AP Environmental Science

## Learning Outcomes

- Define **carrying capacity (K)** and explain why it depends on resource supply
- Distinguish between **exponential growth** and **logistic growth**
- Explain how shrinking resources reduce population growth by lowering fecundity and increasing mortality
- Identify **limiting factors** and classify them as density-dependent or density-independent
- Interpret population graphs showing stabilization, overshoot, and dieback
- Apply the logistic growth idea to human and nonhuman examples
- Use simple quantitative reasoning, including the Rule of 70, in population questions

## AP Environmental Science Syllabus

For the AP Environmental Science, you are expected to understand how shrinking resources reduce population growth, with a focus on the following syllabus points:

- Know that **carrying capacity (K)** is the maximum population size an environment can sustainably support
- Identify key limiting resources, including food, water, space, shelter, and nutrients
- Explain the difference between **exponential growth** and **logistic growth**
- Understand how density-dependent limiting factors become stronger as population size rises
- Recognise that shrinking resources can lower birth rate, raise death rate, or both
- Interpret graphs showing population growth near carrying capacity, including overshoot and dieback
- Understand that carrying capacity is not fixed and can decrease if the environment is degraded
- Distinguish density-dependent factors such as competition and disease from density-independent factors such as drought and fire

## Test Your Knowledge

_Attempt these questions before reading this article. If you find some difficult or cannot remember the answers, look more closely at that area during your revision._

1. What is carrying capacity, and why can it change over time?
2. How does logistic growth differ from exponential growth?
3. Why do shrinking resources reduce population growth?
4. What is the difference between a density-dependent and a density-independent limiting factor?
5. What usually happens when a population overshoots carrying capacity?

## Introduction

Population growth in nature is never just about how many organisms are born. It is also about whether the environment can keep supplying what those organisms need. A population may grow quickly for a time, but if food, water, space, or other resources become scarce, that growth slows and may even reverse.

This is a core AP Environmental Science idea because it links ecology to real environmental problems. Populations do not grow forever. Resource limits control them. On the exam, you may be asked to explain this in words, read it from a graph, or apply it to a scenario such as deer in a forest, bacteria in a flask, or humans in a drought-prone region.

> **Key Term: carrying capacity**
> The maximum population size that an environment can sustainably support over time with its available resources.

### Why shrinking resources slow population growth

At first, a population with abundant resources may increase rapidly. Births are high, deaths are relatively low, and individuals can obtain what they need. But as population size rises, the amount of resources available per individual falls. The key idea is not just that resources exist, but that each organism must get enough of them.

A simple cause-and-effect chain is:

Shrinking resources -> more competition -> less food or space per individual -> lower survival and lower reproduction -> slower population growth

This is the logic behind why populations level off instead of rising forever.

> **Key Term: limiting factor**
> Any resource or environmental condition that restricts the growth, size, or distribution of a population.

A limiting factor can be the scarcest resource, even if everything else is abundant. For example, a grassland may have enough sunlight and space, but if drought reduces water, plant growth falls. Herbivores then have less food, so their population growth also slows. This is an example of resource shortage passing through the food web.

Liebig's Law of the Minimum helps explain this. Population growth is controlled by the resource in shortest supply relative to need, not by the total amount of all resources combined. Students often miss this point and say a habitat is "resource rich" overall, so the population should grow. That is not enough. One missing requirement can still limit the entire population.

Consider a deer population in a forest. In wet years, vegetation grows well, so the forest may support many deer. If drought cuts plant growth and dries water sources, the carrying capacity drops. Even if the deer population has not changed yet, the environment can now support fewer deer. Competition increases, weaker individuals die first, and reproduction may drop because undernourished females are less likely to carry healthy offspring.

This is why shrinking resources reduce growth in two main ways:

- **Mortality increases** because individuals starve, become dehydrated, or are more vulnerable to disease
- **Fecundity decreases** because individuals have less energy to reproduce successfully
  > **Key Term: fecundity**
  > The reproductive capacity of an organism or population; in practice, how many offspring are produced.

A common exam error is to explain slower growth only by saying "more organisms die." That may be true, but APES expects you to recognise that fewer organisms may also be born, or both processes may happen together.

> **Test Tip:** In a free-response answer, do not stop at "resources become scarce." Add the mechanism: scarcity increases competition, which raises death rate and lowers birth rate.

### Exponential growth, logistic growth, and what graphs really show

When resources are effectively unlimited, population growth can be **exponential**. This produces a J-shaped curve. The larger the population gets, the more individuals are reproducing, so the growth rate gets faster and faster.

> **Key Term: exponential growth**
> Population growth in which the rate of increase becomes faster as the population gets larger, usually shown as a J-shaped curve.

This can happen in short-lived situations, such as bacteria in a fresh nutrient medium or an introduced population entering a new habitat with little immediate competition. But it usually does not last in nature because finite environments run into resource limits.

More realistic population growth is **logistic growth**. In logistic growth, a population may begin with a fast increase, but as it approaches carrying capacity, growth slows. The graph becomes S-shaped.

> **Key Term: logistic growth**
> Population growth that starts rapidly but slows as resources become limiting and the population approaches carrying capacity.

Why does the curve bend and flatten? Because environmental resistance becomes stronger. When population size is small relative to carrying capacity, resources are plentiful enough that growth is close to exponential. As the population approaches **K**, each individual faces more competition for food, water, oxygen, nesting sites, or other essentials.

Conceptually, the logistic model is:

dN/dt = rN(1 - N/K)

You do not always need to use the formula on the AP exam, but you should understand its meaning.

- **N** = population size
- **r** = intrinsic growth rate
- **K** = carrying capacity
- **dN/dt** = population growth rate over time

The crucial part is the term **(1 - N/K)**.

- If **N** is much smaller than **K**, then **N/K** is small, so **(1 - N/K)** stays close to 1. Growth is rapid.
- If **N** gets close to **K**, then **N/K** gets close to 1, so **(1 - N/K)** gets close to 0. Growth slows.
- If **N = K**, net population growth is 0.
- If **N > K**, the term becomes negative, so the population tends to decline.

This explains why shrinking resources reduce growth: shrinking resources often mean a lower **K**. If carrying capacity drops while population size stays high, the population suddenly becomes closer to, or even above, the new limit.

A useful classroom example is bacteria in a petri dish. At first, nutrients are abundant and waste levels are low, so the bacteria divide rapidly. Later, nutrients shrink and waste builds up. Some bacteria die, reproduction slows, and the colony levels off. The system has shifted from near-exponential growth to logistic growth because of limiting conditions.

> **Test Tip:** If you see an S-shaped graph, describe the stages: initial slow growth, rapid increase, slowing growth, then stabilization near carrying capacity.

### Density-dependent regulation and the role of limiting factors

Not all limiting factors work in the same way. APES often tests whether you can classify them correctly.

**Density-dependent limiting factors** become stronger as population density increases. These are especially important when discussing shrinking resources reducing growth.

Examples include:

- competition for food, water, or space
- disease spread
- parasitism
- predation
- stress from overcrowding
- waste buildup

If there are only a few individuals scattered across a habitat, disease spreads less easily and competition is lower. But when many individuals crowd into the same area, every individual is more affected.

> **Key Term: density-dependent limiting factor**
> A limiting factor whose effect becomes stronger as population size or population density increases.

For example, in a dense rodent population, food can be eaten faster than it regrows. At the same time, disease can spread quickly because individuals encounter one another more often. Both factors lower growth. That is why logistic growth is often described as density-dependent regulation.

By contrast, **density-independent limiting factors** affect populations regardless of their density.

Examples include:

- drought
- floods
- fires
- hurricanes
- freezes
- extreme temperatures

A wildfire can kill organisms whether a population is dense or sparse. But after that density-independent event, density-dependent effects may still follow. For example, drought may reduce plant biomass, then the remaining herbivores compete more intensely for what is left.

> **Key Term: density-independent limiting factor**
> A limiting factor that affects populations regardless of how crowded or sparse they are.

This distinction matters because exam questions often ask what happens after a change in resource availability. If a drought reduces water and plant growth, the drought itself is density-independent, but the resulting food competition among herbivores is density-dependent.

Another subtle point: carrying capacity is not a fixed magic number. It changes with environmental conditions. A wetter year may raise **K** for a grazing species. A polluted lake with lower dissolved oxygen may reduce **K** for fish. Deforestation may lower **K** for a forest specialist species by removing food and shelter.

So when you explain shrinking resources, be precise: the shrinking resource either makes existing limiting factors stronger or creates a new one, which lowers carrying capacity and slows growth.

### Overshoot, dieback, and why populations may crash instead of stabilise smoothly

Textbook diagrams often show a clean S-curve rising and flattening neatly at carrying capacity. Real populations are often messier. They may overshoot the carrying capacity before the limiting effects fully take hold.

> **Key Term: overshoot**
> When a population exceeds the carrying capacity of its environment.

Overshoot usually happens because population responses are not instantaneous. Organisms may keep reproducing based on past good conditions, even when the resource base is already shrinking. This time lag is critical.

Imagine rabbits in a fenced grass enclosure. During spring, grass is abundant and the rabbit population grows rapidly. But rabbits continue reproducing even as the grass becomes sparse. By the time food shortage strongly affects survival, the population may already be above what the enclosure can support.

The likely result is **dieback**.

> **Key Term: dieback**
> A rapid decline in population size after overshoot, usually caused by depleted resources or intensified limiting factors.

Dieback can occur through starvation, disease, conflict, reduced reproduction, or a combination of these. In some cases, the environment later recovers and the population stabilises again. In other cases, the damage is more severe and carrying capacity remains permanently lower.

A useful example is a deer population in a forest after drought. Suppose the forest once supported about 200 deer. A drought reduces vegetation and water so the effective carrying capacity falls to 120. If the deer population is still close to 200, it has overshot the new carrying capacity. The likely result is a sharp decline due to starvation and disease.

There are several possible outcomes after overshoot:

- mild overshoot followed by small oscillations around carrying capacity
- overshoot that damages the environment and lowers carrying capacity permanently
- catastrophic overshoot leading to local extinction

Students often make the mistake of saying a population above carrying capacity "keeps growing until resources are gone." A better answer is that once the population exceeds carrying capacity, negative growth is expected because deaths rise and births fall.

You can also connect this to human populations in local settings. A town depending on one reservoir may support a certain population during average rainfall years. If a long drought reduces water supply, the region's carrying capacity drops. Even if the population does not immediately fall, the area experiences resource stress, rising costs, migration pressure, and lower quality of life.

This does not mean Earth has one simple fixed carrying capacity for humans. Human technology, trade, and social systems complicate that question. But at local and regional scales, shrinking resources clearly reduce the capacity to support a population.

### Applying the idea with numbers and AP-style reasoning

APES also rewards simple quantitative reasoning. One tool is the **Rule of 70**, which estimates doubling time during exponential growth.

> **Key Term: Rule of 70**
> A shortcut used to estimate doubling time by dividing 70 by the annual growth rate as a whole number.

Worked example:

If a population grows at **5% per year**,

Doubling time = 70 / 5  
Doubling time = **14 years**

This matters because shrinking resources usually make such rapid doubling unsustainable over time. The Rule of 70 helps you see how quickly exponential growth can run into limits.

Another AP-style example:

A fish population in a lake grows rapidly after a few predator species are removed. For several years, the lake has enough nutrients and dissolved oxygen to support the increase. Then nutrient depletion and oxygen stress appear.

How should you explain the change?

1. Predator removal reduced an earlier limiting factor
2. Population size rose quickly
3. More individuals consumed more food and oxygen
4. Resource availability per individual fell
5. Competition and stress increased
6. Mortality rose and reproduction fell
7. Growth slowed toward carrying capacity, or overshoot caused dieback

That step-by-step logic is stronger than a short statement like "the fish population got too big."

A final distinction students miss: **biotic potential** is the maximum possible growth under ideal conditions, but actual growth is almost always lower because of environmental resistance. Do not treat biotic potential as if it describes what usually happens in nature.

## Key Point Checklist

_This article has covered the following key knowledge points:_

- Carrying capacity **(K)** is the maximum population size an environment can sustain over time
- Shrinking resources reduce population growth by increasing competition
- Reduced resource access can lower **fecundity**, increase **mortality**, or both
- **Exponential growth** produces a J-shaped curve and usually requires abundant resources
- **Logistic growth** produces an S-shaped curve because growth slows near carrying capacity
- In the logistic model, when **N** approaches **K**, population growth rate falls
- When **N = K**, net population growth is zero
- When **N > K**, negative growth is expected and population size tends to decline
- **Density-dependent limiting factors** include competition, disease, predation, and parasitism
- **Density-independent limiting factors** include drought, floods, fires, and extreme temperatures
- **Overshoot** happens when a population exceeds carrying capacity, often because of time lag
- **Dieback** is the decline that follows overshoot when resources are depleted

## Key Terms and Concepts

- carrying capacity
- limiting factor
- fecundity
- exponential growth
- logistic growth
- density-dependent limiting factor
- density-independent limiting factor
- overshoot
- dieback
- Rule of 70


Population Growth and Resource Availability - Shrinking resources reduce growth