Multivariate Ordination Antony Rodger

Edwin Lopez

Todays Presentation

Why use multivariate ordination?

What is “ordination”?

Distance metrics (Ecological distances)

Common transformations

Types of ordination

Examples of multivariate ordination analyses

Why do it??

What is ordination ???

Ordination methods geometrically arrange sites so that distances between them in the

graph represent their ecological distances. In an ordination graph, sites are plotted so

that distances between them in the graph reflect the ecological differences between

them.

Ordination Visualize complex data in few dimensions

Find patterns and combinations of the variables that can be use in subsequent analysis

The goal of ordination is to find axes of the greatest variablility in the community composition (the ordination axes) for a set of samples and to visualize (using an ordination diagram)

Large and messy

matrices of

Variables Multivariate

Analysis

Distance Metrics (Ecological Distance)

• Euclidean Distance

• Bray-Curtis Distance

• Kulczynski Distance

• Hellinger Distance

• Chi-Square Distance

Euclidean Distance

Bray-Curtis Distance

Kulczynski Distance

Hellinger Distance

Chi-Square Distance

Pricipal Component Analysis

Redundancy Discriminant

Analysis

Correspondence Analysis

Canonical Correspondence

Analysis

Common Transformations

Square-root

Log-transformation

Remove rare species

Proportions (species profiles)

Presence/Absence

Hellinger

Euclidean to minimize impact of

species abundance

Bray-Curtis, Kulczynski to minimize

impact of dominant species

Community composition data that

usually contains many zero values

Chi-square to minimize impact of

rare species

Ordination

Types

Unconstrained

Constrained

Are only based on the

species matrix

• Use information from both the species and the environmental

matrices

• Attempt to explain difference in species composition between sites by

differences in environmental variables

• The aim of constrained ordination is to find the variability in species

composition that can be explained by the measured environmental

variables

Direct gradient analysis

Indirect gradient analysis

Multivariate Ordination Analyses

Principal Component Analysis (PCA)

Correspondence Analysis (CA)

Non-Metric Multidimensional Scaling (NMDS)

Principal Coordinates Analysis (PCOA, MDS)

Discriminant Analysis (DA)

Redundancy Discriminant Analysis (RDA)

Canonical Correspondence Analysis (CCA)

Distance-based redundancy analysis (db-RDA)

Canonical analysis of principal coordinates (CAP)

Constrained Unconstrained

Correspondence Analysis (CA)

Canonical Correspondence Analysis (CCA)

Canonical Correspondence Analysis (CCA)

References

Kindt, R. and R. Coe. 2005. Tree diversity analysis. A manual and software for

common statistical methods for ecological and biodiversity studies. Nairobi:

World Agroforestry Centre (ICRAF).

http://www.worldagroforestry.org/downloads/publications/PDFs/B13695.pdf

Leps, J. and P. Smilauer. 2003. Multivariate analysis of ecological data using

CANOCO. Cambridge University Press, New York.

http://www.planta.cn/forum/files_planta/multivariate_analysis_of_ecological_dat

a_using_canoco_390_173.pdf

Additional Resources Vegan Package

http://cran.r-project.org/web/packages/vegan/vegan.pdf

Vegan: An Introduction to Ordination

http://cran.r-project.org/web/packages/vegan/vignettes/intro-vegan.pdf

Multivariate Analysis of Ecological Communities in R: vegan tutorial

http://cc.oulu.fi/~jarioksa/opetus/metodi/vegantutor.pdf

R Lab for Vegetation Ecologists

http://ecology.msu.montana.edu/labdsv/R/labs/

Ordination Methods for Ecologists

http://ordination.okstate.edu/

Community Analysis

http://cc.oulu.fi/~jarioksa/opetus/metodi/

Multivariate Statistics Summary

http://www.umass.edu/landeco/teaching/multivariate/schedule/summary.handouts.pdf

Ecologically Meaningful Transformations

http://adn.biol.umontreal.ca/~numericalecology/Reprints/Legendre_&_Gallagher.pdf