1. Basic Concepts for Ordination Tanya, Nick, Caroline

2. What is ordination? Puts information in order of importance to the researcherPuts information in order of importance to the researcher There are two types of ordinationThere are two types of ordination –Direct Ordination –Indirect Ordination

3. Direct Ordination Places information in order with respect to a pre-defined environmental measurePlaces information in order with respect to a pre-defined environmental measure –Time (Generation) –Distance –Elevation

4. Example of Direct Ordination

5. Indirect Ordination

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

7. Indirect Ordination vs. Regression Regression makes one variable dependent on the othersRegression makes one variable dependent on the others Indirect Ordination treats all variables as equalsIndirect Ordination treats all variables as equals Indirect Ordination works well for co- correlated data whereas regression does notIndirect Ordination works well for co- correlated data whereas regression does not

8. Raw Data vs. Ordinated Data In raw data axes correspond to some measurement made by the researcherIn 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 scoresIn 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 dataOrdination scores – abstract way of measuring ordinated data –Has no relation to raw data

9. 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 measurementsPoints that are close together are similar and contain similar measurements, while points that are far apart are very different and contain different measurements

10. Setting Up Ordination Choosing variables is subjectiveChoosing variables is subjective Excluding variables should be robustExcluding variables should be robust –Repeat ordination several times Typical to restrict to one type of variableTypical to restrict to one type of variable –Ex. Given biological data or chemical data or climate data etc.

11. Bray-Curtis Ordination Can be done by hand without a computerCan be done by hand without a computer –Simplest of all indirect ordinations 1.Rectangular matrix of data is created 2.Matrix is converted into a square matrix that quantifies differences between samples 3.Two samples are chosen as the end points and are used to construct a scale diagram 4.Second set of samples is chosen to construct another axis 5.Process is repeated

12. Limitations of Bray-Curtis Being subjective and arbitraryBeing subjective and arbitrary Many permutations to select endpoints and distance indicesMany permutations to select endpoints and distance indices –Many techniques possible to describe the same data set – this gives 40 different possible permutations Sensitive to outliersSensitive to outliers Geometry may fail to workGeometry may fail to work Not a simple calculation – amount of work goes with the square of the number of samplesNot a simple calculation – amount of work goes with the square of the number of samples

13. Dissimilarity Matrix Essentially this matrix is made up of numbers (dissimilarity indices) that represent the difference between pairs of samplesEssentially 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 indicesFor different types of data, there are different formulas for calculating the dissimilarity indices

14. Defining End-Points Once we have the dissimilarities between all samples have been calculated, two samples need to be chosen as the end-pointsOnce 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) 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)

15. Graphing Ordination Scores First you have to construct the first ordination axis with the endpointsFirst 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 endpointThen 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