spca: Spatial principal component analysis

In adegenet: Exploratory Analysis of Genetic and Genomic Data

Spatial principal component analysis

Description

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").

Usage

spca(...)

## Default S3 method:
spca(x, ...)

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

## S3 method for class 'spca'
summary(object, ..., printres=TRUE)

## S3 method for class 'spca'
plot(x, axis = 1, useLag=FALSE, ...)

## S3 method for class 'spca'
screeplot(x, ..., main=NULL)

## S3 method for class 'spca'
colorplot(x, axes=1:ncol(x$li), useLag=FALSE, ...)

Arguments

x	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.
obj	a genind or genpop object.
xy	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).
cn	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).
matWeight	a square matrix of spatial weights, indicating the spatial proximities between entities. If provided, this argument prevails over cn (see details).
center	a logical indicating whether data should be centred to a mean of zero; used implicitely for genind or genpop objects.
scale	a logical indicating whether data should be scaled to unit variance (TRUE) or not (FALSE, default).
scannf	a logical stating whether eigenvalues should be chosen interactively (TRUE, default) or not (FALSE).
nfposi	an integer giving the number of positive eigenvalues retained ('global structures').
nfnega	an integer giving the number of negative eigenvalues retained ('local structures').
type	an integer giving the type of graph (see details in chooseCN help page). If provided, ask is set to FALSE.
ask	a logical stating whether graph should be chosen interactively (TRUE,default) or not (FALSE).
plot.nb	a logical stating whether the resulting graph should be plotted (TRUE, default) or not (FALSE).
edit.nb	a logical stating whether the resulting graph should be edited manually for corrections (TRUE) or not (FALSE, default).
truenames	a logical stating whether true names should be used for 'obj' (TRUE, default) instead of generic labels (FALSE)
d1	the minimum distance between any two neighbours. Used if type=5.
d2	the maximum distance between any two neighbours. Used if type=5.
k	the number of neighbours per point. Used if type=6.
a	the exponent of the inverse distance matrix. Used if type=7.
dmin	the minimum distance between any two distinct points. Used to avoid infinite spatial proximities (defined as the inversed spatial distances). Used if type=7.
object	a spca object.
printres	a logical stating whether results should be printed on the screen (TRUE, default) or not (FALSE).
axis	an integer between 1 and (nfposi+nfnega) indicating which axis should be plotted.
main	a title for the screeplot; if NULL, a default one is used.
...	further arguments passed to other methods.
axes	the index of the columns of X to be represented. Up to three axes can be chosen.
useLag	a logical stating whether the lagged components (x$ls) should be used instead of the components (x$li).

Details

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

Value

The class spca are given to lists with the following components:

eig	a numeric vector of eigenvalues.
nfposi	an integer giving the number of global structures retained.
nfnega	an integer giving the number of local structures retained.
c1	a data.frame of alleles loadings for each axis.
li	a data.frame of row (individuals or populations) coordinates onto the sPCA axes.
ls	a data.frame of lag vectors of the row coordinates; useful to clarify maps of global scores .
as	a data.frame giving the coordinates of the PCA axes onto the sPCA axes.
call	the matched call.
xy	a matrix of spatial coordinates.
lw	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.

Author(s)

Thibaut Jombart [e-mail]

References

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.

See Also

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.

Examples

## data(spcaIllus) illustrates the sPCA
## see ?spcaIllus
##
## Not run: 
example(spcaIllus)
example(rupica)

## End(Not run)

adegenet documentation built on Feb. 16, 2023, 6 p.m.