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F. Population Dynamics · Population Dynamics

Population Dynamics: Unit Review

F1.1 F1.2 F2.1 F2.2 F2.3 F3.1 F3.2 F3.3 A1.1 A1.2 A1.3 A1.4 A1.5 A1.6 A1.7 A1.8 A1.9 A1.10 A1.11 A1.12 A1.13 A2.1 A2.2About 40 minutes
Learning goals
  • I can recall and apply the key terms, formulas and models of population dynamics.
  • I can identify which lesson to revisit for each kind of mistake.

Words to know

carrying capacity (K)
The largest population an environment can support indefinitely.
per capita growth rate
Change in population size relative to population size (ΔN ÷ N, or r in continuous models).
density-dependent factor
A limiting factor whose effect grows stronger as density increases.
ecological footprint
The productive land and water area needed to supply a population's resources and absorb its wastes.

Let's review!

In this unit you learned to describe populations (size, density, dispersion, age structure, minimum viable size), to estimate them (quadrats, transects, mark-recapture), and to read life tables and survivorship curves. You used models: ΔN = (b + i) − (d + e), geometric and exponential growth, logistic growth with carrying capacity, and predator-prey and host-parasitoid simulations. You explained what limits populations (density-dependent and density-independent factors, r- and K-selected life histories) and how species interact (competition, predation and defences, symbiosis). Finally, you applied it all to humans: population growth and the demographic transition, consumption and the ecological footprint, Canadian technologies and projects to feed growing populations, and sustainable management that includes First Nations, Métis and Inuit knowledge.

Each set of questions below matches one lesson. Answers are hidden behind the buttons.

How to use this review

Do two or three sections at a time. For calculations (density, Chapman, R₀, λ and r, doubling time, logistic N(t), K from birth and death rates, equilibria, MSY, Earths from overshoot days), write the formula first, then substitute, then check whether the answer makes sense. For explanation questions, use the unit's key words (per capita, density-dependent, carrying capacity, lag, trade-off, outcome versus output). For every question you get wrong, write down why and revisit that lesson (see the notes for parents at the end).

GeometricNₜ = N₀λᵗExponentialNₜ = N₀eʳᵗLogisticdN/dt = rN(K − N)/KKbreeding seasonsJ-curveS-curve
The three growth models of the unit: geometric (in steps, one per breeding season), exponential (J-curve) and logistic (S-curve levelling at K).
ΔN = (b + i) − (d + e)population NDensity-dependentcompetition, predation,parasites and diseaseregulate N toward KDensity-independentweather, fire, flood,droughtcause sudden booms or crashes
What changes and limits a population: four processes change N; density-dependent factors regulate it toward K, while density-independent factors cause sudden changes.

What Is a Population? Size, Density, Distribution and Minimum Viable Size

1

A 3.0 km² marsh has 750 muskrats. What is the density?

2

Quadrat counts have mean 5 and variance 1. Classify the dispersion.

3

Give two reasons very small populations face extra risk of extinction.

Estimating Population Size: Quadrats, Transects and Mark-Recapture

1

M = 30, C = 25, R = 5. Find N by Lincoln-Petersen and by Chapman.

2

Five 0.25 m² quadrats contain 2, 3, 1, 2, 2 plants. Find the density.

3

Marked animals are easier for predators to catch. Is N over- or underestimated?

Fecundity, Mortality, Life Tables and Survivorship Curves

1

Fecundity or fertility: the number of eggs a hen actually laid this year?

2

n₀ = 200, n₁ = 50. Find l₁ and q₀.

3

lₓmₓ values are 0, 0.5, 0.4, 0.2. Find R₀ and interpret.

4

Which survivorship type: most deaths in old age?

Measuring Population Change: Births, Deaths, Immigration and Emigration

1

N = 500; b = 80, d = 60, i = 10, e = 30. Find ΔN and cgr.

2

A population grows from 1250 to 1400 in a year. Find cgr.

3

What is environmental resistance?

Geometric and Exponential Growth Models

1

N₀ = 400, λ = 1.5. Find N₃.

2

r = 0.07 per year. Find the doubling time.

3

A culture grows from 1000 to 8000 cells in 3 hours. Find r.

Logistic Growth and Carrying Capacity

1

r = 0.5, K = 600. Find dN/dt at N = 200.

2

For the same population, what is the maximum growth rate and where?

3

K = 1000, N₀ = 100, r = 0.4. Find N after 5 years.

Limiting Factors: Density-Dependent and Density-Independent

1

Density-dependent or independent: (a) an early frost; (b) competition for nest sites.

2

b = 0.5 − 0.001N and d = 0.1 + 0.001N. Find K.

3

What did the Lake 226 experiment show?

Life-History Strategies: r-Selection and K-Selection

1

Classify: matures at 4 years, one young every 2 years, long parental care.

2

Which strategy usually recovers faster after a crash, and why?

3

Semelparous or iteroparous: a chinook salmon? A moose?

Competition, Niches and Resource Partitioning

1

State the competitive exclusion principle.

2

In Connell's study, why was Chthamalus absent low on the rocks?

3

Give an example of resource partitioning.

Predation, Herbivory and Defence Mechanisms

1

Batesian or Müllerian: a stingless hoverfly with wasp stripes?

2

Name the defence: skunk spray; snowshoe hare's white coat.

3

Why are sea otters called a keystone species?

Symbiosis: Mutualism, Commensalism and Parasitism

1

Give the symbols for mutualism, commensalism and parasitism.

2

Which host is the intermediate host of the meningeal worm?

3

How does a parasitoid differ from a typical parasite?

Investigation: Modelling Predator-Prey and Host-Parasite Populations

1

r = 0.5, a = 0.01, b = 0.2, m = 0.4. Find the Lotka-Volterra equilibrium.

2

Why do predator peaks lag prey peaks?

3

Give one limitation of the Lotka-Volterra model.

Human Population Growth and the Demographic Transition

1

CBR = 18, CDR = 6. Find the rate of natural increase and doubling time.

2

Which stage of the demographic transition has falling death rates but high birth rates?

3

Why does Canada's population usually grow despite a TFR of about 1.25?

Consumption, Technology and the Ecological Footprint

1

A country's overshoot day is day 73. How many Earths would its lifestyle need?

2

P rises 10% and A rises 10%. What change in T keeps I constant?

3

What is the rebound effect?

Feeding a Growing Population: Canadian Technologies and Projects

1

Output or outcome: 500 tonnes of grain delivered?

2

Name two Canadian crop innovations and what each did.

3

Give two criteria for judging a food-security project's effectiveness.

Managing Populations: Indigenous Knowledge, Sustainable Harvests and Careers

1

r = 0.6, K = 10 000. Find the MSY.

2

Why is harvesting at exactly MSY risky?

3

Give one example of Indigenous knowledge or co-management helping sustain a population.

Just for fun

Population dynamics in one breath: everything grows exponentially until it doesn't, and the interesting biology is in the "doesn't".

Check your understanding

Quiz

1.

A 2.0 ha meadow (20 000 m²) has a density of 6 plants/m². The population is:

2.

In a mark-recapture study, M = 40, C = 50 and R = 10. The Lincoln-Petersen estimate is:

3.

A cohort has R₀ = 0.7. The population is:

4.

A population with r = 0.035 per year doubles in about:

5.

Logistic growth is fastest when:

6.

Which is density-independent?

7.

Two species competing for exactly the same resources cannot coexist indefinitely. This is:

8.

Ticks on a moose are an example of:

9.

In 2026, Earth Overshoot Day fell on July 30. Humanity used about:

10.

Maximum sustainable yield in the logistic model equals:

For parents and teachers

How to use the results: each section of this review matches one lesson. Revisit the lesson that matches the kind of mistake:

  • Density units, crude versus ecological density, dispersion and the variance-to-mean ratio, minimum viable population → What Is a Population? Size, Density, Distribution and Minimum Viable Size.
  • Quadrat scaling, edge rules, Lincoln-Petersen or Chapman arithmetic, direction of bias → Estimating Population Size: Quadrats, Transects and Mark-Recapture.
  • Fecundity versus fertility, lₓ, dₓ, qₓ, R₀, survivorship types and log scales → Fecundity, Mortality, Life Tables and Survivorship Curves.
  • ΔN signs, growth rate versus per capita growth rate, rates per 1000 → Measuring Population Change: Births, Deaths, Immigration and Emigration.
  • λ versus r, Nₜ = N₀λᵗ and N₀eʳᵗ, doubling time, logarithms → Geometric and Exponential Growth Models.
  • Logistic rates, K/2, the N(t) formula, overshoot → Logistic Growth and Carrying Capacity.
  • Classifying factors, finding K from birth and death equations, Liebig and Shelford → Limiting Factors: Density-Dependent and Density-Independent.
  • r- versus K-selection, semelparity, recovery times → Life-History Strategies: r-Selection and K-Selection.
  • Competitive exclusion, fundamental versus realized niche, partitioning → Competition, Niches and Resource Partitioning.
  • Defence types, Batesian versus Müllerian mimicry, keystone species, functional response → Predation, Herbivory and Defence Mechanisms.
  • + / − / 0 classification, host types, parasitoids → Symbiosis: Mutualism, Commensalism and Parasitism.
  • Lotka-Volterra terms and equilibria, spreadsheet steps, model limitations → Investigation: Modelling Predator-Prey and Host-Parasite Populations.
  • Rates of natural increase, demographic transition stages, age pyramids, current figures → Human Population Growth and the Demographic Transition.
  • Overshoot-day arithmetic, I = P × A × T, rebound effect → Consumption, Technology and the Ecological Footprint.
  • Outputs versus outcomes, evaluating Canadian initiatives, judging sources → Feeding a Growing Population: Canadian Technologies and Projects.
  • MSY and harvest stability, the cod collapse, Indigenous knowledge and co-management, careers → Managing Populations: Indigenous Knowledge, Sustainable Harvests and Careers.

Tip: many university first-year biology and environmental science courses begin ecology with exactly these models, so time spent mastering them now pays off.