Why does the population not become exactly the background colour?

Mutation keeps injecting new colours every generation, and predation is probabilistic, so a few mismatched beetles always survive by chance. The mean settles close to the background and fluctuates around it; the standard deviation stays near a balance between mutation adding spread and selection removing it.

What happens when the mutation σ is set to 0?

No new variation enters. Selection removes the most contrasting colours each generation while offspring are exact copies of their parents, so the colour range shrinks until every beetle is identical and the histogram collapses to one bar. The population is then "stuck" and cannot re-adapt if the background changes.

Do the beetles choose or change their colour to match the background?

No. An individual never changes colour during its life. Only the population changes, because beetles that happen to match survive and pass their colour to more offspring. That difference between individual change and population change is the heart of natural selection.

Why are two runs with identical settings different?

Which beetles get eaten and which mutations appear are random draws, as in a real population. Small populations show larger run-to-run differences; raise the population size to see the mean colour curve become smoother.

Natural Selection: Beetles, Predators and Camouflage

Beetles with a colour trait on an adjustable background: predators eat high-contrast ones, survivors breed with mutation σ.

Environment

Background colour (0 light … 1 dark)0.3

Predation strength0.7

Population

Mutation σ (colour per offspring)0.03

Population size (carrying capacity)120

Generations per second2

Each generation has two phases: predators remove beetles with probability growing with the contrast between beetle and background, then survivors breed back to the carrying capacity; each offspring inherits its parent’s colour ± a random mutation. Changing population size restarts the run; the other sliders act live.

Tastenkürzel

Space / Enter — play / pause
R — reset population

Gemessene Größen

Generation0

Mean colour0.500

Background colour0.30

|mean − background|0.200

Std. deviation σ_pop0.120

Survivors last generation120 / 120

Removed by predators0.0%

Zum Modell

This is an individual-based model of natural selection acting on one continuous, heritable trait. Each beetle carries a colour value c between 0 (light) and 1 (dark) and sits on a background of colour b. A generation has two phases. In the predation phase every beetle is removed with probability P = min(0.95, 1.5·s·|c − b|), where s is the predation strength: the greater the contrast with the background, the more likely a predator spots it. In the reproduction phase the survivors breed back to the carrying capacity N; each offspring copies a randomly chosen surviving parent and adds a Gaussian mutation with standard deviation σ. Nothing else is modelled: there are no sexes, no genes or alleles, no age structure, no predator population dynamics, and the background does not react to the beetles. The mean colour drifts toward b over roughly 15–30 generations and the spread narrows; a sudden change of background shows re-adaptation, and σ = 0 shows that without new variation selection eventually fixes a single colour. Because selection is random sampling, every run differs — compare several runs before drawing conclusions. For the same ideas expressed with discrete alleles and frequencies p and q, continue with the Hardy–Weinberg Population Genetics simulator (earth-life-fluids/hardy-weinberg-population-genetics).

Für wen: Middle- and high-school biology (grades 7–11) introducing adaptation, variation, heredity and natural selection with a visual, hands-on model.

Wichtige Begriffe

Natural selection
Variation
Heritability
Mutation
Camouflage
Selection pressure
Carrying capacity
Adaptation

So funktioniert es

A population of beetles carries a continuous colour trait from 0 (light) to 1 (dark) and lives on a background with its own colour. In each generation predators spot and remove beetles with probability proportional to the contrast |colour − background| times the predation strength; the survivors then reproduce until the population is back at the carrying capacity, with each offspring inheriting its parent’s colour plus a small random mutation σ. Over generations the mean colour of the population drifts toward the background — natural selection acting on heritable variation — and the histogram narrows. Flip the background suddenly and watch the population re-adapt; set σ = 0 and the variation is eventually lost altogether.

Wichtige Gleichungen

P(eaten) = min(0.95, 1.5 · s · |c − b|) (s = predation strength, b = background)

c_offspring = clamp(c_parent + N(0, σ²), 0, 1)

mean c̄ = Σc/N, σ_pop = √(Σ(c − c̄)²/N)

Häufige Fragen

Why does the population not become exactly the background colour?: Mutation keeps injecting new colours every generation, and predation is probabilistic, so a few mismatched beetles always survive by chance. The mean settles close to the background and fluctuates around it; the standard deviation stays near a balance between mutation adding spread and selection removing it.
What happens when the mutation σ is set to 0?: No new variation enters. Selection removes the most contrasting colours each generation while offspring are exact copies of their parents, so the colour range shrinks until every beetle is identical and the histogram collapses to one bar. The population is then "stuck" and cannot re-adapt if the background changes.
Do the beetles choose or change their colour to match the background?: No. An individual never changes colour during its life. Only the population changes, because beetles that happen to match survive and pass their colour to more offspring. That difference between individual change and population change is the heart of natural selection.
Why are two runs with identical settings different?: Which beetles get eaten and which mutations appear are random draws, as in a real population. Small populations show larger run-to-run differences; raise the population size to see the mean colour curve become smoother.

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Natural Selection: Beetles, Predators and Camouflage

Zum Modell

So funktioniert es

Wichtige Gleichungen

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Wichtige Gleichungen

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