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Managing Dimensionality (but not acronyms) PCA, CA, RDA, CCA, MDS, NMDS, DCA, DCCA, pRDA, pCCA PowerPoint PPT Presentation


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Managing Dimensionality (but not acronyms) PCA, CA, RDA, CCA, MDS, NMDS, DCA, DCCA, pRDA, pCCA. Type of Data Matrix. Ordination Techniques. Models of Species Response. There are (at least) two models:- Linear - species increase or decrease along the environmental gradient

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Managing Dimensionality (but not acronyms) PCA, CA, RDA, CCA, MDS, NMDS, DCA, DCCA, pRDA, pCCA

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Managing Dimensionality (but not acronyms)PCA, CA, RDA, CCA, MDS, NMDS, DCA, DCCA, pRDA, pCCA


Type of Data Matrix


Ordination Techniques


Models of Species Response

There are (at least) two models:-

  • Linear - species increase or decrease along the environmental gradient

  • Unimodal - species rise to a peak somewhere along the environmental gradient and then fall again


A Theoretical Model


Linear


Unimodal


Alpha and Beta Diversity

  • alpha diversity is the diversity of a community (either measured in terms of a diversity index or species richness)

  • beta diversity (also known as ‘species turnover’ or ‘differentiation diversity’) is the rate of change in species composition from one community to another along gradients; gamma diversity is the diversity of a region or a landscape.


A Short Coenocline


A Long Coenocline


Inferring Gradients from Species (or Attribute) Data


Indirect Gradient Analysis

  • Environmental gradients are inferred from species data alone

  • Three methods:

    • Principal Component Analysis - linear model

    • Correspondence Analysis - unimodal model

    • Detrended CA - modified unimodal model


PCA - linear model


PCA - linear model


Terschelling Dune Data


PCA gradient - site plot


PCA gradient - site/species biplot

standard

biodynamic& hobby

nature


Site A B C D E F SpeciesPrunus serotina 6 3 4 6 5 1Tilia americana2 0 7 0 6 6Acer saccharum0 0 8 0 4 9Quercus velutina0 8 0 8 0 0Juglans nigra3 2 3 0 6 0

Reciprocal Averaging


Site A B C D E F Species ScoreSpecies Iteration 1Prunus serotina 6 3 4 6 5 11.00Tilia americana2 0 7 0 6 60.63Acer saccharum0 0 8 0 4 90.63Quercus velutina0 8 0 8 0 00.18Juglans nigra3 2 3 0 6 00.00

Iteration11.00 0.00 0.86 0.60 0.62 0.99SiteScore

Reciprocal Averaging


Site A B C D E F Species ScoreSpecies Iteration 12Prunus serotina 6 3 4 6 5 1 1.00 0.68Tilia americana2 0 7 0 6 6 0.63 0.84Acer saccharum0 0 8 0 4 9 0.63 0.87Quercus velutina0 8 0 8 0 0 0.18 0.30Juglans nigra3 2 3 0 6 0 0.00 0.67

Iteration 1 1.00 0.00 0.86 0.60 0.62 0.99Site20.65 0.00 0.88 0.05 0.78 1.00Score

Reciprocal Averaging


Site A B C D E F Species ScoreSpecies Iteration 1 23Prunus serotina 6 3 4 6 5 1 1.00 0.68 0.50Tilia americana2 0 7 0 6 6 0.63 0.84 0.86Acer saccharum0 0 8 0 4 9 0.63 0.87 0.91Quercus velutina0 8 0 8 0 0 0.18 0.30 0.02Juglans nigra3 2 3 0 6 0 0.00 0.67 0.66

Iteration 1 1.00 0.00 0.86 0.60 0.62 0.99Site 2 0.65 0.00 0.88 0.05 0.78 1.00Score30.60 0.01 0.87 0.00 0.78 1.00

Reciprocal Averaging


Site A B C D E F Species ScoreSpecies Iteration 1 2 3 9Prunus serotina 6 3 4 6 5 1 1.00 0.68 0.50 0.48Tilia americana2 0 7 0 6 6 0.63 0.84 0.86 0.85Acer saccharum0 0 8 0 4 9 0.63 0.87 0.91 0.91Quercus velutina0 8 0 8 0 0 0.18 0.30 0.02 0.00Juglans nigra3 2 3 0 6 0 0.00 0.67 0.66 0.65

Iteration 1 1.00 0.00 0.86 0.60 0.62 0.99Site 2 0.65 0.00 0.88 0.05 0.78 1.00Score 3 0.60 0.01 0.87 0.00 0.78 1.0090.59 0.01 0.87 0.00 0.78 1.00

Reciprocal Averaging


Site A C E B D F Species SpeciesScoreQuercus velutina8 8 0 0 0 0 0.004Prunus serotina6 3 6 5 4 10.477Juglans nigra0 2 3 6 3 0 0.647Tilia americana0 0 2 6 7 6 0.845Acer saccharum0 0 0 4 8 9 0.909Site Score0.000 0.008 0.589 0.778 0.872 1.000

Reordered Sites and Species


Arches - Artifact or Feature?


The Arch Effect

  • What is it?

  • Why does it happen?

  • What should we do about it?


From Alexandria to Suez


CA - with arch effect (sites)


CA - with arch effect (species)


Long Gradients

A

B

C

D


Gradient End Compression


CA - with arch effect (species)


CA - with arch effect (sites)


Detrending by Segments


DCA - modified unimodal


Making Effective Use of Environmental Variables


Direct Gradient Analysis

  • Environmental gradients are constructed from the relationship between species environmental variables

  • Three methods:

    • Redundancy Analysis - linear model

    • Canonical (or Constrained) Correspondence Analysis - unimodal model

    • Detrended CCA - modified unimodal model


CCA - site/species joint plot


CCA - species/environment biplot


Removing the Effect of Nuisance Variables


Partial Analyses

  • Remove the effect of covariates

    • variables that we can measure but which are of no interest

    • e.g. block effects, start values, etc.

  • Carry out the gradient analysis on what is left of the variation after removing the effect of the covariates.


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