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Q8:
With the help of suitable diagram describe the logistic population growth curve.
Solution :
Theoretical Foundation: The Logistic Growth Model
The logistic growth model describes population growth under conditions of limited resources. Unlike exponential growth, which assumes infinite resources, logistic growth accounts for environmental resistance, leading to an S-shaped (sigmoid) curve. It is defined by the mathematical expression:
$\frac{dN}{dt} = rN \left( \frac{K - N}{K} \right)$
- $N$: Population density at time $t$.
- $r$: Intrinsic rate of natural increase.
- $K$: Carrying capacity (the maximum population size an environment can sustain).
- $\frac{K-N}{K}$: The fraction of carrying capacity remaining.
Visual Representation: Logistic Growth Curve
Step-by-Step Analysis of Growth Phases
| Phase | Description | Mechanism |
|---|---|---|
| Lag Phase | Initial slow growth period. | Organisms are adapting to the new environment. [Per biological lag-time requirements]. |
| Log/Exponential Phase | Rapid increase in population numbers. | Abundant resources allow the population to grow at its maximum biotic potential. |
| Deceleration Phase | Growth rate begins to decline. | Environmental resistance (intra-specific competition, resource depletion) increases as $N$ approaches $K$. |
| Stationary Phase | Population levels off at $K$. | Birth rate equals death rate ($N = K$). The population reaches equilibrium with the environment. |
Mathematical Derivation Insight
When $N$ is small, the term $\frac{K-N}{K}$ is close to $1$, making the growth nearly exponential. As $N$ approaches $K$, the term $\frac{K-N}{K}$ approaches $0$, effectively stopping population growth. This mechanism ensures that population dynamics are constrained by the physical limits of the habitat, an observation known as the Verhulst-Pearl Logistic Growth model.
Final Solution: The logistic population growth curve represents a realistic model of population dynamics where, due to resource limitation, growth follows a sigmoid pattern characterized by a lag phase, an exponential phase, a deceleration phase, and a stationary phase at the carrying capacity ($K$).
More Questions from Class 12 Biology Organisms and Populations EXERCISES
- Q1: List the attributes that populations possess but not individuals.
- Q1: List the attributes that populations possess but not individuals.
- Q2: If a population growing exponentially double in size in 3 years, what is the intrinsic rate of increase (\(r\)) of the population?
- Q2: If a population growing exponentially double in size in 3 years, what is the intrinsic rate of increase ((r)) of the population?
- Q3: Name important defence mechanisms in plants against herbivory.
- Q3: Name important defence mechanisms in plants against herbivory.
- Q4: An orchid plant is growing on the branch of mango tree. How do you describe this interaction between the orchid and the mango tree?
- Q4: An orchid plant is growing on the branch of mango tree. How do you describe this interaction between the orchid and the mango tree?
- Q5: What is the ecological principle behind the biological control method of managing with pest insects?
- Q5: What is the ecological principle behind the biological control method of managing with pest insects?
- Q6: Define population and community.
- Q6: Define population and community.
- Q7(a): Define the following terms and give one example for each: (a) Commensalism
- Q7(a): Define the following term and give one example for it: Commensalism
- Q7(b): Define the following terms and give one example for each: (b) Parasitism
- Q7(b): Define the following term and give one example for it: Parasitism
- Q7(c): Define the following terms and give one example for each: (c) Camouflage
- Q7(c): Define the following term and give one example for it: Camouflage
- Q7(d): Define the following terms and give one example for each: (d) Mutualism
- Q7(d): Define the following term and give one example for it: Mutualism
- Q7(e): Define the following terms and give one example for each: (e) Interspecific competition
- Q7(e): Define the following term and give one example for it: Interspecific competition
- Q8: With the help of suitable diagram describe the logistic population growth curve.
- Q9: Select the statement which explains best parasitism.
- Q9: Select the statement which explains best parasitism.
- Q10: List any three important characteristics of a population and explain.
- Q10: List any three important characteristics of a population and explain.
CBSE Solutions for Class 12 Biology Organisms and Populations
Chapters in CBSE - Class 12 Biology
- Reproduction in Organisms
- Human Reproduction
- Reproductive Health
- Principles of Inheritance and Variation
- Molecular Basis of Inheritance
- Evolution
- Human Health and Disease
- Strategies for Enhancement in Food Production
- Microbes in Human Welfare
- Biotechnology: Principles and Processes
- Biotechnology and Its Applications
- Ecosystem
- Biodiversity and Conservation
- Environmental Issues
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