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Measurements of Ecological Diversity

How to measure Diversity in an ecological system

Laila, Vimal, & Rozie

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?

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

Each of the Indices mention require the calculation

of a Population Proportion Pi

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

Procedure: Convert the count for each species in a sample to a proportion of the total number of individuals within the sample.

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 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.

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 low- growing, 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 a sample:

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

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

Data for Homework problem 3