# Population Dynamics

## Background

A major component of modern ecological research focuses on understanding what influences the abundance of organisms within a population, and why this abundance changes over time. A population is a group of individuals of the same species that occupy a specific area over a certain period of time. Population dynamics refers to how populations of a species change over time. The study of a species’ population dynamics usually seeks to answer questions such as:

• What explains average abundance of a population?
• What causes fluctuations in abundance?

There are several processes that occur simultaneously that can affect population size and dynamics. First, population size is influenced by the per capita population growth rate, which is the rate at which the population size changes per individual in the population. This growth rate is determined by the birth, death, emigration, and migration rates in the population. When the per capita growth rate remains constant, the population can experience exponential growth followed by exponential decline. Interestingly, Charles Darwin was one of the first scientists to realize that high rates of population growth can cause massive mortality events –  he related this to evolutionary changes in heritable traits or genes. The maximum per capita growth rate for a population is called the intrinsic rate of increase.

As a population grows in an area, a population may experience the effects of increased densities. In a given area, is the maximum population size of the species that the environment can sustain is called the carrying capacity. Carrying capacity is determined by the amount of available resources (food, habitat, water). As the density of individuals in a population increases, these individuals must begin competing for limited resources with each other (same species, or intra-specific competition) or with other species (inter-specific competition). If the population grows indefinitely, less and less resources will be available to sustain the population. This process in which per capita population growth changes when population density changes is referred to as density dependence.

The Ricker model is a classic population model which gives the expected number of individuals in a generation as a function of the number of individuals in the previous generation. It is commonly used to represent the dynamics of a population that is affected by density-dependent processes.  The equation is: where the parameter r represents the intrinsic growth rateK is the carrying capacity, and N0 is the initial population size. It is important to note that simplified population models such as the Ricker model are extremely valuable for understanding and learning ecological processes involved in population dynamics. However, many simple models are not always realistic when observing natural populations.

## Lesson Plan

The following activity has been designed to teach basic principles of ecological population dynamics to high school and college level students. The activity utilizes online, interactive tools that allow students to manipulate characteristics of populations and analyze how these changes affect population sizes in real-time. This activity is best paired with a lecture on concepts such as (but not limited to) populations in ecology, carrying capacity, limited resources, or population growth. Students can complete the lesson with just a computer or tablet and internet access. Click here for the full lesson plan document.

## Student Objectives

• Explain what a population is in ecology.
• Describe what r, K, and Nare in a population.
• Analyze how r, K, and Ncan change population sizes over time both individually and together.
• Devise a way to stabilize a hypothetical fish population by varying r, K, and Nand propose a set of management strategies using these concepts.
• Justify this proposal in a group presentation.

## Activity Procedure

### Part 1: Changing r

We will first focus on understanding r (the intrinsic growth rate of a population) and how it affects population dynamics (or the size of populations over time). The intrinsic growth rate is the theoretical maximum rate of increase of a population per individual. Write your answers to the bolded questions on a separate sheet of paper.

1. Use the interactive app above to complete the activity.
2. The model begins with r=4, meaning that the population is growing by 4 for every 1 individual. First, become acquainted with the graph.
1. What are the x and y axes?
2. How does the population size change over time when r=4?
3. Move the slidebar to make r=1.
1. Describe how the size of the population changes over time when r=1.
2. What does it mean when r=1, or the intrinsic growth is 1?
4. Use the slidebar to slowly increase the value of r, noting when the dynamics in the plot changes.
1. Describe the pattern of how the dynamics change as r increases. Note any changes in scaling of the y axis.
2. How does this parameter (or “characteristic”) influence population dynamics?

### Part 2: Changing K and N0

Now that we have a better sense for how r, or the intrinsic growth rate, affects population sizes over time, let’s now learn how carrying capacity and initial population size are also important.

For full page, click here.

1. Use the interactive app above to complete the activity.
2. In our first activity, K and N0 were kept constant: K = 20 and N0 = 10. Begin by making r=1. Use the slidebar to change the value of K (the carrying capacity).
1. Describe what happens to the population when r=1 and K is changed.
2. Explain why this observed pattern is happening in terms of growth rate and carrying capacity.
3. Return K to 20, and set r=2.
1. Describe what happens to the population size over time.
2. How much does the population size vary?
4. Now, set r=1 and K=20. Move the slidebar to increase the value of N0.
1. How does population size respond to changes in this parameter?
2. Explain why you see this pattern.
5. Set r=2 and K=10. Move the slidebar to increase the value (starting at 0) of N0.
1. Describe what happens to the population size over time.
6. Explore moving all 3 of the population parameters.
1. How does K (carrying capacity) influence population dynamics?
2. How does N0 (initial population size) influence population dynamics?

### Part 3: Applying concepts for fisheries management

#### Real-world context of populations

Population dynamics of fishes are of particular interest for people involved in fisheries, from fishermen to managers to ecologists. The application of population dynamics enables fisheries scientists to understand changing patterns of the population and determine sustainable yields.

## Evaluation

This activity includes two forms of evaluation: questions designed to guide the student through the activity and describe how population dynamics change with each task, and a rubric which will assess student knowledge of concepts during a group presentation of a proposal (Part 3 of activity above). The example rubric is located on page 3 of the lesson plan (link above).

## Education Standards

This activity is designed to meet the following standards:

• North Carolina Science Standard Bio.2.1: Analyze the independence of living organisms within their environments. Bio.2.1.3: Explain various ways organisms interact with each other and with their environments resulting in stability within ecosystems. Bio.2.1.4: Explain why ecosystems can be relatively stable over hundreds or thousands of years, even though populations may fluctuate.
• North Carolina Science Standard Bio.2.2: Understand the impact of human activities on the environment (one generation affects the next). Bio.2.2.1: Infer how human activities may impact the environment. Bio.2.2.2: Explain how the use, protection and conservation of natural resources by humans impact the environment from one generation to the next.
• NC Next Generation Science Standard HS-LS2-1: Use mathematical and/or computational representations to support explanations of factors that affect carrying capacity of ecosystems at different scales.
• NC Next Generation Science Standard HS-LS2-6: Evaluate the claims, evidence and reasoning that the complex interactions in ecosystems maintain relatively consistent numbers and types of organisms in stable conditions, but changing conditions may result in a new ecosystem.