Red Queen Coevolution

Host-parasite arms race: allele frequencies cycle endlessly as each species evolves to counter the other. The Red Queen hypothesis (Van Valen 1973) — constant running just to stay in place — explains why sex is maintained.

Model

Selection s 0.15

Mutation μ 0.005

Host initial p₀ 0.30

Parasite init q₀ 0.70

Host p (A₁)

—

Parasite q (B₁)

—

Gen

Cycle period

—

Match-allele: parasite infects when alleles match. Δp ∝ s·p(1-p)·(2q-1)
Gene-for-gene: host resists unless parasite has virulence allele. Δq ∝ s·q(1-q)·p
Both models produce persistent cycling — Red Queen dynamics. Period ~ 2π/s.