Biology · Grade 12 · Population Dynamics and Ecology · Term 4

Population Growth Models: Exponential and Logistic

Students use mathematical models to predict how populations change over time, comparing exponential and logistic growth patterns.

• Ontario Curriculum Expectations
• HS-LS2-1

About This Topic

Community interactions examine the complex web of relationships between different species living in the same area. Students study symbiosis (mutualism, commensalism, and parasitism), competition, and predation. They also explore the concept of the ecological niche and how niche partitioning allows similar species to coexist by using different resources or hunting at different times.

Within the Ontario curriculum, a major focus is on the role of keystone species and the impact of invasive species on local ecosystems. Students learn how a change in one population can trigger a trophic cascade, affecting the entire community. This topic is ideal for gallery walks and case study analysis where students can trace the ripple effects of a single species' arrival or removal from a Canadian ecosystem.

Key Questions

1. What happens to a population when it exceeds the carrying capacity of its environment?
2. Compare and contrast exponential and logistic growth models.
3. Predict the future size of a population given its intrinsic rate of increase and carrying capacity.

Learning Objectives

• Calculate the future population size using both exponential and logistic growth equations.
• Compare and contrast the graphical representations of exponential and logistic population growth.
• Analyze the impact of carrying capacity on population growth rates in a given ecosystem.
• Explain the assumptions and limitations of exponential and logistic growth models.
• Predict how environmental changes might affect a population's carrying capacity.

Before You Start

Introduction to Ecology

Why: Students need a foundational understanding of ecological concepts like ecosystems, habitats, and biotic/abiotic factors before modeling population dynamics.

Basic Algebraic Equations and Graphing

Why: Students must be able to solve simple equations and interpret graphical data to work with population growth models.

Key Vocabulary

Exponential Growth	Population growth that occurs when resources are unlimited, resulting in a J-shaped curve where the growth rate is constant.
Logistic Growth	Population growth that occurs when resources are limited, resulting in an S-shaped curve that levels off at the carrying capacity.
Carrying Capacity (K)	The maximum population size of a species that an environment can sustain indefinitely, given the available resources.
Intrinsic Rate of Increase (r)	The rate at which a population would grow under ideal conditions with unlimited resources.
Limiting Factors	Environmental conditions that restrict population growth, such as food availability, predation, disease, and space.

Watch Out for These Misconceptions

Common Misconception

Symbiosis always means both organisms benefit.

What to Teach Instead

Clarify that symbiosis is simply a 'living together' relationship, which includes parasitism (one benefits, one is harmed) and commensalism (one benefits, one is unaffected). Using a '+/-/0' chart for various real-world examples helps students categorize these relationships correctly.

Common Misconception

Predators are 'bad' for a prey population.

What to Teach Instead

Explain that predators often keep prey populations healthy by removing the weak and preventing overpopulation, which could lead to habitat destruction. A simulation showing what happens to a forest when deer have no natural predators can quickly change this perspective.

Active Learning Ideas

Gallery Walk: Trophic Cascades in Canada

Display posters of different Canadian ecosystems (e.g., the return of wolves to a park or the impact of sea otters on kelp forests). Students move in groups to map out the 'who eats whom' relationships and identify the keystone species in each scenario.

40 min·Small Groups

Formal Debate: The Invasive Species Dilemma

Assign students to represent different stakeholders (e.g., a fisherman, an ecologist, a government official) regarding an invasive species like the Zebra Mussel or Emerald Ash Borer. They must debate the best course of action for management, considering both ecological and economic impacts.

50 min·Small Groups

Think-Pair-Share: Niche Partitioning

Provide students with data on three species of birds that live in the same tree but eat different insects at different heights. Students discuss in pairs how this behavior reduces competition and allows for higher biodiversity in the forest.

20 min·Pairs

Real-World Connections

• Wildlife biologists use logistic growth models to manage populations of endangered species, such as the Greater Sage-Grouse in the Canadian prairies, by estimating carrying capacity and identifying limiting factors for habitat restoration.
• Fisheries managers in British Columbia employ population growth models to set sustainable catch limits for commercially important fish stocks like salmon, balancing harvesting with the species' ability to reproduce and maintain population levels.
• Urban planners consider carrying capacity when designing new developments, assessing how increased human populations will impact local resources like water, energy, and waste management systems.

Assessment Ideas

Quick Check

Provide students with a data set showing population size over time for a specific species (e.g., yeast in a culture, deer in a park). Ask them to graph the data and identify whether it most closely resembles exponential or logistic growth, justifying their choice with reference to the graph's shape.

Exit Ticket

Present students with a scenario: 'A population of rabbits is introduced to an island with abundant food and no predators.' Ask them to write one sentence describing the initial growth pattern and one sentence describing how the growth pattern will change as the population increases. Then, ask them to define carrying capacity in their own words.

Discussion Prompt

Facilitate a class discussion using the prompt: 'Imagine a population of wolves is introduced into an area with a stable deer population. How might this introduction affect the deer population's growth rate, and what factors would determine the carrying capacity for both species?'

Frequently Asked Questions

What is a keystone species?

A keystone species is an organism that has a disproportionately large effect on its natural environment relative to its abundance. If a keystone species is removed, the ecosystem often undergoes dramatic changes, potentially leading to the loss of many other species and a total shift in the community structure.

How does resource partitioning reduce competition?

Resource partitioning occurs when species divide a niche to avoid direct competition for the same resources. For example, different species of lizards might live in the same area but hunt in different parts of the canopy or at different times of day, allowing them to coexist peacefully.

What is the difference between primary and secondary succession?

Primary succession begins in an area with no soil, such as after a volcanic eruption or glacier retreat. Secondary succession occurs in an area where an existing community has been disturbed (e.g., by a fire or logging) but the soil remains, allowing life to return much faster.

How can active learning help students understand community interactions?

Active learning helps students visualize the 'web' of life. By mapping out trophic cascades or debating the management of invasive species, students see that ecosystems are not static but are held in a delicate balance. This systems-thinking approach is much more effective than simply memorizing definitions of symbiotic relationships.