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Measurements of Ecological DiversityHow to

measure Diversity in an ecological

systemLaila, Vimal, Rozie

Diversity-Stability Hypothesis McArthur (1955)

WHY ?

Ecologists describe distribution of diversity on

a spatial scale

in three classifications.

a

The diversity of organisms within a selected

habitat or sample.

ß

Index of the rate of increase of alpha as new

habitats are sampled.

?

The full species diversity/ species richness.

Alpha, Beta, and Gamma diversity measures are

Scale Dependent. Whats that mean?

Ecologist one studies

One acre of land and calls this one habitat

measuring alpha diversity.

Ecologist two studies microbial organisms,

therefore one acre of land would contain an

infinite amount of microhabitats under his

consideration. The one acre of land would be

measuring Gamma Diversity.

What are the properties of the community that

can be measured to indicate its alpha diversity?

- The total number of species within the sample
- although relative frequencies are unknown.

- Richness and Balance

- Refer to Figure 2.1 pg 31

There an infinite number of different

mathematical functions to describe diversity

indices by encapsulating different aspects of

the balance between richness and balance.

The Shannon Index

The Simpson Index

Each of the Indices mention require the

calculation of a Population Proportion Pi

Procedure Convert the count for each species in

a sample to a proportion of the total number of

individuals within the sample.

S the total number of species in the sample. Ni

the number of individuals in the ith

species. Total number of individuals in a sample

may be calculated as ?N The proportion made up

by species i (denoted pi ) is given by

Pi Ni / ?N

The Simpson Index

- measures the probability that two consecutive

random samples from a population will find the

same species. - The probability that a random sample from a

population will pick out a given species is

assumed to be equal to that species contribution

to the whole population. - Pi Ni/?N
- The probability of sampling species i in two

consecutive samples is found as follows - p(sampling species i twice) pi pi
- A more realistic model equation
- P(sampling species I twice) Ni(Ni-1)/ ?N(?N-1)
- The probability of sampling any species twice in

two consecutive samples can be found as - P(sampling any species twice) ?(pi pi)

Interpreting the Simpson Index

- If there is only one species, pi 1, hence ?(pi

pi) 1. This is called the zero diversity

condition. - As the number of species tends to infinity, ?(pi

pi) tends to zero, which is the high diversity

condition. - Simpsons index is usually altered to reverse the

above arrangement. - D 1-?(pi pi)
- So this equation calculate the probability of two

consecutive samples will be of different species. - D is the standard symbol for the Simpson index.

The Shannon Index

- Most commonly used diversity index.

A

- H -?pi x log(pi)

- H Symbol for Shannon Index.
- Negative sign (-) makes sure f value is

received.

- Community with one species (Pi 1.0), diversity

is zero.

- If a community with S of species, maximum

possible value of the - Shannon index is log(S)- this occurs when all

species occur at - equal frequency.

- For ecological studies, logarithms base 10 are

used.

- Converting between logarithms of different bases

Loga(X) Logb(X)/Logb(a)

B

A

B

- Combine

H(base2) -? pi x log10(pi)/ log10(2)

3.3219 x H(base 10)

Equitability

- Let us calculate the ratio of calculated

diversity with maximum possible diversity - for the number of species found.
- E H/Hmax -?pi x

log(pi)/ log(S) - Does not matter what sort of logarithm is used.
- Reflects evenness of species distribution within

sample. - An equitability near zero shows the community to

be dominated by one species. - An equitability near 1.0 indicates an equal

balance between all species.

Jack-Knifing

Both the indices mentioned do not come with

estimates of variability. Why would a

scientist be interested in estimates of

variability?

Jack-Knifing is an extension of the resampling

process, performed by a computer using the

completed final dataset. It obtains estimates of

the variability within parameter estimates in a

wide range of settings, including diversity

indices.

The Wimbledon Common Dataset

Liphook Pine Forest Fungal

- Successional changes in community
- structure, such as a bare habitat
- where colonization starts with a few
- colonist species, followed by a
- gradual increase in numbers as
- new species arrive.
- First year low-species diversity
- 281 individuals, 280 one species.
- Simpson diversity 0.007
- Shannon diversity 0.034

First graphed unclear trend, no stabilizing

of values due to dominance of one species. The

species richness diversity index shows a clear

pattern increases consistently every year.

Nutrient enrichment of Dutch grasslands

Five experimental plots Brachypodium pinnatum

was present, not dominant. different

concentrations of nitrogen, phosphorus,

potassium fertilizers. increase

in biomass, decrease in number of

species. Data summarized using Shannon index.

Interest the effects of increased atmospheric

pollution on the growth of coarse grasses.

Problem high levels of nitrogen deposits due

to ammonia release.

Effect stimulates coarse grasses in preference

to the rich community of low- growing, less

vigorous herbs.

Ecological Conclusion Brachypodium pinnatum

is able to flourish on high levels of

nitrogen low levels of phosphorus. The

coarse grass was able to use its

height to shade out other species therefore

1. Reducing Biodiversity

2. Reducing conservation value of habitat.

The Brillouin Index

- Used when the randomness of sampling is not

guaranteed. - HB ln(N!)-?ln(ni!) / N
- HB Brillouin Index
- N Total number of individuals in the sample
- ni number of individuals of species
- Unlike the Shannon the Simpson indices, this

index varies with sample size - as well as with the relative proportions of

species. Why?

The Berger-Parker Index

- Only calculates the proportion of the most

common species in a sample - d Nmax/ N

The Macintosh Index of Diversity

D N-(?ni2)1/2 / N-N1/2

Homework

- What are the three distributions of diversity on

a spatial scale within ecology? - What does the Simpson index measure?
- Calculate the species richness, Simpson Index and

Shannons Index (base 10)? - Please show all your calculation ?

Data for Homework problem 3

Raw Data

Achillea millefolia 0

Arrhenatherium elatius 0

Calluna vulgaris 95

Deschampsia flexuosa 0

Festuca rubra 10

Heracleum sphondylium 0

Trifolium repenas 0

Vicia sativa 0