Measurements of Ecological Diversity Diversity Laila, Vimal, & Rozie

Measurements of
Ecological Diversity
How to measure Diversity in an ecological system
Laila, Vimal, & Rozie
Diversity-Stability Hypothesis
McArthur (1955)
WHY ?
Ecologists describe distribution of diversity on a spatial scale
in three classifications.
α
The diversity of organisms within a
selected habitat or sample.
β
Index of the rate of increase of alpha
as new habitats are sampled.
γ
The full species diversity/ species richness.
Alpha, Beta, and Gamma diversity measures are Scale Dependent.
What’s 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.
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 b
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.
• Simpson’s 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.
• 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)
• Combine
+
= H’(base2)= [-∑ pi x log10(pi)]/ log10(2) =
3.3219 x H’(base 10)
• Let us calculate the ratio of calculated diversity with
for the number of species found.
maximum possible diversity
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.
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.
• 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.
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 lowgrowing, less vigorous herbs.
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.
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.
• 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?
• Only
calculates the proportion of the most common species in
d= Nmax/ N
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 Shannon’s 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