NEET2026BiologyChapterActual
A population of Paramecium is cultured in a laboratory flask with a limited and fixed supply of nutrients, exhibiting Verhulst-Pearl logistic growth. When the population density ( N ) eventually reaches the carrying capacity ( K ) of the flask, what will be the rate of change in population density ( dN dt ) and the primary mathematical reason for it?
Options
- AdN dt = 0 , because the expression ( K-N K ) becomes zero.
- BdN dt = 0 , because the intrinsic rate of natural increase ( r ) becomes zero.
- CdN dt = rN , because the population size has reached its maximum limit.
- DdN dt becomes negative, because the available resources are completely exhausted.
Correct answer
A. dN dt = 0 , because the expression ( K-N K ) becomes zero.
Step-by-step solution
The Verhulst-Pearl logistic growth equation is given by dN dt = rN ( K-N K ) . When the population density ( N ) reaches the carrying capacity ( K ), we substitute N = K into the equation. dN dt = rK ( K-K K ) = rK 0 = 0 . The rate of change in population density becomes zero because the environmental resistance term ( K-N K ) becomes zero. The intrinsic rate of natural increase ( r ) remains constant. Answer: dN dt = 0 , because the expression ( K-N K ) becomes zero.