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How to Calculate the Shannon-Weaver Diversity Index

The Shannon-Weaver diversity index helps determine species diversity in a community at a particular time. This diversity index, also known as the Shannon-Wiener species diversity index or simply the Shannon index, calculates the number of different species in a community (species richness), and the proportion of individuals in a single species compared to the number of individuals of other species in the same community. This comparison shows how rare or common a species is in a group. The Shannon-Weaver diversity index is expressed as the formula H = -sum(Pi ln[Pi]). In this formula H represents the Shannon-Weaver diversity index and Pi is the number of individuals in a particular species divided by the total number of individuals of all species in the community. The diversity index can be use to measure species diversity in any defined study; for this illustration we̵7;ll determine the diversity of trees in a yard.

Instructions

- 1
  Identify the different tree species in the yard using their scientific names. For this example, we have red maple (Acer rubrum), silver maple (Acer saccharinum), Virginia pine (Pinus virginiana ) and live oak (Quercus virginiana) for a total of four species. Remember to identify each tree to species level and not genus. For example, red maple (Acer rubrum) and silver maple (Acer saccharinum) are in the same genus, but are different species.
- 2
  Count the number of trees in each species in the study area. In this case, the count yields 10 red maple, four silver maple, three Virginia pine and one live oak for a total of 18 trees spread across four species.
- 3
  Calculate Pi for each species by dividing the number of a given species by the total number of all trees in the study area. Pi for red maple is 10 divided by 18, which equals 0.556. Pi for the remaining species is: silver maple 0.222, Virginia pine 0.167 and live oak 0.056.
- 4
  Multiply Pi for each species by the natural log of its Pi. For red maple, (Pi ln[Pi]) is (0.556 ln[0.556]) with a result of -0.326. Note, the result is a negative number. (Pi ln[Pi]) for the other species is: silver maple -0.334, Virginia pine -0.299 and live oak -0.161.
- 5
  Add together the results of (Pi ln[Pi]) for all species. Because the diversity index formula starts with a negative sign, H = -sum(Pi ln[Pi]), multiply the result by -1. The Shannon-Weaver diversity index for this community is 1.12. A Shannon-Weaver diversity index of zero indicates that only one species is in the community; as diversity increases, so does the index number. The most diverse communities have an index of seven or higher. The community in this illustration is moderately diverse.

Nature