WK8 - COMMUNITIES & ECOSYSTEMS: Abundance & Diversity: Part 2: Species Diversity

Simpson's Diversity Index (d)

Combines richness and relative abundance into a single metric.
Formula: d = \frac{1}{\sum p_i^2}
- Where p_i is the number of individuals of a single species divided by the total number of individuals in a given area or community.
- \sum indicates summing the p_i^2 values for each species in the community.
- Example with three species (a, b, c): d = \frac{1}{pa^2 + pb^2 + p_c^2}
Higher d indicates higher diversity.
d starts at 1, representing no diversity (only one species in the community).
- If only one species, the number of individuals of that species equals the total, so p_i = 1, and d = \frac{1}{1} = 1.
Simpson's index gives more weight to common species than to rare species.
- A community with one common species and many rare species will have a lower diversity index than a community with fewer species but more even abundance.
Recommendation: Import fake data into the equation to observe how d changes with varying species richness and abundances.

Formula: h' = -\sum (pi * ln(pi))
- Where p_i is the number of individuals of a species divided by the total number of individuals in the community (same as in Simpson's index).
- ln is the natural logarithm.
- The negative sign ensures the index is positive since the values inside the sum are negative.
Example with three species: h' = - (pa * ln(pa) + pb * ln(pb) + pc * ln(pc))
Here, diversity represented by h' starts at zero and increases as diversity goes up.
Balances rare species better than the Simpson's diversity index.
- Gives a better diversity index when there are more rare species.

The choice depends on study objectives and research questions.
Example:
- Three communities (x, y, z), each with five species, but different abundances.
  - Community x: All five species evenly balanced (high diversity).
  - Community y: Decreasing abundance of species (less evenness, drop in indices).
  - Community z: One dominant species (species a) and very rare other species (very uneven).
Observations:
- Community x: High diversity in both Simpson's and Shannon Weaver indices.
- Community y: A drop is observed in both indices due to reduced evenness.
- Community z: Significant drop in Simpson's index (d) but a smaller change in Shannon Weaver index (h').
- This demonstrates that the Shannon Weaver Index treats rare species with more weight.

Diversity increases with richness and evenness.
Evenness measures how evenly distributed species are in a community.
To calculate, first find h_{max}, the highest possible diversity.
- h_{max} = ln(s), where s is the total number of species.
- h_{max} is calculated this way because the highest diversity occurs when all species have the same number of individuals.
Evenness (E) is calculated as: E = \frac{h'}{h_{max}}
- Where h' is the observed diversity at the site.
When all species are evenly distributed in abundance, evenness equals one (highest possible value).
The value of E decreases as evenness decreases, approaching zero.

Terms for species richness at different scales and comparisons between regions.
Alpha Diversity: Within-habitat diversity; the number of species found in one area (species richness).
- Different communities can have the same alpha diversity if they contain the same number of species.
Beta Diversity: Similarity or dissimilarity between species in different communities.
- Allows for comparison between different communities.
- Measured using:
  - Binary data and Jaccard's coefficient of similarity (C).
    - Formula: C = \frac{\text{number of species in both j and k}}{\text{number of species in both j and k + number of species only in j + number of species only in k}}
    - If communities j and k have the same 15 species, then C = \frac{15}{15} = 1 (complete overlap).
    - C close to one indicates little difference between communities.
    - As C decreases towards zero, the communities are more different.
  - Abundance data and Euclidean distance.
    - Formula: \sqrt{\sum (N{ij} - N{ik})^2} , where N{ij} is the number of individuals of species i in community j, and N{ik} is the number of individuals of species i in community k.
Gamma Diversity: Regional or geographic diversity.
- The sum of alpha and beta diversities.
- Considers diversity within communities (alpha) and the differences between them (beta).

Alpha diversity: Diversity within a habitat.
Beta diversity: Difference between communities.
Gamma diversity: Diversity of the whole region.
Important to understand how indices work and when to use each one, rather than memorizing equations.
Consider what values indicate high or low diversity for each index.
Understand how rarity impacts diversity measures.