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Author Topic: What exactly is the Williams's index of diversity?  (Read 1363 times)

NFossil

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What exactly is the Williams's index of diversity?
« on: March 30, 2009, 12:30:59 am »
Got a handout from this conservation stuff course, with this Williams index about which I can't find almost any information on the web (there was plenty for Shannon's and others). The formula is: S = a*ln(1+(N/a)). S and N are known, and you'll need to calculate a. Is it really possible with reasonable ease, or is there just some typo on the handout? The examples given have some results that don't come out equal when put into the formula.
S=13,N=27,a=9.9
S=13,N=21,a=13
S=10,N=29,a=8.5
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Jim Groovester

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Re: What exactly is the Williams's index of diversity?
« Reply #1 on: March 30, 2009, 02:27:06 am »
Ech, there's no algebraic way of solving it that I can think of. It looks like it could be the result of integration, but without more information about how it came about and more information about the variables I doubt I'll be able to help you.

And the results do come out close, but not exact, except for the third one. I don't know what's up with that one.
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Quote from: Jim Groovester on April 16, 2021, 04:58:54 pm
I understood nothing, contributed nothing, but still got to win, so good game everybody else.

NFossil

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Re: What exactly is the Williams's index of diversity?
« Reply #2 on: March 30, 2009, 08:14:44 am »
Thanks. Just did some more search and found another name for this thing, then stuff started turning up, such as this one.
http://www.mc.edu/campus/users/rhamilto/Website%20Rocky%20Springs%201/fisher.html
However, I still can't get anything out of it - I guess any differentiation & integration must have gone from me. Saw someone mentioning that it's easy enough to be calculated by hand - definitely not for me.
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Jim Groovester

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Re: What exactly is the Williams's index of diversity?
« Reply #3 on: March 30, 2009, 10:47:31 am »
Did they mention any sort of techniques to solve it by hand? The best I can figure is the infinite series expansion for the ln(1-x), but I may be barking up the wrong tree.

I feel like I should know how to solve this, but I haven't wrote it down on paper and tried to solve it by hand myself, so I can't figure it out.
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Quote from: Jim Groovester on April 16, 2021, 04:58:54 pm
I understood nothing, contributed nothing, but still got to win, so good game everybody else.

NFossil

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Re: What exactly is the Williams's index of diversity?
« Reply #4 on: March 30, 2009, 09:57:23 pm »
Nevermind. Looked over some books at the library today and one mentioned there were tables to derive the value from S/N ratios. I'll just hope that the exam doesn't actually ask us to do it by hand. Judging from the focus of the course, it seems unlikely that such calculations would be required.
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