Multi-Scale Pattern Analysis

The multi-scale pattern analysis (MSPA, Jombart et al 2009) investigates the main scales of spatial variation in a multivariate dataset. This implementation allows one to perform a MSPA using any multivariate analysis (stored as a dudi object), and a list of spatial weights (class listw) or an object of class orthobasisSp.

mspa(
  dudi,
  lwORorthobasisSp,
  nblocks,
  scannf = TRUE,
  nf = 2,
  centring = c("param", "sim"),
  nperm = 999
)

# S3 method for class 'mspa'
scatter(
  x,
  xax = 1,
  yax = 2,
  posieig = "topleft",
  bary = TRUE,
  plot = TRUE,
  storeData = TRUE,
  pos = -1,
  ...
)

# S3 method for class 'mspa'
print(x, ...)

Arguments

dudi: a duality diagram (i.e. a reduced space ordination) obtained by a dudi function (for instance dudi.pca).
lwORorthobasisSp: either a list of weights (class listw) that san be obtained easily using the function chooseCN or an object of class orthobasisSp
nblocks: an integer indicating the number of blocks to divide MEMs.
scannf: logical, indicating whether the screeplot should be displayed to choose the number or retained factors.
nf: the number of retained factors
centring: a character string indicating if parametric ("param") or non-parametric ("sim") centring should be used
nperm: an integer giving the number of permutations used to compute the theoretical coefficients of determination (999 by default); used if centring="sim".
x: a mspa object.
xax: an integer indicating the x axis to be displayed.
yax: an integer indicating the y axis to be displayed.
posieig: a character indicating the position of the screeplot (any of the four combination between "top", "bottom", "left" and "right").
bary: a logical indicating whether the barycenter of the variables should be displayed.
plot: a logical indicating if the graphics is displayed
storeData: a logical indicating if the data should be stored in the returned object. If FALSE, only the names of the data arguments are stored
pos: an integer indicating the position of the environment where the data are stored, relative to the environment where the function is called. Useful only if storeData is FALSE
...: additional graphical parameters (see adegpar and trellis.par.get)

Value

An object having the classes mspa and dudi: mspa objects are dudi objects with the following extra slots:
- ls: principal components of the MSPA. These are the coordinates of variables onto principal axes, to be used for plotting. Correspond to matrix B in Appendix A of Jombart et al (2009).
- R2: matrix of R2 between variables and MEMs. Corresponds to S in Jombart et al (2009).
- meanPoint: coordinates of the 'mean variable' onto principal axes. The 'mean variable' is an hypothetic variable whose scale profile is the average of those of all variables of the analysed dataset.
- varweights: the weights of variables. Corresponds to d in Jombart et al. (2009).

Details

The scatter method is used for plotting the results. Compared to the original version of the method, this new implementation allows to specify a number of blocks (nblocks). In this case, the multiscale decomposition is performed by dividing MEMs into several blocks and summing R2 values. This could facilitate the interpretation of results.

References

Jombart T, Dray S, and Dufour, A-B. (2009) Finding essential scales of spatial variation in ecological data: a multivariate approach. Ecography 32: 161-168.

Author

Thibaut Jombart t.jombart@imperial.ac.uk

Examples



####################################
### using oribatib mites dataset ###
####################################

if(require("ade4", quietly = TRUE)){
## load data
data(oribatid)

## get the list of spatial weights
cn <- chooseCN(oribatid$xy, res = "listw", ask = FALSE, type = 1)

## Hellinger transformation
hellTrans <- function(X){
  if (!( is.matrix(X) | is.data.frame(X) )) stop("Object is not a matrix.")  
  if (any(is.na(X))) stop("na entries in table.")
  
  sumRow <- apply(X,1,sum)
  Y <- X/sumRow
  Y <- sqrt(Y)
  
  return(Y)
}


## ENVIRONMENTAL VARIABLES ##
## Hill and Smith analysis for environmental variables
## (for a mixture of quantitative / qualitative variables)
hsEnv <- dudi.hillsmith(oribatid$envir,scannf=FALSE)

## detrending of the analysis (residuals of regression onto xy coordinates)
hsEnv.detr <- pcaivortho(hsEnv,oribatid$xy,scannf=FALSE)

## MSPA of the detrended analysis
mspaEnv <- mspa(hsEnv.detr,cn,scannf=FALSE,nf=2)
scatter(mspaEnv)



## SPECIES DATA ##
## PCA of species abundances, after Hellinger transformation
pcaFau <- dudi.pca(hellTrans(oribatid$fau),scale=FALSE,scannf=FALSE)

## detrending of this PCA
pcaFau.detr <- pcaivortho(pcaFau,oribatid$xy,scannf=FALSE)

# MSPA of the detrended analysis
mspaFau <- mspa(pcaFau.detr,cn,scannf=FALSE,nf=2)
scatter(mspaFau)



## CANONICAL MSPA ##
## RDA species ~ envir
## (species abundances predicted by environment)
## note: RDA = 'PCAIV' (PCA with Instrumental Variables)
rda1 <- pcaiv(dudi=pcaFau.detr, df=oribatid$envir,scannf=FALSE,nf=2)

## canonical MSPA (species predicted by environment)
mspaCan1 <- mspa(dudi=rda1, lw=cn, scannf=FALSE, nf=2)
scatter(mspaCan1)

## same analysis, using a non-parametric centring
mspaCan1NP <- mspa(dudi=rda1, lw=cn, scannf=FALSE, nf=2,cent="sim",nper=999)
scatter(mspaCan1NP) # basically no change



## PARTIAL CANONICAL MSPA ##
## partial RDA species ~ envir
## (species abundances not predicted by environment)
rda2 <- pcaivortho(dudi=pcaFau.detr,df=oribatid$envir,scannf=FALSE,nf=2)

## partial canonical MSPA
mspaCan2 <- mspa(dudi=rda2, lw=cn, scannf=FALSE, nf=2)
scatter(mspaCan2) # nothing left
}
#> Error in s.arrow(dfxy = mspaEnv$c1, xax = 1, yax = 2, plot = FALSE, storeData = TRUE,     pos = -3, plabels = list(cex = 1)): non convenient selection for dfxy (can not be converted to dataframe)