Simpson’s Diversity Index Study Notes

Biological Diversity: Key Concepts

• Biological diversity (biodiversity) = the great variety of life within a defined area.
• Quantification hinges on two independent but complementary components:
  • Richness – number of distinct taxa present (usually species).
  • Evenness – how evenly individuals are distributed among those taxa.
• High biodiversity = simultaneously high richness and high evenness.

Richness

• Simple count of species/taxa per sample.
• Does not incorporate population size:
  • $1$ daisy contributes as much to richness as $1000$ buttercups.
• “Richer” sample = contains more distinct species regardless of their abundance.

Evenness

• Describes relative abundance patterns among species making up the richness.
• Example (two wild-flower fields, each with $1000$ individuals & 3 species):
  • Sample 1: $300$ daisies, $335$ dandelions, $365$ buttercups ⇒ high evenness.
  • Sample 2: $20$ daisies, $49$ dandelions, $931$ buttercups ⇒ low evenness.
• Same richness, same total N, but Sample 1 ≫ Sample 2 in diversity because of higher evenness.
• General rule: community dominated by one/few species = less diverse.

Simpson’s Diversity: Three Closely-Related Indices

• Collectively called “Simpson’s Diversity Index,” but the name is used loosely. Always confirm which variant is reported.

1. Simpson’s Index (D)

• Measures probability that two randomly selected individuals belong to the same species.
• Formula (two equivalent forms, but be internally consistent):
  • $D = \sum<em>{i=1}^{S} \left( \frac{n</em>i}{N} \right)^2$
  • or $D = \frac{\sum n<em>i(n</em>i-1)}{N(N-1)}$
  • where:
  • $n_i$ = number of individuals in species $i$
  • $N$ = total number of individuals, $N = \sum n_i$
• Range: $0 \le D \le 1$.
  • $D \to 0$ ⇒ infinite diversity.
  • $D \to 1$ ⇒ no diversity (all individuals belong to one species).
• Interpretation is counter-intuitive (higher D = lower diversity).

2. Simpson’s Index of Diversity ($1 - D$)

• Simply $1 - D$.
• Represents probability that two randomly selected individuals belong to different species.
• Range still $0 \le 1-D \le 1$ but now larger values = greater diversity, which feels logical.

3. Simpson’s Reciprocal Index ($1/D$)

• Takes reciprocal to remove counter-intuition.
• Minimum possible value = $1$ (monoculture).
• Maximum possible value = richness $S$ (occurs when all species are perfectly even).
• Larger number ⇒ higher diversity.

Sampling & Data Collection

• Calculate any Simpson index only after sampling the community.
• Typical ecological approach:
  • Place random quadrats.
  • Record species identity (or morpho-type) and number of individuals per species.
  • Correct identification not essential; distinguishability is what matters.
• Use multiple samples; pool data for reliable estimate.
• Question “How many samples?” depends on habitat heterogeneity and desired confidence; more samples ⟹ lower variance.

Worked Example (Single Quadrat of Woodland Ground Flora)

Step-by-step calculations:

1. Simpson’s Index:
   $D = \frac{\sum n<em>i(n</em>i-1)}{N(N-1)} = \frac{64}{15\times14} \approx 0.3$
2. Simpson’s Index of Diversity:
   $1 - D = 1 - 0.3 = 0.7$
3. Simpson’s Reciprocal Index:
   $\frac{1}{D} \approx 3.3$

All three values describe the same community, but numerical meaning & range differ; never compare raw numbers from different variants.

Interpretation & Properties

• $D$ gives greater weight to abundant species; rare species shift the index only slightly.
• Addition of a low-abundance species to a community ⇒ small drop in $D$, modest rise in $1-D$, modest rise in $1/D$.
• Because of weighting, Simpson’s indices are particularly sensitive to dominance patterns, complementing indices that emphasise richness (e.g.
  Shannon index).

Practical / Real-World Relevance

• Widely used in conservation biology, habitat assessment, pollution monitoring, and sustainable resource management.
• High diversity (low $D$, high $1-D$, high $1/D$) often correlated with ecosystem stability, resilience, and provisioning of services.
• Ethical implication: emphasises importance of managing not just number of species, but their population balance.

Connections & Comparisons

• Contrast with Shannon–Wiener Index (information-theoretic, more sensitive to rare species).
• All diversity metrics rely on sound sampling; biases (e.g.
  time of day, seasonality, observer skill) can distort estimates.
• When reading literature, verify which Simpson variant, sampling protocol, and taxonomic resolution were used before drawing conclusions.