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Basic Concepts for Ordination

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Basic Concepts for Ordination

Tanya, Nick, Caroline

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

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

- 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

- 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

- 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

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

- 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.

- 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

- 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

- 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

- 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)

- 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