Population Ecology — Practice · Grade 12 Science

Chapter: Ecology, Populations & Biodiversity

What this practice covers

By the end of Population Ecology you should be able to:

9 questions, multiple choice, numeric and written answer, each with a worked explanation.

Vocabulary used: population, exponential growth, logistic growth, carrying capacity (K), limiting factor, survivorship curve.

Problem 1

A population reproducing with unlimited resources, doubling again and again, produces which growth curve?
  1. An S-shaped logistic curve
  2. A flat horizontal line
  3. A bell-shaped curve
  4. A J-shaped exponential curve
Answer and explanation

A J-shaped exponential curve

Constant per-capita growth with no limits accelerates into a J-shaped exponential curve.

Problem 2

For N=200, r=0.5/year, and K=1000, find the instantaneous rate dN/dt=rN(1−N/K), in individuals/year.
Answer and explanation

80 rabbits/yr

(1,000 - 200)/1,000 = 0.8; 0.5 × 200 × 0.8 = 80. This is an instantaneous rate in the continuous model, not an exact finite-year increase.

Problem 3

A population of 4,000 has 240 births and 40 deaths in a year (ignore migration). What is the annual growth rate, as a percent?
Answer and explanation

5 %

Net change = 240 - 40 = 200; 200/4,000 = 0.05 = 5%.

Problem 4

Which of these is a density-DEPENDENT limiting factor?
  1. Disease spreading through a crowded population
  2. A volcanic eruption
  3. A hurricane that floods the habitat
  4. A sudden hard freeze
Answer and explanation

Disease spreading through a crowded population

Disease spreads faster as density rises, so it intensifies with crowding — a density-dependent factor. The others strike regardless of population size.

Problem 5

Explain why a population may temporarily overshoot its carrying capacity and then crash.
Answer and explanation

If a population grows rapidly, it can climb past K before limiting factors fully catch up. Once there are more individuals than the environment can support, resources run short and deaths spike, so the population crashes back down below K before stabilizing.

Problem 6

For dN/dt=rN with r=0.10/year and N=200, find instantaneous growth. Show the reasoning, not just the conclusion.
Hints

Rates, net numbers and total population are different quantities.

Answer and explanation

20 individuals/year in the exponential model.

Problem 7

In logistic growth, why does growth slow as N approaches K?
Hints

State what the supplied observations or conditions establish, and separate that from any assumption.

Answer and explanation

The model's factor 1−N/K reduces per-capita growth; real mechanisms and K can change with conditions.

Problem 8

Carrying capacity is conditional and can changeCarrying capacity is conditional and can changeLogistic population model N02505007501000036912Time (years)K=1000 here is a fixed model parameter, not an eternal limit.
Calculated logistic curve with N₀=100,r=0.6 yr⁻¹,K=1000; not field observations.
Interpret the supplied visual. For r=0.4 yr⁻¹,K=1000 and N=500, find the instantaneous rate.
Answer and explanation

0.4×500×(1−0.5)=100 individuals/year.

The logistic model uses dN/dt=rN(1−N/K), with K a carrying-capacity parameter under specified conditions. Growth slows as N approaches K in this fixed-parameter model. Real resources, habitat, climate, interactions and disturbance can change K, and delayed responses can produce overshoot or oscillations outside the simple curve. Maximum total logistic growth occurs at N=K/2 for fixed r,K; it is not the same as the highest per-capita growth rate.

0.4×500×(1−0.5)=100 individuals/year.

Response criteria

  • Interpret labels, structures, axes, units and directions correctly.
  • Explain the physical or environmental relationship or mechanism.
  • Respect stated assumptions and distinguish observation from inference.

Problem 9

For continuous logistic growth with r=0.5 yr⁻¹,K=800 and N=200, find dN/dt. Compare with N=400.
Answer and explanation

At200:0.5×200×0.75=75 individuals/year. At400:0.5×400×0.5=100/year. Total growth rises even while per-capita growth falls.

At200:0.5×200×0.75=75 individuals/year.

At400:0.5×400×0.5=100/year.

Total growth rises even while per-capita growth falls.

Response criteria

  • Use the stated measurements or conditions, with correct units.
  • Connect the result to the physical or environmental mechanism or evidence relationship.
  • Identify the assumption, model limit or further evidence requested.

Browse all courses