Basic Concepts for Basic Concepts for OrdinationOrdination

Tanya, Nick, Caroline Tanya, Nick, Caroline

What is ordination?What is ordination?

• Puts information in order of importance Puts information in order of importance to the researcher to the researcher

• There are two types of ordination There are two types of ordination – Direct Ordination Direct Ordination – Indirect Ordination Indirect Ordination

Direct OrdinationDirect Ordination

• Places information in order with Places information in order with respect to a pre-defined environmental respect to a pre-defined environmental measuremeasure– Time (Generation)Time (Generation)– DistanceDistance– ElevationElevation

Example of Direct OrdinationExample of Direct Ordination

Indirect Ordination Indirect Ordination

Indirect OrdinationIndirect Ordination

• Abstract – tries to make a meaningful Abstract – tries to make a meaningful summary of the patterns underlying the summary of the patterns underlying the data data

• Creates graphs or diagrams that show Creates graphs or diagrams that show the relationships among data points the relationships among data points

• Data space Data space – Multidimensional mathematic space where Multidimensional mathematic space where

each variable represents a dimension each variable represents a dimension

Indirect Ordination vs. Indirect Ordination vs. Regression Regression

• Regression makes one variable Regression makes one variable dependent on the others dependent on the others

• Indirect Ordination treats all variables Indirect Ordination treats all variables as equals as equals

• Indirect Ordination works well for co-Indirect Ordination works well for co-correlated data whereas regression correlated data whereas regression does notdoes not

Raw Data vs. Ordinated Data Raw Data vs. Ordinated Data

• In raw data axes correspond to some In raw data axes correspond to some measurement made by the researcher measurement made by the researcher – All axes are equally important All axes are equally important

• In ordinated data the numbers on the axes In ordinated data the numbers on the axes are ordination scores are ordination scores – Axes produced ordination are in descending Axes produced ordination are in descending

order of importance order of importance

• Ordination scores – abstract way of Ordination scores – abstract way of measuring ordinated data measuring ordinated data – Has no relation to raw data Has no relation to raw data

Ordination DiagramOrdination Diagram

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

Setting Up Ordination Setting Up Ordination

• Choosing variables is subjective Choosing variables is subjective

• Excluding variables should be robust Excluding variables should be robust – Repeat ordination several times Repeat ordination several times

• Typical to restrict to one type of Typical to restrict to one type of variable variable – Ex. Given biological data or chemical data Ex. Given biological data or chemical data

or climate data etc. or climate data etc.

Bray-Curtis Ordination Bray-Curtis Ordination

• Can be done by hand without a computer Can be done by hand without a computer – Simplest of all indirect ordinations Simplest of all indirect ordinations

1.1. Rectangular matrix of data is created Rectangular matrix of data is created 2.2. Matrix is converted into a square matrix Matrix is converted into a square matrix

that quantifies differences between that quantifies differences between samples samples

3.3. Two samples are chosen as the end points Two samples are chosen as the end points and are used to construct a scale diagram and are used to construct a scale diagram

4.4. Second set of samples is chosen to Second set of samples is chosen to construct another axis construct another axis

5.5. Process is repeated Process is repeated

Limitations of Bray-CurtisLimitations of Bray-Curtis

• Being subjective and arbitrary Being subjective and arbitrary • Many permutations to select endpoints and Many permutations to select endpoints and

distance indicesdistance indices– Many techniques possible to describe the same Many techniques possible to describe the same

data set – this gives 40 different possible data set – this gives 40 different possible permutations permutations

• Sensitive to outliers Sensitive to outliers • Geometry may fail to work Geometry may fail to work • Not a simple calculation – amount of work Not a simple calculation – amount of work

goes with the square of the number of goes with the square of the number of samples samples

Dissimilarity MatrixDissimilarity Matrix

• Essentially this matrix is made up of Essentially this matrix is made up of numbers (dissimilarity indices) that numbers (dissimilarity indices) that represent the difference between represent the difference between pairs of samplespairs of samples

– Dissimilarity index between a sample and Dissimilarity index between a sample and itself is zero itself is zero

• For different types of data, there are For different types of data, there are different formulas for calculating the different formulas for calculating the dissimilarity indices dissimilarity indices

Defining End-Points Defining End-Points

• Once we have the dissimilarities Once we have the dissimilarities between all samples have been between all samples have been calculated, two samples need to be calculated, two samples need to be chosen as the end-pointschosen as the end-points

• the simplest way to choose the the simplest way to choose the endpoints is to choose the two points endpoints is to choose the two points that are most dissimilar (have the that are most dissimilar (have the largest dissimilarity index – close to 1 largest dissimilarity index – close to 1 being the most dissimilar) being the most dissimilar)

Graphing Ordination ScoresGraphing Ordination Scores

• First you have to construct the first First you have to construct the first ordination axis with the endpoints ordination axis with the endpoints

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

your point is located your point is located