BIO 208L
McMurry
SPRING 2001
Worksheet for Population Dispersion Lab
Turn in your work, including printouts of your Excel file.
Plot methods of measuring dispersion
1. Tally the number of plots with 0-5 junipers, following the example on the lab
handout. Write your findings in the table below.
2. Calculate the observed proportion of plots with 0-5 junipers. Write your findings in
the table below.
3. Calculate the expected proportion of plots by using the Poisson function in Excel and
fill in the table below. (You will need to determine the mean number of junipers per
plot first, see #5 below). Write your findings in the table below.
X
Number of
Observed
Expected
plots
proportion of
proportion of
plots
plots
0
1
2
3
4
5
4. Graph the two sets of numbers (observed vs. expected proportion of plots) and turn
in the figure (appropriately formatted and labeled).
5. Calculate the mean and the variance of the number of junipers per plot in Excel. The
easiest way is to use the descriptive statistics option under "Tools…Data Analysis".
Recall that if "Data Analysis" does not appear under "Tools", you must add it in by
choosing "Add-Ins" under "Tools" and checking the data analysis toolbox.
Variance = ________________ Mean = __________________
6. Divide the variance by the mean. This is your variance-to-mean ratio. Write it in the
space below.
Variance/mean = _____________________
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BIO 208L
McMurry
SPRING 2001
7. Calculate the t value given in Equation 2 on the handout. Show your work here.
8. Look up the critical t value for n-1 degrees of freedom and  = 0.05 in Table 1B.1 in
Brower et al. (1998) and write it in the space below.
9. Is the dispersion pattern significantly different from random? (Compare your value to
the critical value.) If it is nonrandom, is the dispersion pattern clumped or uniform?
Morisita's Index
1. Calculate Morisita's Index, Id, using Equation 4 on the handout.
 For each plot, square the number of junipers. Sum the squares.
 Subtract N, the total number of juniper trees from the summed squares. Divide by
N*(N-1).
 Multiply by n, the number of plots.
Write your answer here: Id = _____________________
1. Calculate 2 using Equation 5 on the handout. Write your answer in the space below.
Write the critical value of 2 for n-1 degrees of freedom at  = 0.05 down below.
2. Is the dispersion pattern significantly different from random? If so, is it clumped or
uniform?
Plotless methods of measuring dispersion
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BIO 208L
McMurry
SPRING 2001
The Holgate Method
1. Calculate A using Equation 6.
 Square d and d' and take the ratio for each point.
 Sum the ratios.
 Divide by the number of points (n).
 Subtract 0.5.
Write your answer here: A =
1. Calculate t by using Equation 7 on the handout. Write your answer in the space
below.
2.
Look up the critical value of t in Table 1B.1 of Brower et al. (1998) for n-1 degrees
of freedom (n = the number of points sampled) and  = 0.05. Write your answer in
the space below.
3. Is the dispersion pattern significantly different from random? If so, is it clumped or
uniform?
Johnson and Zimmer method
1. Calculate A using Equation 8 on the handout.
2. Calculate t using Equation 9 on the handout. Show your work in the space below.
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