diversity exercise- candy

Diversity Exercise

Dr. Mark A. McGinleyTexas Tech University

BIOL 5311Summer 2011

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)

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

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

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

Introducing the Concept

• Question for students to stimulate some thinking about variation and diversity.

What is your favorite type of candy?

Are all kinds of candy the same?

How do different types of candy differ from other types of candy?

Does a particular candy vary within an individual candy?

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

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

Activity

• 1. Break students into groups of 6, each students gets 3 pieces of candy– A) receives 3 Jolly Ranchers of the same color– B) receives 3 Jolly Ranchers of different colors– C) receives 3 small Snickers– D) receives 2 small Snickers and 1 large Snicker– E) receives 2 Jolly Ranchers of different colors and 1

small Snickers– F) receives 1 Jolly Ranchers, 1 small Snickers, and 1

large Snickers

Activity

• 2. Have each student describe to their group all of the ways that their candy varies– Within an individual piece of candy– Across all of the candies in a group

• 3. As a group have the students rank the 6 piles of candy from the least variable to the most variable– Make sure that they can justify why they did this– While students are discussing this, you might suggest that

they think about how they might “measure” the amount of variation.

Activity

• What I think is cool about this activity is that there are different ways to rank the groups of candy from most to least variable– 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

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

• What is important is that students can justify why they ranked their groups in a particular order.

Activity

• How would I rank these?LEAST VARIABLE

1) 3 Jolly Ranchers of the same color2) 3 small snickers3) 2 small Snickers and 1 large Snicker4) 3 Jolly Ranchers of different colors

5) 2 Jolly Ranchers of different colors and 1 small Snickers

6) 1 Jolly Rancher, 1 small Snickers, and 1 large Snickers

MOST VARIABLE

Why do I rank things this way?1) 3 Jolly Ranchers of the same color

-1 type -no variation within a type-all pieces of candy are the same

2) 3 small Snickers- 1 type-all pieces of candy are the same-variation within an individual piece of candy

3) 2 small Snickers and 1 large Snicker-one type-2 variants within in type (small or large)-variation within an individual piece of candy

4) 3 Jolly Ranchers of different colors-1 type-3 variants within type (different colors)

–

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)

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

McGinley’s Diversity Number(MDN)

We assume that diversity is increased1) when the number of types of things is greater2) when there is variation among individuals of the same type3) 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)

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 = 2.5Average variation within individual of type

(0 + 1)/2 =0.5MDI = 2 + 2.5 + 0.5 = 5.0

MDN example3 Jolly Ranchers of the same color

MDN = 1 + 0 + 0 = 13 small snickers

MDN = (1 + 0 + 1) = 2

2 small Snickers and 1 large SnickerMDN = (1 + 2 + 1) = 4

3 Jolly Ranchers of different colorsMDN = (1 + 3 + 0) = 4

2 Jolly Ranchers of different colors and 1 small SnickersMDN = (2 + (2 + 1)/2 + (0 + 1)/2 = 4

1 Jolly Rancher, 1 small Snickers, and 1 large SnickersMDN = (2 + (1 + 2)/2 + (0 + 1)/2 = 4

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

Diversity Indices

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