Unit 5: Population Dynamics — Practice Quiz (AS Learning)

Topic 5.1 — Growth Models

Question 1

Exponential population growth follows the equation:

dN/dt = rN(K−N)/K
dN/dt = rN
dN/dt = K
N = N₀ − rt

Solution: Exponential: dN/dt = rN, with closed form N_t = N₀e^(rt) — J-shape, unlimited resources. Logistic uses K and produces an S-shape.

Question 2

A bacterial culture has N₀ = 100, r = 0.3 hr⁻¹. Approximately how many bacteria after 10 hours of exponential growth? (e^3 ≈ 20)

Solution: N = 100 × e^(0.3×10) = 100 × e^3 ≈ 100 × 20 = 2000 bacteria.

Question 3

In the logistic model, the per-capita growth rate is greatest when:

N = K (population at carrying capacity)
N is small relative to K
N = K/2
N = 0

Solution: Per-capita growth (1/N · dN/dt) = r(K−N)/K is maximum when N is small (close to r). Total dN/dt is greatest at N = K/2 (steepest slope of S-curve).

Question 4

Carrying capacity (K) represents:

The minimum population size
The maximum population size that an environment can sustain indefinitely
The intrinsic rate of increase
The biotic potential

Solution: K is the long-term equilibrium imposed by limiting resources (food, water, space, predators). Populations may overshoot and crash, then oscillate around K.

Topic 5.2 — r vs K Selection

Question 5

Which is most characteristic of an r-selected species?

Few large offspring with extensive parental care
Many small offspring with high mortality (Type III curve)
Long lifespan and late maturity
Stable, predictable habitats

Solution: r-selected: high r, many small young, no/little parental care, fast maturation, short life, Type III survivorship (e.g., insects, weeds, frogs). K-selected: opposite (e.g., elephants, whales, humans).

Question 6

A Type I survivorship curve indicates:

High infant mortality, few survive to old age
Constant probability of death at all ages
Low juvenile mortality, most deaths late in life

Solution: Type I (e.g., humans, large mammals): low mortality until old age. Type II (e.g., birds, rodents): roughly constant. Type III (e.g., fish, oysters): most die young; few make it to adulthood.

Topic 5.3 — Predator-Prey & Succession

Question 7

In classic Canada lynx and snowshoe hare data, the lynx population peaks ___ the hare population.

Slightly before
Slightly after (lagged)
Exactly synchronously
Independently

Solution: Lynx (predator) lag behind hare (prey) by ~1–2 years. Cycle period ~10 years. As hare numbers rise, lynx food supply increases, lynx reproduce; lynx then over-consume hares, hares crash, lynx crash, hares recover.

Question 8

Primary succession differs from secondary succession because primary succession:

Begins on bare rock with no soil (e.g., new volcanic island)
Occurs only in oceans
Starts after a forest fire
Excludes lichens and mosses

Solution: Primary succession: lifeless substrate (rock, glacial till, lava). Pioneer species (lichens, mosses) build soil; succession to grasses, shrubs, trees → climax community. Secondary: after disturbance (fire, logging) where soil remains; faster.

Topic 5.4 — Biodiversity & Human Impact

Question 9

Calculate Simpson's Index of Diversity D = 1 − Σ(p_i)² for a community: 50% sp. A, 30% sp. B, 20% sp. C.

Solution: Σp² = 0.5² + 0.3² + 0.2² = 0.25 + 0.09 + 0.04 = 0.38. D = 1 − 0.38 = 0.62. Higher D = more diversity (max approaches 1).

Question 10

A density-DEPENDENT regulator of population is:

Hurricane
Forest fire
Disease transmission
Drought

Solution: Density-dependent factors intensify with crowding: disease, predation, intraspecific competition, parasitism. Density-independent factors (weather, fire, volcanic eruption) act regardless of population size.

Question 11

A doubling time of 35 years for human population implies an annual growth rate r ≈:

0.2% per year
2% per year
5% per year
10% per year

Solution: Rule of 70: doubling time ≈ 70/r%. r ≈ 70/35 = 2% per year. (Derived from N₀e^(rt) = 2N₀ → t = ln 2 / r ≈ 0.693/r.)

Question 12

Ecological footprint measures:

Number of species in a community
The biologically productive area required to support a person/population's resource use and absorb waste
Population density
Carrying capacity

Solution: Ecological footprint = global hectares (gha) needed per capita. Canada averages ~7–8 gha/person; biocapacity ~1.6 gha/person globally. Indicator of sustainability vs overshoot.