Maria, Bill & all,
A snippet of R code shows how to calculate Simpson's Inverse Index SsubI for a
vector of population sizes, including empty patches.
simp =
function(x)
### simp() calculates the Simpson Reciprocal Index giving a measure of species
diversity
### Patrick Foley 17July2009
{ if(sum(x)==0) return(0)
freq=x/sum(x)
return(1/sum(freq*freq))
}
A quantitative measure of diversity like this fleshes out the intuitive measure
S = species richness. And it accounts for heavy imbalances too. Once you have
such a measure, you can do ANOVA or nonparametric versions for different
substrates. Lots of possible hypotheses can be framed and tested with diversity
measures.
Since one species present represents a greater diversity than none (at least it
does in some sense), SsubI is handier than the S-W index for many purposes. If
it seems important to treat the word 'diversity' as a sacred cow, then use a
different word to express S and SsubI. The ecological literature seems happy
enough with using 'diversity' in a broad sense.
Patrick Foley
[email protected]
________________________________________
From: Ecological Society of America: grants, jobs, news
[[email protected]] On Behalf Of Bill Silvert [[email protected]]
Sent: Friday, July 17, 2009 7:43 AM
To: [email protected]
Subject: Re: [ECOLOG-L] Shannon-Wiener Div Index Question - dealing with zero
species per plot??
After reading this posting and several replies I am getting more and more
confused. Of course both n=0 and n=1 correspond to zero diversity. What is
the issue?
More fundamentally, what is the point of all of this? In the rest of her
posting (which I have omitted) she describes a project for which she wants
an index, but I think that the output of an ecological study should be a
statement about the ecosystem, To say that bees prefer substrate X to
substrate Y is informative, but to simply report the value of some
arbitrarily chosen diversity index is not, at least not so far as I can
tell.
Perhaps if she has some biologically meaningful hypotheses to test it would
be easier to identify some index that can be used to distinguish between
them. She writes "I am studying substrate preferences of ground nesting
bees" but it isn't clear how any diversity index fits into the analysis.
Bill Silvert
----- Original Message -----
From: "Maria Van Dyke" <[email protected]>
To: <[email protected]>
Sent: Thursday, July 16, 2009 6:39 PM
Subject: [ECOLOG-L] Shannon-Wiener Div Index Question - dealing with zero
species per plot??
> 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)
> = -&#8721;(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).
