Measurements of Ecological Diversity How to measure Diversity in an ecological system Laila, Vimal,

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Measurements of Ecological DiversityHow to
measure Diversity in an ecological
systemLaila, Vimal, Rozie
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Diversity-Stability Hypothesis McArthur (1955)
WHY ?
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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?
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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.
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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

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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
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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
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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)

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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.

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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.

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• 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)
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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.

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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.
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The Wimbledon Common Dataset
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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

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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.
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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.
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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.
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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?

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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
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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 ?

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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