Fitness Landscape: Adaptive Walk

Population Genetics

Population size N 40

Mutation step size σ 0.06

Selection strength β 6.0

Live State

Generation

Mean fitness

0.00

Best found

0.00

% of global peak

Effective N (drift)

—

On global peak?

How it works

Each individual's genotype is a point (x, y) on a 2D trait surface; the terrain height W(x,y) is its fitness — Sewall Wright's "adaptive landscape" metaphor (1932). Every generation runs a Wright–Fisher-style life cycle:

1. Mutation:  x' = x + N(0, σ²),  y' = y + N(0, σ²)
2. Fitness:   w_i = W(x_i, y_i)          (terrain height, ≥ 0)
3. Selection: P(parent = i) = exp(β·w_i) / Σ_j exp(β·w_j)
4. Sample N offspring genotypes (with replacement) from step 3

β is selection strength: at β = 0 every genotype is equally likely to reproduce — pure genetic drift, a random walk that can wander anywhere, including downhill. As β grows, reproduction is biased toward high-fitness genotypes — the population climbs the nearest peak and, once there, largely stays.

Population size N sets the strength of drift: a small N means each generation is a small, noisy sample (large sampling variance), so chance alone can carry the whole population off a peak and across a fitness valley to find a taller one nearby — exactly the "shifting balance" escape Wright proposed as one way populations avoid getting stuck on a merely local optimum. A large N averages out that noise and selection dominates, so the population reliably (but not always optimally) climbs whichever peak it started nearest to.

Population size N — number of individuals sampled each generation; smaller = stronger drift.
Mutation step σ — standard deviation of the per-generation genotype change; larger = bigger, riskier jumps.
Selection strength β — how sharply fitness biases reproduction; β = 0 is neutral drift, high β is near-pure hill-climbing.
New landscape — reseeds a fresh multi-peak fitness surface so a strategy that worked on one landscape can be re-tested on another.

Population (genotype, height = fitness) Global fitness peak

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