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

1. Measurements of Ecological DiversityHow to measureDiversity in an ecological systemLaila, Vimal, & Rozie

2. Diversity-Stability Hypothesis McArthur (1955) WHY ?

3. 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?

4. 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.

5. 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

6. 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

7. 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

8. 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)

9. 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.

10. 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.

11. 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)

12. 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.

13. 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.

14. The Wimbledon Common Dataset

15. 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

16. 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.

17. 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.

18. 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.

19. 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?

20. 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

21. 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 

22. Data for Homework problem 3