Question

Consider the logistic population growth model, given by \[ \frac{dn}{dt} = r n \left( 1 - \frac{n}{k} \right) \] where \(r\) is the intrinsic growth rate, \(n\) is the population size, and \(k\) is the carrying capacity. Which one or more of the following is/are assumption(s) of the model?

• A. Carrying capacity is constant
• B. Density dependence is quadratic
• C. Continuous growth with no time-lags
• D. No genetic, age or size structure

Hint:

The logistic population growth model assumes continuous growth, a constant carrying capacity, and no structure in terms of age, size, or genetics.

Answer 1

The Correct Option is A, C, D

Step 1: Understanding the logistic model assumptions.
The logistic growth model assumes that the population grows continuously, without time-lags, and that the carrying capacity (\(k\)) remains constant. The model also assumes that density dependence is linear and does not account for genetic, age, or size structure.

Step 2: Explanation of each option.
(A) Carrying capacity (\(k\)) is assumed to be constant in the logistic model. (B) The logistic model assumes linear density dependence, not quadratic. (C) The logistic model assumes continuous growth with no time-lags, meaning population growth responds immediately to changes in population size. (D) The logistic model does not include genetic, age, or size structure, assuming a homogeneous population.

Step 3: Conclusion.
The correct answers are (A), (C), and (D) as they represent the assumptions of the logistic growth model.