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#population decline

4 public questions tagged with this topic.

Population Growth

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

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

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Predator Prey Model

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 fee

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

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