ENV 311/EEB 320: Polluted Streams Lab—Winter 2007
Due in lab on Th 3/22 or M 3/26.
1. Using the chemistry data and flow measurements taken at each site, calculate the
discharge (m3/sec), daily load (kg/day), and yield (kg/ km2/day) for total reactive
phosphorous (TRP) and nitrite/nitrate-nitrogen (NOx-N). Remember that some unit
conversions will be necessary. Briefly describe your results and explain whether they
make sense given the conditions unique to each watershed. 5 pts
2. Using the family-level site taxa list provided (includes insects and crustaceans only),
compare the diversity [number of families] at each site. Include the Kalamazoo taxa in
your comparison.
What does this imply about pollution and biodiversity in rivers? Refer to the land use,
surficial geology, and other maps for the area as well as your knowledge of pollution
sources to help you answer this question. Assume equal sampling effort was used at all
sites. 5 pts
3. EXTRA CREDIT. Plot the water quality measurements against invertebrate family
biodiversity. How correlated are they? Are there any surprises? If so, can you explain
them? If not, why not? 1 pt
A Few Words on Stream Discharge and Diversity Indices
So, you’ve just received this assignment and you’re wondering where to start. We
haven’t practiced calculating diversity indices or discharge in class and you’d like to be
sure you’re doing it the right way. Below, you’ll find a brief intro and an example for
each topic.
Discharge
In the field we’ve sampled the depth-averaged (60% depth) velocity along a transect
perpendicular to the average direction of flow for each site. Once you’ve converted all
units, you can use a little simple geometry to approximate the discharge through a twodimensional cross-section on each stream reach. Because you have velocity readings at
several verticals in the cross-section, you can divide the transect into vertical subareas.
Start from the left edge (where the depth is zero), set the width at that point to zero and
then work your way across the stream, using the velocity and depth averaged over the
verticals bounding each subarea. To get the total discharge, just sum up the discharge for
all the subareas, i.e.:
N 1
  d  d n1  vn  vn1 

Q     n

wn1  wn 
2
2


n 1  

where d is depth, v is velocity, w is width and N is the total number of points in the
transect (including edges).
For instance, in the diagram below, the discharge for subarea (A) is just the average of
depth 1 and 2 times the average of velocity 1 and 2 times width (a). If we know that
depth 1 = 0.00m and depth 2 = 0.10 m, a=0.10 m, velocity 1=0.00 m/s and velocity
2=0.20 m/s then:
 0.00m  0.10m  0.00m / s  0.20m / s 
3
QA  

0.10m   0.05m 0.10m / s 0.10m   0.0005m / s
2
2



Then do the same for subarea B, C, etc. through G and add them up at the end.
Diversity Indices
Biodiversity is not easy to quantify or even to define. Few authors agree on appropriate
methods. Many choose to use so-called biodiversity indices for comparison of diversity
between sites or at the same site over time. While these indices produce relatively
arbitrary numbers that have little meaning in and of themselves, they are frequently
encountered in the literature and, as such, it is a good idea to be familiar with at least the
most common ones.
Basically, these indices attempt to quantify one or both of the following:
 Heterogeneity—how varied is the assemblage of organisms at the site?
 Evenness—how evenly are the abundances of these organisms distributed? Are
there just a few really common taxa and many rare ones or are most of the taxa of
an intermediate abundance (e.g., an assemblage with 10 individuals of species A,
B and C is more even than an assemblage with 28 individuals of species A and
one individual each in species B and C)?
There are three indices you may need to use to complete this assignment:
1. Richness, which is not really an index but just a simple count of all the taxa (of a
given level) encountered. In this assignment, it will be the total number of
families (you do not need to incorporate abundances into this measure). Richness
measures can get much more complicated than this and may involve statistical
estimates of the true total number of taxa present at a site. For our purposes,
however, you may assume that we collected all taxa present.
2. The Shannon-Wiener index (often erroneously called the Shannon-Weaver
index) has been widely used in ecological studies for decades. However, it
suffers from some serious drawbacks, including the fact that it tends to be very
dependent on sample size. If an assemblage is incompletely sampled (as is almost
always the case—because it is often impractical to collect all individuals or
species at a site), the estimator of this index will always be biased. Also, while
the richness measure (above) makes intuitive sense, the Shannon-Wiener index
produces a value (H') that usually varies between 1.5 and 3.5, numbers that do not
mean anything in and of themselves. These values only have meaning relative to
each other, i.e. a site scoring a 2.2 may reflect a more diverse community than a
site scoring only 1.9.
To counter the second problem, the exponential Shannon Wiener index (eH' ) was
derived. The results you get from this modified index can be thought of as the
number of families you would expect to see if all families were equally common.
You will be using this modification for the assignment.
Modified Shannon-Wiener index: e H , where H'=    pi  ln  pi 
'
and pi is the proportion of individuals in the ith family.
3. The Simpson index of diversity (1/D) is less sensitive to sample size than the
Shannon-Wiener index. Even with incomplete sampling of the taxonomic
assemblage, it tends to reflect the underlying abundance distribution, especially
when the number of taxa in the sample is 10 or greater. Since D represents
dominance, assemblages with higher values of 1/D can be thought of as more
heterogeneous and even.
Simpson’s index of diversity : 1/D, where D is dominance
 ni (ni 1) 
 N ( N 1) 


and D   
ni is the number of individuals in family i and N is the total number of individuals.
Higher values of Simpson’s index of diversity indicate more diverse (and more
even) communities.
Examples
Assume that you have found the following abundances in one of your samples:
Number
Taxon
Abundance
1
A
9
2
B
3
3
C
1
The richness would be 3.
The exponential Shannon-Wiener index would be:
e
  9  9   3  3   1  1  
    ln      ln      ln  
  13   13   13   13   13   13  
 e 0.8  2.2
The Simpson index would be:
9  (9  1)  3  (3  1)  1 (1  1)  72  6  0  0.5
13  (13  1)
156