In the equation for S-shaped population growth `(dN)/(dt)=rN[(K-N)/(K)]` , r represents

Options

A. Carrying capacity
B. Environmental resistance
C. Biotic potential
D. Population size

Answer

To solve the question regarding the representation of 'r' in the equation for S-shaped population growth `(dN)/(dt)=rN[(K-N)/(K)]`, we can break it down into the following steps:

### Step-by-Step Solution:

1. **Understand the Equation**: The equation `(dN)/(dt)=rN[(K-N)/(K)]` describes the rate of change of a population (N) over time (t). This is a logistic growth model, which is characterized by an S-shaped curve.

2. **Identify the Components**:
- **N**: This represents the current size of the population.
- **K**: This is the carrying capacity of the environment, which is the maximum population size that the environment can sustain.
- **r**: This is the parameter we need to define.

3. **Interpret 'r'**: In population ecology, 'r' is known as the intrinsic growth rate or biotic potential. It indicates the maximum rate at which a population can grow under ideal conditions, without any limitations such as food, space, or competition.

4. **Conclusion**: Therefore, 'r' represents the biotic potential of the population, which is the maximum growth rate of the population when resources are unlimited.

5. **Final Answer**: In the given equation, 'r' represents the biotic potential of the population.