In a logistic model, what happens when K-N = 0?
If K - N equals zero, then N equals K. The density-dependent factor (K - N)/K in the logistic equation is therefore zero, and multiplying it by rN gives dN/dt = 0. Population size is at the model s carrying-capacity equilibrium, even though individuals continue to be born and die. Logistic predictions depend on assumptions that managers should not overlook. Carrying capacity changes with habitat and climate, and removing individuals may alter age structure, social organization, or genetic diversity. Thus an algebraic optimum is a benchmark, not a guarantee that a real harvested or conserved population will behave identically. Reading the terms biologically, rather than memorizing labels, shows how individual survival and reproduction scale up to population change. Ecological predictions remain conditional on the stated environment, because changing resources, mortality, or interactions can alter the observed demographic pattern. This interpretation connects individual-level processes with measurable changes in survival, reproduction, recruitment, or abundance across the population.
Ref: Ecology: Concepts and Applications, Molles, 9th Ed., Ch. 11