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

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Presentation on theme: "Managing Dimensionality (but not acronyms) PCA, CA, RDA, CCA, MDS, NMDS, DCA, DCCA, pRDA, pCCA."— Presentation transcript:

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

2 Type of Data Matrix

3 Ordination Techniques Linear methodsWeighted averaging unconstrainedPrincipal Components Analysis (PCA) Correspondence Analysis (CA) constrainedRedundancy Analysis (RDA) Canonical Correspondence Analysis (CCA)

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

15 Terschelling Dune Data

16 PCA gradient - site plot

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

18 Reciprocal Averaging Site A B C D E F Species Prunus serotina Tilia americana Acer saccharum Quercus velutina Juglans nigra

19 Reciprocal Averaging Site A B C D E F Species Score Species Iteration 1 Prunus serotina Tilia americana Acer saccharum Quercus velutina Juglans nigra Iteration Site Score

20 Reciprocal Averaging Site A B C D E F Species Score Species Iteration 1 2 Prunus serotina Tilia americana Acer saccharum Quercus velutina Juglans nigra Iteration Site Score

21 Reciprocal Averaging Site A B C D E F Species Score Species Iteration Prunus serotina Tilia americana Acer saccharum Quercus velutina Juglans nigra Iteration Site Score

22 Reciprocal Averaging Site A B C D E F Species Score Species Iteration Prunus serotina Tilia americana Acer saccharum Quercus velutina Juglans nigra Iteration Site Score

23 Reordered Sites and Species Site A C E B D F Species Species Score Quercus velutina Prunus serotina Juglans nigra Tilia americana Acer saccharum Site Score

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 ABCD

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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