Post on 04-Feb-2017
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