2. Ask the class what their expectations are for how tar spots
will be distributed among leaves. Given that the fungus is
at the whim of air currents to get dispersed, the class may
expect spores to be randomly distributed. However, spores
are likely released in pulses and probably have patchy survival because of variation in habitat. Moreover, susceptible
hosts are probably not randomly distributed. This may lead
to clumped distributions of symbionts. The procedure for
testing for a random distribution is described below.
3. Should leaves on the tree have more spots than those on the
ground? If the tree tries to rid itself of diseased leaves, the
prediction would be fewer spots on leaves still on the tree.
If the fungus–tree symbiosis is a mutualism, the opposite prediction would be made.
4. Should yellow leaves have more tar spot than green leaves? If
the fungus is harming the leaves, the tree may respond by
resorbing green pigments, or the fungus may tap into those
pigments for nutrition, potentially leaving the leaves yellow.
Harm is predicted to be greater for leaves with more fungus
spots. Another reason that yellow leaves might have more
tar spots is that leaves are simply older and have therefore
been exposed to more spores and, on top of this, are senesc-ing. If the symbiosis is a mutualism, the opposite pattern
would be predicted.
5. Does the class predict more tar spots in a particular habitat?
Depending on the habitats being compared, several factors
may be important. In the case of residential versus forest habitats, the former may receive more fertilizers and so the trees
there may be better at resisting fungi. On the other hand,
raking of leaves may facilitate the spread of spores. Differences in humidity between habitats may affect spore dispersal,
and different conditions in soil where fallen leaves lie may
affect overwinter survival. In addition, there may be differences in the density and diversity of suitable hosts in the two
habitats. As another consideration, competition may differ
among habitats; trees may have more resources to devote to
fighting off fungi where competition is lower. There are many
other possible influences.
To start, calculate prevalence (proportion of infected hosts), mean
intensity (mean number of spots per leaf), and standard deviation
(SD) in intensity. If using Excel, to obtain means, type “=average
()” and then put the cursor inside parentheses, and drag the cursor
from the top of the column with data entries to the bottom. For the
SDs, use the same procedure with “stdev()”. Plot a histogram of
intensity (the number of symbionts per individual; in this case
the number of spots per leaf). Was tar spot randomly distributed
on leaves? If so, the mean and SD of intensity should be similar –
a defining characteristic of Poisson distributions. A more rigorous
test can be done by calculating expected values for each interval
in the histogram. Sample calculations are provided in Table 2.
Next, calculate prevalence and mean + SD intensity separately for
each habitat, for each location, and for each leaf color, and compare
these values using analysis of variance (ANOVA).
The following are results from actual implementation of this lab
activity. Data were collected from 1550 leaves; the mean number of
spots was 3.75 and the SD was 3.84, which is relatively consistent
with a Poisson distribution (Figure 2). Whereas ~60% of leaves in
the forest were green, ~72% were green in the residential habitat
(Table 3). About 94% of leaves sampled from trees were green versus only 36% on the ground (Table 3). The more important analyses are on tar spots. There were more tar spots on leaves on trees
than on leaves on the ground (Table 4). Also, the number of spots
did not differ between green versus yellow leaves. Finally, there
were far more spots on leaves of forest trees than on leaves of residential trees (Table 4). These analyses do not control for repeated
sampling of a tree; this would require using a mixed statistical
model with tree identity as a random factor.
MacArthur (1972) wrote that “to do science is to search for
repeated patterns.” If this perspective on science is not already
awake in your students, the exercise described here has the potential to awaken it. The content of the lab introduces students to the
entire range of the scientific process, beginning with simply
Table 2. Calculating expected frequencies under the null expectation of a random distribution of tar spot
fungi based on a hypothetical sample of 1000 leaves.
Number of Spots Observed Frequency Expected Frequency Contribution to Chi-square
0 109 23. 6 309.0
1 188 88.5 111.9
2 166 165.7 0.0
3 143 206.9 19. 7
4 112 193.7 34. 5
5 74 145.1 34. 8
> 5 208 176.5 5. 6
Notes: To calculate the expected frequency, you first need to calculate the mean, which for these data was 3.746. Expected frequencies for a Poisson distribution are
e−x̄ X̄ / x factorial N. For the first cell, this is 0.0236 3.7460 / 0! 1000. Note that 0! is 1. The contribution to the χ2 statistic is (Observed-Expected)2/Expected; the
final χ2 6 stat is the sum of these values. Without doing the calculations, the first line indicates significant deviation from a Poisson distribution; P will be much less