Basic concepts for ordination
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Basic Concepts for Ordination. Tanya, Nick, Caroline . What is ordination?. Puts information in order of importance to the researcher There are two types of ordination Direct Ordination Indirect Ordination . Direct Ordination.

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Basic Concepts for Ordination

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Basic Concepts for Ordination

Tanya, Nick, Caroline

What is ordination?

  • Puts information in order of importance to the researcher

  • There are two types of ordination

    • Direct Ordination

    • Indirect Ordination

Direct Ordination

  • Places information in order with respect to a pre-defined environmental measure

    • Time (Generation)

    • Distance

    • Elevation

Example of Direct Ordination

Indirect Ordination

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

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

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

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

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.

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

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

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

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)

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

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