Butterfly Butterfly diversity……………………diversity……………………

in rain in rain forestforest

What is ecological What is ecological diversity?diversity?

Based onBased on 1) 1) Species richnessSpecies richness, i.e. number of , i.e. number of

species presentspecies present But also greater if most species have But also greater if most species have

equal numbers than if one or two equal numbers than if one or two predominate, so includespredominate, so includes

2) 2) Species abundanceSpecies abundance

Relative abundance Relative abundance ppii from fieldfrom field samplessamples

Two types of display commonly used. Two types of display commonly used.(data from an English field study over many (data from an English field study over many

years) years) Rank OrderRank Order individuals in each individuals in each

species in species in descending order descending order of rankof rank

Species abundanceSpecies abundance species with 1,2,3,species with 1,2,3,

… etc individuals … etc individuals on number of on number of individualsindividuals

Useful too to have a Useful too to have a diversity indexdiversity index

NN individuals in a community, with individuals in a community, with S S species, each at frequency species, each at frequency ppi i

Diversity increases with Diversity increases with SS But also affected by But also affected by species compositionspecies composition For given For given SS diversity is: diversity is: Least when 1 species predominatesLeast when 1 species predominates Greatest when all Greatest when all ppii = 1/ = 1/S S So a diversity index has to measure So a diversity index has to measure

bothboth

A well known one is Simpson’s A well known one is Simpson’s indexindex

Based on Based on ppii, the probability of picking an , the probability of picking an individual of species i estimated from individual of species i estimated from frequencyfrequency

Probability of picking two of species i is Probability of picking two of species i is ppii22

Probability of getting two any species = Probability of getting two any species = ΣΣppii

22. . ( = information content of a sample)( = information content of a sample) Gets Gets smallersmaller as diversity goes up as diversity goes up Sometimes expressed as 1/Sometimes expressed as 1/ΣΣppii

22 or -log or -logΣΣppii22

which which increaseincrease with increased diversity with increased diversity

Short digressionShort digression Simpson’s index is 1/Simpson’s index is 1/ΣΣppii

22 or -log or -logΣΣppii22

Shannon Index, H, is -Shannon Index, H, is -ΣΣppii.log p.log pii

both both increaseincrease with increased diversity with increased diversity

Evenness is defined as nearness of index to Evenness is defined as nearness of index to maximummaximum

Evenness (Simpson) = (-logEvenness (Simpson) = (-logΣΣppii22)/logS)/logS

Evenness (Shannon) = (-Evenness (Shannon) = (-ΣΣppii.log p.log pii)/log S)/log S

Relation of H to Simpson:Relation of H to Simpson: H = -log/H = -log/ΣΣppii

22 if all p if all pii = 1/S = 1/S

H ≈ 2.5 log (1/H ≈ 2.5 log (1/ΣΣppii22) if distribution extreme) if distribution extreme

Sampling location, Sampling location, EcuadorEcuador

San JosSan Joséé de Payamino, Orellana de Payamino, Orellana ProvinceProvince

Arrival at Coca Arrival at Coca Payamino research site Payamino research site

At Payamino siteAt Payamino site

Probably ca 1000 butterfly speciesProbably ca 1000 butterfly species No good identification guidesNo good identification guides Several reasons not to catch and kill Several reasons not to catch and kill

themthem

But we might try to measure But we might try to measure ecological diversity, which is a ecological diversity, which is a useful measure of habitat qualityuseful measure of habitat quality

Indexes like Simpson’s Index Indexes like Simpson’s Index usually estimated by counting usually estimated by counting numbers in each species.numbers in each species.

But But ΣΣppii

22 (i.e. the probability that two (i.e. the probability that two individuals in a pair are the same individuals in a pair are the same species)…….species)…….

can be found directly by can be found directly by observationobservation

Field data book:Field data book:

/////////// = a = number of like /////////// = a = number of like pairspairs

/////////////// = b = unlike pairs /////////////// = b = unlike pairs

n = a+b = total pairsn = a+b = total pairs ////////// = ////////// = S S = species seen= species seen ------------------------------------------------------------------------------------------------------------------------ a/n = fraction of like pairs seen a/n = fraction of like pairs seen which is an estimate of which is an estimate of ΣΣppii

22

So sequential estimate So sequential estimate is:is:

D = a/nD = a/n which does not need relative which does not need relative

abundance counts,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

Data collected from two Data collected from two sides of Payamino riversides of Payamino river

Conclusion from data Conclusion from data

These estimates show that: These estimates show that: 1. 1. repeatable estimates of D can be repeatable estimates of D can be

made (mean SEmade (mean SED D about the same as about the same as standard deviation of D)standard deviation of D)

2. 2. differences in diversity between differences in diversity between sites can be detected (mean D sites can be detected (mean D significantly different at the two sites)significantly different at the two sites)

Some problems of Some problems of accuracy of Daccuracy of D

1. Aggregation, courtship etc. affect 1. Aggregation, courtship etc. affect estimate, so sampling must be as random as estimate, so sampling must be as random as possiblepossible

2. Binomial variance of D is 2. Binomial variance of D is ab/nab/n33, , larger than large-sample var of Simpson’s larger than large-sample var of Simpson’s

index, index, 2[2[ΣΣppii

3 3 - (- (ΣΣppii22))22]/n]/n

3. but data for D are easier to gather and 3. but data for D are easier to gather and little knowledge of species is neededlittle knowledge of species is needed

To test accuracy we To test accuracy we couldcould

compare relative compare relative abundance abundance estimates with estimates with sequential sequential estimates made estimates made from the same from the same series of series of observations.observations.

and compare results of and compare results of simulationssimulations

P1P1 P2P2 P3P3 P4P4 P5P5 P6 ……P6 …… P1P1 ff1111 ff1212 ff1313 ff1414 ff1515 ff1616 ….…. P2P2 ff2121 ff2222 ff2323 ff2424 ff2525 ff2626 ….…. P3P3 ff3131 ff3232 ff3333 ff3434 ff3535 ff3636 P4P4 ff4141 ff4242 ff4343 ff4444 ff4545 ff4646 P5P5 ff5151 ff5252 ff5353 ff5454 ff5555 ff5656 P6P6 ff6161 ff6262 ff6363 ff6464 ff6565 ff6666 .. .. .. .. .. .. .. ((ΣΣff11))22+(+(ΣΣff22))22+ etc ……....+ etc …….... ΣΣffiiii for frequencies for for frequencies for

sequentialsequential If some mistakes are made they have similar If some mistakes are made they have similar

accuracy accuracy

Should we use overlapping or Should we use overlapping or independent pairs?independent pairs?

Sequence overlap D independent DSequence overlap D independent DFor k observations k-1 k/2For k observations k-1 k/2If k = 4 3 2 If k = 4 3 2 Possible order if 2 species at equal Possible order if 2 species at equal

frequency:frequency: yyzz 2/3 2/2yyzz 2/3 2/2 yzyz 0/3 0/2yzyz 0/3 0/2 yzzy 1/3 0/2yzzy 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

Overlapping or Overlapping or independent?independent?

So estimates from overlapping data So estimates from overlapping data tend to the same mean as tend to the same mean as independent ones and are more independent ones and are more closely grouped closely grouped

Relationship of indexesRelationship of indexes Indexes are related by Indexes are related by RRéényi’snyi’s equation equation NNaa = ( = (ΣΣppii

aa) ) 1/(1-a)1/(1-a) = generalized entropy of = generalized entropy of order a order a

aa N Naa relates to relates to --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

-inf-inf 1/p 1/pminmin freq(rarest species)freq(rarest species) 00 S S number of speciesnumber of species 11 e eHH Shannon indexShannon index 22 1/D 1/D Simpson indexSimpson index +inf+inf 1/p 1/pmaxmax Berger-Parker indexBerger-Parker index

Graffiti in CocaGraffiti in Coca

Why butterflies?Why butterflies?

Butterflies are part of Butterflies are part of the public awareness the public awareness of ecological richness of ecological richness of the region for both of the region for both

local people local people and and

visitors visitors It is worth finding out It is worth finding out

more about them, more about them, including their including their diversity diversity

General conclusionsGeneral conclusions

Diversity and evenness can be estimated Diversity and evenness can be estimated from sequential observationsfrom sequential observations

Repeat trials produce consistent estimates Repeat trials produce consistent estimates and show a difference between habitatsand show a difference between habitats

Method is easy to apply and practical when Method is easy to apply and practical when there is little taxonomic expertisethere is little taxonomic expertise

Cook LM (2008) Diversity and evenness from sequential Cook LM (2008) Diversity and evenness from sequential sightings. sightings. Insect Conservation and Diversity Insect Conservation and Diversity 11, 263-265, 263-265

Simpson EH (1949) Measurement of diversity. Simpson EH (1949) Measurement of diversity. Nature, LondNature, Lond. . 163163,388,388