In study of the influence of cattle grazing on day butterfly populations, in northern Israel (Ish Am & Oron 2018: Effect of cattle grazing on day butterfly populations (Lepidoptera: Rhopalocera) in the Mediterranean Maqui Har-Hermon Reserve in Israel) we found in some sites, which were under cattle grazing, a lower mean richness (half to a quarter), compared with ungrazed control sites, though almost a similar mean abundance. In the grazing sites almost all the monophagous and endangered butterfly species were gone. Since most of these butterfly species consist of very small population, we calculated in the ungrazed control a lower evenness, compared with the grazed sites. Since Shannon diversity index is positively correlated with both evenness and richness indices we calculated a higher mean Shannon diversity index for the grazed sites. In this case I don't really understand what is the ecological mining of the Shannon diversity index? Watching richness and evenness indices, plus species lists, I understand that the cattle grazing hurt niches that are essential for the monophagous butterfly species. However, since these species are rare even in the ungrazed sites the mean richness there was almost similar to that in the grazed sites.
Is there any addition insight from the Shannon diversity index here?
The same question is applied for the Simpson's diversity Index as well.
Hello dear Gad Ish-Am.
I know that the Shannon index (H') is very criticized because it does not measure diversity per se. It instead measures entropy in each community. It means that one community with H' = 1 and a second one with H'= 2, is not necessarily two times more diverse. Then the ecologists employed a correction to transform it into an effective-species index (1D) as follows: 1D= exp(H') (as the suggestion by Jost, 2006).
Starting from your question, I think that monophagous and endangered butterflies are more susceptible to perturbations (grazing). Then the lowest value of H' index was found on this site.
Regards
The Shannon diversity index (H) is another index that is commonly used to characterize species diversity in a community. Like Simpson's index, Shannon's index accounts for both abundance and evenness of the species present. http://www.tiem.utk.edu/~gross/bioed/bealsmodules/shannonDI.html
In the Shannon index, p is the proportion (n/N) of individuals of one particular species found (n) divided by the total number of individuals found (N), ln is the natural log, Σ is the sum of the calculations, and s is the number of species. .http://entnemdept.ufl.edu/hodges/protectus/lp_webfolder/9_12_grade/student_handout_1a.pdf
The Shannon-Wiener Diversity Index, H, is calculated using the following equation: H = -å Pi(lnPi) where Pi is the proportion of each species in the sample. Given a very large sample size, with more than 5 species, the S-W index values (H) can range of 0 to ~4.6 using the natural log (ln). http://www.manhassetschools.org/cms/lib8/NY01913789/Centricity/Domain/681/Lab5%20Shannon%20Diversity%20Index.doc
You could also perform ordination and anova with post hoc tests, which will show patterns and compare sites
http://www.tiem.utk.edu/~gross/bioed/bealsmodules/shannonDI.html.
Cristian Adrian Martínez-Adriano
Thanks for your informative and relevant answer
Renyi entropy of Alfa more than 0 and less than 1 is Shannon entropy (H). It is amount of information, however it's not indicating diversity directly but effect number is species (ENS) can be calculated as exponential of H
The Hill's numbers or effective numbers of species recently have been recommended to replace various diversity indices for a number of statistical advantages. However, these "new" diversity measures are subject to the same flaw, i.e., their biological relevancies never established. When applied to restoration and conservation, they are hard to interpret and can be very misleading. You might like to check: Article Weighting effective number of species measures by abundance ...
Yong Cao
Thank you for the relevant information, which is worth for consideration
Most of these replies discuss the indices and their value. Ages ago I di my Master's thesis on the effects of clear-cutting in Finnish boreal forest. In those days Shannon-Weaner dominated discussions. My results were exacty thr same as in huge Polish studies earlier. After the forest was cut away, the SW index increased. In Poland they had been able to study equal sized clear-cut plots of different age simultaneously (1, 10, 20, 40, 60 years). The result was that after the initial increase, the value finally decreased to the original non-cut value. My study had areas of different age and the same could be observed. Looking at all the beetle species
...cut off, sorry! ...it became clear that dominant forest species had crushed in numbers and new open habitat species invaded causing a richer more even fauna. After the new trees grow, finally this all returns to the original state. Now, in your case there might be a simple answer as well. The rare butterflies utilizing the rare plants are very likely to have specialized in such a world and thus the grazing may effect them only marginally. After all, like you said they were rare outside the grazing area already. Had the grazer been sheep, I suspect they would have vanished, many other mammals are less thorough. As to Shannon-W index, I think it can give you a hint as to what has happened, but it certainly does not measure something that is good = high and bad = low.
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