Practice question

For logistic growth, maximum dN/dt equals rK/4 and occurs at N = K/2. With r = 0.15 and K = 400, the calculation is 0.15 �� 400 �� 4 = 15 individuals per time unit. The keyed value 30 is therefore inconsistent with the standard logistic equation; 30 would not result from the supplied parameters. Graphically, logistic abundance through time is sigmoid, whereas its instantaneous increment plotted against abundance is a downward-opening parabola. Confusing these two plots leads to incorrect curve descriptions. The time trajectory approaches K, while the production curve peaks at K/2 and is zero at both model equilibria. The example should therefore be understood as an application of a general model, with its assumptions kept explicit. 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.