Summary

Summary Ecological Methods: Multivariate (visual)

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Course
Ecological Methods (WEC31806)

Institution
Wageningen University (WUR)

This is a summary of the second part of Ecological Methods (WEC31806), namely Multivariate analyses. The summary shows all the lectures in the Multivariate section and has been made extra visual in order to understand the material quickly and properly. In addition, with plenty of examples.

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Uploaded on October 2, 2024
Number of pages 22
Written in 2024/2025
Type Summary

data analysis
ecology
ecology
statistics
multivariate
regression
correlation
ca
cca
pca
rca

Institution
Wageningen University (WUR)
Education
Forest and Nature Conservation
Course
Ecological Methods (WEC31806)

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1. Summary - Summary ecological methods: multivariate (visual)
2. Summary - Summary ecological methods: univariate (visual)
3. Summary - Summary ecological methods: applied statistics (visual)
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12. Distance based ordination
Many response variables: more than one dependent variable
 plant/animal communities
 Microbiome studies
 Genetic studies

Multivariate analysis (MVA): simultaneously analysing multiple response variables

Community ecology: the variation in many dependent variables (e.g. species abundance) across sites
in the landscape
 may be explained by one or more environmental predictor variables
 often, we thus look for spatial gradients across sites (in species abundance and environmental
variables)

Ordination
Ordination: a way of ordering samples based on similarity
(e.g. Dutch political landscape)

Ordination is the placing of objects (= site, samples) along axes
(gradients), based on their properties (often species composition). –
Ramensky, 1929
 and relate these to environmental variables

2 main types of ordination

- Unconstrained ordination: only examines 1 dataset with response variables; the resulting
output reflects overall variation in the data, which is good for exploring data
- Constrained ordination: focussing on particular effects of interest: it attempts to explain the
variation in a set of response variables by the variation in a set of explanatory variables.

3 types of ordination plots

Scatterplot Biplot Triplot
Sites Sites + species Sites + species + predictors

 the closer the point are, the more similar they are
 triplots plots both variables, so also the predictors

,Polar ordination
Polar ordination: a foundational ordination technique

Steps of polar ordination:

1. Compute distance between sites in terms of species composition and plot in a distance
matrix
2. Select two most different sites: these are placed on opposite ends (poles) of axis 1
3. Order the remaining sites between the poles
 eventually leading to calculate an ordination score x, where x is coordinates of the site
4. Choose sites for axis 2 perpendicular to axis 1: select 2 other sies which are close together on
axis 2, but very dissimilar
5. Order all sites between these poles on axis 2

Start of dataset

Compute distances between sites (objects)
Distance: dissimilarity between objects

Euclidean distance: form of computing distances

d jk= √∑ ( y − y )
j k
2

, For a bigger dataset

Select two most different sites
Find the biggest value of difference between two sites in
the matrix
 the two sides are placed on opposite ends (poles) of
axis 1

Order remaining sites between the poles
E.g. axis score of site S2
 take the distance from S2 from both poles on the matrix and plot it
on the axis

Distance S2 – S1 = 128
Distance S2 – S5 = 74

Repeat that for every site

Can be computed by using the altered theorem of Pythagoras

2 2 2
X =( L + D1−D2 )/2 L

L = Distance between poles
D1 = Distance from pole 1
D2 = Distance from pole 2

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