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




Models of species response
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





Alpha and beta diversity
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.





Indirect gradient analysis
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 gradient site species biplot
PCA gradient - site/species biplot

standard

biodynamic& hobby

nature


Reciprocal averaging

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


Reciprocal averaging1

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


Reciprocal averaging2

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


Reciprocal averaging3

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


Reciprocal averaging4

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


Reordered sites and species

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



The arch effect
The Arch Effect

  • What is it?

  • Why does it happen?

  • What should we do about it?












Direct gradient analysis
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





Partial analyses
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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