PopulationDynamics_NABT worksheet_2019B-4765

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Biology

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Jan 9, 2024

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Ecology NABT Sample www.BioInteractive.org Page 1 of 5 Click & Learn NABT Example Worksheet Population Dynamics OVERVIEW This worksheet complements the Population Dynamics Click & Learn and provides a sample of procedures students could perform using this tool. The published versions of the student worksheet and educator materials are available on the Population Dynamics Click & Learn page. This worksheet also includes a preview of activities from a forthcoming Click & Learn that uses the lionfish invasion in the Caribbean to teach students about logistic population growth and mechanisms regulating populations (available in 2020). KEY CONCEPTS • Scientists construct mathematical models to predict the growth of populations and understand factors that can affect the rate at which a population changes over time. • In the exponential growth model, the rate of population growth depends on the per capita growth rate and population size. • In the logistic growth model, population growth slows down as the population size approaches a maximum number called the carrying capacity ( k ). A variety of density-dependent factors contribute to k . EXAMPLE STUDENT LEARNING TARGETS • Explain how changing the variables of time, per capita growth rate, and the initial population size affect population growth. • Explain the differences between an exponential growth model and logistic growth model. • Describe assumptions of the population growth models and how those assumptions align with biological populations. PART 1: Exploring Exponential Growth Proceed to the exponential model simulator. Click on the “How to Use” button and notice the explanations provided to students regarding the components of the tool. Click on the gear icon to change the scale of the graph and the range of values you can select for each parameter. The worksheet questions are designed to get students exploring the slider tools and recording the outcomes of changing the parameters for exponential growth. After gaining familiarity with the tool, students should be able to change the parameters to generate particular scenarios. Identify the parameter levels (e.g., large or small growth rate, large or small initial population size) that generate the following graphs: 1. A long period of almost no growth—the curve looks nearly flat. 2. A long period of slow but clearly accelerating growth—the curve starts to become steeper at the end. 3. Extremely rapid growth from the very beginning.

Population Dynamics Ecology NABT Sample www.BioInteractive.org Page 2 of 5 Click & Learn NABT Example Worksheet PART 2: Applying Parameters from a Natural Population Students can use the Population Dynamics Click & Learn to explore hypothetical scenarios for any organism or situation. The first example in the currently available student worksheet asks students to consider waterbuck populations in Gorongosa National Park in Mozambique that are recovering after a devastating civil war (using b = 0.67, d = 0.06, N 0 = 140 as the starting values, where students use the equation: r = b – d to determine that the waterbuck population would exponentially grow at a rate of r = 0.61 ). Today, we will explore the simulation using lionfish data! Below are some sample questions from the Population Dynamics Click & Learn (C&L) Student Worksheet adjusted for lionfish. You can adjust the questions to any organism or system, or consider this a preview for the Lionfish C&L coming soon! 4. In a study by Côté and Smith (2018), lionfish were surveyed in the Bahamas in 2004, when 2 individuals were first sighted. Fill in the chart below using the exponential model simulator to predict how the population is expected to grow under the early years of the invasion. Use r = 0.95 as the estimate of lionfish population growth rate in a novel habitat. Time 1 (2005) 2 (2006) 3 (2007) 4 (2008) 5 (2009) Population size ( N t ) Slope ( 𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑 ) 5. How do your model estimates compare to the field data collected by Côté and Smith (2018) in the Bahamas? Note: The data above is reported as number of sightings of lionfish per dive. This measure can be used to estimate density based on the amount of area surveyed. As reported here, this measure can only be used as an index to represent lionfish density and not as a direct measure of population size (N).

Population Dynamics Ecology NABT Sample www.BioInteractive.org Page 3 of 5 Click & Learn NABT Example Worksheet PART 3: Logistic Growth Models A. Exploring Carrying Capacity The logistic model adds the concept of carrying capacity, k when modeling changes in population size over time. This is the maximum number of individuals that the community can support without exhausting resources. 6. Given the data in the previous figure, what would be an appropriate carrying capacity to include in a logistic model for lionfish? Note: You may need to use the settings to adjust the range of the input variables. B. Extensions in Lionfish Click & Learn: Exploring Changes in Instantaneous Growth Rate 7. How does slope ( 𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑 ) change in relation to N ? Refer to the graphs and practice questions:

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