# Introducing Endangered Birds to Ulva, NZ -- Modeling exponential and logistic growth of the yellowhead population

This material is replicated on a number of sites as part of the SERC Pedagogic Service Project

#### Summary

In this Spreadsheet Across the Curriculum activity, students build an Excel spreadsheet to model exponential and logistic growth of a population, in this case an endangered species introduced to a remote island. First, the students use difference equations and generate graphs showing exponential growth of the population. They experiment with changing the variables and see from the results of the simulation that the population exceeds reasonable expectations of the number of birds the island can sustain. Then the students modify the model to include a carrying capacity, and they analyze graphs of the logistic model. "What-if" questions are emphasized throughout the activity.

## Learning Goals

In this module, students will
• Use Excel to model exponential and logistic population growth.
• Make predictions about the effects of changing variables in the models.
• Test these predictions by doing numerical experiments with the spreadsheets.
In the process, students will
• Develop Excel skills including entering equations, filling cells, and graphing.
• See the purpose and limitations of population models.
• Understand the relationship between algebraic equations and resulting graphs.
• Analyze the exponential and logistic curves.
• See how rates of change are represented in exponential and logistic curves.

## Context for Use

This module is designed for an introductory ecology class. Students are not expected to know calculus, so we use difference equations instead of differential equations in the simulation. If students have some familiarity with Excel, it will help, but the activity can be done with Excel novices. This is a simple module that can be followed with a more complex one such as the author's SSAC2007.QH540.BS1.1, Predator-Prey Interactions – Modeling the Number of Fishers and Porcupines in New Hampshire, which uses the same Excel skills. A third module, Modeling Competition, is being developed. Or, as another follow-up, an instructor could ask students to develop a competition model on their own, using the predator-prey modulle as a starting point. Students who have had calculus can explore mathematical aspects of simulation using the logistic model by working through David McAvity's module, SSAC2007.QH352.DM1.1, Chaos in Population Dynamics – Understanding Chaos in the Logistic Model

## Description and Teaching Materials

SSAC2007.QH352.BS1.2-stdnt (PowerPoint 1.4MB Aug4 07)
This module is a PowerPoint presentation with embedded spreadsheets. Students work though the presentation, answering questions and developing the spreadsheet. If the embedded spreadsheets are not visible, save the PowerPoint file to a disk and open it from there.

This PowerPoint file is the student version of the module. An instructor version is available by request. The instructor version includes the completed spreadsheet. Send your request to Len Vacher (vacher@usf.edu) by filling out and submitting the Instructor Module Request Form.

## Teaching Notes and Tips

The module works best in a small class or with several roving tutors to help students. It could probably be done as homework, but is designed for in-class use. Each student or pair of students will need a computer. Students with experience with Excel can be paired with novices, but with novices, you should expect some frustration.
Note that there might be multiple correct answers for some of the pre-post test questions (Instructor version). In the first question, B could be logistic and a math student might know this. Also, the model examples might be arguable.

## Assessment

Students are directed to complete an assignment at the end that tests understanding of the key concepts. Answers can be compared to similar questions in the pre-test that is included in the instructor version.

## References and Resources

More information about the example used in this module can be found at Stewart Island Department of Conservation
and Briskie, James V. 2006. Introduced Birds As Model Systems For The Conservation Of Endangered Native Birds. The Auk, Oct 2006