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Organisms and Populations - Populations: Growth, Attributes and Age Pyramids

Grade 12CBSEBiology

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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A population is a group of individuals of the same species living in a particular geographical area. Unlike individuals, populations have attributes such as birth rates, death rates, and sex ratios.

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Natality (BB) refers to the number of births during a given period in the population that are added to the initial density.

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Mortality (DD) is the number of deaths in the population during a given period.

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Immigration (II) is the number of individuals of the same species that have come into the habitat from elsewhere during the time period under consideration.

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Emigration (EE) is the number of individuals of the population who left the habitat and gone elsewhere during the time period under consideration.

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The Age Pyramid is a graphic representation of different age groups (Pre-reproductive, Reproductive, and Post-reproductive). The shape of the pyramid reflects the growth status of the population: Expanding (Triangular), Stable (Bell-shaped), or Declining (Urn-shaped).

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Exponential Growth occurs when resources (food and space) are unlimited. The population grows in a geometric fashion, resulting in a J-shaped curve.

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Logistic Growth (Verhulst-Pearl Logistic Growth) occurs when resources are finite. 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 (KK). This results in a Sigmoid (S-shaped) curve.

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Intrinsic rate of natural increase (rr) is a very important parameter chosen for assessing impacts of any biotic or abiotic factor on population growth.

📐Formulae

Nt+1=Nt+[(B+I)−(D+E)]N_{t+1} = N_t + [(B + I) - (D + E)]

dNdt=(b−d)×N\frac{dN}{dt} = (b - d) \times N

dNdt=rN\frac{dN}{dt} = rN

Nt=N0ertN_t = N_0 e^{rt}

dNdt=rN(K−NK)\frac{dN}{dt} = rN \left( \frac{K - N}{K} \right)

💡Examples

Problem 1:

In a laboratory population of 4040 fruit flies, 44 individuals died during a specific time interval (say, a week). Calculate the death rate for the population during that period.

Solution:

Death rate=440=0.1Death\ rate = \frac{4}{40} = 0.1 individuals per fruit fly per week.

Explanation:

The death rate is calculated by dividing the number of individuals who died by the total initial population size.

Problem 2:

If a population of size NN shows exponential growth, and the birth rate is 0.150.15 and the death rate is 0.050.05 per capita per year, calculate the intrinsic rate of natural increase (rr).

Solution:

r=b−d=0.15−0.05=0.1r = b - d = 0.15 - 0.05 = 0.1 per capita per year.

Explanation:

The intrinsic rate of natural increase (rr) is the difference between the per capita birth rate (bb) and the per capita death rate (dd).

Problem 3:

Identify the components of the logistic growth equation: dNdt=rN(K−NK)\frac{dN}{dt} = rN \left( \frac{K - N}{K} \right).

Solution:

NN = Population density at time tt; rr = Intrinsic rate of natural increase; KK = Carrying capacity.

Explanation:

This formula accounts for the environmental resistance as the population size NN approaches the carrying capacity KK.

Populations: Growth, Attributes and Age Pyramids Revision - Class 12 Biology CBSE