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Diversity by lanyuehua

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```									Diversity
Which SU is most diverse?

Species   Species   Species   Species   Species
TOTAL
1         2         3         4         5

SU 1     96         1         1         1         1       100

SU 2     55        23        11         8         3       100

SU 3     20        20        20        20        20       100
Popular Diversity Indices
• Richness: S
• Shannon-Wiener index: H’
• Complement or reciprocal of Simpson’s
dominance index
Expressing abundances as
proportions of total abundance
in an SU

xi   Abundance

pi     s
of species i

Proportional
abundance
of species i
 xi
i 1
Total abundance
of all species
Expressing abundances as
proportions of total abundance
in an SU

Species   Species   Species   Species   Species
TOTAL
1         2         3         4         5

x     12        45         1        0         2       60

p   0.2000    0.7500    0.01667   0.0000    0.0333   1.0000
Hill’s General Diversity Index

1
     S
      1 a
Da    pi 
a

 i 1 
Species Richness (S)

• number of species present in an SU
• when the parameter a is 0, Hill’s Index
reduces to species richness
• simplest, most intuitive measure of
diversity, but:
– depends non-linearly on area sampled (species-
area curves)
– sensitive to skill of observer
– high sampling error when species are small,
cryptic, mobile or difficult to identify
Shannon-Wiener Index: H’
• popular diversity index
• “Information content” of an SU
• measures the degree of uncertainty
about the species of one individual
chosen at random from an SU
• uncertainty decreases as:
– richness decreases
– evenness decreases (SU is dominated by
a few species)
Evenness or Equitability

• degree to which abundances of
species within an SU are equal
• intuitively, greater evenness also
equates with higher diversity
• diversity indices often combine
richness and evenness
Shannon-Wiener Index: H’

s
H    pi log pi
i 1
Shannon-Wiener Index: H’
• minimum value is 0 when only 1 species is
present
• maximum value is log(S), when all S species
have equal abundances
• need to state the base of logarithms used
(usually e, 2 or 10)
• strictly defined only when abundances are
counts (number of individuals), though often
applied to other measures (cover, biomass
etc…)
Shannon-Wiener Examples

Species   Species   Species   Species   Species
H’
1         2         3         4         5

SU 1     96         1         1         1         1      0.097

SU 2     55        23        11        8         3       0.528

SU 3     20        20        20        20        20      0.699

Note: 0.699 = log(5) – all species have equal abundances
Simpson’s Index of Dominance
(or Concentration)

• probability that two individuals drawn
randomly from an SU belong to the
same species
• increases as evenness decreases
• high values when one or a few species
dominate the SU
Simpson’s Index of
Dominance or Concentration
s
Cp            2
i
i 1
Diversity Indices Derived from
Simpson’s Index
• reciprocal:   1 / C
– minimum value of 1, when only one
species is present
– maximum value is S, when abundances of
all species are equal

• complement: 1 - C
– probability that two individuals drawn
randomly from an SU belong to different
species
Hill’s General Diversity Index
• three most popular diversity indices:
• When a = 0, Da = S (richness)
• As a → 1, Da → log-1(H’)
• When a = 2, Da = 1/C (reciprocal of
Simpson’s index).
Hill’s General Diversity Index

• as a increases, greater weight is
given to the more abundant species
– a=0 (richness) all species have equal
weight
– a=1 (antilog of Shannon) is intermediate
– a=2 (reciprocal of Simpson) dominant
species have relatively high weight
Indices
• Richness is conceptually simple, but
very sensitive to SU area and
sampling effort / error
• Shannon and 1 / Simpson are less
sensitive to SU area and sampling
effort / error, but conceptually more
complex
Evenness Indices
• Diversity indices combine richness and
evenness
• Evenness indices are an attempt to
factor out the richness component
• Simplest method is to divide diversity
index by its maximum value
Pielou’s J
• Shannon-Wiener divided by log(S) (also
known as Shannon’s equitability – EH)
• maximum of 1 when species have equal
abundances
• approaches zero as one species dominates
s
  pi log pi
H
J                       i 1

H max                    log( S )
Simpson Equitability E
• reciprocal of Simpson (D2) divided by S
• maximum of 1 when species have equal
abundances
• approaches 1/S as one species dominates.

D2                            1
E                              s
S p
D2 max                                 2
i
i 1
Species-Area Curves
• graph of relationship between number
of species (richness) and area sampled
• applications
– estimate sampling adequacy (no. of SU’s)
– island biogeography
Methods of Constructing
Species-Area Curves
• Bootstrapping
– take random samples of SU’s from data
matrix, with replacement, and count
number of species
then groups of 3, 4, 5, etc...
– plot mean number of species against
number of SU’s (or area).

64 m2

16 m2   32 m2

2
4 m2 8 m
2 m2
1 m2
Species-Area Curve
40
Number of Species (Richness)

30

20

10

0
0   10   20      30       40       50   60   70

Levels of Diversity

• Alpha diversity
– Diversity of individual sampling units
(SU’s)
• Beta diversity
– Between SU diversity: amount of
compositional variation among a set of
SU’s
• Gamma diversity
– Overall diversity of a set of SU’s
– “Landscape-level” diversity
Alpha Diversity
• diversity at the SU level
• calculate as average species richness
per plot
Beta Diversity
• Between SU diversity: amount of
compositional variation among a set of
SU’s
• Several different concepts
– heterogeneity in composition among SU’s,
• calculated as gamma diversity – alpha diversity
– amount (or rate) of compositional change
– amount of compositional change along an
ordination axis
Gamma Diversity
• diversity of the total collection of
SU’s
• can use the same kinds of indices as
for alpha diversity
– Richness (total number of species in
entire data matrix)
– Shannon-Wiener or Reciprocal of
Simpson’s Index calculated on total or
average abundances of species over all
SU’s.

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