AP Environmental Science

## Learning Outcomes

- Define **sustainable yield** accurately for AP Environmental Science
- Distinguish between **sustainable yield** and **maximum sustainable yield (MSY)**
- Explain how sustainable yield links to **renewable resources**, **population growth**, and **carrying capacity**
- Use the **logistic growth model** to explain why growth is highest near **K/2**
- Calculate simple **MSY** values using **MSY = rK/4**
- Identify examples of sustainable use and overharvesting in fisheries, forestry, and water systems
- Avoid common exam mistakes, especially confusing sustainable yield with carrying capacity or nonrenewable resource use

## AP Environmental Science Syllabus

For the AP Environmental Science, you are expected to understand sustainable yield definition, with a focus on the following syllabus points:

- Know that **sustainable yield** is the amount of a renewable resource that can be harvested without reducing future supply
- Identify that sustainable yield applies mainly to **renewable resources**, not nonrenewable resources
- Explain how **overharvesting** occurs when removal exceeds the rate of replenishment
- Understand the difference between **sustainable yield** and **maximum sustainable yield (MSY)**
- Know that in the simple **logistic growth model**, population growth is greatest at about **half the carrying capacity**
- Interpret **K** as carrying capacity, **r** as intrinsic growth rate, and **N** as population size
- Use the idea that **MSY occurs near K/2** and, in the simplified model, **MSY = rK/4**
- Apply these ideas to renewable resource examples such as fisheries and forests

## 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 meant by **sustainable yield**?
2. How is **maximum sustainable yield** different from sustainable yield?
3. Why does a population usually produce the largest harvestable surplus at an intermediate size rather than at a very low or very high size?
4. What does **overharvesting** mean in a fishery?
5. In the simple logistic model, at what population size is growth greatest?

## Introduction

Sustainability in AP Environmental Science is about using resources in ways that do not reduce future availability. That idea becomes much more precise when you study **sustainable yield**. The term appears simple, but exam questions often test whether you can connect it to population ecology, renewable resources, and human resource use.

Sustainable yield matters because many human activities depend on living systems that can recover only up to a point. Fisheries, forests, and some freshwater systems can provide ongoing benefits, but only if the rate of harvest does not exceed the rate of replacement. Once removal goes beyond replenishment, the system moves from sustainable use to depletion.

> **Key Term: sustainable yield**
> The amount of a renewable resource that can be harvested or used without reducing the future supply of that resource.

### What sustainable yield actually means

A common mistake is to define sustainable yield too vaguely as “using resources carefully.” That is part of the general idea of sustainability, but for the AP exam you need a sharper definition. Sustainable yield refers specifically to the **amount** of a **renewable** resource that can be taken without lowering the amount available in the future.

That definition contains three parts students should notice.

First, the resource must be **renewable**. Fish populations, forests, groundwater recharge in some systems, and wildlife populations can renew over time. Coal, oil, copper ore, and uranium do not fit the idea in the same way because they are not replaced on a human timescale.

> **Key Term: renewable resource**
> A resource that can be naturally replenished on a timescale relevant to human use, if it is not used faster than it is replaced.

Second, sustainable yield is about **rate**, not just amount. A forest may contain 10,000 trees, but that does not mean cutting 5,000 at once is sustainable. What matters is how many can be removed while allowing regrowth and continued ecological balance function.

Third, the future supply must stay stable. If harvest this year makes next year’s stock smaller, the harvest was above sustainable yield.

A fishery example makes this clearer. Suppose a lake fish population naturally adds about 200 fish per year under current conditions. If people harvest 150 fish per year, the stock can likely remain stable. If they harvest 200, they may be at the upper edge of sustainable use. If they harvest 300, the population declines over time. That last case is overharvesting.

> **Key Term: overharvesting**
> The removal of individuals from a renewable resource population at a rate greater than the population can replenish.

This is why the textbook focus on sustainability links directly to renewable resource use. A renewable resource is not automatically sustainable. It becomes unsustainable when the harvest rate exceeds replenishment.

> **Test Tip:** If a multiple-choice question includes coal, petroleum, or metal ores, be cautious. Sustainable yield mainly applies to renewable resources, not nonrenewable ones.

### Sustainable yield, carrying capacity, and logistic growth

To understand why sustainable yield works, you need population ecology. Many renewable resources are living populations, so harvest depends on how populations grow.

A simple population model is **logistic growth**. In this model, population growth starts fast when resources are available, then slows as the population approaches environmental limits.

> **Key Term: carrying capacity (K)**
> The maximum population size that an environment can support over time.

In the logistic model, population change is written as:

$$
\frac{dN}{dt} = rN\left(1-\frac{N}{K}\right)
$$

Where:

- **N** = population size
- **r** = intrinsic growth rate
- **K** = carrying capacity
  > **Key Term: intrinsic growth rate (r)**
  > The maximum potential rate of population increase under ideal conditions.

The key reasoning is more useful than the formula itself.

If population size is **very low**, growth is limited because there are not many reproducing individuals. Even if resources are plentiful, a tiny population does not generate much total new biomass or many new individuals.

If population size is **very high**, close to carrying capacity, growth is again low because competition for resources becomes intense. Food, space, dissolved oxygen, or other limiting factors reduce net increase.

So growth is low at both extremes. That means the largest surplus available for harvest must occur somewhere in the middle.

In the simple logistic model, that maximum growth occurs when:

$$
N = \frac{K}{2}
$$

This is a very high-yield exam idea. Half of carrying capacity is where the population adds individuals at the fastest rate under the simple model. That added amount is the theoretical surplus humans might remove without long-term decline.

Students often confuse this with carrying capacity itself. **K** is the size the environment can support, not the sustainable harvest amount. Harvest is the surplus growth, not the total population.

Imagine a fish stock with carrying capacity of 1,000 fish:

- At **N = 100**, the stock is small and total reproduction is limited
- At **N = 500**, growth is highest
- At **N = 950**, the lake is near full capacity, so competition limits additional growth

This is why the “best” harvest level is not taken from the largest stock size. A stock near carrying capacity is large, but it is not growing very fast.

> **Test Tip:** When an FRQ asks why MSY occurs at an intermediate population size, explain both sides: low populations have too few breeders, while high populations are limited by competition near carrying capacity.

### Sustainable yield versus maximum sustainable yield

The AP exam may ask you to separate the broad concept of sustainable use from the more precise benchmark called **maximum sustainable yield**.

> **Key Term: maximum sustainable yield (MSY)**
> The largest long-term average harvest that can be taken from a renewable population without causing long-term depletion.

Sustainable yield means any harvest level that does not reduce future supply. Maximum sustainable yield is the **highest** harvest level that still meets that condition.

So if a forest can regrow 100 trees per year under current conditions:

- Harvesting 40 trees per year is sustainable yield
- Harvesting 70 trees per year is also sustainable yield
- Harvesting 100 trees per year may be maximum sustainable yield
- Harvesting 130 trees per year is overharvesting

This distinction matters because students often treat the terms as synonyms. They are not.

Under the simple logistic model, if growth is greatest at **K/2**, then the maximum value of the growth function becomes:

$$
MSY = \frac{rK}{4}
$$

This comes directly from substituting $N = K/2$ into the logistic growth expression.

Worked example:

A fish population has:

- $r = 0.8$
- $K = 2{,}000$ fish

Step 1: Find population size at maximum growth

$$
N = \frac{K}{2} = \frac{2000}{2} = 1000
$$

Step 2: Use the MSY formula

$$
MSY = \frac{rK}{4}
$$

$$
MSY = \frac{(0.8)(2000)}{4}
$$

$$
MSY = \frac{1600}{4} = 400
$$

So the theoretical maximum sustainable yield is **400 fish per year**.

You can also reason through it with the full logistic expression:

$$
\frac{dN}{dt} = rN\left(1-\frac{N}{K}\right)
$$

$$
= (0.8)(1000)\left(1-\frac{1000}{2000}\right)
$$

$$
= 800(1-0.5)
$$

$$
= 800(0.5)=400
$$

Same result.

This does **not** mean managers should always harvest exactly 400 fish. Real populations do not behave perfectly like simplified equations.

### Why real-world sustainable yield is harder than the model

The logistic model is useful because it gives clear reasoning, but real systems are more complicated. This is where AP Environmental Science expects application and evaluation.

Real renewable resource populations are affected by:

- changing temperature
- disease
- predator-prey shifts
- habitat quality
- pollution
- age structure
- weather variation
- human technology

A fish stock might support a certain harvest one year and not the next. A drought can reduce streamflow and oxygen levels. A marine heat wave can change food supply. Deforestation can reduce breeding habitat. All of these can lower actual replenishment.

This is why NOAA and other fisheries agencies define MSY in terms of the largest long-term average catch under **prevailing conditions**. That wording matters. MSY is not a permanent universal number.

There is also environmental risk. A harvest may appear sustainable for one target species while harming:

- predators that eat it
- prey relationships
- seafloor habitat
- by-catch species
- biodiversity overall

For AP Environmental Science, this means you should avoid absolute statements like “harvesting at MSY is always safe.” In practice, uncertainty makes harvesting right at the theoretical maximum risky. Many managers set catch levels below the maximum to leave a safety margin.

A forestry example shows the same problem. If a forest is cut at a rate equal to average regrowth, it might still lose biodiversity, soil quality, and wildlife habitat if the harvest method is too intense. Sustainable yield in ecological system terms is not only about replacing numbers; it is also about keeping the system functioning.

### Applying sustainable yield to fisheries, forests, and water

Fisheries are the clearest APES example. If fish are removed faster than they reproduce, the stock shrinks. Improved technology, larger fleets, and by-catch can increase pressure even when fishers think they are maintaining harvest.

A sustainably managed fishery keeps catch at or below replenishment. An overfished stock shows long-term decline because the harvest exceeds that replenishment.

Forestry works similarly, but students should think beyond tree count. Sustainable forestry means harvest rates that allow regrowth over time, while protecting soil, biodiversity, and watershed function. Cutting only the annual regrowth is closer to sustainable yield than removing mature trees faster than replacement.

Water is a bit different because “sustainable yield” in water management can mean withdrawal rates that do not exceed natural recharge. But even there, a good answer should mention that enough water must remain for streamflow, wetland support, and aquatic habitat.

This is a useful contrast:

- in fisheries and wildlife, sustainable yield is often expressed as harvest of organisms
- in forestry, it is often harvest of biomass or trees
- in water systems, it is withdrawal relative to recharge and environmental flow support

The common principle is the same: use must not reduce future availability.

## Key Point Checklist

_This article has covered the following key knowledge points:_

- Sustainable yield is the amount of a **renewable resource** that can be used without reducing future supply
- Sustainable yield applies mainly to **renewable**, not nonrenewable, resources
- Overharvesting occurs when harvest exceeds the rate of replenishment
- **Carrying capacity (K)** is the maximum population size an environment can support, not the harvest amount
- In the logistic growth model, population growth is low at very small and very large population sizes
- Maximum growth in the simple logistic model occurs at **K/2**
- **Maximum sustainable yield (MSY)** is the largest long-term average harvest that can be maintained without long-term depletion
- Sustainable yield and MSY are not the same; MSY is the highest sustainable level
- In the simplified model, **MSY = rK/4**
- Real-world MSY changes with environmental conditions and should not be treated as a fixed number
- A harvest can seem sustainable for one species but still damage habitats and food webs
- Fisheries and forestry are common AP Environmental Science examples of sustainable yield

## Key Terms and Concepts

- sustainable yield
- renewable resource
- overharvesting
- carrying capacity (K)
- intrinsic growth rate (r)
- maximum sustainable yield (MSY)


Introduction to Sustainability - Sustainable yield definition