4D2EE8CFd01

# 4D2EE8CFd01 - Multivariate analysis Prof dr Ann Vanreusel...

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Multivariate analysis Prof dr Ann Vanreusel - Principal component analysis (PCA)

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Ordination = collective term for multivariate techniques that arrange sites along axes on the basis of data on species composition or other variables ( e.g .environmental) The results of an ordination in two dimensions (two axes) is a diagram in which sites are represented by points in a two dimensional space. The aim of ordination is to arrange points such • that points that are close together represent sites that are similar in species composition • and points that are far apart correspond to sites that are dissimilar in species composition The diagram is a graphical summary of data
Ordination h Definitions Indirect gradient analysis b Sites are arranged along axes based on the environmental data or species species composition composition Direct gradient analysis b Integrated analysis of species AND environmental data : sites are aranged based on combination of both b Only reliable when correct (relevant) environmental variables are measured and used in the analysis b To estimate impact of different environmental variables b Always has to be combined with an indirect gradient analysis

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Ordination Two types of respons curves considered Species abundanc h Types of ordinations (only in case of biological assemblage data) Unimodal Linear Abundance of a species increases along the (environmental) gradient until an optimum is reached, followed by a decrease in abundance with increasing values for the (environmental) gradient Anbundance of the species increases linear along (environmental) gradient Environmental variable ce Different techniques assuming underlying respons model is Linear or Unimodal (euclidian distance) ( chi square distance)
Ordination Different techniques assuming underlying respons model is Linear or Unimodal h Types of ordinations Linear Unimodal Indirect PCA CA DCA Direct RDA CCA DCCA

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Ordination h When to use what ? To estimate lenght of gradient SD : standard deviation units
Samples represented by points in a multi-dimensional space with as much dimensions as species e.g. 3 species b 3 axes b species abundances are co-ordinates for samples mples with comparable species composition ( 29 - = 2 jk ik ij x x ED Euclidean distance = Pythagoras’ theorem generalized to n dimensions. X ik = abundance of species k in sample i X jk = abundance of species k in sample j b samples with comparable species composition close together in 3 dimensional space . Dissimilarity index b The larger the distance The smaller the similarity

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In case we have 9 samples and 2 species 9 samples represented as points in two dimensional space (cfr Euclidean distance)
Suppose we need a 1 dimensional ordination which we represent by only 1 species In this way we neglect information on species 2 b Inaccurate representation of sample relationships Better 1 dimensional representation when using the perpendicular projection of

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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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4D2EE8CFd01 - Multivariate analysis Prof dr Ann Vanreusel...

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