Download Diversity/Similarity

Butterfly diversity……………………
 in
rain forest
What is ecological diversity?
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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
Relative abundance pi from field samples
Two types of display commonly used.
(data from an English field study over many years)
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Rank Order
individuals in each
species in descending
order of rank
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Species abundance
species with 1,2,3,… etc
individuals on number of
individuals
Useful too to have a diversity index
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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
A well known one is Simpson’s index
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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
Short digression
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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
Sampling location, Ecuador
San José de Payamino, Orellana Province
Arrival at Coca
Payamino research site
At Payamino site
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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
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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
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Field data book:
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///////////
= 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
So sequential estimate is:
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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
Data collected from two sides of
Payamino river
Conclusion from data
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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)
Some problems of accuracy of D
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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
To test accuracy we could
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compare relative
abundance estimates
with sequential estimates
made from the same
series of observations.
and compare results of simulations
P1
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P2
P3
P4
P5
P6 ……
P1 f11
f12
f13
f14
f15
f16
….
P2 f21
f22
f23
f24
f25
f26
….
P3 f31
f32
f33
f34
f35
f36
P4 f41
f42
f43
f44
f45
f46
P5 f51
f52
f53
f54
f55
f56
P6 f61
f62
f63
f64
f65
f66
. .
.
.
.
.
.
(Σf1)2+(Σf2)2+ etc ……....
Σfii
for frequencies
for sequential
If some mistakes are made they have similar accuracy
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
Overlapping or independent?
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So estimates from overlapping data tend to the
same mean as independent ones and are more
closely grouped
Relationship of indexes
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Indexes are related by Rényi’s equation
Na = (Σpia) 1/(1-a) = generalized entropy of
order a
 a
Na
relates to
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-inf
0
1
2
+inf
1/pmin
S
eH
1/D
1/pmax
freq(rarest species)
number of species
Shannon index
Simpson index
Berger-Parker index
Graffiti in Coca
Why butterflies?
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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
General conclusions
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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