The formula to calculate the Shannon Weiner Index (SWI) is:
\[ SWI = - \sum (p_i \cdot \ln(p_i)) \]
Where:
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.
Let's consider an example with three species with proportions 0.5, 0.3, and 0.2:
Using the formula to calculate the Shannon Weiner Index:
\[ SWI = - \left( 0.5 \cdot \ln(0.5) + 0.3 \cdot \ln(0.3) + 0.2 \cdot \ln(0.2) \right) \approx 1.0297 \]
This means that the Shannon Weiner Index for this example is approximately 1.0297.
