1. Measurement of Biological Diversity: Shannon Diversity Index and Shannon’s Equitability Comparing the diversity found in two or more habitats

2. What is Biological Diversity? (from Whitaker, 1960) alpha diversity: diversity within a sample alpha diversity: diversity within a sample beta diversity: diversity associated with changes in sample composition along an environmental gradient (between samples) beta diversity: diversity associated with changes in sample composition along an environmental gradient (between samples) gamma diversity: diversity due to differences among samples when they are combined into a single sample (this tells us something about how samples are collected – not about communities in nature) gamma diversity: diversity due to differences among samples when they are combined into a single sample (this tells us something about how samples are collected – not about communities in nature)

3. Biological Diversity Includes: Number of different species (species diversity) Number of different species (species diversity) Relative abundance of different species (species evenness) Relative abundance of different species (species evenness) Ecological distinctiveness of different species, e.g., functional differentiation – often done in microbiology (Functional Diversity). Ecological distinctiveness of different species, e.g., functional differentiation – often done in microbiology (Functional Diversity). Evolutionary distinctiveness of different species Evolutionary distinctiveness of different species (The last two of these are rarely addressed)

4. Why is Biological Diversity Important? It is commonly believed that the more diverse a system is, the more stable it will be. It is commonly believed that the more diverse a system is, the more stable it will be. Studies with plants suggest that productivity in more diverse plant communities is more resistant to, and recovers more fully from, a major drought. Studies with plants suggest that productivity in more diverse plant communities is more resistant to, and recovers more fully from, a major drought. Diverse communities are more resistant to invasion by exotic species than are less diverse communities. Diverse communities are more resistant to invasion by exotic species than are less diverse communities.

5. The Shannon Diversity Index (SDI) – what is it? Claude Shannon was not a biologist – he was a mathematician and communications engineer who worked for Bell Laboratories. Claude Shannon was not a biologist – he was a mathematician and communications engineer who worked for Bell Laboratories. Shannon originated a field called Information Theory. Shannon originated a field called Information Theory. The Shannon Diversity Index is a mathematical measure of species diversity in a community. The Shannon Diversity Index is a mathematical measure of species diversity in a community.

6. What does the Shannon Diversity Index tell us about biological diversity? It provides information about community composition beyond just species richness (how many different species are present). It provides information about community composition beyond just species richness (how many different species are present). It also takes the relative abundance of each species into account. It also takes the relative abundance of each species into account. It provides important information about rarity and commonness of species in a community. It provides important information about rarity and commonness of species in a community.

7. The Variables examined when calculating the SDI H = the SDI H = the SDI S = the total number of species in the community (richness) S = the total number of species in the community (richness) p i = the proportion of S made up of the “ith” species (the number of individuals of a particular species divided by the total number of all species) p i = the proportion of S made up of the “ith” species (the number of individuals of a particular species divided by the total number of all species) E H = Shannon’s Equitability (species evenness). E H = Shannon’s Equitability (species evenness).

8. The SDI accounts for both abundance and evenness of the species present. The SDI accounts for both abundance and evenness of the species present. The proportion of species i relative to the total number of species (we call it p i ) is calculated, and then multiplied by the natural logarithm of this proportion (ln pi). The proportion of species i relative to the total number of species (we call it p i ) is calculated, and then multiplied by the natural logarithm of this proportion (ln pi). The resulting product is summed across species and multiplied by -1. The resulting product is summed across species and multiplied by -1.

9. Let’s assume the following data set: Species found Numberfound Proportion (p i ) (number ÷ total) Beetle6 6/13 = 0.462 Earwig3 3/13 = 0.231 Spider2 2/13 = 0.154 Centipede2 1/13 = 0.154 Total (Sum) 13

10. The formula for SDI is:

11. H = -1 times the sum of all p i ln p i = -1 x -1.271 = 1.271 Species found Numberfound Proportion (p i ) (number ÷ total) p i ln p i Beetle6 6/13 = 0.462 - 0.357 Earwig3 3/13 = 0.231 - 0.338 Spider2 2/13 = 0.154 - 0.288 Centipede2 1/13 = 0.154 - 0.288 Total13 - 1.271

12. Now that we have calculated the SDI for our sample, we can calculate Shannon’s Equitability Shannon’s Equitability (E H ) is a measure of species evenness or relative abundance. Shannon’s Equitability (E H ) is a measure of species evenness or relative abundance. Equitability assumes a value between 0 and 1, with 1 being complete evenness (equal numbers of every species in the sample). Equitability assumes a value between 0 and 1, with 1 being complete evenness (equal numbers of every species in the sample).

13. Shannon’s Equitability for our example would be: Shannon’s Equitability (E H ) = SDI (H) divided by the natural log of H MAX or… Shannon’s Equitability (E H ) = SDI (H) divided by the natural log of H MAX or… H/ln S (where S = 4) H/ln S (where S = 4) In this case, E H = 1.27/1.39 =.91 In this case, E H = 1.27/1.39 =.91 Knowing that E H is always between zero and one, our sample has pretty high equitability. Knowing that E H is always between zero and one, our sample has pretty high equitability.

14. Now, let’s see how SDI and Equitability change under different circumstances. Let’s look at how species richness and species evenness affect SDI and Equitability. Let’s look at how species richness and species evenness affect SDI and Equitability. In the first situation, let’s look at four imaginary samples where the number of species differs, and where there are always an equal number of each species in the sample. In the first situation, let’s look at four imaginary samples where the number of species differs, and where there are always an equal number of each species in the sample. We’ll call these our “even” communities. We’ll call these our “even” communities.

15. SDI and Equitability for “Even” Communities (equal number of each species in the sample) Number of Species in the Sample SDIEquitability 51.611.0 102.311.0 203.001.0 503.911.0

16. But what if the number of species in each sample are NOT equal (Equitability is low)? In this second situation, let’s look at four imaginary samples where the number of species again differs, and where there are always an unequal number of each species in the sample. In this second situation, let’s look at four imaginary samples where the number of species again differs, and where there are always an unequal number of each species in the sample. In this case, one species makes up 90% of the total number of individuals in the sample and the remaining species each make up an equal proportion of the remaining 10%. In this case, one species makes up 90% of the total number of individuals in the sample and the remaining species each make up an equal proportion of the remaining 10%. We’ll call these our “uneven” communities. We’ll call these our “uneven” communities.

17. SDI and Equitability for “Uneven” Communities (one species makes up 90% of the total sample and the rest each make up an equal portion of the last 10%) Number of Species in the Sample SDIEquitability 50.460.29 100.540.23 200.620.21 500.710.18

18. There are two methods to calculate SDI – one uses natural log, the other uses log base 10 As it turns out, Microbiologists often use one method (the natural log version) in their publications, while botanists and biologists often use the log 10 version. As it turns out, Microbiologists often use one method (the natural log version) in their publications, while botanists and biologists often use the log 10 version. Either way, you always use the same method when you compare the SDI of one sample to that of another to determine which has more diversity. Either way, you always use the same method when you compare the SDI of one sample to that of another to determine which has more diversity.

19. Calculating e H or the exponent of SDI Finally, if we calculate the exponent of our SDI or e H, we get a number between 1 and S for that sample. You can use your calculator to do this (use the e x ) function and put your H (SDI) in for the x. You can also do this in excel (see the Word file that explains this). If, for example, you have Finally, if we calculate the exponent of our SDI or e H, we get a number between 1 and S for that sample. You can use your calculator to do this (use the e x ) function and put your H (SDI) in for the x. You can also do this in excel (see the Word file that explains this). If, for example, you have

20. Calculating e H or the exponent of SDI What does this tell us? If, for example, you have a sample with species richness of 12 and your e H is approximately 8.5, this means that your sample has the same evenness as a perfectly even sample with 8.5 species. In other words, your sample of 12 species is dominated by about 8.5 species. If you had a sample with S = 12 and your eH is 12, it is perfectly even and not dominated by any species – they are equally distributed. What does this tell us? If, for example, you have a sample with species richness of 12 and your e H is approximately 8.5, this means that your sample has the same evenness as a perfectly even sample with 8.5 species. In other words, your sample of 12 species is dominated by about 8.5 species. If you had a sample with S = 12 and your eH is 12, it is perfectly even and not dominated by any species – they are equally distributed.

21. Now you do it Using the numbers of ants from the pitfall data, calculate the SDI, Evenness, Species Richness, and exponent of SDI for three forest types Using the numbers of ants from the pitfall data, calculate the SDI, Evenness, Species Richness, and exponent of SDI for three forest types Melina forest – sylvaculture forest Melina forest – sylvaculture forest Primary forest – rainforest, never cut Primary forest – rainforest, never cut Secondary forest – rainforest, selectively logged 30 years ago Secondary forest – rainforest, selectively logged 30 years ago