Species diversity concepts for high school students or freshman and sophomore students depends on the curriculum.

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?