IB Biology HLPopulations & CommunitiesPaper 1 & 2~11 min read
Population Growth Curves
Populations of every kind — seals, yeast, pond weed — tend to follow the same S–shaped path when they establish or recover. Three phases, one carrying capacity, and one clever trick with a log scale that proves growth is genuinely exponential.
📘 What you need to know
A sigmoid (S–shaped) growth curve has three phases: exponential, transition, plateau.
Exponential phase (also the logarithmic phase): no factors limit growth, so numbers and the rate of growth both increase.
Transition phase: limiting factors start to act, so the rate of growth slows — but the population is still increasing.
Plateau phase (also the stationary phase): death rate equals birth rate, growth stops, and this occurs at the carrying capacity.
Growth is exponential when the speed of growth is proportional to the number of individuals.
Plot population size on a logarithmic y axis against time on a non–logarithmic x axis: exponential growth appears as a straight line.
NOS: the sigmoid curve is an idealised graphical model. Few real populations follow it perfectly.
Yeast and duckweed can be used to model the curve in the lab.
The three phases
Antarctic fur seals were hunted heavily through the 1800s. After hunting stopped, the recovering population at Cape Shirreff traced almost exactly this curve between 1960 and the early 2000s.
Phase
Also called
What is happening
Exponential
Logarithmic phase
No factors limit growth. The number of individuals increases, and so does the rate of growth.
Transition
—
Limiting factors start to act: competition increases, predators are attracted to large prey populations. The rate of growth slows, though the population is still increasing.
Plateau
Stationary phase
Limiting factors cause the death rate to equal the birth rate, so growth stops. This occurs at the carrying capacity, and the population often fluctuates slightly around it.
Nature of science: an idealised model
Scientists use models to represent real world ideas, organisms, processes and systems that cannot easily be investigated directly. Models are useful for experimentation and testing predictions, but they are not perfect representations of biological systems.
The growth curve is a good example. It is genuinely useful for conceptualising the different stages in the growth of a population — but real ecosystems are complex, and many factors are at play in determining population size. There are few real–world situations where populations follow perfect sigmoid curves. The Antarctic fur seal population above is itself the warning: its recovery did not continue through the early 21st century, and climate change has since caused severe declines in many seal populations.
This is a lovely NOS point to have ready, because it works on almost any modelling question. A model is a deliberate simplification. It earns its place by making a system easier to think about and predict — not by being true in every detail.
Testing for exponential growth with a log scale
Growth is exponential when the speed of growth is proportional to the number of individuals. A population of 20 individuals will reproduce at twice the rate of a population of 10.
To test whether growth really is exponential, plot population size on a logarithmic y axis against time on a normal x axis. If growth is exponential, the plot comes out as a straight line.
Logarithmic scales are useful whenever a factor varies over several orders of magnitude — they let tens and millions be shown on the same easily readable axis.
“Orders of magnitude” refers to whether values are measured in tens, hundreds, thousands and so on.
The numbers on a logarithmic scale represent logarithms, or powers, of a base number.
On a log₁₀ scale the base is 10, so an axis value of 1 means 10, 2 means 100, and 3 means 1000.
Modelling the curve in the lab
Organisms that grow and reproduce quickly under laboratory conditions can be used to model the sigmoid growth curve. The two on the syllabus are yeast and duckweed.
🧩 Yeast: measuring turbidity
Grow the yeast in a broth culture after inoculating the nutrient broth.
As the yeast reproduce and the population grows, the suspension becomes progressively more turbid.
Turbidity is the cloudiness of a suspension — how much light can pass through it — so it acts as a measure of the number of cells.
Measure how much light passes through at fixed time intervals using a turbidity meter or colorimeter connected to a datalogger.
Plot the results as a population growth curve.
🧩 Duckweed: counting fronds
Place a small number of duckweed fronds in a petri dish of distilled water mixed with liquid fertiliser.
Put the dishes in a brightly lit location, but out of direct sunlight.
Record the number of fronds present after one week.
Repeat the count once a week for a total of six weeks, topping up with distilled water as needed.
Plot the results to show a population growth curve.
Duckweed is ideal because it reproduces quickly and asexually, and newly produced fronds (also called thalli) stay attached to the parent in clusters, which makes counting easy.
Worked examples
WE 1
Explaining the transition phase
Explain what is happening to a population during the transition phase of a sigmoid growth curve. (3 marks)
Point 1: limits appearLimiting factors start to act on the population, for example competition increases and predators are attracted to a large prey population.
Point 2: what slows
The rate of growth slows as a result.
Point 3: what does not
The population itself is still increasing — it has not stopped growing, it is simply growing more slowly.
Growth rate falls, population size still risesthe third point is where most marks are lost — do not say the population decreases
WE 2
Interpreting a log plot
A student plots bacterial numbers on a logarithmic y axis against time and obtains a straight line. What does this show, and why? (2 marks)
Point 1: the conclusion
The population is growing exponentially.
Point 2: the reason
On a logarithmic axis, each equal step upwards represents multiplying by the same factor. A constant multiplication per unit time plots as a straight line, which is exactly what exponential growth means: the speed of growth is proportional to the number of individuals.
A straight line on a log axis means exponential growthnote the x axis stays non–logarithmic — only y is log
WE 3
Evaluating the model
Suggest why real populations rarely follow a perfect sigmoid growth curve. (2 marks)
Point 1: it is a model
The sigmoid curve is an idealised graphical model, useful for conceptualising the stages of growth but not a perfect representation of a biological system.
Point 2: reality is messier
Real ecosystems are complex, with many factors determining population size, so populations may decline rather than remain at a plateau — as happened to Antarctic fur seals when climate change affected them.
Models simplify; real ecosystems do nota named example lifts a vague NOS answer into a marked one
💡 Exam tips
Learn all three phase names and their alternatives: logarithmic and stationary.
In the transition phase, the rate slows while the population still grows.
The plateau occurs at the carrying capacity, with slight fluctuation around it.
Define exponential growth as speed of growth proportional to number of individuals.
A log y axis turns exponential growth into a straight line — the x axis stays normal.
Have the NOS model point and one named example ready.
⚠ Common mistakes
Saying the population falls during the transition phase. It rises — just more slowly.
Saying nothing happens in the plateau phase. Births and deaths continue; they are simply equal.
Putting the log scale on the x axis. Population size goes on the log y axis.
Reading a log axis as if the gaps were equal steps. Each gap is a multiplication by ten.
Treating the sigmoid curve as a law of nature. It is a model, and real populations often deviate.
Forgetting the fertiliser or the weekly counts when describing the duckweed method.
Up next: Intraspecific Relationships. So far the limits have come from outside the species. Next we look at what happens between members of the same one — which turns out to be both the fiercest competition and the closest cooperation in nature.
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