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Models of Population Growth - Practice Questions & MCQ

Edited By admin | Updated on Sep 18, 2023 18:34 AM | #NEET

Quick Facts

  • Models of Population Growth: Exponential Growth, Models of Population Growth: Logistic Growth are considered the most difficult concepts.

  • 17 Questions around this concept.

Solve by difficulty

Which of the following statements is true regarding the relationship between exponential growth and the environment?

A population grows according to the logistic growth equation, dN/dt=rN(1-N/K)  where dN/dt is the rate of population growth, r is the intrinsic rate of increase, N is population size and K Is the carrying capacity of the environment.

According to this equation, population growth rate is maximum at

 

The equation for Verhulst- Pearl Logistic Growth is:

\frac{\mathrm{dN}}{\mathrm{dt}}=\mathrm{rN}\left(\frac{\mathrm{K}-\mathrm{N}}{\mathrm{K}}\right)

Here in this equation “N” denotes Population density (at a point in time ) and “K”dentoes_________?

Given below are growth equations where dN/dt is defined as

P. rN/K

Q. rN

R. rN[(K - N)/N]

S. rN[(K - N)/K]

With reference to the above equations, which one of the following statements is correct?

 

A species whose life history strategies allow for high intrinsic rates of increase (r-strategist) will also exhibit the following except

 

Concepts Covered - 2

Models of Population Growth: Exponential Growth
  • Resource (food and space) availability is obviously essential for the unimpeded growth of a population.
  • Ideally, when resources in the habitat are unlimited, each species has the ability to fully realise its innate potential to grow in number, as Darwin observed while developing his theory of natural selection.
  • Then the population grows in an exponential or geometric fashion.
  • The increase or decrease in population density (N) at a unit time period (t) is calculated as (dN/dt).
  • If in a population of size N, the birth rates are represented as b and death rates as d, then the increase or decrease in N during a unit time period t (dN/dt) will be:

           Let ( b- d) = r then, 

           

  • The r in this equation is called the ‘intrinsic rate of natural increase’ and is a very important parameter chosen for assessing impacts of any biotic or abiotic factor on population growth.
  • The above equation describes the exponential or geometric growth pattern of a population. and results in a J-shaped curve when we plot N in relation to time. 
  • the integral form of the exponential growth equation can be derived as:

 

Where,
= Population density after time t
=  Population density at time zero
 =  intrinsic rate of natural increase
 = the base of natural logarithms (2.71828)

  • Any species growing exponentially under unlimited resource conditions can reach enormous population densities in a short time. 
  • Darwin showed how even a slow growing animal like an elephant could reach enormous numbers in the absence of checks.


                                                             

Models of Population Growth: Logistic Growth
  • 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. 
  • In nature, a given habitat has enough resources to support a maximum possible number, beyond which no further growth is possible. 
  • This limit is known as nature’s carrying capacity (K) for that species in that habitat.
  • A population growing in a habitat with limited resources shows 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 as follows:

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.

 

Study it with Videos

Models of Population Growth: Exponential Growth
Models of Population Growth: Logistic Growth

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Reference Books

Models of Population Growth: Logistic Growth

Biology Textbook for Class XII

Page No. : 231

Line : 26

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