Maria --
If you're getting sample counts so low as zero, you might well question
whether the they are reasonable estimators for the population
proportions the Shannon-Wiener index depends on. As a practical matter,
your resulting variances may be too high to enable you to distinguish
among treatments.
A more sensible use of your data would be to look at the Shannon-Wiener
diversity for some aggregation of your samples for each treatment (thus
comparing the populations associated with each treatment). Simply
totaling and calculating H' doesn't yield enough for a statistical
comparison, but you can get mean Shannon-Wiener +/- SD for a random
resampling using EstimateS (even if you don't use the free software, the
user manual and references are quite helpful):
http://viceroy.eeb.uconn.edu/EstimateSPages/EstSUsersGuide/EstimateSUsersGuide.htm
Moreover, you might want to use some of the included estimators of
species richness, which take into account the relative abundance of rare
species. With any of these methods, the zero-counts wouldn't present a
problem.
I agree with the comments of others that Shannon-Wiener diversity should
be reported as exp(H'), as discussed by Jost (2006).
Best of luck!
-- Kurt Moser (M.S. Environmental Science & Policy, George Mason University)
Maria Van Dyke wrote:
Dear ECO loggers,
I have a question about utility of the Shannon-Wiener diversity index in
regards to sampling units that have no species in them at a given sampling
time. Normally this would get a value of zero, however with Shannon-Wiener a
sampling unit that has only one individual of one species would also earn
the value of zero when input into the formula -∑(1*ln1) =
-∑(1*0) = 0;
therefore there becomes an issue of two different species scenarios having
the same values (0 for no species individuals and 0 for 1 ind of one species).
For example:
I am studying substrate preferences of ground nesting bees in which I
created three different substrate treatment types for bees to nest in. In
all, I have 20 plots that have the 3 different treatments (subplots) within
each plot. I sampled all subplots of all plots 7 times throughout the bee
flight season. During some rounds I would collect no bees from a subplot and
therefore have no species to calculate diversity from in my data set. How do
I deal with these subplots that actually had no (zero) bee species in them?
I would use Simpson Diversity instead but I am interested in rare species so
I thought it would not be sensitive enough.
I know this is somewhat of a strange predicament b/c the data sets that
Shannon-Wiener is usually applied to normally have at least one species per
plot at the very least but the nature of my study forces me to deal with
these true zero values.
Has anyone out there had to deal with this before? I am open to any and all
suggestions or varying approaches. Is there a better index to use for this
analysis? I intend to use the results from diversity to calculate evenness
as well. Please enlighten me
Maria Van Dyke
Department of Environmental Sciences
University of Virginia
