pres - Tamu.edu

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
Pricipal Component Analysis
Redundancy Discriminant
Analysis
Bray-Curtis Distance
Kulczynski Distance
Hellinger Distance
Chi-Square Distance
Correspondence Analysis
Canonical Correspondence
Analysis
Common Transformations
Bray-Curtis, Kulczynski to minimize
impact of dominant species

Square-root

Log-transformation

Remove rare species

Proportions (species profiles)

Presence/Absence

Hellinger
Chi-square to minimize impact of
rare species
Euclidean to minimize impact of
species abundance
Community composition data that
usually contains many zero values
Ordination
•
Constrained
Direct gradient analysis

•
•
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
Types
Unconstrained
Indirect gradient analysis
Are only based on the
species matrix
Multivariate Ordination Analyses
Unconstrained
Constrained

Principal Component Analysis (PCA)

Redundancy Discriminant Analysis (RDA)

Correspondence Analysis (CA)

Canonical Correspondence Analysis (CCA)

Non-Metric Multidimensional Scaling (NMDS)

Distance-based redundancy analysis (dbRDA)

Principal Coordinates Analysis (PCOA, MDS)

Canonical analysis of principal coordinates
(CAP)

Discriminant Analysis (DA)
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


Vegan: An Introduction to Ordination


http://cc.oulu.fi/~jarioksa/opetus/metodi/
Multivariate Statistics Summary


http://ordination.okstate.edu/
Community Analysis


http://ecology.msu.montana.edu/labdsv/R/labs/
Ordination Methods for Ecologists


http://cc.oulu.fi/~jarioksa/opetus/metodi/vegantutor.pdf
R Lab for Vegetation Ecologists


http://cran.r-project.org/web/packages/vegan/vignettes/intro-vegan.pdf
Multivariate Analysis of Ecological Communities in R: vegan tutorial


http://cran.r-project.org/web/packages/vegan/vegan.pdf
http://www.umass.edu/landeco/teaching/multivariate/schedule/summary.handouts.pdf
Ecologically Meaningful Transformations

http://adn.biol.umontreal.ca/~numericalecology/Reprints/Legendre_&_Gallagher.pdf