1. Calculating Diversity Class 3 Presentation 2

2. Outline Lecture Class room exercise to calculate diversity indices

3. Why quantify biodiversity? Initially thought that more diversity = more stable ecosystem* Now used to measure and track changes *MacArthur, R. 1955. Fluctuations of animal populations and a measure of community stability. Ecology 35:533-536

4. How do we measure biodiversity? Use functional categories –Ecosystem, species, genetic Use theoretical categories* –Alpha –Beta –Gamma * Whittaker, R.H. 1960. Vegetation of the Siskiyou Mountains, Oregon and California. Ecol. Mono. 30:279-338.

5. Alpha diversity Diversity within a particular sample E.g. the number of species surveyed

6. Beta Diversity Changes in sample composition along an environmental gradient E.g. composition of forest stands on the slope of a mountain

7. Gamma Diversity Diversity due to differences in samples when all samples combined E.g. diversity of a forest landscape

8. Describing Communities Two methods –Describe physical attributes (e.g. age class, size class) –Describe number of species and their abundance

9. Biodiversity Diversity of living things Term often misused and overused Current focus in conservation studies Includes interest in genetic, species and ecosystem diversity We will use species as our focus but concepts can be used for genetic and ecosystem diversity as well.

10. Species Richness Number of species in a community The simplest measure Can count all spp only is few simple ecosystems Does not consider number of individuals Difficulties –When is it a specie? Aphids Clonal plants –Cannot count all species with limited time

11. Species Richness How? Identify organism groups of interest Identify boundaries of community Survey area for organisms of interest

12. Species diversity Species richness not very informative Each community has 5 spp & 50 individuals Spp 1 Spp 2 Spp 3 Spp 4 Spp 5 Comm A 10 Comm B 461111

13. Diversity indices To get a better description of the community we need to get a measure of spp richness and evenness of their distribution We usually use an index to represent several different measures –E.g. stock markets, air pollution, etc.

14. Diversity indices Over 60 indices used in ecology Indices used to measure proportional abundance Two major forms: –Dominance indices (e.g. Simpson index) –Information indices (e.g. Shannon Weiner index)

15. Simpson Diversity Index (D) –Simpson’s index considered a dominance index because it weights towards the abundance of the most common species. –measures the probability two individuals randomly selected from a sample will belong to the same category –For example, the probability of two trees, picked at random from a tropical rainforest being of the same species would be relatively low, whereas in the boreal forest would be relatively high.

16. Simpson Diversity Index (D) D s =  (n 1 (n 1 -1)/N(N-1)) Where: D s = Bias corrected form for Simpson Index n 1 = number of individuals of spp 1 N = Total number of spp in community In this form as diversity increases index value gets smaller

17. Simpson Diversity Index (D) To make it easier to read the index is often read as: Reciprocal i.e. 1/ D s Complimentary form: 1- D s Here as diversity increases Index value increases

18. Simpson Diversity Index (D) Sugar Maple Red Maple Yellow Birch Red Oak White Ash Total # Trees 56481263125 ((56*55)/(125*124))+ ((48*47)/(125*124)) + …………. ….((3*2)/125*124)) = 0.35509 See Excel Show how index changes

19. Simpson Diversity Index (D) Complimentary form = 1-D = 1-0.35509 = 0.6449 Reciprocal 1/D 1/0.35509 = 2.816

20. Shannon-Weiner Index (H') The index measures the uncertainty of a category in a particular set It is a measure of evenness For example, very low uncertainty the letter y is the next letter in this string: yyyyyyy (H' = 0)

21. Shannon-Weiner Index (H') Assumptions: –All species represented –Sample randomized (equal probability of being selected in the sample) H' = -  p i lnp i p i= proportion of the i th species ln=natural logarithm

22. Shannon-Weiner Index (H') Sugar Maple Red Maple Yellow Birch Red Oak White Ash Total # Trees 56481263125 p 56/125 0.44 48/125 0.38 12/125 0.096 6/125 0.048 3/125 0.024 -plnp0.3590.3670.2240.1460.089 1.187

23. Shannon-Weiner Index (H') Index affected by both number of species and evenness of their population Diversity increases as both increase Diversity maximum when all species equally abundant

24. Evenness Can use Shannon Weiner index to get a measure of evenness First calculate H max Evenness = H‘/ H max Evenness will vary between 1 and 0

25. Evenness In the last example H‘= 1.1875 Hmax = 1.609 Therefore E = 1.1875/1.609 = 0.738 The closer to 1 the more even the populations that form the community

26. Questions?