Rugged Fitness Landscape Evolution

NK model — epistasis, local optima, and evolutionary search

Landscape

Generation: 0
Best fitness:
Mean fitness:
Unique peaks:

NK Fitness Landscapes

Kauffman's NK model (1993) generates tunable rugged fitness landscapes. N is the genome length (binary string of N bits); K is the number of other loci each locus interacts with (epistasis).

f(σ) = (1/N) Σᵢ fᵢ(σᵢ, σ_{i₁},...,σ_{iK})
Each fᵢ drawn uniformly from [0,1]

K=0: smooth landscape, single global peak (multiplicative, no epistasis). K=N-1: maximally rugged — uncorrelated landscape, exponentially many local optima.

The landscape (top) is visualized in 2D via random projection of the high-dimensional binary genotype space. Each color dot is one individual; brighter = higher fitness.

The trajectory panel shows best (green) and mean (white) fitness over generations. Increasing K makes evolution harder — populations get trapped on local optima, and the number of optima grows exponentially with K.