Lamarck vs Darwin: Two Theories of Inheritance

Inheritance Model

Darwin: necks already vary; short-necked animals starve more often, survivors' genes pass on.

Environment & Genetics

Foliage height 3.20 m

Mutation / stretch rate σ 0.12

Speed 1.0×

Population State

Generation

Alive

Mean neck

2.80 m

Trait variance (σ²)

0.000

Deaths this gen

How it works

Two rival 19th-century explanations for why giraffes have long necks, run as actual generational update rules on the same starting population of 40 animals with neck length drawn from N(2.8 m, 0.25 m):

Darwin (natural selection on existing variation):
  P(survive_i) = 1 / (1 + e^-k(neck_i - foodLine))
  survivors breed in random pairs;
  neck_offspring = mean(neck_p1, neck_p2) + N(0, σ)

Lamarck (inheritance of acquired characters):
  neck_i(t+1) = neck_i(t) + r·(foodLine - neck_i(t))   [use-and-disuse growth]
  offspring inherits the *stretched* value directly, unchanged
  no death from short necks — every animal grows toward the food

Darwin mode — variation was already there before any selection happened; the environment only decides who reproduces. Watch the mean climb in visible steps and variance stay roughly stable — selection filters, it doesn't stretch.
Lamarck mode — every individual grows a bit each generation from "trying" to reach the leaves, and that acquired growth (not a gene) is what's passed on. Watch the whole population converge to the foliage height almost uniformly with population size never dropping — no filtering, no death.
Genetics falsified Lamarck's mechanism: DNA in body cells (soma) that "stretch" during life is not the DNA passed to eggs/sperm (germline) — the Weismann barrier. Darwin's mechanism needed genes to work but not to know about them, since it only needs heritable variation plus differential survival, which is exactly what modern population genetics formalizes.

Reaches the foliage Below foliage line

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