Practice question

As population size rises in the logistic model, the factor 1 - N/K declines. Consequently, per-capita growth steadily decreases and total growth eventually falls after reaching its maximum at K/2. The broad statement that growth decreases with population refers most cleanly to per-capita growth; total dN/dt first increases and then decreases. Distinguishing per-capita growth from total growth prevents a common error. In the logistic model, per-capita growth r(1 - N/K) declines linearly with density, but total growth rN(1 - N/K) forms a dome because the number of potential reproducers initially rises. Both quantities reach zero or their maximum at different densities. 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.