Use mathematical or graphical representations to explain how carrying capacity and limiting factors control population size (Tennessee Academic Standards for Science, Biology I, BIO1.LS2).

What this topic is asking

The Tennessee LS2 standards ask you to use mathematical or graphical representations to explain how carrying capacity and limiting factors control population size. For the Biology I EOC that means recognizing exponential and logistic growth on a graph, defining carrying capacity, and classifying limiting factors as density-dependent or density-independent. Items often show a growth curve and ask you to identify the carrying capacity or explain why growth slows.

Exponential and logistic growth

A population can grow exponentially only when resources are abundant and nothing limits it (for example, when it first colonizes a new area). But no environment has unlimited resources, so growth eventually slows. Recognizing the J-shape (exponential) versus the S-shape (logistic) on a graph is a common EOC task.

Carrying capacity

The carrying capacity is set by the environment, so it can change if conditions change (a better food supply raises it; a drought lowers it).

Limiting factors: density-dependent versus density-independent

A limiting factor is anything that restricts the growth of a population. The EOC sorts them into two kinds:

• Density-dependent factors have a stronger effect as the population becomes denser. Examples: competition for food, water, and space; predation; disease (which spreads more easily when individuals are crowded). The more crowded the population, the harder these factors bite.
• Density-independent factors affect the population regardless of its density. Examples: weather and climate events, drought, floods, fires, and other natural disasters. A hard freeze affects a sparse and a dense population alike.

Telling these apart is the most-tested distinction here: ask whether the factor's effect depends on how crowded the population is.

Reading a population graph

On a growth graph, look for the shape and the level-off:

• A curve that keeps climbing steeply is exponential (J-shaped).
• A curve that rises, then bends and flattens is logistic (S-shaped); the flat level is the carrying capacity.
• A curve that fluctuates up and down around a level is a population staying near its carrying capacity as births and deaths balance.

Try this

Q1. Define carrying capacity and state how you would find it on a logistic growth graph. [2]

• Cue. The maximum population size an environment can support over time; on an S-shaped graph it is the level at which the curve flattens out.

Q2. Classify each as density-dependent or density-independent: predation, a flood, competition for space, a wildfire. [2]

• Cue. Predation, density-dependent; flood, density-independent; competition for space, density-dependent; wildfire, density-independent.