The document outlines a presentation on calculating biodiversity, including methods for measuring diversity indices such as Simpson's and Shannon-Weiner indices. It discusses the importance of biodiversity in ecosystems, different forms of diversity (alpha, beta, gamma), and challenges in assessing species richness. The presentation also emphasizes the role of indices in quantifying community composition and evenness to better understand ecological stability.

1. Calculating Diversity
Class 3
Presentation 2

2. Outline
• Lecture
• Class room exercise to calculate diversity
indices

3. Why quantify biodiversity?
• Initially thought that more diversity = more
stable ecosystem*
• Now used to measure and track changes
*MacArthur, R. 1955. Fluctuations of animal
populations and a measure of community stability.
Ecology 35:533-536

4. How do we measure
biodiversity?
• Use functional categories
– Ecosystem, species, genetic
• Use theoretical categories*
– Alpha
– Beta
– Gamma
* Whittaker, R.H. 1960. Vegetation of the
Siskiyou Mountains, Oregon and California.
Ecol. Mono. 30:279-338.

5. Alpha diversity
• Diversity within a particular sample
• E.g. the number of species surveyed

6. Beta Diversity
• Changes in sample composition along an
environmental gradient
• E.g. composition of forest stands on the
slope of a mountain

7. Gamma Diversity
• Diversity due to differences in samples
when all samples combined
• E.g. diversity of a forest landscape

8. Describing Communities
• Two methods
– Describe physical attributes (e.g. age
class, size class)
– Describe number of species and their
abundance

9. Biodiversity
• Diversity of living things
• Term often misused and overused
• Current focus in conservation studies
• Includes interest in genetic, species and
ecosystem diversity
• We will use species as our focus but
concepts can be used for genetic and
ecosystem diversity as well.

10. Species Richness
• Number of species in a community
• The simplest measure
• Can count all spp only is few simple ecosystems
• Does not consider number of individuals
• Difficulties
– When is it a specie?
• Aphids
• Clonal plants
– Cannot count all species with limited time

11. Species Richness
• How?
• Identify organism groups of interest
• Identify boundaries of community
• Survey area for organisms of interest

12. Species diversity
• Species richness not very informative
• Each community has 5 spp & 50 individuals
Spp
1
Spp
2
Spp
3
Spp
4
Spp
5
Comm
A
10 10 10 10 10
Comm
B
46 1 1 1 1

13. Diversity indices
• To get a better description of the
community we need to get a measure of spp
richness and evenness of their distribution
• We usually use an index to represent
several different measures
– E.g. stock markets, air pollution, etc.

14. Diversity indices
• Over 60 indices used in ecology
• Indices used to measure proportional
abundance
• Two major forms:
– Dominance indices (e.g. Simpson index)
– Information indices (e.g. Shannon Weiner
index)

15. Simpson Diversity Index (D)
– Simpson’s index considered a dominance
index because it weights towards the
abundance of the most common species.
– measures the probability two individuals
randomly selected from a sample will belong
to the same category
– For example, the probability of two trees,
picked at random from a tropical rainforest
being of the same species would be
relatively low , whereas in the boreal
forest would be relatively high.

16. Simpson Diversity Index (D)
Ds = Σ(n1(n1 -1)/N(N-1))
Where:
Ds= Bias corrected form for Simpson Index
n1= number of individuals of spp 1
N = Total number of spp in community
In this form as diversity increases index value
gets smaller

17. Simpson Diversity Index (D)
• To make it easier to read the index is often
read as:
• Reciprocal i.e. 1/ Ds
• Complimentary form: 1- Ds
• Here as diversity increases Index value
increases

18. Simpson Diversity Index (D)
Sugar
Maple
Red
Maple
Yellow
Birch
Red
Oak
White
Ash
Total
#
Trees
56 48 12 6 3 125
((56*55)/(125*124))+ ((48*47)/
(125*124)) + …………. ….
((3*2)/125*124)) = 0.35509
See Excel
Show how
index
changes

19. Simpson Diversity Index (D)
• Complimentary form = 1-D
• = 1-0.35509 = 0.6449
• Reciprocal 1/D
• 1/0.35509 = 2.816

20. Shannon-Weiner Index (H')
• The index measures the uncertainty of a
category in a particular set
• It is a measure of evenness
• For example, very low uncertainty the letter
y is the next letter in this string: yyyyyyy
(H' = 0)

21. Shannon-Weiner Index (H')
• Assumptions:
– All species represented
– Sample randomized (equal probability of being selected
in the sample)
H' = -Σ pilnpi
pi=proportion of the ith
species
ln=natural logarithm

22. Shannon-Weiner Index (H')
Sugar
Maple
Red
Maple
Yellow
Birch
Red
Oak
White
Ash
Total
#
Trees
56 48 12 6 3 125
Pi 56/125
0.44
48/125
0.38
12/125
0.096
6/125
0.048
3/125
0.024
-plnp 0.359 0.367 0.224 0.146 0.089 1.187

23. Shannon-Weiner Index (H')
• Index affected by both number of species
and evenness of their population
• Diversity increases as both increase
• Diversity maximum when all species
equally abundant

24. Evenness
• Can use Shannon Weiner index to get a
measure of evenness
• First calculate Hmax
• Evenness = H‘/ Hmax
• Evenness will vary between 1 and 0

25. Evenness
• In the last example
• H‘= 1.1875
• Hmax = 1.609
• Therefore E = 1.1875/1.609 = 0.738
• The closer to 1 the more even the
populations that form the community

26. Questions?