Question

You sample a plant bed in a lake a few years after Eurasian watermilfoil has been introduced. You find the following plants in the plot (data are plant species name and number found):

Eurasian watermilfoil 71

White waterlily 3

Yellow waterlily 4

Water mustard 3

Curly leaf pondweed 1

Narrowleaf pondweed   6

Cattail 4

Pond sedge 5

Pickerelweed 2

Calculate the Shannon-Wiener Index for this sample. The correct value of the Shannon-Wiener diversity index for this sample is

Select one:

a. 0.913

b. 1.595

c. 1.145

d. 1.865

Answer 1

Okay let's start with the formula used for the Shannon Weiner diversity index:

Where p is the proportion of the species in the sample (number of individuals of one species divided by the total number of individuals sampled). ln is the natural log, we will multiply the natural log of p by p for each species, and then sum all of them. Let's use a table to summarize it:

Species	Incidence	Proportion	lnp	(p)(lnp)
Eurasian watermilfoil	71	0.71	-0.34	-0.241
White eaterlily	3	0.03	-3.5	-0.105
Yellow Water lily	4	0.04	-3.2	-0.128
Water mustard	3	0.03	-3.5	-0.105
Curly leaf pondweed	1	0.01	-4.6	-0.046
Narrow leaf pondweed	6	0.06	-2.8	-0.168
Cattail	4	0.04	-3.2	-0.128
Pond sedge	5	0.05	-2.9	-0.145
Pickerelweed	2	0.02	-3.9	-0.078
Sum				-1.144

Now, remember we have to change the sign as the formula indicates it, so the value is 1.144. The answer is option C.