Simpson's Diversity index has two forms, one equation for finite populations and one for infinite populations. Which version should I use if working with vegetation % cover values from quadrats? A brief survey of published papers shows both equations used with such data suggesting that either there is no meaningful difference or that authors have not considered the options.
Have you thought of using Hill numbers instead? Hill 1 and 2 are equivalent to Shannon and Simpson, respectively. But have much better properties thann the traditional use. Firstly, they have units, that is the value provided is in number of species (SW &S are unitless) thus are comparable and more meaningful. Secondly, they comply with the doubling principle. That is, if true diversity doubles, their value does so (SW &S don't). You can read Jost or Chao for more information. Lastly, the use of Shannon or Simpson (or their equivalents) depends on how much weight you want to give to common species. Hope this helps.
Dear Sir,
You should go with the finite population as it is considered most adopted and reliable method to study the diversity indices of the unit area. Infinite population did not has much more difference but not accepted by all the coworkers in the field of biodiversity.
Thanks for your input. However, I read this in a recent Journal of Ecology paper:
"When applying the index to vegetation data, it is common practice to use the proportional cover or biomass of each species rather than the proportion of individuals; and hence an adjustment to prevent bias in a finite sample of individuals (Simpson 1949) is not applied here."
http://onlinelibrary.wiley.com/doi/10.1111/j.1365-2745.2010.01762.x/pdf
It is better to use Shannon-Weiner index for defining diversity than Simpson Index, as it incorporates the proportion of species / their property. The details may be found in the following two books.
1. Fundamentals of Ecology by E.P. Odum and
2. Field Biology and Ecology by Smith.
The choice between Shannon-Weiner and Simpson index is very much open to debate. It is by no means widely accepted that SW is better, and in recent years opinion has moved away from SW. I would urge anyone interested in using these indices/functions to read around in the contemporary literature. See this thread for starters.
https://www.researchgate.net/post/what_is_the_deference_between_Shannon_Wiener_diversity_Index_and_Simpson_diversity_Index
Have you thought of using Hill numbers instead? Hill 1 and 2 are equivalent to Shannon and Simpson, respectively. But have much better properties thann the traditional use. Firstly, they have units, that is the value provided is in number of species (SW &S are unitless) thus are comparable and more meaningful. Secondly, they comply with the doubling principle. That is, if true diversity doubles, their value does so (SW &S don't). You can read Jost or Chao for more information. Lastly, the use of Shannon or Simpson (or their equivalents) depends on how much weight you want to give to common species. Hope this helps.
What is clear is that there is little consensus about the use of finite or infinite versions. If you are free to use alternative indices, then Hill's numbers is the best choice (as advised by @Jaime Pinzon. If for some reasons you are restricted in your choice and have to use Simpson's index and nothing else, then finite or infinite version can be decided by additional criteria. Is your sample a part of a very large population? Then infinite version can be chosen. If the population is small or local, the finite one can do.
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