Frequency-dependent selection drives perpetual cycling — "running to stay in place"
ẋ = x(1−x)[β·y − γ·(1−y)] | ẏ = y(1−y)[α·x − δ·(1−x)] | cycling in allele-frequency space
Red Queen hypothesis (Van Valen 1973): Species must keep evolving just to maintain fitness relative to coevolving partners — like the Red Queen in Alice in Wonderland who runs to stay in place.
Model: Host resistance allele frequency x, parasite virulence allele frequency y. Fitness depends on the opponent's frequency (negative frequency-dependent selection). This creates Lotka-Volterra-like cycling in allele space.
Implications: Explains maintenance of sexual reproduction (sex generates novel allele combinations, staying ahead of parasites). Hamilton & Zuk (1982): sexual selection signals parasite resistance. Also explains geographic mosaics of coevolution, local adaptation, and rapid evolution in host-parasite systems.