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Can I compare the Shannon-Wiener (a.k.a. Shannon-Weaver) Index of diversity ($H'$) of plots (communities) with varying sizes (areas)?

If not, what steps do I need to take and/or which tests should I use to compare the diversity of different-sized plots?

I also wonder if this is possible for Simpson's Index of diversity?

Shannon-Wiener Index:

$$H' = -\sum \limits_{i=1}^S p_i \ln p_i$$

Simpson Index:

$$D = 1 -\sum \limits_{i=1}^S {p_i}^2$$

Where $p_i$ is the proportion of species $i$, and $S$ is the number of species.

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  • $\begingroup$ Welcome to Biology.SE. I am not an ecologist and I don't know the Shannon-Wiener index (and don't remember by heart the definition of the Simpson's index). However, if you were to include the definitions of those indices, I (and others) might be able to answer without having to search the literature for those definitions. When you say different-sized plot, do you mean different total number of individuals (total abundance) per plot? $\endgroup$ – Remi.b Aug 6 '15 at 17:33
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    $\begingroup$ Different sized plots strictly in terms of each plot having inconsistent physical AREA. For example, 1 plot might be 500m2, while another might be 1100m2. $\endgroup$ – theforestecologist Aug 6 '15 at 17:49
  • $\begingroup$ Oh Shannon-wiener index is just what I would call the Shannon Index. This is why I did not recognize it at first place. Thanks for the edit +1 $\endgroup$ – Remi.b Aug 6 '15 at 17:51
  • $\begingroup$ No problem. I think the science community needs to make up their minds about what to call it ha! $\endgroup$ – theforestecologist Aug 6 '15 at 17:58
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Theoretically the index for two habitats of different areas are not directly comparable. Consider the species area relationship. You see more species when you look over a larger area. So you will potentially see a different index just from considering a larger area, and not necessarily because there is something different about the habitats.

Borda-de-Agua et al tackle this head on. They use fractals to account for differences in area when comparing diversity indexes. It's complicated and I won't try to put the methods here because I don't understand them. Definietly worth looking at yourself though.

I would also consider using species abundance distribution (SAD) curves for comparison. They give information about diversity but don't sum it up in one nice number like indexes. I feel they are area invariant too. Since if you keep increasing the area of your sample, the total species will only increase from relatively few rare species, while abundances will increase mostly with the abundant species. This will not change the slope of the curve but just the intercept (My hypothesis, not sure if it's actually true). Checkout a good comparison of SAD's and diversity indexes in the intro to McGill et al.


References

Borda‐de‐Água, L., Hubbell, S. P., & McAllister, M. (2002). Species‐area curves, diversity indices, and species abundance distributions: a multifractal analysis. The American Naturalist, 159(2), 138-155. Link

McGill, B. J., Etienne, R. S., Gray, J. S., Alonso, D., Anderson, M. J., Benecha, H. K., Dornelas, M., Enquist, B. J., Green, J. L., He, F., Hurlbert, A. H., Magurran, A. E., Marquet, P. A., Maurer, B. A., Ostling, A., Soykan, C. U., Ugland, K. I. and White, E. P. (2007), Species abundance distributions: moving beyond single prediction theories to integration within an ecological framework. Ecology Letters, 10: 995–1015. Link

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