I’ve got a little confused with the interpretation of Simpsons’ index and Simpson’s inverse index for assessing diversity. My understanding was that the higher the value of the output from Invsimpson the greater the diversity. However, someone pointed out to me that being the inverse of the Simpson’s index should it not be the other way around? Sorry if its a bit of a stupid question but i’m not that familiar with the different diversity indices. Also is there any advantage of using Simpson’s instead of Shannon’s? As the latter seems to be the more commonly used index from what I’ve seen.
From Zhou et al 2002. Spatial and Resource Factors Influencing High Microbial Diversity in Soil. AEM:
"The use of 1/D instead of the original formulation of Simpson’s index ensures that an increase in the reciprocal index reflects an increase in diversity (Magurran, E. 1988. Ecological diversity and its measurement. Princeton University Press, Princeton, N.J.)."
Simpson’s diversity index can basically be thought of as the probability that upon randomly selecting an individual from a community, the individual has already been observed.
So the higher the SDI is, the less diverse your sample will be (if you’re constantly observing previously recorded individuals you must be getting close to complete coverage). Since this isn’t very intuitive - as you say, you would expect that the higher the diversity index is, the more diverse the community is - the inverse or reciprocal are used to make the results more intuitive.
Another interpretation of the inverse simpson: it is the richness you’d have for a community with perfect evenness and the same diversity as the community you were sampling.