1. Butterfly diversity…………………… in rain forest

2. What is ecological diversity? Based on Based on 1) Species richness, i.e. number of species present 1) Species richness, i.e. number of species present But also greater if most species have equal numbers than if one or two predominate, so includes But also greater if most species have equal numbers than if one or two predominate, so includes 2) Species abundance 2) Species abundance

3. Relative abundance p i from field samples Two types of display commonly used. (data from an English field study over many years) Rank Order Rank Order individuals in each species in descending order of rank individuals in each species in descending order of rank Species abundance species with 1,2,3,… etc individuals on number of individuals

4. Useful too to have a diversity index N individuals in a community, with N individuals in a community, with S species, each at frequency p i S species, each at frequency p i Diversity increases with S Diversity increases with S But also affected by species composition But also affected by species composition For given S diversity is: For given S diversity is: Least when 1 species predominates Least when 1 species predominates Greatest when all p i = 1/S Greatest when all p i = 1/S So a diversity index has to measure both So a diversity index has to measure both

5. A well known one is Simpson’s index Based on p i, the probability of picking an individual of species i estimated from frequency Based on p i, the probability of picking an individual of species i estimated from frequency Probability of picking two of species i is p i 2 Probability of picking two of species i is p i 2 Probability of getting two any species = Σp i 2. Probability of getting two any species = Σp i 2. ( = information content of a sample) ( = information content of a sample) Gets smaller as diversity goes up Gets smaller as diversity goes up Sometimes expressed as 1/Σp i 2 or -logΣp i 2 Sometimes expressed as 1/Σp i 2 or -logΣp i 2 which increase with increased diversity which increase with increased diversity

6. Short digression Simpson’s index is 1/Σp i 2 or -logΣp i 2 Simpson’s index is 1/Σp i 2 or -logΣp i 2 Shannon Index, H, is -Σp i.log p i Shannon Index, H, is -Σp i.log p i both increase with increased diversity both increase with increased diversity Evenness is defined as nearness of index to maximum Evenness is defined as nearness of index to maximum Evenness (Simpson) = (-logΣp i 2 )/logS Evenness (Simpson) = (-logΣp i 2 )/logS Evenness (Shannon) = (-Σp i.log p i )/log S Evenness (Shannon) = (-Σp i.log p i )/log S Relation of H to Simpson: Relation of H to Simpson: H = -log/Σp i 2 if all p i = 1/S H = -log/Σp i 2 if all p i = 1/S H ≈ 2.5 log (1/Σp i 2 ) if distribution extreme H ≈ 2.5 log (1/Σp i 2 ) if distribution extreme

7. Sampling location, Ecuador San José de Payamino, Orellana Province

8. Arrival at Coca Payamino research site

10. At Payamino site Probably ca 1000 butterfly species Probably ca 1000 butterfly species No good identification guides No good identification guides Several reasons not to catch and kill them Several reasons not to catch and kill them But we might try to measure ecological diversity, which is a useful measure of habitat quality But we might try to measure ecological diversity, which is a useful measure of habitat quality

11. Indexes like Simpson’s Index usually estimated by counting numbers in each species. But Σp i 2 (i.e. the probability that two individuals in a pair are the same species)……. can be found directly by observation

12. Field data book: /////////// = a = number of like pairs /////////// = a = number of like pairs /////////////// = b = unlike pairs /////////////// = b = unlike pairs n = a+b = total pairs n = a+b = total pairs ////////// = S = species seen ////////// = S = species seen ------------------------------------------------------------ ------------------------------------------------------------ a/n = fraction of like pairs seen a/n = fraction of like pairs seen which is an estimate of Σp i 2 which is an estimate of Σp i 2

13. So sequential estimate is: D = a/n D = a/n which does not need relative abundance counts, which does not need relative abundance counts, or, if preferred, use 1/D (or –log D) or, if preferred, use 1/D (or –log D) Evenness of D can be measured as Evenness of D can be measured as E = (1-D)/(1-1/S) E = (1-D)/(1-1/S) If S large this is close to 1-D If S large this is close to 1-D

14. Data collected from two sides of Payamino river

15. Conclusion from data These estimates show that: These estimates show that: 1. repeatable estimates of D can be made (mean SE D about the same as standard deviation of D) 1. repeatable estimates of D can be made (mean SE D about the same as standard deviation of D) 2. differences in diversity between sites can be detected (mean D significantly different at the two sites) 2. differences in diversity between sites can be detected (mean D significantly different at the two sites)

16. Some problems of accuracy of D 1. Aggregation, courtship etc. affect estimate, so sampling must be as random as possible 1. Aggregation, courtship etc. affect estimate, so sampling must be as random as possible 2. Binomial variance of D is 2. Binomial variance of D is ab/n 3, ab/n 3, larger than large-sample var of Simpson’s index, larger than large-sample var of Simpson’s index, 2[Σp i 3 - (Σp i 2 ) 2 ]/n 2[Σp i 3 - (Σp i 2 ) 2 ]/n 3. but data for D are easier to gather and little knowledge of species is needed 3. but data for D are easier to gather and little knowledge of species is needed

17. To test accuracy we could compare relative abundance estimates with sequential estimates made from the same series of observations. compare relative abundance estimates with sequential estimates made from the same series of observations.

18. and compare results of simulations P1P2P3P4P5P6 …… P1P2P3P4P5P6 …… P1f 11 f 12 f 13 f 14 f 15 f 16 …. P1f 11 f 12 f 13 f 14 f 15 f 16 …. P2f 21 f 22 f 23 f 24 f 25 f 26 …. P2f 21 f 22 f 23 f 24 f 25 f 26 …. P3f 31 f 32 f 33 f 34 f 35 f 36 P3f 31 f 32 f 33 f 34 f 35 f 36 P4f 41 f 42 f 43 f 44 f 45 f 46 P4f 41 f 42 f 43 f 44 f 45 f 46 P5f 51 f 52 f 53 f 54 f 55 f 56 P5f 51 f 52 f 53 f 54 f 55 f 56 P6f 61 f 62 f 63 f 64 f 65 f 66 P6f 61 f 62 f 63 f 64 f 65 f 66.............. (Σf 1 ) 2 +(Σf 2 ) 2 + etc …….... Σf ii (Σf 1 ) 2 +(Σf 2 ) 2 + etc …….... Σf ii for frequencies for sequential for frequencies for sequential If some mistakes are made they have similar accuracy If some mistakes are made they have similar accuracy

19. Should we use overlapping or independent pairs? Sequence overlap D independent D For k observations k-1 k/2 If k = 4 3 2 Possible order if 2 species at equal frequency: yyzz 2/3 2/2 yyzz 2/3 2/2 yzyz 0/3 0/2 yzyz 0/3 0/2 yzzy 1/3 0/2 yzzy 1/3 0/2 Mean D estimate 0.33 0.33 Mean D estimate 0.33 0.33 Slope of overlap on independent = 0.5 Slope of overlap on independent = 0.5

20. Overlapping or independent? Overlapping or independent? So estimates from overlapping data tend to the same mean as independent ones and are more closely grouped So estimates from overlapping data tend to the same mean as independent ones and are more closely grouped

21. Relationship of indexes Indexes are related by Rényi’s equation Indexes are related by Rényi’s equation N a = (Σp i a ) 1/(1-a) = generalized entropy of order a N a = (Σp i a ) 1/(1-a) = generalized entropy of order a a N a relates to a N a relates to ---------------------------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------- -inf 1/p min freq(rarest species) -inf 1/p min freq(rarest species) 0 Snumber of species 0 Snumber of species 1 e H Shannon index 1 e H Shannon index 2 1/DSimpson index 2 1/DSimpson index +inf 1/p max Berger-Parker index +inf 1/p max Berger-Parker index

22. Graffiti in Coca

25. Why butterflies? Butterflies are part of the public awareness of ecological richness of the region for both Butterflies are part of the public awareness of ecological richness of the region for both local people local people and visitors and visitors It is worth finding out more about them, including their diversity It is worth finding out more about them, including their diversity

26. General conclusions Diversity and evenness can be estimated from sequential observations Diversity and evenness can be estimated from sequential observations Repeat trials produce consistent estimates and show a difference between habitats Repeat trials produce consistent estimates and show a difference between habitats Method is easy to apply and practical when there is little taxonomic expertise Method is easy to apply and practical when there is little taxonomic expertise Cook LM (2008) Diversity and evenness from sequential sightings. Insect Conservation and Diversity 1, 263-265 Cook LM (2008) Diversity and evenness from sequential sightings. Insect Conservation and Diversity 1, 263-265 Simpson EH (1949) Measurement of diversity. Nature, Lond. 163,388 Simpson EH (1949) Measurement of diversity. Nature, Lond. 163,388