Exercises: Simpson's Diversity Index

Define biodiversity and state what is meant by species richness and species evenness. Explain why a high value of Simpson's Diversity Index indicates a more diverse habitat when the index is calculated as $D = 1-\sum\left(\frac{n}{N}\right)^2$.

A quadrat survey of a meadow in County Kildare found: 10 daisies, 10 buttercups, 10 clover and 10 dandelions. Using $D = 1-\sum\left(\frac{n}{N}\right)^2$, calculate Simpson's Diversity Index for the meadow.

A sample from a field contains only one species, with 40 individuals. Calculate Simpson's Diversity Index using $D = 1-\sum\left(\frac{n}{N}\right)^2$ and state what the value tells you about the field.

A student records invertebrates in a stream in County Wicklow:

1. a) Calculate $N$.

1. b) Calculate $D = 1-\sum\left(\frac{n}{N}\right)^2$.

1. c) State what the result suggests about water quality if mayfly and stonefly nymphs are pollution-sensitive.

Two hedgerows are sampled.

1. a) Calculate $D$ for each hedgerow using $D = 1-\sum\left(\frac{n}{N}\right)^2$.

1. b) Compare species richness and evenness in the two hedgerows.

1. c) Explain which hedgerow is likely to support more wildlife and why.

A formula sometimes used is $D = \frac{\sum n(n-1)}{N(N-1)}$, where a lower value of $D$ means higher diversity. A sample of a woodland floor has 6 beetles of species X, 4 of species Y and 2 of species Z.

1. a) Calculate $D$ using this formula.

1. b) Calculate $1-D$.

1. c) Explain why the two forms of the index are inverse in interpretation.

A bog in County Offaly is surveyed before and after drainage for peat extraction.

1. a) Calculate Simpson's Diversity Index $D = 1-\sum\left(\frac{n}{N}\right)^2$ before and after drainage.

1. b) Interpret the change, commenting on richness and evenness.

1. c) Explain why the index alone may not show the full ecological damage to the bog, and name a limitation of the sampling.

Farm A is an intensive ryegrass monoculture with $D = 0.12$. Farm B is a mixed organic farm with hedgerows and wildflower margins, with $D = 0.78$.

1. a) Explain why a monoculture has a low index.

1. b) Discuss two ecological consequences of the difference for pollinators and soil health.

1. c) A researcher claims that Farm B is always better for conservation. Evaluate this claim, considering that $D$ ignores which species are present.

In a sample, species A has $n$ individuals and species B has $20-n$ individuals, so $N = 20$.

1. a) Write an expression for $D = 1-\sum\left(\frac{n}{N}\right)^2$ in terms of $n$.

1. b) Calculate $D$ for $n = 10$, $n = 15$ and $n = 19$.

1. c) Deduce the value of $n$ that gives maximum diversity and explain why.

1. d) State the maximum possible value of $D$ for a community of $S$ equally abundant species, giving your reasoning.