Statistics - Shannon Wiener Diversity Index

Statistics – Shannon Wiener Diversity Index

Within the literature, the phrases species richness and species variety are generally used interchangeably. We recommend that on the very least, authors ought to outline what they imply by both time period. Of the various species variety indices used within the literature, the Shannon Index is probably mostly used. On some events it’s known as the Shannon-Wiener Index and on different events it’s known as the Shannon-Weaver Index. We recommend a proof for this twin use of phrases and in so doing we provide a tribute to the late Claude Shannon (who handed away on 24 February 2001).

Shannon-Wiener Index is outlined and given by the next perform:

H=[(pi)×ln(pi)]H=∑[(pi)×ln(pi)]

The place −

  • pipi = proportion of complete pattern represented by species ii. Divide no. of people of species i by complete variety of samples.
  • SS = variety of species, = species richness
  • Hmax=ln(S)Hmax=ln(S) = Most variety attainable
  • EE = Evenness = HHmaxHHmax

Instance

Downside Assertion:

The samples of 5 species are 60,10,25,1,4. Calculate the Shannon variety index and Evenness for these pattern values.

Pattern Values (S) = 60,10,25,1,Four variety of species (N) = 5

First, allow us to calculate the sum of the given values.

sum = (60+10+25+1+4) = 100

Species (i)(i) No. in pattern pipi ln(pi)ln(pi) pi×ln(pi)pi×ln(pi)
Huge bluestem 60 0.60 -0.51 -0.31
Partridge pea 10 0.10 -2.30 -0.23
Sumac 25 0.25 -1.39 -0.35
Sedge 1 0.01 -4.61 -0.05
Lespedeza 4 0.04 -3.22 -0.13
S = 5 Sum = 100 Sum = -1.07

 

H=1.07Hmax=ln(S)=ln(5)=1.61E=1.071.61=0.66Shannon diversity index(H)=1.07Evenness=0.66