Question

Give a brief account of different population growth models.

Hint:

The exponential model assumes unlimited resources, while the logistic model accounts for environmental constraints and carrying capacity.

Answer 1

There are two main types of population growth models used to describe how populations change over time: 1. Exponential Growth Model: - In this model, populations grow at a constant rate when resources are abundant, and there are no limiting factors. - The growth rate is proportional to the size of the population, leading to a J-shaped curve. - The equation for exponential growth is: \[ N(t) = N_0 e^{rt} \] Where: - \( N(t) \) is the population size at time \( t \), - \( N_0 \) is the initial population size, - \( r \) is the rate of growth (birth rate - death rate), - \( t \) is the time period. - Example: Bacteria in a culture under ideal conditions. 2. Logistic Growth Model: - In this model, population growth is initially exponential but slows down as the population reaches the carrying capacity of the environment. - The logistic model includes a limiting factor (carrying capacity) that prevents indefinite growth. - The equation for logistic growth is: \[ N(t) = \frac{K}{1 + \frac{K - N_0}{N_0} e^{-rt}} \] Where: - \( N(t) \) is the population size at time \( t \), - \( K \) is the carrying capacity, - \( N_0 \) is the initial population size, - \( r \) is the growth rate, - \( t \) is time. - Example: A population of deer in a forest with limited resources.
Final Answer: The exponential growth model describes unlimited population growth, while the logistic growth model incorporates a carrying capacity that limits growth as the population reaches environmental limits.