2. Homepage. IntroductionExercise 1: Recognizing Individuals as Unique Exercise 2: Matching Leaves Exercise 3: Using Math to Make Decisions about Variation in the Characteristics of LeavesExercise 4: Matching Shells . Exercise List continued. . 3. Exercise 5: Making Sense of Variation: The G
2. 2 Homepage Introduction
Exercise 1: Recognizing Individuals as Unique
Exercise 2: Matching Leaves
Exercise 3: Using Math to Make Decisions about Variation in the Characteristics of Leaves
Exercise 4: Matching Shells
3. 3 Exercise 5: Making Sense of Variation: The Game
Exercise 6: Finding Species
Exercise 7: Mechanisms
Exercise 8: Mystery Identification,
Suggested Readings & Links
4. 4 Introduction There are over 2 million named species of plants and animals on Earth and many scientists feel that the actual number of types of organisms is well over 5 million.
To start with, we need to know what variation is. It means to be a little bit different from others or from some typical pattern.
Organisms vary because:
The Earth offers many different types of places to live: physical structures such as mountains and water bodies create habitat variation.
Climate adds to the environmental variability offered by physical structure in habitats. Climate (the weather patterns different parts of the world experience over time) is influenced by the shape of the Earth and its pattern of rotation around the sun
5. 5 The Student Will… Learn the different methods scientists use to separate species by the characteristics that vary between them.
Use both qualitative (observational) and quantitative (measurement) methods to make decisions about which organisms should be grouped together versus placed in different groups.
6. 6 Materials
35 unique Leaves
30 leaves each of two species
31 mollusc shells with red dot on each
30 mollusc shells with blue dot on each
7. 7 Objectives Exercise 1 helps students recognize the individual organism’s unique traits by testing your skills in committing a leaf to memory that will vary a lot from many of the leaves available but only slightly from some.
9. 9 Directions 1st Run: Before discussion
Locate the Container marked A, which holds 35 leaves from trees and shrubs that have been laminated. Each leaf has a unique number on its underside.
The teacher will spread these out on the front table.
Each student should select one leaf.
Examine the top of this leaf for a few minutes with the object of committing it to memory.
After studying the leaf, turn it over and copy the number that is on the back onto a sheet of paper. (Alternatively, the teacher might also keep track of the numbers for the students).
Return each leaf to the front table.
10. 10 Check the number of the leaf you picked from the table against the number written down for the leaf you originally examined.
Count the number of students that were successful in finding their leaves. What was the class or group success rate (number correct/total number X 100)?
Example: if 10 individuals out of 30 found their leaves, the success rate was 30%.
Discuss what characteristics the students used to remember their leaves and make an ordered list from the most frequently used characteristic to the least used trait.
11. 11 Fig. 1 Leaf traits that might vary among species and even individuals.
12. 12 For older students, prepare a bar graph, showing the relative importance of the characteristics the class used in identifying their leaves.
Fig. 2 Example of relative importance of various characteristics in distinguishing among leaves. A. Absolute count. B. Relative count expressed as percent of individuals (Number of individuals using a particular trait/total number of individuals).
14. 14 Exercise 2: Leaf Match (very simple) Materials:
Leaves from container A
Picture guide to tree leaves (Leaf Guide)
How to play:
The tree guide sheet has pictures of all of the leaves that might be found in container A of this unit.
Your goal is to find leaves in the batch that match each picture of a leaf that is shown to you.
Below the picture is the common name (what local people call the tree or shrub) and scientific name (internationally registered name that reflects this species relationship to other trees as well as its unique characteristics.
The scientific name consists of two parts: the Genus (close relatives will all have this name) and species (only individual trees that might possibly interbreed share this name).
15. 15 Objective Exercise 2 helps students learn how to make comparisons among individual leaves to find those that are more similar to one another than are the majority of leaves in a sample.
16. 16 Directions Separate the class into groups of three or four students
Partition the leaves in container A into piles so that each group has a unique pile of leaves to examine.
The teacher will show on the screen three leaf species at a time.
Each group of students should check their pile to match leaves in it to the images shown
A representative from each group should bring potential matches up to the front for comparison with the image.
Form piles of the different leaf species on the front table with all correctly matched leaves.
label each pile by its common name and scientific name
24. 24 Exercise 3. Using math to make decisions about variation in the characteristics of leaves For scientists, it is not enough to look at two individuals and decide that they differ in one or more characteristics (i.e., are ‘qualitatively’ different).
The differences must be ‘quantified.’
The traits must be measured and expressed in numbers so that the differences between them can be statistically compared.
Statistics is that branch of mathematics that organizes data such that central tendency (average or mean value) and the levels of variation around it can be found and compared between or among samples.
26. 26 3a. What is the expected value for a trait? Traits vary but within a local group of individuals there is a trait value that can be considered as typical (mean or central tendency)
27. 27 As a class, decide what measure of leaf size you would like to measure on one of the two sets of 30 leaves in container B.
You might want to base your estimate on the width of the leaf blade at its widest point, or its blade length from its tip to its base at the attachment of the petiole (Fig. 1). You could also get a rough estimate of the leaf’s blade area by multiplying the leaf blade width (W) times its length (L) as in (W X L).
To Fig. 1
Each student will receive a leaf and take the measures the class or group has agreed on.
Let’s say that you will round off each measurement to the nearest 1 cm (centimeter).
Make a column for the trait on the board as shown in table 1.
For Table Template, see Table 1
30. 30 It is time to make a graph.
In the example shown in Fig. 1, the horizontal line at the bottom (X-axis) of the graph has 23 1-cm intervals as this was the width of the largest leaf in the sample data set presented in Table 1.
The Y-axis should have more intervals placed on it than the number of individuals of any one leaf size.
In the example in Table 1, the largest number of individuals of a given size was 8 for a leaf width of 8 cm (Look in column 3.). The height of the Y-axis in the graph was thus set at 9.
You are ready to plot your data. Put a dot for the leaf numbers present (Y- axis) for each width (X-axis) as shown in the sample graph.
Finally, draw a line between each dot. This is your distribution of leaves with respect to an estimate of size (leaf width in the example).
31. 31 Fig. 1. Example plot of leaf width distribution from 30 leaf sample. Y-axis
32. 32 The mean or average is calculated by adding up all of the leaf widths in column 1 of Table 1 and dividing this sum by the total number (n) of leaves measured (30 in this case): 238/30 = 7.9. Because we are measuring our leaves to the nearest cm, 7.9 is rounded off to 8.
The median is determined by dividing the total number of leaves measured (n) by 2 and counting down the list of leaves ranked by size (from column 1) to the size designating that leaf. In the example 30 leaves/2 = the 15th leaf and from column 1, we see that the 15th leaf = 8 cm in width.
The mode is equal to the most numerically prominent or common leaf. From columns 2 and 3 in Table 1, we see that the maximum number of leaves of a particular width in the sample was 8 (from column 3) and that these eight leaves were each 8 cm in width (from column 2).
33. 33 Note that these measures of central tendency or typical trait value do not always come out to be the same number.
The estimate that is used most is the mean as it provides the most accurate number (i.e., 7.9 compared to 8 for median and 8 for mode).
The spread of leaf widths to the left and right of the peak at 8 cm on the graph provides a measure of variation in leaf width. The wider the number of intervals on the X-axis, the greater is the variation.
Calculate the mean, median, and mode for leaf width in your sample of 30 leaves from Container B. Mark the location of the mean, median and mode on the graph you have made.
34. 34 Just as the typical value can be calculated, so can the variation in trait values around this typical value.
Variance is the most common measure of how variable a trait is.
Variance is calculated from the mean.
Calculate variance for your sample of leaves using the equation summarized on the next slide.
35. 35 Subtract each leaf width value from the mean value you calculated under 8 and square the result of each subtraction ((mean leaf width – value leafn)2). (Leaf values would come from column 1 of Table 1 but would not need to be sorted as in this column).
Write your results down as you complete these difference calculations.
Then add (sum (S)) all the new values together, and divide this sum by the quantity (n–1), where n = the total number of leaves in the sample.
The following equation prescribes the calculation of variance:
Variance = S((mean – value leaf1)2 + (mean – value leaf2)2 + mean – value leaf3)2 + mean – value leaf4)2 . . . ) /n-1.
The larger the value for variance relative to its mean, the greater is the variability in leaf size among leaves in the sample.
36. 36 3b. Comparing the sizes of leaves from two samples. Container B contains two batches of 30 leaves collected from two different trees or shrubs.
In this exercise we will quantitatively compare the typical leaf sizes of two species of trees.
37. 37 Develop a distribution curve for each species as you did under Exercise 3a
first making a table with the needed columns
and then developing a graph with two axes.
*(You can use the data from the leaf sample you measured under 3a and only measure the other leaf sample here).
This time you will plot two sets of points on your graph. Be sure to use different symbols for the two sets so that you do not confuse them when you are drawing your lines between points.
Fig. 2 provides a model for you to follow in preparing this graph. Be sure to make the X-axis long enough to accommodate the largest size leaf present in the two samples and the Y-axis should accommodate the largest number of individuals of a given size.
38. 38 Fig. 2. Example of two species comparison of leaf size distributions as estimated by leaf width.
39. 39 Calculate the mean, median, and mode for the two species you are comparing and show these results with arrows on your figure.
Calculate the variances of leaf widths for species A and B. Do your numerical results fit what you would conclude from looking at your graph? They should, unless the two species are very similar in size.
40. 40 We can actually determine whether the two means (central tendencies) noted for your leaf widths or other measures differ enough from one another to be able to say that the difference is meaningful or significant.
Scientists conclude that two samples differ significantly from one another in trait value if at a probability of 95%, the difference could not be accounted for by chance.
When we make such comparisons, we are doing statistics or a statistical analysis. We apply a Student’s t-test to determine whether two sample means differ from one another.
41. 41 The student's t-test for the comparison of two means uses the samples sizes (N), means, variances and standard deviations of the two samples.
Because you know the sample sizes and have already calculated the mean and variance for species A and also for species B, you will not need to recalculate these here.
Instead, find these values and list them as follows on a sheet of paper or the blackboard:
MeanA = VarianceA = NA = SDA =
MeanB = VarianceB = NB = SDB =
42. 42 Take the square roots of VarianceA and VarianceB and record your values in the table you are setting up under species SDA and SDB.
Now you need to calculate the pooled estimate of standard deviation for the two species samples A and B. Let’s call it SDAB.
To calculate SDAB, you need to:
1. Multiply the number of leaves minus one (NA -1) for species A times its variance. Write this value down: (NA -1) VarianceA = _____.
2. Do the same for species B: (NB-1) VarianceB =________.
3. Add the two numbers together ((NA -1) VarianceA + (NB -1) VarianceB =_______
4. Take the square root of the sum just calculated under step 3. Write this number down as SDAB.
5. Sum the two sample sizes (NA + NB) and subtract 2 from this sum as in (NA + NB)-2 =____
6. Finally Divide the values calculated under step 4 by the sum calculated under step 5. value4/value 5 = SDAB
43. 43 The equation that describes these calculations looks like this:
SDAB = (NA -1) VarianceA + (NB -1) VarianceB
(NA + NB) - 2
Congratulations! You have calculated the pooled standard deviation of the two means.
We also have to calculate the test statistic t that will be compared to a standard from a table to determine whether the means differ significantly.
___ MeanA - Mean B
SDAB 1/NA + 1/ NB = t
44. 44 Subtract the mean for species B from that for species A _____
Divide the sample size (number of leaves) of species A into 1 ________.
Divide the sample size (number of leaves) of species B into 1 ________.
Sum the results for steps 2 and 3 and take the square root of this sum.
Multiply the result from 4 by the pooled species estimate of standard deviation. _____
Divide the difference between the two means from 1) by the result of the calculation in 5).
45. 45 Now you need to check your value for t against a predicted distribution.
We have looked this up on a table of statistical values for a sample size of 30 leaves for each of two populations.
If your value for t is greater than 2.83, the sizes of your two species of leaves differ significantly at P < 0.05.
This means that 95% of the time, the differences you measured would not be due to errors in measuring the leaves or some other random effect.
46. 46 Exercise 4: Simple Shell Match (very simple) Materials:
Shells from containers C or D
47. 47 Objective Exercise 2 helps students learn how to discriminate between shells that are of like and unlike type
48. 48 The teacher will spread the shells in Container C out on a desk at the front of the room.
Each student will pick out a shell and take it to his or her seat
The teacher will then display the different shell types on the screen at the front of the room
When a student sees the image of the shell in his possession
raise your hand
bring the shell up to the front for verification and return to the table
49. 49 Directions continued If some students still have shells, remaining at the end of one round of showing pictures, have them bring them up to the front where they can attempt to find a matching shell that has been returned.
At this point, ask the class the name of the unknown shell.
Return to the images to locate that shell type and discuss the characteristics of this shell that make it unique.
Put all of the shells back in Container C
For images and names of the shells in Container C
Repeat the exercise with the shells from Container D
For images and names of the shells in Container D
50. 50 Container C: Moon Shell
51. 51 Container C: Turban Shell
52. 52 Container C: Calico Scallop
53. 53 Container C: Pear Whelk
54. 54 Container C: Spindle Shells
55. 55 Container C: Rose Cockles
56. 56 Container C: Osyters
57. 57 Container C: Nucleus Scallops
58. 58 Container C: Orange Scallop
60. 60 Container D: White Nautica
61. 61 Container D: Ecphora (Fossil)
62. 62 Container D: Nerite
63. 63 Container D: King Crowns (highly variable)
64. 64 Container D: Cebu Beauty
65. 65 Container D: Lettered Olive
66. 66 Container D: Candy Cane
67. 67 Container D: Money Cowrie
68. 68 Container D: Babylon
69. 69 Container D: Horse Conch
70. 70 Container D: Lace Murex
71. 71 Container D: Apple Murex
72. 72 Container D: Yellow Land Snail
74. 74 Exercise 5. Making Sense of Variation: The Matching Game Mollusc shells come in a truly amazing variety of shapes, sculptures, patterns and colors.
There are about 100,000 species in all, each with its own special combination of features.
Each mollusc shell in Container C has characteristics that distinguish it from every other shell in the box. Yet some individuals share more characteristics in common than do others.
We should be able to sort these shells on the basis of size, color pattern, shape, texture, and so on.
This exercise and Exercise 6 demonstrate how biologists make decisions about the relationships among organisms based on the characteristics they share and don’t share with other individuals.
78. 78 Spread the shells from Container C out on a table at the front of the room.
Each student should pick one of these shells.
After everyone has a shell, each individual should seek out others in the class who have shells that resemble his/hers.
Each group then:
Should make up a group name and write this at the top of two sheets of paper
Should develop a list of characteristics that accurately describe the shell type all members of the group share and list these characters on both sheets of paper
On the first sheet of paper, list the numbers found on each shell
79. 79 Return your shells to the front desk and give your teacher the second sheet that has only your group name and the list of shell characteristics you have developed
After all groups have turned in their shells and shell descriptor lists, the teacher will give each group a list of descriptive characteristics made by a different group.
The teacher should now spread the shells out on a long table.
Using the lists of shell descriptive characteristics, the new groups should try to find the correct shells.
Once they think that they have found all of the correct shells:
each group will read the descriptive list of traits out loud to the rest of the class showing the matching shells they found as they do so.
They should also read the numbers on the shells so that the group making the list can compare these numbers to their list of shells.
80. 80 If a new group had trouble identifying the correct shells, the class should discuss what changes might be made in the list of descriptive characters that would make it easier to identify the correct shells.
Please check to see that all red dot shells are placed back in Container C.
At the end, the class can check the names and general types of their shells on the Shell Guide C
82. 82 Exercise 6. Finding Species The Animal Kingdom is at the apex or top of a hierarchy.
This Kingdom consists of multicellular organisms that obtain their food by eating other organisms.
The Kingdom is divided into approximately 30 Phyla, which share similar body plans.
The phylum is at the next highest level of the hierarchy.
83. 83 The Mollusca is a phylum characterized as having a body cavity that houses organs, a mantle cavity that in part provides gas exchange, and some form of shell for protection.
Each Phylum is divided into classes: the Mollusca has five classes. The two classes of molluscs used in this exercise include the Gastropoda (snails) and the Bivalvia (clams and their relatives).
Below the Class level in the hierarchy, there are four additional levels of organization: Order, Family, Genus and finally Species.
84. 84 Objective In this exercise, you will learn about classification and how it is hierarchically based.
85. 85 Your goal in this exercise is to partition the samples of molluscs into two groups down a hierarchical scale to the point at which only very similar shells are present in each group left.
During the process, you will develop a tree similar to the one shown below
88. 88 Fig. 3. Partitioning example
89. 89 Step 2. Spread the shells from Container C (red dot) out on a table in the front of the room.
Step 3. Divide the class into groups of 3-4 students.
Step 4. Each group should have the opportunity to visit the shell sample and complete a number of splits on them to arrive at the individual species, using the handouts at the table:
Characteristics& features of shells
Example of hierarchical scheme
Step 4. Each group should make a drawing of the hierarchy made on a sheet of paper.
Be sure to label the trait differences you used in each split.
Write down the numbers on each shell where it ends up in the diagram
Include the names of all members of the group
When all the groups have completed to exercise, they will each copy their hierarchy onto the board, including the shell numbers
91. 91 Box C: Each shell has a unique number, listed below by type
97. 97 Exercise 7. Mechanisms Thus far in our exploration of variation, we have learned that individuals differ in various traits and that we can measure these differences.
We have also learned that individuals vary in the degree to which they differ from other organisms and that individuals are grouped with other individuals that are most similar into species, to those who are a bit less similar into genera, to those who are even less similar into families and so on up a hierarchical scale that deals with the classification of organisms.
This particular exercise introduces you to the mechanisms that may underlie trait variation. We will use leaves and flowers as examples here.
98. 98 Objective Exercise 7 helps students understand why organisms vary.
99. 99 Examine the leaves in Fig. 1. These leaves were collected off of the same tree. In fact, they all came from the same branch but note that the individuals differ in size.
Differences in size as well as other traits frequently are associated with development or growth.
As the young leaf unfolds from its leaf bud, it now has room to grow into a larger size. All it needs is nourishment and time to increase in size to that typical for the mature (adult or fully grown) leaf of this species.
Rank the leaves in Figure 1 from smallest to largest?
STOP ! The answer is next
100. 100 Fig. 1.Variation in leaf size as it is influenced by age.
101. 101 Examine the two sugar maple leaves in Fig 2. Unlike those shown in Fig. 1., these two leaves are both mature. Yet they differ markedly in size.
These two leaves were collected from different parts of the tree: one from a branch near the top of the tree where it is exposed to the sun and the other from one of the lower branches, where there is less sun.
These leaves are influenced by the environment in which they are growing.
102. 102 Fig. 2. Two mature (adult) leaves from different locations on the same tree.
104. 104 Examine the sassafras leaves in Fig. 3.
Note that there are four different leaf shapes:
1. elliptical (balloon-shaped)
2. two lobes, one on either side of the main part of the leaf blade
3. a single lobe on the left side
4. a single lobe on the right side
Morphs 3 and 4 look like left and right-handed mittens. Find each of the four leaves on the diagram.
105. 105 Sassafras is a tree that produces all four leaf types and often on the same branch.
We call a distinct variant that has a genetic basis a morph.
Sassafras exhibits a shape polymorphism (many morphs) consisting of 4 morphs.
Can you think of other examples of polymorphisms?
106. 106 We have learned that leaves vary in size and shape for a number of reasons.
Examine the flowers in Fig. 4 Can you see differences between the two flowers shown from a red lily plant (Fig. 4a) or among the many flowers pictured of purple coneflowers in Fig. 4b?
Of all the parts of a plant, the flower is the least variable. We call traits that show little inter-individual variation conserved traits.
Flowers house the reproductive organs of the plant and to reproduce, flowering plants need animals to carry pollen produced by the male anthers to the female organ (pistil) of another plant.
107. 107 Fig. 4. Examples of lack of variation in flower structure: a) red lily, b) purple coneflower
108. 108 It is important that the animal species that pollinates a particular plant species recognizes its flowers as unique from other species so that it can visit only flowers of the correct type.
Every mistake that a bee makes in visiting the wrong flower is wasted pollen to the plant the bee has visited earlier.
Pollen is very costly to make and is species specific. Seeds will not form if the wrong pollen is encountered. Thus the flowers of a particular plant species do not vary much from one another.
109. 109 Exercise 8. Mystery Shell What is it?
STOP!!! The Answer is next!!!
The mystery shell is actually the operculum of a snail. The operculum is a shell door, which many but not all snails have. With this door, the snail is able to close its shell to survive periods of drought and to gain protection against predators. Snails that live along the seashore are often exposed to air when the tide goes out and there are many animals that feed on snails, especially birds.
111. 111 Suggested Readings
112. 112 Links