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Population Ecology

Author(s): Evan Siemann, PhD

Dynamics of Lagged Logistic Growth Models

Under the discrete-time model, populations often overshoot carrying capacity. These models help predict what happens when the effects of density dependence are not instantaneous.

If there is a delay in feedback, a series of predictable behaviors occur as population growth increases. With a short delay in feedback, the population growth rate will smoothly approach the carrying capacity with small adjustments as shown in the top series of graphs. As population growth accelerates (shown in the second series of graphs), populations will begin to cycle in various periods such as 2 point, 4 point, 8 point, or 16 point cycle. As population growth rates cycle faster and faster, the population can enter into apparent chaos. However, at this point, even though the changes seem random, there is some regularity to the oscillations.