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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
  Tradeoffs Among Diversity
           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
  – determine adequate SU area
  – estimate sampling adequacy (no. of SU’s)
  – island biogeography
     Methods of Constructing
      Species-Area Curves
• Nested quadrat sampling
• Bootstrapping
  – take random samples of SU’s from data
    matrix, with replacement, and count
    number of species
  – start with individual SU’s, then pairs,
    then groups of 3, 4, 5, etc...
  – plot mean number of species against
    number of SU’s (or area).
Nested Quadrat Sampling




                     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

                                                  Quadrat Area (m 2)
        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,
    without reference to specific gradient(s)
    • calculated as gamma diversity – alpha diversity
  – amount (or rate) of compositional change
    along an environmental gradient
  – 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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