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3.8.5Additional lessons

Population Growth Curves: Skills — IB Biology HL Revision Notes & Topical Questions

5 min read 5 parts Lesson 14 of 101

📚 IB Biology HL Hub / Topical Revision
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Part 1 of 5The Sigmoid Curve

3.8.5 Population Growth Curves: Skills

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
  • The graph steepens because the number of reproducing individuals increases with each generation.
Slowing growth
  • Density-dependent factors such as food shortage and disease act more strongly as the numbers climb.
Carrying capacity
  • The plateau marks the limit, and small fluctuations around it reflect changes in resources.
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
  • The slope of the line at any time gives the growth rate, calculated as change in population divided by change in time.
Percentage change
  • Subtract the starting value from the final value, divide by the starting value, and multiply by 100.
Log scale
  • On a logarithmic axis the exponential phase appears as a straight line, which makes the growth rate easier to compare.
Predictions
  • Extending the plateau gives an estimate of the carrying capacity of the habitat.
PhaseBirth rate vs death rateGrowth
LagBirth slightly higherSlow
ExponentialBirth much higherRapid
TransitionalGap narrowsSlowing
PlateauEqualNone

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.

  1. Growth rate = change in population ÷ change in time = (500 − 200) ÷ (7 − 2).
  2. 300 ÷ 5 = 60 cells per day.
  3. 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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