I have data both on the number of families found at each location as well as the abundance of individuals. Through my research, I've deduced that it may be a good idea to use the Simpson or Shannon indices, which I have done. Now that I have this data and have ended with a value between zero and one for both, how do I go about making comparisons between the groups and verifying that any differences may be statistically significant?
Any suggestions are welcome -- I'm trying to tread water without having taken a biostatistics class yet.
Dear Kirby,
What do you mean with "groups"? Do you want to compare the 5 areas (= 5 values for Shannon index and Simpson index)? In this case a statistical comparison will be difficult.
Dear Kirby,
While Simpson's dominance index (D) and complementary diversity index (1-D) rank 0-1, it is relatively uncommon to obtain a Shannon index (H') below one. You need very few groups (families in your case) and one of the groups must be exceedingly abundant while the others must be rare indeed in terms of individuals, i.e. be a sample with high dominance (Simpson's D, not to be confused with Simpson's diversity which is 1-D or 1/D), and low richness (S, or number of families in your case). Is that so with your samples or inventories?
Please bear in mind that although technically it can be calculated for any S>1, H' comparisons lose much meaning when the number of groups is very low, as small changes (e.g. one single group added or substracted to S) may have profound effect on the index.
H' and D can be most meaningfully compared when samples are [EITHER identical in total specimen abundance OR taken under identical conditions as regards to area size, effort, technique, etc.] AND have been assessed for minimal sample size, AT LEAST as regards to richness (all or almost all groups actually existing in the location or community being sampled do appear in the samples).
There are other conditions as well, and corrections can be done prior to comparisons (which generally can be done in pairs), but the above requirements should be met first whenever possible.
Regards
Dear Karpan, I think it best you try to use a comparison for richness estimated by Jackniffe 1, but for this, your data should be raised considering pseudoreplicas. That way you can safely compare the five areas.
Dear Roland,
Yes, you're correct. That is what I was hoping to do.
Dear Arturo,
The 0-1 value I obtained with the Shannon index was with a bit further manipulation of the numbers that I found suggested online. After I obtained the negative of n/N*ln(n/N), I calculated an Hmax value by taking the natural log of the number of total families identified. I then obtained a value that they called Eh by dividing the negative of n/N*ln(n/N) by the Hmax value, and this gave me a value between zero and 1 for all 5 of my areas.
The samples were taken under identical conditions, so I will make it my next step to assess for minimal sample sizes.
Oh I see--you are actually calculating eveness. Indeed, eveness is a 0-1 ratio. The Shannon index is the amount of information and is the "negative" part of your formula, H' = -SUM[pi·log2(pi)], and is measured in bits. You can find a link to a short presentation below. As you are using natural logarithms instead, H' is defined instead in natbits. But this may be of no real consequence for your study.
You are using a formula which is correct as long as your relative proportions (pi, or your n/N) are exactly known: that is, both n and N tend to infinite. This is almost never the case as you are presumably working with finite samples from a much larger area, so a correction should be applied; however, as long as N is sufficiently large and there are enough groups (sample meets minimal requirements) the bias becomes negligible and you can safely use the simplified formula. On the other hand, if you are e.g. working with census data (for example, tree vegetation) and you have total numbers, it would be more appropriate to calculate H through the Brillouin series.
At any rate, as you want to make statistical comparisons you should be concerned with the significance of those tests. For that you need to estimate the variance of your H' readings; once you have the variance, a t test can be performed as the distribution of H has often been found to be relatively normal. The tricky parts can be obtaining that estimate of variance for H' as well as the degrees of freedom, although some people have used common comparisons as if they were parametric tests (actually, H' is non-parametric but its distribution might be).
The variance can possibly be best obtained through jackknifing or bootstrapping, although there's also a direct estimate proposed long ago by Hutcheson (1970), not used very often as far as I know. The degrees of freedom depend on the actual values of the variance and N. You can find the formulae in Zar (1974), Biostatistical Analysis. If you can't access it I can send you the Hutcheson formulae or even an Excel template to do the calculations directly. I often prefer to bootstrap the samples and then proceed normally once I have bootstrap averages and variances for H'.
There is no universally accepted method (or even definition) to ensure minimal sample size. Most approaches rely on species accumulation curves. I also attach a reference to a paper describing one such method. Alternatively, a Whittaker plot (see ref. on beta below) may help you infer whether your samples' distributions have captured basically all groups, even rare ones, which should be enough.
Hope this helps. Regards
Chapter Optimal Sampling for Complexity in Soil Ecosystems
Conference Paper Beta diversity
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