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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. Type of Data Matrix. species. attributes. desert macroph inverts. uses. species. sites. attributes. attributes. watervar rain. gulls. individuals. sites. Ordination Techniques.

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

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

  2. Type of Data Matrix species attributes desert macroph inverts uses species sites attributes attributes watervar rain gulls individuals sites

  3. Ordination Techniques

  4. 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

  5. A Theoretical Model

  6. Linear

  7. Unimodal

  8. 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.

  9. A Short Coenocline

  10. A Long Coenocline

  11. Inferring Gradients from Species (or Attribute) Data

  12. 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

  13. PCA - linear model

  14. PCA - linear model

  15. Terschelling Dune Data

  16. PCA gradient - site plot

  17. PCA gradient - site/species biplot standard biodynamic& hobby nature

  18. 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

  19. 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

  20. 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

  21. 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

  22. 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

  23. 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

  24. Arches - Artifact or Feature?

  25. The Arch Effect • What is it? • Why does it happen? • What should we do about it?

  26. From Alexandria to Suez

  27. CA - with arch effect (sites)

  28. CA - with arch effect (species)

  29. Long Gradients A B C D

  30. Gradient End Compression

  31. CA - with arch effect (species)

  32. CA - with arch effect (sites)

  33. Detrending by Segments

  34. DCA - modified unimodal

  35. Making Effective Use of Environmental Variables

  36. 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

  37. CCA - site/species joint plot

  38. CCA - species/environment biplot

  39. Removing the Effect of Nuisance Variables

  40. 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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