Question
Explain logistic growth with equation.
✓
Answer
→ No population of any species in nature has at its disposal unlimited resources to permit exponential growth.
→ This leads to competition between individuals for limited resources.
→ Eventually, the 'fittest' individual will survive and reproduce.
→ The governments of many countries have also realised this fact and introduced various restraints with a view to limit human population growth.
→ In nature, a given habitat has enough resources to support a maximum possible number, beyond which no further growth is possible.
→ This limit is nature's carrying capacity (K) for that species in that habitat.
→ A population growing in a habitat with limited resources show initially a lag phase, followed by phases of acceleration and deceleration and finally an asymptote, when the population density reaches the carrying capacity.
→ A plot of N in relation to time (t) results in a sigmoid curve. This type of population growth is called Verhulst-Pearl Logistic Growth.
→ The Verhulst-Pearl Logistic Growth equation :
$
dN / dt = rN ( K - N / K )
$
Where $N =$ Population density at time t
$r =$ Intrinsic rate of natural increase
$K=$ Carrying capacity
→ Since resources for growth for most animal populations are finite and become limiting sooner or later, the logistic growth model is considered a more realistic one.
→ Gather from Government Census data the population figures for India for the last 100 years, plot them and check which growth pattern is evident.
→ This leads to competition between individuals for limited resources.
→ Eventually, the 'fittest' individual will survive and reproduce.
→ The governments of many countries have also realised this fact and introduced various restraints with a view to limit human population growth.
→ In nature, a given habitat has enough resources to support a maximum possible number, beyond which no further growth is possible.
→ This limit is nature's carrying capacity (K) for that species in that habitat.
→ A population growing in a habitat with limited resources show initially a lag phase, followed by phases of acceleration and deceleration and finally an asymptote, when the population density reaches the carrying capacity.
→ A plot of N in relation to time (t) results in a sigmoid curve. This type of population growth is called Verhulst-Pearl Logistic Growth.
→ The Verhulst-Pearl Logistic Growth equation :
$
dN / dt = rN ( K - N / K )
$
Where $N =$ Population density at time t
$r =$ Intrinsic rate of natural increase
$K=$ Carrying capacity
→ Since resources for growth for most animal populations are finite and become limiting sooner or later, the logistic growth model is considered a more realistic one.
→ Gather from Government Census data the population figures for India for the last 100 years, plot them and check which growth pattern is evident.
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