Biology • Year 11 • Module 4 • Lesson 7
Population Growth — Exponential, Logistic and Carrying Capacity
Apply population growth concepts to real data, graph analysis and new ecological scenarios.
1. Interpret rabbit population data (South Australian region, 1930–1960)
The table below shows estimated European rabbit numbers in a South Australian region. Study the data carefully, then answer the questions. 10 marks
| Year | 1930 | 1935 | 1940 | 1945 | 1950 | 1952 | 1955 | 1960 |
|---|---|---|---|---|---|---|---|---|
| Population (millions) | 2 | 15 | 60 | 120 | 180 | 20 | 45 | 70 |
1.1 Describe the growth pattern from 1930 to 1950. Is this exponential or logistic growth? Justify your answer using at least two specific data points from the table. 3 marks
1.2 The population dropped from 180 million (1950) to 20 million (1952). Calculate the percentage decrease and identify the event responsible. State whether this represents a density-dependent or density-independent factor; justify your answer. 3 marks
1.3 Describe the growth pattern from 1952 to 1960. What does this suggest about the new carrying capacity compared to before 1952? 2 marks
1.4 Suggest two density-dependent factors that would have limited rabbit recovery between 1952 and 1960. 2 marks
2. Interpret graph — bacterial culture growth over time
The graph below shows the growth of a bacterial population in a closed culture flask over 24 hours. Nutrients were unlimited for the first 12 hours, then a metabolic waste product began accumulating. 6 marks
Figure 2. Bacterial population growth over 24 hours in a closed culture flask. K ≈ 800 million cells.
2.1 Describe the shape of the growth curve from 0 to 12 hours and the shape from 12 to 24 hours. Use the correct biological terms for each phase. 2 marks
2.2 Explain why growth slows after 12 hours, using the concept of carrying capacity and limiting factors. 2 marks
2.3 Would the limiting factor operating after 12 hours be density-dependent or density-independent? Justify your answer. 2 marks
3. Apply to a new scenario — koala population after bushfire
A koala population in a eucalypt forest has reached carrying capacity at K = 200 individuals. A severe bushfire destroys 80% of the forest. 8 marks
3.1 Is the bushfire a density-dependent or density-independent factor? Explain your reasoning. 2 marks
3.2 Predict the short-term impact on the koala population (within the first year). Estimate the new population size, showing your reasoning. 2 marks
3.3 As the forest regenerates over 10 years, what type of population growth curve would you expect the koalas to show, and why? Explain what happens to K over the same period. 2 marks
3.4 Once the forest has fully regenerated, what density-dependent factors would slow koala population growth as it approaches the new K? Name two specific factors relevant to koalas. 2 marks
Q1 — Rabbit population data (10 marks)
1.1 (3 marks) Exponential growth from 1930 to 1950. The population increased from 2 million to 180 million in 20 years — a 90-fold increase [1]. The rate of increase accelerated over time: from 2 to 15 million (a gain of 13 million in 5 years, 1930–1935) up to 120 to 180 million (a gain of 60 million in 5 years, 1945–1950) [1]. This acceleration, where the increment per unit time increases proportionally with population size, is the defining characteristic of exponential growth [1].
1.2 (3 marks) Percentage decrease = (180 − 20) ÷ 180 × 100 = 88.9% [1]. The event was the introduction of the myxoma virus (myxomatosis) in 1950–1952 [1]. This was initially a density-independent factor because the disease spread through mosquito vectors regardless of local rabbit density, killing animals across the entire range. However, it became partly density-dependent over time because transmission is higher where rabbits are more concentrated [1]. Accept either category with a clear justification.
1.3 (2 marks) Logistic growth from 1952 to 1960 — the population recovered from 20 to 70 million but the growth rate slowed, suggesting an S-curve approaching a new carrying capacity [1]. The new K (estimated ~70–100 million) is substantially lower than before 1952 (old K ~180 million) because myxomatosis remains endemic as a permanent density-dependent regulator [1].
1.4 (2 marks) Any two: food competition with livestock (sheep, cattle) and native herbivores (kangaroos) [1]; disease (myxomatosis or RHDV) — transmission increases as density rises [1]; predation by foxes, cats and dingoes [1]. Award 1 mark each, maximum 2.
Q2 — Bacterial growth graph (6 marks)
2.1 (2 marks) From 0 to 12 hours: exponential (J-shaped) growth — the population increases at an accelerating rate, doubling at regular intervals [1]. From 12 to 24 hours: logistic growth levelling to a plateau near K — the growth rate slows progressively until the population stabilises around 800 million (the S-curve plateau) [1].
2.2 (2 marks) After 12 hours, accumulating metabolic waste acts as a limiting factor. As waste concentration increases with population density, it becomes harder for bacteria to survive and reproduce, reducing the net growth rate [1]. Growth stops when birth rate ≈ death rate, which is the carrying capacity K (~800 million cells for this flask’s conditions) [1].
2.3 (2 marks) Density-dependent. Waste accumulates proportionally to the number of bacteria producing it — the more bacteria present, the faster waste builds up and the more intensely it limits growth [1]. Because the intensity of the limiting factor increases with population density, it is density-dependent [1].
Q3 — Koala after bushfire (8 marks)
3.1 (2 marks) Density-independent [1]. A bushfire destroys habitat and kills organisms regardless of how many koalas are present — a population of 10 koalas and a population of 200 koalas in the same fire zone both suffer equivalent proportional destruction. The intensity of the factor does not increase with population density [1].
3.2 (2 marks) The bushfire destroys 80% of the forest habitat, so it will reduce K by approximately 80% (from 200 to ~40 individuals). The koala population would crash to approximately 40 individuals in the short term [1]. The actual loss may be higher due to direct mortality from fire and starvation as surviving koalas compete for the remaining 20% of forest [1]. Accept any estimate ≈20–50 with appropriate reasoning.
3.3 (2 marks) As the forest regenerates, koalas would initially show exponential growth because density-dependent factors (food competition, territorial conflict) would be temporarily reduced due to the low population size [1]. K would increase progressively as forest area recovers, eventually returning toward 200 (or possibly a new value depending on the extent of regeneration), producing an S-curve as the population approaches the recovering K [1].
3.4 (2 marks) Any two relevant factors: food availability — competition for eucalyptus leaves intensifies as koala numbers rise in the recovering forest [1]; territorial conflict / nesting tree availability — koalas are territorial and fight for home-range trees, limiting density [1]; disease (e.g. chlamydia) — spreads more easily at higher densities [1]. Award 1 mark each for two named and relevant density-dependent factors.