Basic Concepts for Ordination

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Basic Concepts for Ordination

• Tanya, Nick, Caroline

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What is ordination?

• Puts information in order of importance to the
  researcher
• There are two types of ordination
• Direct Ordination
• Indirect Ordination

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Direct Ordination

• Places information in order with respect to a
  pre-defined environmental measure
• Time (Generation)
• Distance
• Elevation

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Example of Direct Ordination
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Indirect Ordination
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Indirect Ordination

• Abstract tries to make a meaningful summary of
  the patterns underlying the data
• Creates graphs or diagrams that show the
  relationships among data points
• Data space
• Multidimensional mathematic space where each
  variable represents a dimension

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Indirect Ordination vs. Regression

• Regression makes one variable dependent on the
  others
• Indirect Ordination treats all variables as
  equals
• Indirect Ordination works well for co-correlated
  data whereas regression does not

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Raw Data vs. Ordinated Data

• In raw data axes correspond to some measurement
  made by the researcher
• All axes are equally important
• In ordinated data the numbers on the axes are
  ordination scores
• Axes produced ordination are in descending order
  of importance
• Ordination scores abstract way of measuring
  ordinated data
• Has no relation to raw data

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Ordination Diagram

• Points that are close together are similar and
  contain similar measurements, while points that
  are far apart are very different and contain
  different measurements

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Setting Up Ordination

• Choosing variables is subjective
• Excluding variables should be robust
• Repeat ordination several times
• Typical to restrict to one type of variable
• Ex. Given biological data or chemical data or
  climate data etc.

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Bray-Curtis Ordination

• Can be done by hand without a computer
• Simplest of all indirect ordinations
• Rectangular matrix of data is created
• Matrix is converted into a square matrix that
  quantifies differences between samples
• Two samples are chosen as the end points and are
  used to construct a scale diagram
• Second set of samples is chosen to construct
  another axis
• Process is repeated

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Limitations of Bray-Curtis

• Being subjective and arbitrary
• Many permutations to select endpoints and
  distance indices
• Many techniques possible to describe the same
  data set this gives 40 different possible
  permutations
• Sensitive to outliers
• Geometry may fail to work
• Not a simple calculation amount of work goes
  with the square of the number of samples

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Dissimilarity Matrix

• Essentially this matrix is made up of numbers
  (dissimilarity indices) that represent the
  difference between pairs of samples
• Dissimilarity index between a sample and itself
  is zero
• For different types of data, there are different
  formulas for calculating the dissimilarity
  indices

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Defining End-Points

• Once we have the dissimilarities between all
  samples have been calculated, two samples need to
  be chosen as the end-points
• the simplest way to choose the endpoints is to
  choose the two points that are most dissimilar
  (have the largest dissimilarity index close to
  1 being the most dissimilar)

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Graphing Ordination Scores

• First you have to construct the first ordination
  axis with the endpoints
• Then you have to draw a circle with the radius
  representing the distance between the first
  endpoint and the point your are plotting and
  repeat the process with the second endpoint
• Where the two circles intersect is where your
  point is located