These functions implement the spatial principal component analysis
(sPCA). The function spca is a generic with methods for:
matrix: only numeric values are accepted
data.frame: same as for matrices
genind: any genind object is accepted
genpop: any genpop object is accepted
The core computation use multispati from the ade4 package.
Besides the set of spca functions, other functions include:
print.spca: prints the spca content
summary.spca: gives variance and autocorrelation
statistics
plot.spca: usefull graphics (connection network, 3 different
representations of map of scores, eigenvalues barplot and
decomposition)
screeplot.spca: decomposes spca eigenvalues into variance and
autocorrelation
colorplot.spca: represents principal components of sPCA in
space using the RGB system.
A tutorial on sPCA can be opened using:
adegenetTutorial(which="spca").
spca(...)# S3 method for default
spca(x, ...)
# S3 method for matrix
spca(x, xy = NULL, cn = NULL, matWeight = NULL,
center = TRUE, scale = FALSE, scannf = TRUE,
nfposi = 1, nfnega = 1,
type = NULL, ask = TRUE,
plot.nb = TRUE, edit.nb = FALSE,
truenames = TRUE,
d1 = NULL, d2 = NULL, k = NULL,
a = NULL, dmin = NULL, ...)
# S3 method for data.frame
spca(x, xy = NULL, cn = NULL, matWeight = NULL,
center = TRUE, scale = FALSE, scannf = TRUE,
nfposi = 1, nfnega = 1,
type = NULL, ask = TRUE,
plot.nb = TRUE, edit.nb = FALSE,
truenames = TRUE,
d1 = NULL, d2 = NULL, k = NULL,
a = NULL, dmin = NULL, ...)
# S3 method for genind
spca(obj, xy = NULL, cn = NULL, matWeight = NULL,
scale = FALSE, scannf = TRUE,
nfposi = 1, nfnega = 1,
type = NULL, ask = TRUE,
plot.nb = TRUE, edit.nb = FALSE,
truenames = TRUE,
d1 = NULL, d2 = NULL, k = NULL,
a = NULL, dmin = NULL, ...)
# S3 method for genpop
spca(obj, xy = NULL, cn = NULL, matWeight = NULL,
scale = FALSE, scannf = TRUE,
nfposi = 1, nfnega = 1,
type = NULL, ask = TRUE,
plot.nb = TRUE, edit.nb = FALSE,
truenames = TRUE,
d1 = NULL, d2 = NULL, k = NULL,
a = NULL, dmin = NULL, ...)
# S3 method for spca
print(x, ...)
# S3 method for spca
summary(object, ..., printres=TRUE)
# S3 method for spca
plot(x, axis = 1, useLag=FALSE, ...)
# S3 method for spca
screeplot(x, ..., main=NULL)
# S3 method for spca
colorplot(x, axes=1:ncol(x$li), useLag=FALSE, ...)
The class spca are given to lists with the following
components:
a numeric vector of eigenvalues.
an integer giving the number of global structures retained.
an integer giving the number of local structures retained.
a data.frame of alleles loadings for each axis.
a data.frame of row (individuals or populations) coordinates onto the sPCA axes.
a data.frame of lag vectors of the row coordinates; useful to clarify maps of global scores .
a data.frame giving the coordinates of the PCA axes onto the sPCA axes.
the matched call.
a matrix of spatial coordinates.
a list of spatial weights of class listw.
Other functions have different outputs:
- summary.spca returns a list with 3 components: Istat
giving the null, minimum and maximum Moran's I values; pca
gives variance and I statistics for the principal component analysis;
spca gives variance and I statistics for the sPCA.
- plot.spca returns the matched call.
- screeplot.spca returns the matched call.
a matrix or a data.frame of numeric values,
with individuals in rows and variables in columns; categorical
variables with a binary coding are acceptable too; for print
and plotting functions, a spca object.
a genind or genpop object.
a matrix or data.frame with two columns for x and y
coordinates. Seeked from obj$other$xy if it exists when xy is not
provided. Can be NULL if a nb object is provided in
cn.
Longitude/latitude coordinates should be converted
first by a given projection (see 'See Also' section).
a connection network of the class 'nb' (package spdep). Can be NULL if xy is provided. Can be easily obtained using the function chooseCN (see details).
a square matrix of spatial weights, indicating the
spatial proximities between entities. If provided, this argument
prevails over cn (see details).
a logical indicating whether data should be centred to a mean of zero; used implicitely for genind or genpop objects.
a logical indicating whether data should be scaled to unit variance (TRUE) or not (FALSE, default).
a logical stating whether eigenvalues should be chosen interactively (TRUE, default) or not (FALSE).
an integer giving the number of positive eigenvalues retained ('global structures').
an integer giving the number of negative eigenvalues retained ('local structures').
an integer giving the type of graph (see details in
chooseCN help page). If provided, ask is set to
FALSE.
a logical stating whether graph should be chosen interactively (TRUE,default) or not (FALSE).
a logical stating whether the resulting graph should be plotted (TRUE, default) or not (FALSE).
a logical stating whether the resulting graph should be edited manually for corrections (TRUE) or not (FALSE, default).
a logical stating whether true names should be used for 'obj' (TRUE, default) instead of generic labels (FALSE)
the minimum distance between any two neighbours. Used if
type=5.
the maximum distance between any two neighbours. Used if
type=5.
the number of neighbours per point. Used if type=6.
the exponent of the inverse distance matrix. Used if
type=7.
the minimum distance between any two distinct points. Used
to avoid infinite spatial proximities (defined as the inversed
spatial distances). Used if type=7.
a spca object.
a logical stating whether results should be printed on the screen (TRUE, default) or not (FALSE).
an integer between 1 and (nfposi+nfnega) indicating which axis should be plotted.
a title for the screeplot; if NULL, a default one is used.
further arguments passed to other methods.
the index of the columns of X to be represented. Up to three axes can be chosen.
a logical stating whether the lagged components
(x$ls) should be used instead of the components
(x$li).
Thibaut Jombart t.jombart@imperial.ac.uk
The spatial principal component analysis (sPCA) is designed to
investigate spatial patterns in the genetic variability. Given
multilocus genotypes (individual level) or allelic frequency
(population level) and spatial coordinates, it finds individuals (or
population) scores maximizing the product of variance and spatial
autocorrelation (Moran's I). Large positive and negative eigenvalues
correspond to global and local structures.
Spatial weights can be obtained in several ways, depending how the
arguments xy, cn, and matWeight are set.
When several acceptable ways are used at the same time, priority is as
follows:
matWeight > cn > xy
Jombart, T., Devillard, S., Dufour, A.-B. and Pontier, D. Revealing cryptic spatial patterns in genetic variability by a new multivariate method. Heredity, 101, 92--103.
Wartenberg, D. E. (1985) Multivariate spatial correlation: a method for exploratory geographical analysis. Geographical Analysis, 17, 263--283.
Moran, P.A.P. (1948) The interpretation of statistical maps. Journal of the Royal Statistical Society, B 10, 243--251.
Moran, P.A.P. (1950) Notes on continuous stochastic phenomena. Biometrika, 37, 17--23.
de Jong, P. and Sprenger, C. and van Veen, F. (1984) On extreme values of Moran's I and Geary's c. Geographical Analysis, 16, 17--24.
spcaIllus and rupica for datasets illustrating the sPCA
global.rtest and local.rtest
chooseCN, multispati,
multispati.randtest
convUL, from the package 'PBSmapping' to convert longitude/latitude to
UTM coordinates.
## data(spcaIllus) illustrates the sPCA
## see ?spcaIllus
##
if (FALSE) {
example(spcaIllus)
example(rupica)
}
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