1. A first lesson in mathematical modeling for biologists: Rocs S1 Rocs.pptx Anne-Marie Hoskinson Michigan State University hoskin29@msu.edu 0

2. 1 Not “Rocks!” http://en.wikipedia.org/wiki/Roc_(mythology) Arabian Rocs

3. 2 “When the Rocs no longer fly over Baghdad, the Caliphs will no longer rule.” Your Objective: Caliph has drafted the class to advise him about the prospects for the Caliphate over the next 1,000 years.

4. 3 Arabian Rocs: Some Facts They are enormous birds. The only population is in Persia. Current population = approximately 742. Build nests high in the Persian mountains. Each Roc builds a single nest and lays a single clutch of eggs in its lifespan. All Roc chicks hatch on the 100 th birthday of the parent, who then flies out into the desert and dies.

5. 4 Arabian Rocs: What do you still Need to Know? In your teams, generate a list of as many questions you can think to ask in order to build a population model that predicts the future Roc population. Rank your list from 1=most important to N=least important to know. Five minutes!

6. 5 Arabian Rocs: What do you still Need to Know?

7. How many generations will our model include? 6 Arabian Rocs: Developing the model

8. Discuss as a team: How will you figure out the future population? Think about: 1.Rocs in this generation 2.Rocs in next generation 3.Other factors As a team, write out a statement that includes 1, 2, and 3. Three minutes! 7 Arabian Rocs: Developing the model

9. 8 Arabian Rocs model

10. 9 Arabian Rocs model: From words to math Rocs in the next generation will be the Rocs in this generation, that didn’t get shot by silver bullets, which then reproduce.

11. 10 Arabian Rocs model: From words to math Rocs in the next generation will be the Rocs in this generation, that didn’t get shot by silver bullets, which then reproduce.

12. 11 Arabian Rocs model: From words to math Rocs in this generation will be the Rocs in the last generation, that didn’t get shot by silver bullets, which then reproduce. R t = (R t-1 - s)*c

13. 12 Arabian Rocs model: From words to math R t = (R t-1 - s)*c Write this equation in your notes. Model’s OBJECTIVE: Predict Roc population 1,000 years into the future and advise the Caliph. Rocs in this generation will be the Rocs in the last generation, that didn’t get shot by silver bullets, which then reproduce.

14. Use “Roc model setup for students.xlsx” 13 Arabian Rocs model: Spreadsheet model development