Give a population unlimited food and space and it explodes. Give it a real environment and it slows down and levels off. Those two stories produce the two curves you have to know — the J and the S — and almost every population question comes back to one of them.
📚 What you need to know
Carrying capacity (K) is the maximum population size an environment can support over time.
A J-curve shows exponential growth with no limits, and usually ends in an overshoot and a crash.
An S-curve shows growth in a resource-limited environment, levelling off at K.
Density-dependent factors get stronger as the population gets denser: competition, predation, disease.
Density-independent factors hit the population regardless of its density: storms, fire, drought.
Density-dependent factors drive negative feedback, which pulls a population back towards K.
Carrying capacity in plain words
Every individual could in theory reproduce and add to the population. In practice, food runs short, shelter runs out, predators arrive and diseases spread. Carrying capacity is the point where those limits balance the reproduction, so the population stops growing.
It is not a fixed number carved into the landscape. A wet year with good grass raises it; a drought lowers it. That is why real populations wobble around K rather than sitting exactly on it.
Population change in a year
change = (births + immigration) − (deaths + emigration)
Two kinds of limiting factor
Type
How it behaves
Examples
Density-dependent
The denser the population, the harder it bites. These are the factors that regulate a population around K.
Competition for food, predation, disease and parasites
Density-independent
Hits the population just as hard whether it is crowded or sparse. It can knock numbers down but does not regulate them.
Storms, fire, flood, drought, extreme cold
Think about it from the organism’s point of view. A disease spreads faster when animals are packed together, so crowding makes it worse — density-dependent. A hailstorm flattens a field of seedlings whether there are ten of them or ten thousand — density-independent.
🧩 How negative feedback holds a population near K
Population rises above K.
Food per individual falls, competition rises, disease spreads more easily.
Deaths rise and births fall, so numbers drop back down.
Below K there is food to spare, so births rise again and numbers climb.
The result is a population that fluctuates around K instead of running away.
Negative feedback does not mean “bad”. It means the response works against the change, like a thermostat. Population goes up, the pressure pushing it down goes up too. That is stability, not decline.
The J-curve: growth with nothing in the way
Put a few organisms into an environment with unlimited resources and growth accelerates. Ten becomes twenty, twenty becomes forty, and the curve turns almost vertical. Nothing in the real world supplies unlimited resources for long, so a J-curve usually ends the same way: the population shoots past what the environment can support, resources collapse, and so does the population.
The lag phase is not a slow-growth phase. Doubling twelve organisms adds twelve; doubling twelve thousand adds twelve thousand. Same rate, very different picture.
The S-curve: growth that meets its limits
Most populations follow this one. Growth starts slowly, accelerates, then slows as resources run short, and finally levels off. The four phases have names and examiners use them, so learn them in order.
The transitional phase is where the answer usually lies: growth is still happening, but it is slowing because density-dependent factors have started to bite.
What is happening in each S-curve phase
Lag phase — few individuals, few births, so the total change is small.
Exponential phase — resources are still plentiful, limiting factors are weak, numbers accelerate.
Transitional phase — competition for food, space and light increases, so the rate of increase falls even though numbers are still rising.
Plateau phase — the population has reached K and fluctuates around it as limiting factors vary.
Watch the wording. “The population is decreasing” and “the rate of increase is decreasing” mean very different things. In the transitional phase the second one is true and the first one is not.
Worked examples
WORKED EXAMPLE
A deer population of 2 400 records 300 births, 180 deaths, 40 animals moving in and 60 moving out in one year. Calculate the change and the growth rate.
Step 1: write the equation
change = (births + immigration) − (deaths + emigration)
Step 2: substitutechange = (300 + 40) − (180 + 60) = 340 − 240change = +100 deerStep 3: growth rate as a percentage(100 ÷ 2400) × 100 = 4.17%growth rate = 4.2% per yearThe new population size is 2 500. Always check whether the question wants the change or the new total.
WORKED EXAMPLE
Rabbits are released onto an island with plenty of grass and no predators. Sketch and describe how their numbers will change.
Step 1: identify the curve
No predators and abundant food, so growth is unlimited at first — a J-curve.
Step 2: describe the phases
Slow lag phase while numbers are small, then exponential growth as each generation adds more than the last.
Step 3: explain the ending
The population overshoots the carrying capacity, grass is eaten faster than it regrows, food runs out and there is a sudden crash.
J-curve: lag, exponential growth, overshoot, crashThe word “overshoot” is worth including — it is the link between the growth and the crash.
WORKED EXAMPLE
Explain why the plateau of an S-curve is wavy rather than a straight flat line.
Step 1: say what K depends on
Carrying capacity depends on limiting factors such as food supply, weather and disease, and these change from year to year.
Step 2: bring in negative feedback
When numbers rise above K, competition and disease increase, so deaths rise and numbers fall back.
Step 3: complete the loop
When numbers dip below K, resources per individual improve, births rise and numbers climb again.
The population fluctuates around K, controlled by negative feedbackNaming negative feedback explicitly is usually worth a mark on its own.
💡 Exam tip
Label a sketched curve with the phase names and a dashed K line. Both are commonly credited.
To tell the curves apart in a question, ask whether resources are limited. Limited means S; unlimited means J.
Never say growth stops “because the population runs out of space” alone. Name the density-dependent factor: competition, predation or disease.
If asked to describe a graph, quote numbers and units from the axes. Describing shape only caps your marks.
Keep lag phase and slow growth separate in your head. The lag phase is slow in total numbers, not in rate.
⚠ Common mix-up
Reading the transitional phase as a decline. Numbers are still rising there; only the rate is falling.
Treating K as a permanent number. It moves whenever conditions move.
Calling drought density-dependent. Drought hits crowded and sparse populations alike, so it is density-independent.
Mixing up negative feedback and negative effects. Negative feedback stabilises; it is the reason populations do not run away.
Drawing the crash as a gentle curve. A crash after an overshoot is steep and sudden — that is what makes it a crash.
Forgetting immigration and emigration in a population change calculation. Births and deaths are only half the equation.
Up next: Human Populations in Ecosystems — why our species has escaped so many limiting factors, and why our carrying capacity is so hard to pin down.
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