The big idea: When a few organisms first move into a new habitat with plenty of food and space, the population grows quickly.
But no habitat can support unlimited numbers. Eventually limiting factors — shortage of food, water, space, or the spread of disease — slow the growth down.
The population then levels off at the largest size the environment can support. This maximum sustainable size is the carrying capacity.
The sigmoid (S-shaped) growth curve: a slow lag start, a rapid exponential phase, then a plateau at the carrying capacity (K) where births balance deaths.
Interactive diagram
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- Population
- All the organisms of the same species living in the same area at the same time.
- Carrying capacity (K)
- The maximum population size of a species that a habitat can support over a long period, given its resources.
- Limiting factor
- Any factor that slows or stops a population from growing — for example a shortage of food, water or space, or the spread of disease.
- Sigmoid (S-shaped) curve
- The shape of a graph of population size against time as a population grows up to its carrying capacity: a slow start, a rapid rise, then a plateau.
- Exponential growth
- Rapid growth in which the population increases by ever-larger amounts because resources are plentiful and there are few limiting factors.
Why it levels off: A population can only grow while births outnumber deaths.
As numbers rise, individuals compete for the same limited food, water and space, and disease spreads more easily. Deaths rise and births fall.
When births equal deaths, the population stops growing — it has reached its carrying capacity (K).
Plot population size against time and you get the sigmoid (S-shaped) curve.
It is easiest to read in four parts: a slow lag start, a steep exponential rise, a transitional slowing, and a flat plateau at the carrying capacity.
| Phase of the curve | What the population is doing | Why |
|---|---|---|
| Lag phase | Grows slowly at first | Few individuals are present, so few are reproducing |
| Exponential phase | Grows rapidly | Plenty of resources and space; few limiting factors, so births greatly outnumber deaths |
| Transitional phase | Growth slows down | Limiting factors start to bite as the population gets crowded |
| Plateau phase | Levels off and stays roughly steady | Births ≈ deaths; the population has reached the carrying capacity (K) |
The exponential phase — why it is so fast: Early on there is plenty of food, water and space and few limiting factors.
Almost every individual survives and reproduces, so the population increases by ever-larger amounts — this is exponential growth.
It cannot last: the faster the population grows, the sooner resources start to run short.
As the population nears the carrying capacity, limiting factors slow growth — the exponential rise flattens into the plateau at K.
Interactive diagram
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The plateau — what makes growth stop: As the population becomes crowded, limiting factors take effect: there is not enough food, water or space for everyone, waste builds up, disease spreads, and predators may increase.
Deaths rise until births ≈ deaths, and the curve flattens into the plateau at the carrying capacity (K).
So if an exam labels the flat top of the curve as region X and asks for the factor causing it, the answer is a limiting factor such as competition for food or limited space.
Two kinds of limiting factor: Limiting factors come in two types, and exams love the difference.
A density-dependent factor acts more strongly when the population is crowded — for example competition, disease and predation get worse as numbers rise.
A density-independent factor acts regardless of population density — for example a drought, fire, flood or extreme cold kills a similar proportion whether the population is large or small.
| Type of limiting factor | Does its effect depend on how crowded the population is? | Examples |
|---|---|---|
| Density-dependent | Yes — the effect gets STRONGER as the population gets denser | Competition for food, water or space; disease spread; predation; build-up of waste |
| Density-independent | No — it acts the SAME whatever the population density | Drought, flood, fire, extreme cold, a storm or other extreme weather |
Density-dependent
- Effect gets stronger as the population gets denser
- Competition for food, water and space
- Disease spreads faster in crowds
- Predation and waste build-up
Density-independent
- Effect is the same whatever the density
- Drought, flood or fire
- Extreme cold or a storm
- Hits a large and a small population alike
A memory hook: Density-DEPENDENT depends on the crowd — competition and disease get worse the more individuals there are.
Density-INDEPENDENT ignores the crowd — a drought or a frost does not care how many organisms are present.
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How this is tested: On Paper 1A a multiple-choice question often shows a population growth curve with a region labelled (such as region X) and asks you to identify the factor causing it — for the flat plateau, that is a limiting factor such as competition for food.
A Paper 1B data question can give a graph or table of a population (for example duckweed grown at different temperatures) and ask you to explain how an abiotic factor such as temperature influences the growth — read the data, then link the factor to the growth rate.
You may also be asked to identify a density-independent factor limiting a named population (such as a drought for kangaroos).
IB-style question — explain how temperature affects population growth
Duckweed (a small floating plant) is grown in identical dishes at 15 °C, 25 °C and 35 °C. After two weeks the population is largest at 25 °C, smaller at 15 °C and smallest at 35 °C. Explain how temperature influences the population growth of the duckweed. [2]
How to score both marks
- Read the data first. Population growth is fastest / greatest at 25 °C, and lower at the cooler (15 °C) and hotter (35 °C) temperatures — so there is an optimum temperature for growth.
- Explain using the factor. Temperature affects the rate of enzyme-controlled reactions (such as photosynthesis). Near the optimum (25 °C) these reactions are fastest, so duckweed reproduces quickly and the population grows most; when it is too cold reactions are slow, and when it is too hot enzymes start to denature, so growth is reduced. (Mark 1: identifies an optimum / 25 °C gives most growth. Mark 2: links temperature to rate of reactions / reproduction, with too cold = slow and too hot = denatures.)
Final answer
Growth is greatest at the optimum temperature (25 °C) and lower above and below it: temperature controls the rate of enzyme reactions such as photosynthesis, so reproduction (and population growth) is fastest near the optimum, slow when too cold, and reduced when too hot because enzymes denature.
✓ Why this scores full marks: It does both jobs an 'explain' wants: it uses the data (an optimum at 25 °C, less at 15 °C and 35 °C) and gives the reason (temperature changes the rate of enzyme-controlled reactions / reproduction).
Just describing the numbers without a reason would only be a 'describe', not an 'explain'.
| Phase of the curve | What the population is doing | Why |
|---|---|---|
| Lag phase | Grows slowly at first | Few individuals are present, so few are reproducing |
| Exponential phase | Grows rapidly | Plenty of resources and space; few limiting factors, so births greatly outnumber deaths |
| Transitional phase | Growth slows down | Limiting factors start to bite as the population gets crowded |
| Plateau phase | Levels off and stays roughly steady | Births ≈ deaths; the population has reached the carrying capacity (K) |