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#population decline

4 public questions tagged with this topic.

In logistic growth, growth rate decreases as:

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.

Ref: Ecology: Concepts and Applications, Molles, 9th Ed., Ch. 11

In the absence of prey, predator population will:

Without prey or another usable food source, predator intake falls to zero while metabolic maintenance, mortality, and emigration continue. In the Lotka–Volterra equation dP/dt = baNP − mP, setting prey density N to zero gives dP/dt = −mP. Predator abundance then declines exponentially at rate m, assuming a closed population and no immigration. Stabilization would require replacement of deaths through feeding-supported reproduction or external subsidy, while increase is impossible under the model because prey conversion supplies the positive growth term. Oscillation also requires reciprocal feedback between both populations and cannot continue when one is absent. Real predators may persist temporarily on stored reserves, enter dormancy, migrate, scavenge, or switch to alternative prey, so “absence of prey” must mean absence of all effective food. Those mechanisms change the model assumptions rather than the basic energetic conclusion. The population-level decline arises from the balance of births and deaths, not because every individual dies immediately when prey disappear.

Ref: Ecology: Concepts and Applications, Molles, 9th Ed., Ch. 14