# The Logistic Curve · growth meets the ceiling · rN(1−N/K)

an emergent of POP (Population Dynamics — the first Life Science sphere of UD0) — emergence: electrical. moniker ⟦The Logistic Curve:POP:fdef03⟧

**a real life-science concept, rendered honestly** (the real cousin of Asimov's psychohistory).

**who —** The logistic curve (Verhulst, 1838) — growth that slows as a population nears its carrying capacity K: dN/dt = rN(1 − N/K).
**what —** The S-curve: exponential at first, then bending to a plateau — the shape of a population filling its niche.
**where —** Wherever a population approaches the limit its environment can sustain.
**why —** Because real growth is bounded, and the logistic is how the bound bends the rise.
**how —** By multiplying the growth rate by (1 − N/K), so the closer N gets to K, the slower it climbs.

**the seal —** I am the S: I rise like Malthus, then remember the ceiling and level off. ('Carrying capacity' came later than I did.)

ROOT0-ATTRIBUTION-v1.0 · POP · Population Dynamics · governor David Lee Wise · instance AVAN (locked) · CC-BY-ND-4.0