Which is not an assumption for logistic growth?

Options

A. K is constant
B. All individually reproduce equally
C. Immigration and emigration
D. the relation between density and rate of increase is linear.

Answer

To solve the question "Which is not an assumption for logistic growth?", we need to analyze the assumptions associated with logistic growth models. Here’s a step-by-step breakdown:

### Step 1: Understand the Logistic Growth Model
The logistic growth model describes how a population grows in an environment with limited resources. The equation is given by:
\[ \frac{dn}{dt} = r \cdot n \left(1 - \frac{n}{K}\right) \]
where:
- \( n \) = population size
- \( r \) = intrinsic rate of natural increase
- \( K \) = carrying capacity of the environment

### Step 2: Identify Key Assumptions of Logistic Growth
1. **Carrying Capacity (K) is Constant**: The carrying capacity remains constant over time.
2. **No Immigration or Emigration**: The model assumes that the population is closed, meaning there are no individuals moving in or out of the population.
3. **Density-Dependent Growth**: The growth rate decreases as the population density approaches the carrying capacity.
4. **Resources are Limited**: The model assumes that resources are limited, which affects the growth rate.

### Step 3: Analyze the Options
Now, let's evaluate the options provided in the question:
1. **K is constant**: This is a correct assumption of logistic growth.
2. **All individuals reproduce equally**: This implies a survival of the fittest scenario, which is also an assumption in logistic growth.
3. **Immigration and Emigration**: This is NOT an assumption of logistic growth, as the model assumes a closed population.
4. **The relation between density and rate of increase is linear**: This is a correct assumption, as the growth rate is affected by the population density.

### Step 4: Conclusion
Based on the analysis, the option that is NOT an assumption for logistic growth is **Immigration and Emigration**.

### Final Answer
The correct answer is: **Immigration and Emigration**.

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