3.8.5Additional lessons
Population Growth Curves: Skills — IB Biology HL Revision Notes & Topical Questions
5 min read 5 parts Lesson 14 of 101
Curriculum Equation Key قوانين الرقم الهيدروجيني والاتزان الأيوني - pH & Acid-Base Equilibrium FormulasFast Exam Solution
pH = -log[H⁺] | pOH = -log[OH⁻] | pH + pOH = 14 | [H⁺][OH⁻] = 10⁻¹⁴
Word Equation & Conditions: الرقم الهيدروجيني = -لوغاريتم تركيز أيون الهيدروجين | pH + pOH = 14
Location & Specifications: الاتزان الأيوني، كيمياء 3 ثانوي، التحصيلي، و AP Chemistry.
Part 1 of 5The Sigmoid Curve
A population entering a new habitat typically shows an S-shaped curve.
1
Lag phase: a few individuals colonise a new habitat and numbers rise slowly because there are few breeding adults.
2
Exponential phase: resources are plentiful, birth rate is far greater than death rate, and the population doubles at regular intervals.
3
Transitional phase: resources become scarcer and competition increases, so birth rate falls and death rate rises, and growth slows.
4
Plateau phase: birth rate equals death rate, and population size stays around the carrying capacity set by the environment.
Part 2 of 5Explaining Each Phase
Exponential growth
- Exponential growth The graph steepens because the number of reproducing individuals increases with each generation.
Slowing growth
- Slowing growth Density-dependent factors such as food shortage and disease act more strongly as the numbers climb.
Carrying capacity
- Carrying capacity The plateau marks the limit, and small fluctuations around it reflect changes in resources.
Overshoot and crash
- Overshoot and crash Some populations rise above the carrying capacity and then fall sharply when resources are used up.
Part 3 of 5Reading and Using Graphs
Reading and Using Graphs
Growth rate
- Growth rate The slope of the line at any time gives the growth rate, calculated as change in population divided by change in time.
Percentage change
- Percentage change Subtract the starting value from the final value, divide by the starting value, and multiply by 100.
Log scale
- Log scale On a logarithmic axis the exponential phase appears as a straight line, which makes the growth rate easier to compare.
Predictions
- Predictions Extending the plateau gives an estimate of the carrying capacity of the habitat.
| Phase | Birth rate vs death rate | Growth |
|---|---|---|
| Lag | Birth slightly higher | Slow |
| Exponential | Birth much higher | Rapid |
| Transitional | Gap narrows | Slowing |
| Plateau | Equal | None |
Part 4 of 5Worked Example
Question
- A yeast culture has 200 cells per unit volume at day 2 and 500 at day 7, during the exponential phase.
- Calculate the mean growth rate and the percentage change.
- Growth rate = change in population ÷ change in time = (500 − 200) ÷ (7 − 2).
- 300 ÷ 5 = 60 cells per day.
- Percentage change = (500 − 200) ÷ 200 × 100 = 150%.
Answer The mean growth rate is 60 cells per day and the population increased by 150%.
Part 5 of 5Exam Checklist & Tips
3.8.5 – Key Points for the Exam
- Sigmoid curve S-shaped graph of population growth over time.
- Exponential growth Growth in which the population multiplies by a constant factor per time period.
- Carrying capacity The population size at which the plateau occurs.
- Growth rate The change in population size per unit time.
- Lag phase The initial slow phase of growth.
Common Mistakes
- Saying the population stops reproducing at the plateau; births continue but equal deaths.
- Assuming growth stays exponential for ever, when the phase ends once resources become limiting.
- Reading the carrying capacity from the highest point of a temporary overshoot.
- Forgetting to divide by the starting value when calculating percentage change.
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