No, not really. They are important but they deal with different components of species distributions. There are many more indices that suit different data set. I would refer you to two worthwhile text on the subject:
Hayek and Buzas "Surveying natural populations" and Magurran "Measuring biological diversity".
Both discuss the fors and against for different indices and their use.
Eddy is right. Shannon-Wiener has good scientific background as is elaborated from physics (Boltzmann equation) but it is complex index. It consists of species number and equitability or evenness. Interesting question: how to calculate role of every component? Long time ago (1884) I elaborated method, how to do (look my site paper - Structurally-functional features of the basic ciliocenosis groups in Kiev reservoir. (Структурно-функциональные особенности важнейших групп цилиоценозов Киевского водохранилища). (In Russian). Some traits of behavior of Sh index, or its parts even can forecast changes from structural parameters. But they are (or can be) specific for different ciliocoenoses! Direct estimation of evenness (equitability) can do by index of Bray-Curtis (=Hurlbert). Its modification you can see as well in my site:
Влияние донных инфузорий на придонный фитопланктон (Influence of benthic infusoria on near-bottom phytoplankton). (In Russian). 1984 (equation 1). I'm going to translate it into English!
Except of famous Magurran book I can recommend a lot of articles, one important is attached.
You can also read some articles of Lou Jost about this issue. I recommend you to read: Jost, L. 2006. Entropy and diversity. Oikos 113(2):363-375. and Jost, L. 2010. The relation between evenness and diversity. Diversity 2:207-232.
One more note. Yesterday i got the telephone call from Dr. Natalia Kovalchuk that followed this small discussion. She is a specialist in microinvertebrates esp copepods. So, she noted that it is problematic to use this index for small invertebrates where larvae cannot be identified to species level! So, if you have e g more than one species of Cyclops or Nematods with larval stages - no chance to use index in right way! Efforts to try it in Genera’s' level I'm not appreciating as it guide to the loss of main idea of this approach...
Scientists, including hydrobiologists, are very interested in finding adequate index to measure diversity.
Unfortunately, often, discussion about the mentioned indexes goes into a discussion about the authors of the indices. The role of indices is to describe the diversity of natural systems, in particular the index of Shannon (or Shannon-Weaver) has a few unresolved issues:
- First – life (eco-) form of hydrobionts to link the required method of sampling. Otherwise, it makes no sense to calculate the index. For example, zooplankton: zooplankton samples, in the best case, is taken by the the standard Jedi plankton net (inlet diameter 37 cm, capron conical filter with mesh size of 73 μm (the water column have been taken). According to our research of microzoobenthos of deep reservoirs (rhizopods, nematodes, oligochaetes, rotifers, copepods, cladocerans, tardigrades) in its content had been found many species of crustaceans in the upper 2 cm of the soil. This community is generally impossible to study by plankton nets. (Article available in my site in RG.
Second – how the different stages of development that are not determinable, are calculated for the index ? (abundance and biomass?).
- Thirdly, biomass is generally derived from the abundance. Why use it if only not to take into account the role of large predators?
- In the fourth – depending on the time of sampling will vary with indices. When to take samples?