A population growth curve usually passes through lag, exponential, stationary and decline phases. The skill is to describe each stage with figures from the graph or table, then give a biological reason for the change.
It builds on reading graphs and on the cycling ideas in linking decomposition with nutrient recycling. It leads to explaining a limiting factor, and sits within nutrient cycles and populations.
How does the idea build up?
Start with a small population in a new, suitable environment.
- Lag phase: the count hardly changes. Organisms are adjusting, and few are reproducing yet.
- Exponential phase: reproduction is fast and resources are plentiful. The population increases by the same proportion in equal time intervals, such as doubling.
- Stationary phase: the count levels off. Food, space or oxygen become limited, or waste builds up, so births roughly equal deaths.
- Decline phase: deaths exceed births. Resources are exhausted or waste is toxic.
To describe a phase, give its time range and the start and end values.
Worked example
A student counts yeast cells in a sugar solution. The data are invented for practice.
| Time (h) | 0 | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 |
|---|---|---|---|---|---|---|---|---|---|
| Cells (×1000 per cm³) | 10 | 12 | 24 | 48 | 90 | 100 | 100 | 70 | 30 |
Question: Identify the phases, show the growth is exponential between 2 and 6 hours, and explain the level and the fall.
Step 1, lag: 0 to 2 h: the count rises only from 10 to 12 thousand.
Step 2, exponential: 2 to 6 h: 12 → 24 → 48. Each step of 2 h doubles the count (12 × 2 = 24, 24 × 2 = 48), so the population doubles every 2 hours.
Step 3, slowing: 6 to 8 h: the count rises from 48 to 90, a factor of about 1.9, just short of a doubling (48 × 2 = 96). From 8 to 10 h it adds only 10 more. Growth is slowing.
Step 4, stationary: 10 to 12 h: the count stays at 100 thousand.
Step 5, decline: 12 to 16 h: the count falls from 100 to 30 thousand.
Step 6, explain: as yeast grows it uses sugar and releases waste such as ethanol. Sugar becomes limiting and waste builds up, so growth slows and stops. Later, deaths exceed births and the count falls.
The cause of the decline here is probably sugar running out and waste building up. The data alone do not prove it, so a good answer says “likely”.
What mistake should I watch for?
Mistaken answer: “From 4 to 6 hours the population increases quickly, by 24 thousand, so it is exponential.”
A large increase is not the same as exponential growth. Exponential growth is a steady proportion, so check whether the count multiplies by the same factor each equal interval.
Corrected: “From 4 to 6 h the count rises from 24 to 48 thousand. That is a doubling, the same factor as from 2 to 4 h, so growth is exponential.”
Use ratios to test, not only differences.
Check yourself
1. In the table above, how many cells were there at 8 h, and what was the increase from 6 h?
Show answer
90 thousand per cm³ at 8 h. Increase = 90 − 48 = 42 thousand.
2. A population goes 5, 10, 20 (thousand) at equal time intervals. Is it growing exponentially? Give a reason.
Show answer
Yes. It doubles each interval (5 × 2 = 10, 10 × 2 = 20), so the proportion of growth is constant.
3. Suggest one reason a population enters the stationary phase.
Show answer
A resource such as food, space or oxygen becomes limited, or waste builds up, so births roughly equal deaths.
Where does this lead next?
Now practise turning a limit into a cause in explaining a limiting factor from data. The mixed practice set then combines all the phases.
If you want a teacher to check that your descriptions quote figures and your causes are precise, online one-to-one Biology tuition can review them with you.