Adaptive Landscape: Natural Selection Walk

Landscape

Shape

Population genetics

Population size 120

Selection strength s 3.0

Mutation σ 0.35

Generations / s 3

Population state

Generation

Mean fitness

0.00

Mean trait x̄

0.00

Trait variance

0.00

How it works

Every organism carries one quantitative trait x (think beak depth, camouflage darkness, body size). The environment defines a fitness landscape W(x) — Sewall Wright's 1932 "adaptive landscape" — built from one or more Gaussian peaks:

W(x) = Σ_k A_k · exp( -(x-μ_k)² / (2σ_k²) )

Each generation, parents are drawn with fitness-proportionate selection sharpened by a strength exponent s (higher s = harsher culling of the unfit):

p(pick i) ∝ W(x_i) ^ s

Offspring inherit the parent's trait plus mutation, a Gaussian nudge with standard deviation σ_mut:

x_child = x_parent + N(0, σ_mut²)

Selection strength — at s = 0 reproduction is random (pure drift); higher s makes the population climb faster toward a peak, at the cost of losing variation.
Mutation σ — the raw material of variation. Too low and a small population can get stuck; too high and it never settles on a peak.
Population size — small populations drift: chance alone can carry the mean away from the optimum even under selection, exactly as in real conservation genetics.
Shift environment — moves the peak(s), forcing a previously well-adapted population to climb again (directional selection), the way a changing climate or a new predator resets what "fit" means.
Two peaks — shows a population can become trapped on a local optimum, unable to cross the fitness valley to a taller peak without a lucky run of mutation and drift.

The gold trail traces the population's mean trait and its fitness across generations, receding into the landscape — a literal "walk" up the adaptive landscape, the mechanism behind everything from Darwin's finches to antibiotic resistance.

Individuals (current generation) Population mean, over time

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