Mathematica will check your work, so please press the Check
button after entering your result to see if you did the calculation correctly (Figure 1A).
2. Now, for each species, we will compute the proportional
abundance, pi ¼ ni N, where ni is the number of individuals
of the species. Enter your answer rounded to the thousandth place (3 digits after the decimal point). For example,
p1 ¼73 111 ¼ 0:658.
3. Complete the table with the proportional abundance for the
other species. Again, check your work by pressing the Check
button. It will check each answer individually. Do not continue until all your answers are correct (Figure 1B).
4. The rank abundance curve is the graph of rank versus the proportional abundance. The rank abundance curve has been
started for you. Complete it by clicking and dragging the points
for ranks 2 through 6 to the appropriate positions (Figure 2).
Simpson’s Diversity Index (for students)
1. Simpson’s Diversity Index is a number that represents the
diversity, in terms of species, of an area. It is calculated using
the formula DS ¼ 1 ∑ip2 i. You just computed the proportional abundance for each species in the sample data. Those results
are duplicated in the next table.
2. To compute Simpson’s Diversity Index, first square each of
the proportional abundance values. For example, for species A, the proportional abundance was p1 ¼0:658, so
p2 1 ¼ 0:4330 (rounded to the nearest ten-thousandth, i.e.,
4 digits after the decimal point) (Figure 3A).
3. Now, add the p2 i values and finally compute Simpson’s
Diversity Index by dividing 1 by that sum, rounding your
answer to the nearest thousandth (Figure 3B).
Evaluation Questions (for students)
1. How does the slope of the rank abundance curve vary with
increasing species evenness? Why?
2. Species diversity measurements take into account both species richness and species evenness. Why would these measurements be preferred to species richness alone?
3. What do rank abundance curves add to one’s knowledge
about community structure?
4. You can make up your own sample data in the table, and the
rank abundance curve and Simpson’s Index will be computed for you. How does the rank abundance curve change
if all the species are equally abundant? (Figure 4)
5. The table in Figure 5 shows data obtained from a mature
deciduous forest stand in northern West Virginia, together
with a rank abundance curve and the value of Simpson’s
Diversity Index (data from Smith & Smith, 2012). You can
move the sliders to change the numbers of individuals of
each species, and see the effect on the curve and the index
Figure 1. Screen shots of the proportional abundance calculation. (A) Step 1 of the methods and (B) step 2 of the methods as
described. We have shown the example with an incorrect answer.
Figure 2. This image shows how the rank abundance graph
appeared to students. They practiced graphing using this