NK Fitness Landscape — Evolutionary Dynamics

N genes, K epistatic neighbors — ruggedness scales with K; local optima ~ 2^N/(N+1)

Genome length N 12

Epistasis K 3

Mutation rate μ 0.02

Population size 50

Selection strength 5

Walk type

NK model (Kauffman 1987): Each of N binary genes has fitness contribution dependent on its value and K randomly chosen epistatic partners. Total fitness = average of N contributions. K=0: smooth, single-peak (Mt. Fuji); K=N−1: fully random (House of Cards). Intermediate K gives tunably rugged landscapes with many local optima. Number of local optima ~ 2^N/(N+1). Colors: fitness landscape projection via PCA/MDS of Hamming space. Trajectories show adaptive walks.