can be easily modified), but there are general principles that apply to
any sampling regime. The first is being able to generate a random
starting point, and the number of potential starting points should
coincide with how many random options one needs. If only two
are needed, flipping a coin works. If six are needed, a die; if 12,
two dice, etc. Random number tables can be found in ecology and
statistics books, or one could close one’s eyes and point to a phone
number in a phone book, choosing however many digits one wants
to use. One can also type in “random number generator” on the web
and find numerous options. Another option is spreadsheets. If you
have access to Excel, type “=rand()” into a cell (leaving out the quotations) and a random number between 0 and 1 will be generated.
Multiplying this value by a fixed value and using the “Number”
pull-down menu to control the number of decimals can generate a
range of random numbers suited to any exercise one chooses (e.g.,
“=rand()*100” with no decimal places will give random numbers
between 0 and 100). Many stats packages also have random number
generators. The worst way to sample in this exercise would be to just
approach a tree and gravitate, for example, to leaves that are eye-catching.
Exploring Dispersion in Leaf
Tell students to bring a ruler, pad and pencil, and suitable clothing
for spending two or more hours outdoors. To get students calibrated on procedure (below), take the whole class to an infected
tree that is at least 150 cm tall, with branches that are within arm’s
length. Run through the procedure below, ensuring that everyone
knows what to do. Once everyone is confident they know what
to do, have them break into pairs and disperse in different directions so that everyone collects independent data. Each pair of students should be able to sample three or more trees per hour.
Procedure Using Random Sampling
1. When the presence of a symbiont on a tree is confirmed (do
not work with trees that have no symbionts, and work only
with a single species of Acer), toss a pencil or other linear
object in the air. Use the orientation of the linear object to
decide which side of the tree to start sampling. Identify a
point approximately halfway between the trunk and the far-
thest reach of the lower branches. Close your eyes, and reach
up and choose a leaf (don’t pull it off).
2. Record the data indicated in Table 1: habitat, location, leaf
color, and number of spots. Depending on what is available,
find a contrast in sampling habitats; this could be “urban,”
“forest,” “residential,” etc. Try to divide sampling effort
roughly equally among habitats. For location, choose either
“tree” (= still on the tree regardless of color) or “ground,”
and for color choose either “green” or “yellow.” Alternatively,
one could quantify the proportion of each leaf that is green
(excluding areas occupied by the fungus).
3. After collecting data for the first leaf, close your eyes and take
one step in a clockwise direction in the circle that you could
draw around the tree between the trunk and halfway to the
farthest reach of the lower branches.
4. Repeat until you have collected data for 20 leaves on each tree.
5. Next, search the ground under the tree for fallen leaves. If there
are many more than 20 fallen leaves, toss your pencil in the air
and record the same data for the leaf closest to the pencil. Use
the same procedure as above to find the next fallen leaf to sam-
ple. If there are fewer than 20 leaves in sight, sample as many as
you can find that are likely to have come from the focal tree.
6. Do not preferentially sample leaves that have spots; once
you’ve confirmed that a tree is infected, zero values for a leaf
are an important part of the data.
7. For columns with numeric entries, write only numbers ( i.e.,
never write “> 10” or “ 15”), and do not leave empty cells
in the data sheet.
8. For columns with text entries (other than student names),
write only lowercase.
9. Continue to collect data until a predetermined time; then return
to the lab. Data can be pooled for the class prior to analysis.
Questions to Ponder
1. Ask the students how they think the fungi get on maple leaves.
Because the fungi arrive as tiny airborne spores shortly after
leaves open, this will affect answers to subsequent questions.
Table 1. Sample data. Enter all text variables except student names in lowercase.
Students Habitat Tree Leaf Location Color Spots
A & B urban 1 1 tree green 4
A & B urban 1 2 tree green 0
... ... ... ... ... ... ...
A & B urban 1 20 tree green 12
A & B urban 2 1 tree green 0
A & B urban 2 1 ground yellow 1
C & D forest 1 1 tree yellow 17
C & D forest 2 1 tree green 8
C & D forest 2 2 ground green 2