Threshold population

Definition

The threshold population is the minimum population size required for a specific behavior or phenomenon to occur within a model. In differential equations, it is often associated with the point at which growth rates change.

5 Must Know Facts For Your Next Test

1. The threshold population is crucial in determining the stability of equilibrium points in logistic models.
2. It helps in identifying when a population will grow exponentially or decline.
3. In logistic equations, the carrying capacity can be influenced by the threshold population.
4. The concept is often used to determine the point at which resources become limiting.
5. Threshold population can be calculated using parameters such as growth rate and carrying capacity.

Review Questions

• What role does the threshold population play in determining equilibrium points?
• $\text{How do you calculate the threshold population in a logistic model?}$
• Why is understanding the threshold population important for predicting long-term behavior?

Related terms

Carrying Capacity: The maximum population size that an environment can sustain indefinitely given available resources.

Logistic Growth: A type of growth characterized by an initial exponential increase followed by a leveling off as carrying capacity is approached.

$\text{Equilibrium Point}$: $\text{A state where a system's variables remain constant over time, often found by setting derivatives to zero.}$