How to Use This Page
1. Start with the Key Concepts table — quickly revise all important terms before attempting questions. 2. Attempt MCQs, Fill in the Blanks, and True or False — these test factual recall and are the easiest marks. 3. Match the Following — helps you connect terms with definitions or examples. 4. Answer Briefly (2-mark) — write 3–5 crisp sentences; use biological terms, not vague language. 5. Answer in Detail (5-mark) — use headings or sub-points; draw labelled diagrams wherever possible. 6. Review Common Mistakes to Avoid — these are the exact errors examiners flag. 7. Use the Exam Checklist — tick off each point before you walk into the exam hall.
Key Concepts (Quick Recap)
| Term | Definition |
|---|---|
| Population | A group of individuals of the same species living in a given area at a given time |
| Population density | Number of individuals per unit area or volume (N/area) |
| Natality (Birth rate) | Number of births per 1,000 individuals per year |
| Mortality (Death rate) | Number of deaths per 1,000 individuals per year |
| Carrying capacity (K) | Maximum number of individuals an environment can sustain indefinitely |
| Intrinsic rate of increase (r) | Per capita rate of population increase; r = b − d |
| Exponential growth | Unlimited-resource growth model; J-shaped curve; dN/dt = rN |
| Logistic growth | Limited-resource growth model; S-shaped curve; dN/dt = rN[(K−N)/K] |
| Ecological niche | Total functional role and position of a species in its ecosystem |
| Fundamental niche | Full range of environmental conditions a species can theoretically occupy |
| Realised niche | Actual niche a species occupies in the presence of competitors |
| Gause's principle | Two species with identical ecological niches cannot coexist indefinitely |
| Age pyramid | Graphical representation of age distribution in a population |
| Mutualism | Interaction where both species benefit (+, +) |
| Commensalism | Interaction where one benefits, the other is unaffected (+, 0) |
Chapter 20 — Organisms and Populations Exercise Solutions
Population ecology problems require understanding growth equations. Practice substituting values into the logistic growth equation.
Population Growth Models
Exponential Growth (J-curve):
- Nt = N0 × e^(rt), where e = 2.718
- r = b − d (birth rate − death rate)
- Occurs when food, space, and resources are unlimited.
- Example: Bacteria in ideal conditions.
Logistic Growth (S-curve / Sigmoidal):
- K = carrying capacity (maximum sustainable population size)
- As N → K, (K−N)/K → 0, growth slows
- Inflection point at N = K/2 (maximum growth rate)
- More realistic for natural populations.
Age Pyramids
| Type | Shape | Characteristic |
|---|---|---|
| Growing population | Broad base, narrow top | High birth rate, young population |
| Stable population | Bell-shaped (uniform) | Birth rate = Death rate |
| Declining population | Narrow base, broad top | Low birth rate, ageing population |
Ecological Interactions — Summary
| Interaction | Species 1 | Species 2 | Example |
|---|---|---|---|
| Mutualism | + | + | Lichen, mycorrhiza, cleaner fish |
| Commensalism | + | 0 | Orchid on tree, cattle egret with cattle |
| Predation | + | − | Sparrow eating insects |
| Parasitism | + | − | Cuscuta (dodder) on host |
| Competition | − | − | Two species competing for same food |
| Amensalism | 0 | − | Penicillium inhibits Staphylococcus |
Niche Concept
- Ecological niche: Total functional role of an organism in its ecosystem.
- Fundamental niche: The full range of conditions an organism can tolerate.
- Realised niche: Actual conditions it occupies due to competition.
- Competitive exclusion principle (Gause): Two species competing for identical resources cannot coexist — one will exclude the other.
Adaptations
- Thermal adaptation: Rennet's rule (desert animals: long ears); Allen's rule (cold climate animals: compact body).
- High altitude adaptation: More RBCs, efficient haemoglobin, larger lungs.
- Desert adaptation: Camel — concentrated urine, fat in hump, dry faeces; Kangaroo rat — metabolic water.
Worked Examples
Example 1 — Exponential vs logistic growth
Exponential (unlimited resources): dN/dt = rN → J-shaped curve
Logistic (limited resources): dN/dt = rN[(K−N)/K] → S-shaped curve
K = carrying capacity. Growth slows as N approaches K.
Example 2 — Population growth rate
A population of 500 grows with intrinsic rate r = 0.2 /yr (exponential). Find the initial growth rate dN/dt.
dN/dt = rN = 0.2 × 500 = 100 individuals per year
Example 3 — Logistic check at half capacity
For K = 1000 and N = 500, r = 0.2, find dN/dt.
dN/dt = rN[(K−N)/K] = 0.2 × 500 × [(1000−500)/1000]
= 0.2 × 500 × 0.5 = 50 individuals/yr
Growth is fastest near N = K/2.
I. Choose the Best Answer (MCQs)
1. The intrinsic rate of natural increase (r) is calculated as:
2. In logistic growth, the growth rate is maximum when:
3. An age pyramid with a broad base and narrow top indicates:
4. The competitive exclusion principle was proposed by:
5. Which of the following is an example of commensalism?
6. Carrying capacity (K) refers to:
7. Allen's rule states that animals in cold climates have:
8. Metabolic water is produced by which desert animal?
9. Which interaction is represented by (−, −)?
10. The formula Nt = N0 × e^(rt) describes:
II. Fill in the Blanks
1. The total number of individuals in a population is called population size (N).
2. The maximum number of individuals an environment can support is called carrying capacity (K).
3. In an age pyramid, a bell-shaped structure indicates a stable population.
4. Two species with identical niches cannot coexist — this is known as Gause's competitive exclusion principle.
5. The interaction in which one species benefits and the other is unaffected is called commensalism.
6. The S-shaped curve in population growth is also called the sigmoidal curve.
7. Allen's rule explains that animals in cold climates have shorter extremities to reduce heat loss.
8. The relationship between fig tree and fig wasp is an example of mutualism.
9. Penicillium killing nearby bacteria is an example of amensalism.
10. In the logistic growth equation, when N = K, the growth rate dN/dt equals zero.
III. True or False (with corrections)
1. Statement: Exponential growth produces an S-shaped curve.
2. Statement: Carrying capacity is the same as population size.
3. Statement: In mutualism, both species benefit from the interaction.
4. Statement: Gause's principle applies only to intraspecific competition.
5. Statement: A declining population has an age pyramid with a broad base.
6. Statement: Kangaroo rat survives in the desert without drinking water by producing metabolic water.
7. Statement: In amensalism, one species is harmed and the other benefits.
8. Statement: The inflection point in a logistic growth curve occurs when N = K/2.
IV. Match the Following
| Column A | Column B |
|---|---|
| 1. Exponential growth | (c) J-shaped curve |
| 2. Logistic growth | (e) S-shaped curve |
| 3. Gause's principle | (a) Competitive exclusion |
| 4. Mutualism | (f) Lichen (alga + fungus) |
| 5. Commensalism | (g) Cattle egret and cattle |
| 6. Parasitism | (b) Cuscuta on host plant |
| 7. Amensalism | (d) Penicillium inhibits bacteria |
| 8. Allen's rule | (h) Shorter extremities in cold climates |
V. Answer Briefly (2-mark)
1. Define population density. What factors increase population density?
2. What is the difference between fundamental niche and realised niche?
3. State Allen's rule with an example.
4. Why is logistic growth considered more realistic than exponential growth?
5. What is an age pyramid? Name its three types.
VI. Answer in Detail (5-mark)
1. Describe the exponential and logistic growth models with equations and diagrams.
2. Explain the types of ecological interactions with examples and signs (+, −, 0).
3. Discuss the adaptations of organisms to their environment with examples.
Common Mistakes
- Confusing carrying capacity (K) with population size (N).
- Drawing J-curve for logistic growth or S-curve for exponential.
- Confusing commensalism (0,+) with mutualism (+,+) — commensalism: one species is unaffected.
- Writing Gause's principle incorrectly — it says two species with identical niches cannot coexist, not just any two species.
Common Mistakes to Avoid
- ❌ Writing dN/dt = rN for logistic growth — ✅ Logistic growth uses dN/dt = rN[(K−N)/K]; dN/dt = rN is only for exponential growth.
- ❌ Saying carrying capacity (K) means total individuals ever born — ✅ K is the maximum number of individuals the environment can sustain at a given time; it depends on resource availability.
- ❌ Confusing mutualism and commensalism — ✅ Mutualism: both species benefit (+, +). Commensalism: one benefits, the other is completely unaffected (+, 0).
- ❌ Stating Gause's principle applies to any two species — ✅ It applies specifically to species with identical or overlapping niches competing for the same limited resource.
- ❌ Labelling predation and parasitism as the same — ✅ Predation: predator kills prey quickly (+, −). Parasitism: parasite lives on/in host for extended period (+, −) but does not immediately kill the host.
- ❌ Drawing a broad-base pyramid for a declining population — ✅ A declining population has a narrow base and broad top (urn-shaped). A broad base indicates a growing population.
- ❌ Saying Allen's rule means animals in cold climates are larger overall — ✅ Allen's rule specifically refers to shorter extremities (ears, limbs, tail) in cold climates to reduce surface area for heat loss. Bergmann's rule refers to overall body size.
- ❌ Writing that amensalism harms both species — ✅ Amensalism: one species is harmed, the other is completely unaffected (0, −). Competition harms both (−, −).
Exam Checklist
- [ ] I can write and explain the exponential growth equation dN/dt = rN and its integrated form Nt = N0e^(rt).
- [ ] I can write and explain the logistic growth equation dN/dt = rN[(K−N)/K] and identify the inflection point at N = K/2.
- [ ] I can distinguish J-shaped (exponential) and S-shaped (logistic) curves with labelled diagrams.
- [ ] I can define and differentiate: population size, population density, natality, mortality, and sex ratio.
- [ ] I can draw the three types of age pyramids (growing, stable, declining) and label pre-reproductive, reproductive, and post-reproductive groups.
- [ ] I can list all six ecological interactions with correct (+, −, 0) signs and one example each.
- [ ] I can define ecological niche and distinguish fundamental niche from realised niche.
- [ ] I can state Gause's competitive exclusion principle and explain resource partitioning as a way species coexist.
- [ ] I can explain Allen's rule and Rennet's rule with animal examples.
- [ ] I can describe desert adaptations (camel, kangaroo rat) and high-altitude adaptations (increased RBCs, haemoglobin efficiency).
- [ ] I can explain xerophytic, hydrophytic, and halophytic plant adaptations with examples.
- [ ] I can calculate dN/dt given values for r, N, and K in both exponential and logistic models.
Frequently Asked Questions
Population attributes: 1. Population size (N) — total number of individuals. 2. Population density — number per unit area/volume. 3. Birth rate (natality) — new individuals added per capita per unit time. 4. Death rate (mortality) — individuals lost per capita per unit time. 5. Age structure/Age pyramid — ratio of different age age groups. 6. Sex ratio — ratio of males to females. 7. Growth rate — change in N over time.