This document outlines an activity to teach students about variation and diversity. Students will be broken into groups and each given a different assortment of candy. They will describe how their candy varies and then rank the groups from least to most variable. This aims to help students recognize variation within and among objects and develop a way to measure diversity. The document also introduces a "McGinley's Diversity Number" method to numerically quantify diversity based on number of types, variation within types, and variation within individuals.

1. Diversity Exercise Dr. Mark A. McGinley Texas Tech University BIOL 5311 Summer 2011

2. Expected Learning Outcomes By the end of this activity a fully engaged students should be able to Recognize variation among and within objects Describe variation among and within objects Rank groups/objects in how much they vary Develop a metric for measuring amount of variation (intro to diversity index) Recognize that increasing the number of distinct types of objects in a group increases variation (increasing number of types increases diversity)

3. Expected Learning Outcomes Middle School Students At the end of this activity a fully engaged students is expected to be able to- Recognize that objects come in different types and that different parts of the same object can vary describe patterns of variation within and among novel objects Rank different groups of objects in how much the vary within and among objects Describe (either verbally, visually, or using math) why they ranked objects the way they did

4. Expected Learning OutcomesBIG THEMES Variation is common among and within objects When we look at objects it is important to analyze sources of variation Different objects or different groups of objects differ in how variable they are We should be able to examine two groups/objects and determine which are the most/least variable

5. Diversity Biodiversity has become a buzzword in biology Diversity is a relatively complex concept Diversity is interested in measuring variation How things differ from each other The more things vary in more different ways the more diversity

7. Materials Candy Candy bar that varies in size and composition E.g. snickers Candy that varies in color but has the same size and uniform composition Jolly ranchers

8. How do Snickers and Jolly Ranchers Vary? All individual Snickers are the same But an individual Snickers vary within a candy bar All Jolly Ranchers are not the same They have different colors But within an individual Jolly Rancher there is not variation

10. A) receives 3 Jolly Ranchers of the same color

11. B) receives 3 Jolly Ranchers of different colors

12. C) receives 3 small Snickers

13. D) receives 2 small Snickers and 1 large Snicker

14. E) receives 2 Jolly Ranchers of different colors and 1 small Snickers

16. Within an individual piece of candy

17. Across all of the candies in a group

18. 3. As a group have the students rank the 6 piles of candy from the least variable to the most variable

19. Make sure that they can justify why they did this

21. These difference arise because of differences in which components of variation you consider to be most important and how you weight variation within a type

22. Thus, there is no right answer, so students don’t have to worry about getting a particular answer

24. Why do I rank things this way? 3 Jolly Ranchers of the same color -1 type -no variation within a type -all pieces of candy are the same 3 small Snickers - 1 type -all pieces of candy are the same -variation within an individual piece of candy 2 small Snickers and 1 large Snicker -one type -2 variants within in type (small or large) -variation within an individual piece of candy 3 Jolly Ranchers of different colors -1 type -3 variants within type (different colors)

25. Why do I rank things this way? 5) 2 Jolly Ranchers of different colors and 1 small Snickers 2 types of candy No variation within a type 6) 1 Jolly Rancher, 1 small Snickers, and 1 large Snickers 2 types of candy 2 variants within one of the types (large and small)

26. Quantifying Diversity It should be possible to come up with a number that measures our notion of biodiversity. Forces us to clearly state our assumptions about how factors influence diversity Make sure that our answer is logical based on our starting assumptions

27. McGinley’s Diversity Number(MDN) We assume that diversity is increased 1) when the number of types of things is greater 2) when there is variation among individuals of the same type 3) amount of variation within an individual of a type MDI = # types of things + average # variants within a type + amount of variation within an individual (to make it easy add 1 for variation within type and 0 for no variation)

28. MDN Example 1 blue JR, 1 red JR, 1 green JR, 1 small snickers, and 1 large snickers # types = 2 (JR and Snickers) Average number of variants within a type = (3 (colors of JR) + 2 (sizes of Snickers))/2 = 2.5 Average variation within individual of type (0 + 1)/2 =0.5 MDI = 2 + 2.5 + 0.5 = 5.0

29. MDN example 3 Jolly Ranchers of the same color MDN = 1 + 0 + 0 = 1 3 small snickers MDN = (1 + 0 + 1) = 2 2 small Snickers and 1 large Snicker MDN = (1 + 2 + 1) = 4 3 Jolly Ranchers of different colors MDN = (1 + 3 + 0) = 4 2 Jolly Ranchers of different colors and 1 small Snickers MDN = (2 + (2 + 1)/2 + (0 + 1)/2 = 4 1 Jolly Rancher, 1 small Snickers, and 1 large Snickers MDN = (2 + (1 + 2)/2 + (0 + 1)/2 = 4

30. MDN example Thus, my rankings from just thinking about diversity in my head are different than I would get using MDN. Because of differences in how I weighted various components of diversity

31. Diversity Indices There has been lots of work by ecologists and mathematicians to come up with betters ways to quantify diversity Diversity Indices