worse the
   more entangled the skills and the more you mix** (`K=8`, free recombination: ≈ −0.23).
2. **With selection, an optimal rate re-emerges.** Best-of-brood fitness (offspring selection) vs
   rate per `K`, with parents dotted. On rugged landscapes a **nonzero intermediate recombination
   rate** is best — enough mixing to find new combinations, not so much that it shatters good blocks.

### Takeaway
Recombination is not a free lunch. **Merge freely when skills are complementary/additive; merge
sparingly — and always *select* offspring — when they are entangled.** This is the celebrated
population-genetics result (recombination load / outbreeding depression) reproduced for AI model
merging, and it turns the sexual metaphor from a lucky demo into a law with a design rule. The rescue
— directed sex with offspring selection — is E10. **Falsifier (not triggered):** if recombination
rate had no effect, or free recombination never underperformed the parents on rugged landscapes, the
epistasis caveat would be moot.