6D2EE919d01 - Multivariate analysis Prof dr Ann Vanreusel-...

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Unformatted text preview: Multivariate analysis Prof dr Ann Vanreusel- Multidimensional scaling- Simper analysis- BEST NOSIM- ANOSIM site1 site2 site 3 site 4 site 5 species a 1 2 species b 3 1 1 pecies c 1 2 3 4 5 Gradient in species composition Gradient in environment 2 species c 5 5 2 2 3 species d 3 4 6 species e 5 2 site1 site2 site 3 site 4 site 5 100 80 60 40 20 Similarity beach zonation beach zonation site1 site2 site 3 site 4 site 5 Stress: 0 Even when there is contious structure in the data matrix b DISCONTINUOUS OUTPUT b ‘CLUSTERS’ However still useful in ecology, mainly in combination with ordination Clustering or Classification Variation in communities b rather continuous than discontinuous b some disadvantages In order to recognize structure (communities) in large datamatrices. Non metric multidimensional scaling = ordination b points close together = sites similar in (species) composition b points far apart = sites dissimilar in (species) composition MDS b original (species) composition data are replaced by matrix of dissimilarity values between sites b this matrix is used to obtain ordination diagram b Specifies what similar means Measure needed that expresses how well or badly the distances in the ordination diagram correspond to the dissimilarity values = stress function MDS b to choose a configuration that minimizes the degree of stress Metric ordination (CA, PCA) b Stress function depends on the actual numerical values of the dissimilarities Chi square b CA Euclidean distance b PCA Non metric ordination (MDS) b Stress function depends only on the rank order of the dissimilarities Characteristics better flexibility complex algorithm rationale simple few if any assumptions Based on ranks of similarities Raw data similarities ranks ordination The higher similarity has the lowest rank site1 site2 site 3 site 4 site 5 species a 1 2 species b 3 1 1 species c 5 5 2 2 3 species d 3 4 6 species e 5 2 Site 1 site 2 site 3 site 4 Site 2 80 Site 3 44,44 44,44 Site 4 19,04 19,04 63,15 Site 5 10,52 10,52 58,82 70 Bray Curtis similarity matrix Raw counts ite 1 ite 2 ite 3 ite 4 Resemblance: S17 Bray Curtis similarity site1 site2 site 3 site 4 site 5 2D Stress: 0 Site 1 site 2 site 3 site 4 Site 2 1 Site 3 5 5 Site 4 6 6 3 Site 5 7 7 4 2 Ordination ranks 1 2 5 3 and 4 6 and 7 Ordination diagram What are stages in the construction of an MDS diagram ? Iterative procedure (repeated) b Successively refining of the positions of the points until they satisfy as closely as possible the dissimilarity relationships between samples pecify nr of dimensions (usually 2…) I. Specify nr of dimensions (usually 2…) II. Starting configuration of samples (whatever..) III. Regress interpoint distances from this plot on the corresponding dissimilarities Shepard diagram b non-parametric regression = non metric MDS (regression b metric MDS) = best fitting line which moulds itself to the shape of scatterplot = constrained to increase (series of steps) IV. Goodness of fit of the regression by calculating the stress value...
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This note was uploaded on 05/28/2010 for the course WE BIBI010000 taught by Professor Marnikvuylsteke during the Spring '10 term at Ghent University.

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6D2EE919d01 - Multivariate analysis Prof dr Ann Vanreusel-...

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