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Butterfly diversity……………………

Butterfly diversity……………………. in rain forest. What is ecological diversity?. Based on 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 2) Species abundance. Rank Order

wade-mcintosh
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Butterfly diversity……………………

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

  2. What is ecological diversity? • Based on • 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 • 2) Species abundance

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

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

  5. A well known one is Simpson’s index • Based on pi, the probability of picking an individual of species i estimated from frequency • Probability of picking two of species i is pi2 • Probability of getting two any species = Σpi2. • ( = information content of a sample) • Gets smaller as diversity goes up • Sometimes expressed as 1/Σpi2 or -logΣpi2 • which increase with increased diversity

  6. Short digression • Simpson’s index is 1/Σpi2 or -logΣpi2 • Shannon Index, H, is -Σpi.log pi • both increase with increased diversity • Evenness is defined as nearness of index to maximum • Evenness (Simpson) = (-logΣpi2)/logS • Evenness (Shannon) = (-Σpi.log pi)/log S • Relation of H to Simpson: • H = -log/Σpi2 if all pi = 1/S • H ≈ 2.5 log (1/Σpi2) if distribution extreme

  7. Sampling location, EcuadorSan José de Payamino, Orellana Province

  8. Arrival at Coca Payamino research site

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

  10. Indexes like Simpson’s Index usually estimated by counting numbers in each species. But Σpi2 (i.e. the probability that two individuals in a pair are the same species)……. can be found directly by observation blinding glimpse of the obvious

  11. Field data book: • /////////// = a = number of like pairs • /////////////// = b = unlike pairs • n = a+b = total pairs • ////////// = S = species seen • ------------------------------------------------------------ • a/n = fraction of like pairs seen • which is an estimate of Σpi2

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

  13. Data collected from two sides of Payamino river

  14. Conclusion from data • These estimates show that: • 1. repeatable estimates of D can be made (mean SED 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)

  15. Some problems of accuracy of D • 1. Aggregation, courtship etc. affect estimate, so sampling must be as random as possible • 2. Binomial variance of D is • ab/n3, • larger than large-sample var of Simpson’s index, • 2[Σpi3 - (Σpi2)2]/n • 3. but data for D are easier to gather and little knowledge of species is needed

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

  17. and compare results of simulations P1 P2 P3 P4 P5 P6 …… • P1f11 f12 f13 f14 f15 f16 …. • P2 f21f22 f23 f24 f25 f26 …. • P3 f31 f32f33 f34 f35 f36 • P4 f41 f42 f43f44 f45 f46 • P5 f51 f52 f53 f54f55 f56 • P6 f61 f62 f63 f64 f65f66 • . . . . . . . • (Σf1)2+(Σf2)2+ etc …….... Σfii • for frequencies for sequential • If some mistakes are made they have similar accuracy

  18. 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 • yzyz 0/3 0/2 • yzzy 1/3 0/2 • Mean D estimate 0.33 0.33 • Slope of overlap on independent = 0.5

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

  20. Relationship of indexes • Indexes are related by Rényi’s equation • Na = (Σpia) 1/(1-a)= generalized entropy of order a • a Na relates to • ---------------------------------------------------------------------------------------------------- • -inf 1/pmin freq(rarest species) • 0 S number of species • 1 eH Shannon index • 2 1/D Simpson index • +inf 1/pmax Berger-Parker index

  21. Graffiti in Coca

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

  23. General conclusions • Diversity and evenness can be estimated from sequential observations • Repeat trials produce consistent estimates and show a difference between habitats • 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 • Simpson EH (1949) Measurement of diversity. Nature, Lond. 163,388

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