Plot almost any population against time and you get one of two shapes: a J or an S. The J means nothing is holding the population back yet. The S means the environment has started to push back. Learning to name the phases, and to say why each phase looks the way it does, is worth a lot of marks.
📚 What you need to know
Carrying capacity (K) is the largest population an environment can support over the long term.
A J-curve shows exponential growth with no limiting factors, usually ending in a crash.
An S-curve shows growth in a resource-limited environment, levelling off at K.
An overshoot happens when a population passes K before the limiting factors catch up.
Growth rate is worked out from births, deaths, immigration and emigration.
Carrying capacity in plain words
Carrying capacity is not the number of animals you can physically squeeze into a field. It is the number the field can keep alive year after year without being damaged. Push past it and the resources run down, so the ceiling itself drops.
If that total is positive the population grows, if it is negative it shrinks, and if it is zero the population is stable. Every limiting factor on the previous page works by changing one of those four numbers.
The J-curve: growth with the brakes off
A J-curve appears when resources look unlimited — a species arriving in a new habitat, bacteria in fresh nutrient broth, an insect pest reaching a new crop. Growth accelerates because the more individuals there are, the more offspring get produced, and there is nothing to stop them.
The steep part is not “fast growth” but growth that keeps getting faster, because each new individual adds to the breeding stock.
🧩 Describing the J-curve in an exam
Lag phase. Few individuals, so few offspring. Growth is slow even though nothing is limiting it.
Exponential phase. Numbers double in a fixed time. Resources are still plentiful, so births far outnumber deaths.
Overshoot. The population climbs above K because the damage to resources takes time to be felt.
Crash. Food, space or oxygen runs out, or waste builds up, and death rate rises sharply.
The S-curve: growth against a ceiling
Most real populations show an S-curve, because resources are limited from the start. Growth slows smoothly as the population gets closer to K instead of hitting a wall.
The plateau is never a flat line in real data. Numbers rise and fall around K as limiting factors vary from year to year.
J or S? A quick comparison
Feature
J-curve
S-curve
Resources
Effectively unlimited at first
Limited from the start
Limiting factors
Absent until the very end
Increase steadily as density rises
Ending
Overshoot then sudden crash
Levels off and fluctuates around K
Typical species
Fast-breeding colonisers and pests
Established species in a mature ecosystem
Number of phases
Three: lag, exponential, crash
Four: lag, exponential, transitional, plateau
If the graph flattens, it is an S. If it goes almost vertical and then falls off a cliff, it is a J. Do not overthink it.
Worked examples
WORKED EXAMPLE
Calculating a growth rate
A population of deer on an island numbers 8200 at the start of a year. During that year there are 1120 births, 460 deaths, 30 animals brought in by conservationists and 12 animals removed. Calculate the population at the end of the year and the percentage growth rate.
Step 1: work out the change(1120 + 30) − (460 + 12) = 1150 − 472 = 678Step 2: add it to the starting number8200 + 678 = 8878Step 3: growth rate as a percentage(678 ÷ 8200) × 100 = 8.27%8878 deer, a growth rate of 8.3%immigration counts as a gain and emigration as a loss — do not ignore them
WORKED EXAMPLE
Explaining a plateau
A population of rabbits released onto grassland grows quickly for three years and then levels off. Explain the shape of the curve after year three. [4]
Step 1: name the phasethe population has reached the plateau phase at the carrying capacityStep 2: give the limiting factorsgrass becomes scarce, predators increase, disease spreads more easilyStep 3: link to births and deathsthese density-dependent factors lower the birth rate and raise the death ratebirths and deaths become roughly equal, so numbers stop risinga plateau answer is only complete when you mention births AND deaths
💡 Exam tip
Label the axes before you read a growth graph. Population size is nearly always on the y-axis and time on the x-axis.
“Exponential” means the rate of increase is rising, not just that numbers are rising. Say it that way.
Carrying capacity is a long-term ceiling, so use the phrase “can be supported over time”.
When you name a phase, add one reason for it. The name alone is usually only half the mark.
Overshoot questions want the idea of a delay: the damage is done before the population feels it.
Show your working in growth-rate calculations, and give units or a per cent sign.
⚠ Common mix-up
Saying the population stops growing “because K is reached”. That is the observation, not the explanation — name the limiting factors.
Drawing the plateau as a perfectly straight line. Real populations fluctuate around K.
Confusing the lag phase with slow growth caused by limiting factors. In the lag phase, growth is slow simply because there are few breeding individuals.
Thinking K is a fixed number for ever. If the environment is damaged, K falls.
Forgetting migration. Births and deaths are not the only ways a population changes.
Calling every steep curve exponential. Check whether the gradient itself is increasing.
Up next: Human Populations in Ecosystems — we are the one species that keeps moving its own ceiling, and that causes problems.
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