Calculating Diversity

Class 3

Presentation 2

Outline

• Lecture

• Class room exercise to calculate diversity indices

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

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.

Alpha diversity

• Diversity within a particular sample

• E.g. the number of species surveyed

Beta Diversity

• Changes in sample composition along an environmental gradient

• E.g. composition of forest stands on the slope of a mountain

Gamma Diversity

• Diversity due to differences in samples when all samples combined

• E.g. diversity of a forest landscape

Describing Communities

• Two methods

– Describe physical attributes (e.g. age class, size class)

– Describe number of species and their abundance

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.

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

Species Richness

• How?

• Identify organism groups of interest

• Identify boundaries of community

• Survey area for organisms of interest

Species diversity

• Species richness not very informative

• Each community has 5 spp & 50 individuals

Spp1

Spp 2

Spp 3

Spp 4

Spp 5

Comm

A

10 10 10 10 10

Comm

B

46 1 1 1 1

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.

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)

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.

Simpson Diversity Index (D)

Ds = (n1(n1 -1)/N(N-1))

Where:

Ds = Bias corrected form for Simpson Index

n1 = number of individuals of spp 1N = Total number of spp in community

In this form as diversity increases index value gets smaller

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

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

Simpson Diversity Index (D)

• Complimentary form = 1-D

• = 1-0.35509 = 0.6449

• Reciprocal 1/D

• 1/0.35509 = 2.816

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)

Shannon-Weiner Index (H')

• Assumptions:– All species represented– Sample randomized (equal probability of being selected

in the sample)

H' = - pilnpi

pi= proportion of the ith speciesln=natural logarithm

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

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

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

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

Questions?