Topic 19.4 · Core & Supplement
Population Growth and the Sigmoid Curve
Population size isn’t fixed — it responds to food supply, competition, predation and disease, and in an environment with limited resources it tends to follow a recognisable S-shaped pattern. Cambridge wants you to recognise that shape, name its four phases, and — at Extended level — explain in causal terms why each phase happens rather than just what it looks like.
Factors affecting population growth
For this syllabus, the factors affecting the rate of population growth are limited to four: food supply, competition, predation and disease. Each one works by altering survival and reproduction, and it’s that change in survival and reproduction — not the factor itself — that actually changes population size.
Food supply
When plenty of food is available, organisms are more likely to obtain enough energy and nutrients, so more survive and more reproduce successfully, and the population can grow. As population size increases, food can become less available per individual; if it becomes scarce, competition increases, fewer organisms obtain enough food, reproduction may fall and deaths may rise, so the population’s growth rate slows or turns negative.
Competition
Competition occurs when organisms require a resource that is limited. As population size rises, more individuals compete for the same available food or other resources, and strong competition can reduce both survival and reproductive success — which is exactly why competition tends to matter more as resources become scarcer, not as a constant background effect.
Predation
Predators kill and consume prey. If predation increases, more individuals in the prey population die, which can reduce that population’s growth rate; if predation decreases, more prey survive and reproduce, allowing the population to increase. Predator and prey populations can therefore influence one another directly through this single feeding relationship, which is the same reasoning used to interpret food webs more broadly.
Disease
Disease can increase deaths and reduce successful reproduction, and its effect can become especially significant when many susceptible organisms are present and transmission between individuals happens readily. An increase in disease can therefore slow population growth, or cause population size to fall outright.
The sigmoid population growth curve
When a population grows in an environment with limited resources, its size can follow a sigmoid, or S-shaped, growth curve. Cambridge requires four named phases — lag, exponential (also called log), stationary, and death — with time on the horizontal axis and population size on the vertical axis. Being able to recognise and interpret the shape of the curve matters more here than simply memorising the four names in order.
Lag phase
During the lag phase, population growth is slow. There are initially relatively few individuals capable of reproducing, so the number of new individuals added is small, and although the population is increasing, it’s doing so only gradually — which appears on the graph as the shallow beginning of the curve.
Exponential or log phase
During the exponential phase, the population increases rapidly. Resources are still readily available and limiting factors have relatively little effect, so many individuals survive and reproduce, and the number of individuals being added grows larger as the population itself grows larger. On the graph this appears as a steep rise, and this phase is also called the log phase.
Stationary phase
Rapid exponential growth can’t continue indefinitely once resources are limited. As population size increases, food may become limiting, competition becomes stronger, predation may increase, and disease may have a greater effect — so the rate of population growth slows. During the stationary phase, the addition of new individuals is approximately balanced by loss of individuals, so the overall population size remains approximately constant, which appears on the graph as a plateau. A stationary population is not one where nothing happens — individuals can still be born and can still die — the important point is that these changes leave the overall population size roughly unchanged.
Death phase
If limiting factors become severe enough, deaths exceed the addition of new individuals and the population decreases, producing the death phase as a downward section of the graph. Severe food shortage, intensified competition, increased predation or disease can all contribute to this decline.
Why each phase occurs — Supplement
The four phases can be understood as a changing balance between population growth and limiting factors, and Extended candidates are expected to explain the phases this way rather than only recognise their shapes.
In the lag phase, the population is initially small, so relatively few individuals are reproducing and growth is slow. In the exponential phase, resources are abundant relative to population size, competition is low and other limiting factors have relatively little effect, so survival and reproduction allow rapid growth. In the stationary phase, the much larger population places greater pressure on limited resources, and food supply, competition, predation and disease restrict any further increase, so population size becomes approximately stable. In the death phase, limiting factors become strong enough that the population can no longer maintain its size, so deaths exceed the production or survival of new individuals and population size falls.
The curve as a whole represents one central ecological relationship: population growth increases pressure on limited resources, that pressure makes limiting factors stronger, and stronger limiting factors slow growth and can eventually reverse it. It’s the same food-supply, competition, predation and disease logic from the start of this page, just now playing out as a single continuous graph instead of four separate factors.