When does the growth rate of a population following the logistic model equal zero? The logistic model is given as dN/dt = rN(1-N/K):

  • Option 1)

    when N/K is exactly one.

  • Option 2)

    when N nears the carrying capacity of the habitat.

  • Option 3)

    when N/K equals zero.

  • Option 4)

    when death rate is greater than birth rate.

 

Answers (1)

As learnt

Logistic Growth -

No population of any species in nature has 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.

- wherein

A given habitat has enough resources to support a maximum possible number, beyond which no further growth is possible.

 

 

AND

 

 

Equation for logistic growth -

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 and is described by the following equation:

- wherein

d\frac{N}{dt}= \frac{rN(K-N)}{K}

Where,

N = Population density at time t

r = Intrinsic rate of natural increase

K = Carrying capacity

 

 


Option 1)

when N/K is exactly one.

This option is correct

Option 2)

when N nears the carrying capacity of the habitat.

This option is incorrect

Option 3)

when N/K equals zero.

This option is incorrect

Option 4)

when death rate is greater than birth rate.

This option is incorrect

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