Species Diversity

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Species Diversity

• Chapter 16

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Introduction

• 1710, Dutch colonists on the Indonesian island of
  Bangka.
• Over the centuries, mining and deforestation on a
  massive scale.
• Slash and burn agriculture.
• 3 of the primary forest remained intact.

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Introduction

• Minimal restoration efforts and bird diversity.
• First glance restored areas looked the same as
  unrestored sites.

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Introduction

• Further analysis restored sites had more
  diversity.

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Measures of Diversity

• Simplest measure count number of species in an
  area (species richness).
• Major problem does not take into account species
  abundance.
• Community A has 99 individuals of species 1 and 1
  individual of species 2.
• Community B has 50 individuals of species 1 and
  50 individual of species 2.
• Both communities have the same species richness.

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Diversity Indices

• Species richness is highly susceptible to sample
  size.
• The greater the number of individuals in the
  sample, the higher the number of species
  recorded.

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Diversity Indices

• Therefore, we need diversity indices that
  incorporate both abundance and richness.

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Diversity Indices

• Two broad categories dominance indices and
  information-statistic indices.

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Diversity Indices

• Dominance indices
• These indices are weighted toward the abundance
  of the commonest species.
• Berger and Parker dominance index (1970).

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Dominance Indices

• Concept if one species dominates a community,
  then the community is not very diverse.
• Community 1 D 10/100 0.1
• DBP 1/0.1 10
• Community 2 D 55/100 0.55
• DBP 1/0.55 1.82

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Dominance Indices

• Simpsons index (1949)
• Gives the probability that any two individuals
  drawn at random from an infinitely large
  community will belong to different species.
• Disadvantage it is heavily weighted toward the
  most abundant species.
• Common to all dominance indices.
• Rare species fail to change index.
• Regarded as more accurate than Berger-Parker
  Index.

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Diversity Indices

• Information-statistic indices
• Can take into account rare species.
• Based on the rationale that diversity in a
  natural system can be measured in a way that is
  similar to the way information contained in a
  code or message is measured.
• A technique to measure uncertainty.
• The higher the value, the higher the uncertainty
  in predicting a sequence.
• The more diverse a community.

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Information-Statistic Indices

• Shannon index
• Even the rare species contributes to the Shannon
  index, so if an area has many rare species, their
  contributions would accumulate.
• Shannon index for real communities usually fall
  between 1.5 and 3.5.

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Information-Statistic Indices

• Brillouin index
• Index is designed to reflect species abundance.

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Information-Statistic Indices

• Differences between Brillouin index and Shannon
  index
• Shannon index does not change with abundance, as
  long as the proportional abundance remains
  constant. Brillouin index does change.

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Information-Statistic Indices

• Brillouin index uses factorials, which quickly
  produces huge numbers that are unwieldy. Shannon
  index is often chosen for its computational
  simplicity.

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Diversity Indices

• Comparison of Berger-Parker, Simpson, Shannon,
  and Brillouin.
• Generally values of diversity are correlated
  increasing together as diversity increases.

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Diversity Indices

• Example
• Indices generally give the same results.
• 3 out of 4 indicate that bird diversity is
  greater in the restored site.
• If rare species are valued, then
  information-statistic are the most valuable.
• If total abundance of individuals is important,
  then Brillouin is the best index.

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Diversity Indices

• Summary of effectiveness

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Diversity Indices

• It is important to remember that we cant mix the
  indices when comparing communities the SAME
  index must be used throughout.

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Diversity Indices

• Evenness
• Information-statistic indices are affected by
  both number of species and their equitability or
  evenness.
• Compare a communitys actual diversity, HS, to
  the maximum possible diversity, Hmax.
• Evenness H / Hmax
• E is constrained between 0 and 1.0.
• Generally, adding species and increasing evenness
  both increase species diversity.

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Weighting Biodiversity Indices

• Weighting biodiversity indices the use of
  ordinal indices.
• Most indices discussed so far, treat species
  equally (cardinal indices).
• Is this right, or should weight be used?
• Should more weight be given to a large, rare
  predator or a small, rare nematode?

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Applied Ecology

• Ordinal indices indices that attempt to rank
  order species in importance.
• Cardinal indices indices that treat all species
  as equals.

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Applied Ecology

• Vane-Wright, Humphries and Williams (1991).
• Developed methods to weight taxonomically rare
  species in diversity indices.

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Rank Abundance Diagrams

• A more complete picture of the distribution of
  species abundance.
• Plotting proportional abundance (usually on a
  logarithmic scale) against rank abundance.

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Rank Abundance Diagrams

• Rank abundance diagrams can be drawn for the
  number of individuals, biomass, ground area
  covered (and other variables) plotted against
  rank abundance.
• At least 18 different theoretical forms.
• Three most well-known
• Geometric series
• Lognormal
• Broken-stick

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Rank Abundance Diagrams

• Species abundance is most equitable in the
  broken-stick, less equitable in the lognormal,
  and less equitable still in the geometric series.

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Geometric Series

• The first or most dominant species to colonize a
  new area appropriates a fraction of the available
  resources, and by competitive interaction,
  preempts that fraction.
• Second species then preempts a similar fraction,
  and so on.

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Geometric Series

• Model fits
• Plants from sub-alpine communities.
• Benthos in a polluted fjord.
• Best fit for communities of relatively few
  species, where a single environmental factor
  predominates, such as extreme temperature or
  pollution.

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Broken Stick

• Resources (represented by a stick) are divided at
  one time into segments over the length of the
  stick.
• Implying instantaneous colonization by all
  species.
• The segments are ranked in decreasing order of
  their lengths.
• Abundance of species is assumed to be
  proportional to the length of the segment.

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Broken Stick

• Model fits
• A few bird, fish, worm, and predatory gastropod
  communities.
• Realistic on relatively few occasions.

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Lognormal

• Developed by Frank Preston (1948).
• More common than broken stick for most
  communities that are rich in species.
• Graph of species number versus a logarithmic
  scale.

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Lognormal

• Lognormal distribution of a variety of
  communities.

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Lognormal

• Existence of the truncated lognormal
  distribution.
• Plots of number of species (y-axis) against log
  of individuals per species (x-axis), were
  truncated to the left of the mode.
• Truncation due to species that were present in
  the habitat but not in the sample.

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Lognormal

• If larger samples were taken, more species would
  be obtained.
• Mode would move to the right.
• Therefore, it is critical that communities are
  adequately sampled.

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Community Similarity

• Similarity coefficients a method for directly
  comparing diversity of different sites.
• Usually compare the number of species common to
  all areas.

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Community Similarity

• Comparison will involve a simple presence-absence
  matrix for two areas, A and B.
• a number of species common to both sites.
• b number of species in site B, but not in A.
• c number of species in site A, but not in B.
• d number of species absent in both samples.

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Community Similarity

• Is "d", meaningful?
• d is a measure of the negative matches,
  potentially biologically meaningful.
• In reality, it is almost impossible to know.
• Most similarity coefficients rely only on a, b,
  and c.

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Community Similarity

• Community similarity can be measured using
  similarity coefficients such as
• Jaccard coefficient
• Sorenson coefficient
• Simple matching coefficient (incorporates d)

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Cluster Analysis

• Cluster Analysis is used when research is being
  conducted on more than two sites.
• Starts with a table or matrix giving the
  similarity between each pair of sites (by using
  any similarity coefficient).

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Cluster Analysis

• The two most similar sites are combined to form a
  single cluster.
• The analysis then proceeds by successfully
  combining similar sites until all are combined
  into a single figure (dendrogram).

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Cluster Analysis

• Single-linkage clustering method for combining
  sites into clusters.
• Begin with a matrix of similarity coefficients.
• Find most similar pairs (Conifer sites 2 and 3).

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Cluster Analysis

• Second most similar sites (Oak sites 1 and 2).
• Third most similar sites (Conifer sites 1 and 2).
• Therefore, conifer site 1 is linked with cluster
  of conifer site 2 and 3, forming a 3 community
  cluster.
• Last joining is between oak 1 and 2 cluster, and
  conifer 1, 2, and 3 cluster.

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Conclusion

• Measuring biodiversity is essential for effective
  management practices.
• Another important reason to measure biodiversity
• Diversity begets stability!
• Stable ecosystems are easier to manage.

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Summary

• Biodiversity may be expressed in a number of
  ways species richness or by various indices that
  take into account richness and abundance.

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Summary

• Dominance indices include Simpsons index and the
  Berger-Parker index. Both are easy to calculate
  and interpret, but both are biased toward
  dominant or common species. Simpsons index may
  be more realistic.

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Summary

• Information-statistic indices pay more attention
  to rare species. Shannon index and Brillouin
  index are information-statistic indices. The
  Brillouin index is more sensitive to species
  abundance, but is much more difficult to
  calculate.

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Summary

• Each of the various dominance and
  information-statistic indices may give values
  slightly different than those obtained from other
  indices, but all of the values are generally well
  correlated. Each has its own strength.
  Choosing the appropriate index for the
  appropriate situation depends on the question
  being asked.

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Summary

• Most diversity indices can be referred to as
  cardinal indices (they treat species equally).
  Indices that attempt to weight rare species or
  any other type of species are known as ordinal
  indices.

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Summary

• Diversity indices attempt to describe whole
  communities with one statistic. A more complete
  description can be obtained by plotting
  proportional abundance of every species against
  the rank of its abundance. Examples of
  abundance diagrams geometric, lognormal, and
  broken stick.

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Summary

• To compare diversity among areas, compare
  diversity indices or use similarity coefficients.

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Summary

• Cluster analysis may be used to compare the
  similarity of two or more sites.