Enter the proportion of individuals of each species and their natural logarithms into the calculator to determine the Shannon Weiner Index.

Shannon Weiner Index Formula

The following formula is used to calculate the Shannon Weiner Index. 

SWI = - Σ (p_i * ln(p_i))

Variables:

  • SWI is the Shannon Weiner Index
  • p_i is the proportion of individuals of a particular species
  • Σ is the sum of the calculations for each species

To calculate the Shannon Weiner Index, for each species, calculate the proportion of individuals of that species, then multiply this by the natural logarithm of that proportion. Sum all these calculations together and multiply by -1 to get the Shannon Weiner Index. This index measures the biodiversity of a habitat, with higher values indicating greater biodiversity.

What is a Shannon Weiner Index?

The Shannon Weiner Index, also known as the Shannon Diversity Index or the Shannon-Weaver Index, is a mathematical measure used in ecology to quantify the biodiversity within a habitat. It takes into account the number of species present, as well as the relative abundance of each species. The higher the value of the index, the greater the diversity of species in the ecosystem. This index is commonly used in environmental studies to assess the health and diversity of various ecosystems.

How to Calculate Shannon Weiner Index?

The following steps outline how to calculate the Shannon Weiner Index (SWI) using the formula SWI = - Σ (p_i * ln(p_i)).

  1. First, determine the proportion of individuals of each species (p_i).
  2. Next, calculate the natural logarithm (ln) of each proportion (p_i).
  3. Multiply each proportion (p_i) by its corresponding natural logarithm (ln(p_i)).
  4. Sum up all the calculations from step 3.
  5. Multiply the sum from step 4 by -1 to get the Shannon Weiner Index (SWI).

Example Problem:

Use the following variables as an example problem to test your knowledge:

Proportion of species A (p_A) = 0.4

Proportion of species B (p_B) = 0.3

Proportion of species C (p_C) = 0.2

Proportion of species D (p_D) = 0.1

Using the formula SWI = - Σ (p_i * ln(p_i)), calculate the Shannon Weiner Index (SWI) for the given proportions.