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Year 12 Science

Population Ecology

Understand how populations grow, what limits their size, and how species interact -- from exponential growth curves to predator-prey cycles and life history strategies.

Population Growth Models

Ecologists use mathematical models to describe how populations change over time. The two primary models are exponential growth (unlimited resources) and logistic growth (limited resources with a carrying capacity).

Exponential Growth (J-curve)

dN/dt = rN

Population grows at a constant rate proportional to its size.

Occurs when resources are unlimited (e.g., bacteria in fresh medium)

Logistic Growth (S-curve)

dN/dt = rN(K-N)/K

Growth slows as population approaches carrying capacity (K).

Levels off at K due to limiting factors

Variables: N = population size, t = time, r = intrinsic rate of natural increase (per capita growth rate), K = carrying capacity (maximum sustainable population).

Limiting Factors and Carrying Capacity

The carrying capacity (K) of an environment is the maximum population size that can be sustained indefinitely. It is determined by limiting factors, which can be density-dependent or density-independent.

Density-Dependent Factors

Impact increases as population density increases:

  • • Competition for food and space
  • • Predation (more prey attracts predators)
  • • Disease (spreads faster in dense populations)
  • • Waste accumulation

Density-Independent Factors

Impact is the same regardless of population density:

  • • Natural disasters (bushfires, floods)
  • • Extreme weather events
  • • Habitat destruction
  • • Seasonal changes

Predator-prey dynamics: Predator and prey populations cycle together -- as prey increases, predators increase, causing prey to decline, which then causes predators to decline. This produces oscillating population curves with a time lag.

r-Selected vs K-Selected Species

Species adopt different life history strategies depending on their environment. These are modelled as a continuum between r-selected (maximise reproduction rate) and K-selected (maximise competitive ability near carrying capacity).

r-Selected Species

  • • Many offspring, little parental care
  • • Small body size, short lifespan
  • • Early maturity
  • • High mortality rate in young
  • • Colonise unstable environments
  • • Examples: insects, mice, weeds, bacteria

K-Selected Species

  • • Few offspring, extensive parental care
  • • Large body size, long lifespan
  • • Late maturity
  • • Low mortality rate (high survival)
  • • Thrive in stable environments
  • • Examples: elephants, whales, humans

Australian example: Kangaroos are intermediate -- they have relatively few young with significant parental care, but can also reproduce quickly when conditions are favourable (embryonic diapause allows delayed development).

Key Vocabulary

Carrying Capacity (K)

The maximum population size an environment can sustain indefinitely given available resources, space, and other environmental conditions.

Biotic Potential (r)

The maximum per capita rate of increase of a population under ideal conditions with unlimited resources. Also called the intrinsic rate of natural increase.

Intraspecific Competition

Competition between individuals of the same species for limited resources. This is a key density-dependent factor that regulates population size.

Population Overshoot

When a population temporarily exceeds its carrying capacity, often followed by a rapid decline (crash) due to resource depletion.

Worked Examples

1

A population of 500 organisms has a birth rate of 40 per year and a death rate of 15 per year. Calculate the per capita growth rate (r).

Step 1: Net growth = births - deaths = 40 - 15 = 25 individuals per year.

Step 2: Per capita growth rate: r = net growth / N = 25 / 500 = 0.05 per year.

Answer: r = 0.05 per year (or 5% growth rate per year).

2

Using the logistic model, calculate the population growth rate when N = 200, K = 1000, and r = 0.1 per year.

Step 1: Use dN/dt = rN(K - N)/K.

Step 2: dN/dt = 0.1 × 200 × (1000 - 200)/1000 = 0.1 × 200 × 800/1000.

Step 3: dN/dt = 0.1 × 200 × 0.8 = 16 individuals per year.

Answer: The population is growing at 16 individuals per year. Note this is less than the 20 predicted by exponential growth (rN = 20) because resources are already partially used.

3

Explain why predator and prey populations show oscillating cycles.

Step 1: When prey is abundant, predators have plentiful food, so predator numbers increase.

Step 2: More predators consume more prey, causing the prey population to decline.

Step 3: With less prey available, predators face food shortage and their numbers decline.

Step 4: With fewer predators, prey can recover, and the cycle begins again. There is a time lag between changes in prey and predator populations, which produces the oscillation.

Knowledge Check

Select the correct answer for each question. Click "Check Answer" to see if you are right.

Question 1

In the logistic growth model, growth rate is highest when the population is:

Question 2

Disease spreading through a crowded population is an example of a:

Question 3

Which of the following is characteristic of a K-selected species?

Question 4

A bushfire destroying a habitat is an example of a:

Question 5

In the logistic growth equation dN/dt = rN(K-N)/K, when N = K, the growth rate is:

Key Concepts Summary

Year 12: Thermochemistry Year 12: Biodiversity