Unit 3: Populations — Topic 3.5: Population Growth and Resource Availability

Welcome to one of the most important chapters for your AP Exam! In this section, we are looking at the "why" and "how" behind population changes. Why do some populations explode in size while others stay the same? The answer almost always comes down to resources. Understanding how to calculate these changes is a core skill you will need for both the Multiple-Choice and Free-Response sections of the exam.

Note: This chapter builds on what you learned about Carrying Capacity (Topic 3.4) and Survivorship Curves (Topic 3.3). If you need a refresher, remember that carrying capacity is the maximum number of individuals an environment can support based on available resources.

1. The Relationship Between Resources and Growth

Population growth is strictly regulated by resource availability. Resources include everything an organism needs to survive and reproduce, such as food, water, light, and nesting space.

When resources are abundant (lots of food and space):
• The population growth rate usually increases.
• Individuals have higher reproductive success.
• This leads to exponential growth, often represented by a J-curve on a graph.

When resources become limited (food runs low or space gets crowded):
• The population growth rate slows down.
• Competition between individuals increases.
• The population starts to level off at the environment’s carrying capacity.
• This leads to logistic growth, represented by an S-curve on a graph.

Did you know? Even if a population is currently growing exponentially, it eventually hits a limit. No population can grow forever because the Earth has a finite amount of resources!

2. Mathematical Routine: The Rule of 70

On the AP Exam, you will likely be asked to calculate doubling time. Doubling time is the number of years it takes for a population to grow to twice its current size. To find this, we use a handy shortcut called the Rule of 70.

The Formula

The formula for the Rule of 70 is:
\( \text{Doubling Time (in years)} = \frac{70}{r} \)
Where \( r \) is the annual percentage growth rate.

Important Exam Rules for Math:

• Keep the percentage as a whole number: Unlike other math classes, you do not convert the percentage to a decimal for this specific formula. If the growth rate is \( 2\% \), you use the number \( 2 \), not \( 0.02 \).
• Show your work: For Free-Response Question 3 (FRQ 3), you must show your setup and include units (like \( \text{years} \)) to get full credit.
• No formula sheet: You must memorize this formula! It will not be provided during the exam.

Step-by-Step Example:

The Problem: A small country has a population growth rate of \( 3.5\% \). How many years will it take for the population to double?

Step 1: Identify the growth rate (\( r \)).
\( r = 3.5 \)

Step 2: Plug it into the formula.
\( \text{Doubling Time} = \frac{70}{3.5} \)

Step 3: Calculate the final answer.
\( \text{Doubling Time} = 20\text{ years} \)

Key Takeaway: The higher the growth rate (\( r \)), the shorter the doubling time (\( t \)). They have an inverse relationship.

3. Factors Affecting Resource Availability

Why do resources fluctuate? In AP Environmental Science, we look at how different factors change the "resource pie" for a population:

• Density-Independent Factors: These affect a population regardless of its size. Examples include natural disasters (fires, floods, storms) or sudden climate shifts. These can wipe out resources instantly for everyone.
• Density-Dependent Factors: These become more important as the population gets larger. Examples include competition for food, access to clean water, and depletion of soil nutrients. As more individuals move in, the "slice" of resources for each individual gets smaller.

Memory Aid: Think of a classroom. A Density-Independent factor is the fire alarm going off—it affects everyone the same, whether there are \( 5 \) students or \( 50 \). A Density-Dependent factor is the number of textbooks—if there are only \( 10 \) books, having \( 50 \) students creates a huge problem, but \( 5 \) students wouldn't even notice a shortage.

4. Quick Review and Common Mistakes

Quick Review Box:

• Abundant Resources = Exponential Growth (J-curve).
• Limited Resources = Logistic Growth (S-curve).
• Rule of 70: \( \text{Doubling Time} = 70 / r \).
• Carrying Capacity: The limit set by resources (Topic 3.4).

Common Mistakes to Avoid:

• Math Errors: Don't flip the formula! It is \( 70 \) divided by the rate, not the rate divided by \( 70 \).
• Unit Confusion: Always label your answer in \( \text{years} \). If the question asks for the population size after doubling, don't forget to multiply the original population by \( 2 \).
• Jargon Overload: Don't worry if "exponential" sounds scary. It just means the population is growing faster and faster over time because there are more individuals reproducing.

For more information on how these growth patterns apply specifically to humans, see Topic 3.8: Human Population Dynamics.