BiodiversityR (version 1.5)

CAPdiscrim: Canonical Analysis of Principal Coordinates based on Discriminant Analysis

Description

This function provides a method for CAP as described by the authors of the ordination method. The CAP method implemented in vegan through capscale conforms more to distance-based Redundancy Analysis (Legendre & Anderson, 1999) than to the original description for CAP (Anderson & Willis, 2003 ).

Usage

CAPdiscrim(formula,data,dist="bray",axes=4,m=0,permutations=0)

Arguments

formula

Formula with a community data frame (with sites as rows, species as columns and species abundance as cell values) or distance matrix on the left-hand side and a categorical variable on the right-hand side (only the first explanatory variable will be used)

data

Environmental data set.

dist

Method for calculating ecological distance with function vegdist: partial match to "manhattan", "euclidean", "canberra", "bray", "kulczynski", "jaccard", "gower", "morisita", "horn" or "mountford". Thi

axes

Number of PCoA axes (cmdscale) to provide in the result.

m

Number of PCoA axes to be investigated by discriminant analysis (lda). If m=0 then the number of axes that provides the best distinction between the groups is calculated (following the method of Anderson an

permutations

The number of permutations for significance testing.

Value

• The function returns an object with information on CAP based on discriminant analysis. The object contains following elements:
• PCoA
  the positions of the sites as fitted by PCoA
• m
  the number of axes analysed by discriminant analysis
• tot
  the total variance (sum of all eigenvalues of PCoA)
• varm
  the variance of the m axes that were investigated
• group
  the original group of the sites
• CV
  the predicted group for the sites by discriminant analysis
• percent
  the percentage of correct predictions
• x
  the positions of the sites provided by the discriminant analysis
• F
  the squares of the singulare values of the discriminant analysis
• manova
  the results for MANOVA with the same grouping variable
• signi
  the significance of the percentage of correct predictions
• manova
  a summary of the observed randomised prediction percentages
• The object can be plotted with ordiplot, and species scores can be added by add.spec.scores .

Details

This function provides a method of Constrained Analysis of Principal Coordinates (CAP) that conforms to the description of the method by the developers of the method, Anderson and Willis. The method investigates the results of a Principal Coordinates Analysis (function cmdscale) with linear discriminant analysis (lda). Anderson and Willis advocate to use the number of principal coordinate axes that result in the best prediction of group identities of the sites. For permutations > 0, the analysis is repeated by randomising the observations of the environmental data set. The significance is estimated by dividing the number of times the randomisation generated a larger percentage of correct predictions.

References

Legendre, P. & Anderson, M.J. (1999). Distance-based redundancy analysis: testing multispecies responses in multifactorial ecological experiments. Ecological Monographs 69: 1-24. Anderson, M.J. & Willis, T.J. (2003). Canonical analysis of principal coordinates: a useful method of constrained ordination for ecology. Ecology 84: 511-525. Kindt, R. & Coe, R. (2005) Tree diversity analysis: A manual and software for common statistical methods for ecological and biodiversity studies. http://www.worldagroforestry.org/resources/databases/tree-diversity-analysis

Examples

library(vegan)
library(MASS)
data(dune)
data(dune.env)
Ordination.model1 <- CAPdiscrim(dune~Management, data=dune.env,
    dist="bray",axes=2,m=0)
Ordination.model1
plot1 <- ordiplot(Ordination.model1)
ordisymbol(plot1,dune.env,"Management",legend=FALSE)
## CLICK IN THE GRAPH TO INDICATE THE POSITION FOR THE LEGEND
## IN CASE THAT THE OPTION WAS LEGEND=TRUE.