Practice question

“dN/dt = rN[(K-N)/K]” for which of the following equations represents logistic growth. This relationship follows from the ecological mechanism represented by the terms in the item, not merely from an association between their names. Mechanistic support comes from showing how resource limitation, enemies, mate availability, or physiological stress changes demographic performance. A descriptive association alone does not establish regulation or causation. The remaining alternatives—“dN/dt = rN”, “dN/dt = rN/K”, “dN/dt = rN[(K-N)/N]”—refer to different states, processes, or scales and therefore do not express the same causal relationship. Population ecology links individual births, deaths, immigration, and emigration to changes in abundance. Per-capita rates determine the direction of change, while density dependence creates feedback when crowding alters survival or reproduction. This distinction matters because similar surface patterns can arise through different mechanisms, whereas ecological prediction depends on identifying the mechanism that actually changes rates. The cited framing is therefore most useful when treated as a conditional biological claim, with assumptions about scale and environmental context kept explicit.