| Title: | Spatial Interpolation of Genetic Data |
|---|---|
| Description: | The spatial interpolation of genetic distances between samples is based on a modified kriging method that accepts a genetic distance matrix and generates a map of probability of lineage presence. This package also offers tools to generate a map of potential contact zones between groups with user-defined thresholds in the tree to account for old and recent divergence. Additionally, it has functions for IDW interpolation using genetic data and midpoints. |
| Authors: | Pedro Tarroso, Guillermo Velo-Anton, Silvia Carvalho |
| Maintainer: | Pedro Tarroso <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 2.0.2 |
| Built: | 2024-11-01 11:32:37 UTC |
| Source: | https://github.com/cran/phylin |
This package provides functions for the spatial interpolation of genetic distances between samples. The interpolation is based on a modified kriging method that accepts a genetic distance matrix and generates a map of probability of lineage presence. This package also offers tools to generate a map of potential contact zones between groups with user-defined thresholds in the tree to account for old and recent divergence. Additionally, it has functions for IDW interpolation using genetic data and midpoints.
| Package: | phylin |
| Type: | Package |
| Version: | 2.0 |
| Date: | 2016-04-27 |
| License: | GPL-2 |
The kriging algorithm uses a model fitted to the semi-variogram to weight the values of the samples. Here the variogram was modified to fit a model with pairwise comparison between genetic and real distances, describing the spatial dependence in the genetic distance between samples. A map for the lineage can be generated using only a vector that define if each point belong to the a lineage or not.
Since version 2.0, the kriging interpolation can be performed taking into consideration a cost distance instead of simple geographical distances between points. This can help in cases where a landscape resistance explains better the genetic distances between samples than the geographic distances alone.
The IDW can be used to interpolate the genetic distance of each sample against the others, or to interpolate genetic diverge at midpoints between samples. The interpolated value at certain location is obtained by weighting with the distances to the avaialable samples. Similarly to kriging, these distance can be based on a cost distance calculation.
Pedro Tarroso, Guillermo Velo-Anton, Silvia Carvalho
Maintainer: Pedro Tarroso <[email protected]>
Tarroso, P., Velo-Anton, G., & Carvalho, S.B. (2015). PHYLIN: an R package for phylogeographic interpolation. Molecular Ecology Resources, 15(2), 349-357.
Tarroso, P., Carvalho, S.B. & Velo-Anton, G. (2019). PHYLIN 2.0: Extending the phylogeographic interpolation method to include uncertainty and user-defined distance metrics. Molecular Ecology Resources, in press.
## See examples for the included functions.## See examples for the included functions.
This is a matrix of genetic distances between the Vipera latastei samples. The values are cophenetic distances generated from the phylogenetic tree.
data(d.gen)data(d.gen)
'd.gen' is a matrix with 58 rows and columns. Columns and rows are organized with the same order found in the 'vipers' dataset.
Velo-Anton G., Godinho R., Harris D. J. et al. (2012) Deep evolutionary lineages in a Western Mediterranean snake (Vipera latastei/monticola group) and high genetic structuring in Southern Iberian populations. Molecular phylogenetics and evolution, 65, 965–973.
data(d.gen) hc <- hclust(as.dist(d.gen)) plot(hc, hang = -1, main="Vipers genetic distance tree", xlab="Samples", cex=0.7)data(d.gen) hc <- hclust(as.dist(d.gen)) plot(hc, hang = -1, main="Vipers genetic distance tree", xlab="Samples", cex=0.7)
This function extacts pairwise values from a matrix in a specified order in a user provided table.
extract.val(m, samples)extract.val(m, samples)
m |
Matrix with values to extract. |
samples |
Data frame with columns indicating pairs of samples to extract values. Names must correspond to column and row names in the matrix. |
This function extracts the values from a matrix in the same pairs of
populations/samples given in a table. It is useful for merging data
from a distance matrix of samples and the midpoints between samples (in
conjuction with midpoints function).
Returns a vector containing the values from the matrix m in the order given in samples.
Pedro Tarroso <[email protected]>
data(vipers) data(d.gen) # calculate midpoints mp <- midpoints(vipers[,1:2]) # extract values from d.gen. Columns 1 and 2 of mp have the information # about source and target samples. pair.data <- extract.val(d.gen, mp[,1:2]) # it is easier to view in a plot: plot(vipers[,1:2], pch=vipers[,3], main="Midpoints between samples", xlab="Longitude", ylab="Latitude") #trace all connecting lines between samples sps <- rownames(vipers) for (i in 1:nrow(mp)) { sp <- mp[i, 1:2] #source an target samples mask <- c(which(sps == sp[,1]), which(sps == sp[,2])) lines(vipers$x[mask], vipers$y[mask], lty=2, col='lightgrey') } #midpoints with genetic distance acentuated points(mp[,3:4], col='red', pch=16, cex=pair.data*15+0.5)data(vipers) data(d.gen) # calculate midpoints mp <- midpoints(vipers[,1:2]) # extract values from d.gen. Columns 1 and 2 of mp have the information # about source and target samples. pair.data <- extract.val(d.gen, mp[,1:2]) # it is easier to view in a plot: plot(vipers[,1:2], pch=vipers[,3], main="Midpoints between samples", xlab="Longitude", ylab="Latitude") #trace all connecting lines between samples sps <- rownames(vipers) for (i in 1:nrow(mp)) { sp <- mp[i, 1:2] #source an target samples mask <- c(which(sps == sp[,1]), which(sps == sp[,2])) lines(vipers$x[mask], vipers$y[mask], lty=2, col='lightgrey') } #midpoints with genetic distance acentuated points(mp[,3:4], col='red', pch=16, cex=pair.data*15+0.5)
Computes the semi-variance with the real and genetic distances, and with user defined lag parameters.
gen.variogram(x, y, lag = quantile(as.matrix(x), 0.05), tol=lag/2, lmax = NA, bootstraps = 999, verbose = FALSE)gen.variogram(x, y, lag = quantile(as.matrix(x), 0.05), tol=lag/2, lmax = NA, bootstraps = 999, verbose = FALSE)
x |
Real distances matrix. |
y |
Single genetic distances matrix or list of genetic distances matrices. |
lag |
Real distance corresponding to the desired 'lag' interval. This is used to calculate lag centers from 0 to 'lmax'. |
tol |
Tolerance for the lag center to search for pairs ('lag'-'tol', 'lag'+'tol'). |
lmax |
Maximum distance for lag centers. Pairs with distances higher than 'lmax' are not included in the calcualtion of the semi-variance. If 'lmax' is NA (default) then is used the maximum distance between samples. |
bootstraps |
This is the number of bootstraps used to calculate 95% confidence interval for the median, when multiple genetic distances are given. With a single genetic distance, this parameter is ignored. |
verbose |
Boolean for verbosity. When TRUE and with multiple genetic distance matrices, a log of error evolution is printed. |
This function produces a table with real lag centers and
semi-variance. The formula to calculate semi-variance,
, is:
where is the number of pairs with the lag distance
between them, and is the value of the sample at the
the location . The difference between sample
and sample is assumed to
correspond to their genetic distance.
Multiple genetic distance matrices can be used. In this case, a variogram is computed for each genetic distance and the results summarised by the median and a 95% confidence interval calculated with bootstraps.
Returns a 'gv' object with the input data, lag centers and semi-variance.
It is assumed that the order of samples in x corresponds to the same in y.
Pedro Tarroso <[email protected]>
Fortin, M. -J. and Dale, M. (2006) Spatial Analysis: A guide for Ecologists. Cambridge: Cambridge University Press.
Isaaks, E. H. and Srivastava, R. M. (1989) An Introduction to applied geostatistics. New York: Oxford University Press.
Legendre, P. and Legendre, L. (1998) Numerical ecology. 2nd english edition. Amesterdam: Elsevier
data(vipers) data(d.gen) # create a distance matrix between samples r.dist <- dist(vipers[,1:2]) # variogram table with semi-variance and lag centers gv <- gen.variogram(r.dist, d.gen) # plot variogram plot(gv) # fit a new variogram with different lag gv2 <- gen.variogram(r.dist, d.gen, lag=0.2) plot(gv2)data(vipers) data(d.gen) # create a distance matrix between samples r.dist <- dist(vipers[,1:2]) # variogram table with semi-variance and lag centers gv <- gen.variogram(r.dist, d.gen) # plot variogram plot(gv) # fit a new variogram with different lag gv2 <- gen.variogram(r.dist, d.gen, lag=0.2) plot(gv2)
Calculates a geographical euclidean distances matrix based on a list of coordinates for samples and for interpolation locations.
geo.dist(from, to)geo.dist(from, to)
from |
Data frame with coordinates for source locations. Should have two columns (longitude and latitude). |
to |
Data frame with coordinates for destination locations to where distances are calculated. Should have two columns (longitude and latitude). |
Return the matrix of euclidean distances between source locations ('from') to destination ('to') coordinates. The resulting matrix has source locations in rows and destination in columns and respective names are given based on the row names of the 'from' and 'to' data frames.
Pedro Tarroso <[email protected]>
data(vipers) # create a grid of the sampled area grid <- expand.grid(x=seq(-10,10,0.5), y=seq(30, 50, 0.5)) rd <- geo.dist(vipers[,1:2], grid)data(vipers) # create a grid of the sampled area grid <- expand.grid(x=seq(-10,10,0.5), y=seq(30, 50, 0.5)) rd <- geo.dist(vipers[,1:2], grid)
This is a list of coordinates representing the interpolation area in the Iberian Peninsula with a resolution of 0.09 degrees (~10km).
data(grid)data(grid)
The data format is a table with two columns (longitude, and latitude) and 7955 rows (pixels).
data(grid) plot(grid, cex=0.5, asp=1, main="Grid of pixels for interpolation", xlab="Longitude", ylab="Latitude")data(grid) plot(grid, cex=0.5, asp=1, main="Grid of pixels for interpolation", xlab="Longitude", ylab="Latitude")
Plots the interpolated grid.
grid.image(intpl, grid, breaks=10, ic=1, colFUN=heat.colors, main=colnames(intpl)[ic], xlab=colnames(grid)[1], ylab=colnames(grid)[2], sclab=NA, ...)grid.image(intpl, grid, breaks=10, ic=1, colFUN=heat.colors, main=colnames(intpl)[ic], xlab=colnames(grid)[1], ylab=colnames(grid)[2], sclab=NA, ...)
intpl |
A matrix or vector with interpolation results. |
grid |
A table containing longitude and latitude of interpolated locations. |
breaks |
Number of breaks in the scale. |
ic |
Column index or name from 'intpl' table to show. Defaults to the first column. Can be used to plot standard deviation or any other column. This value is ignored of 'intpl' is a vector. |
colFUN |
Function to process colors. Can be any of R base color functions (e.g.
|
main |
Main title. |
xlab |
X axis label. Defaults to name of the first 'grid' column. |
ylab |
Y axis label. Defaults to name of the secont 'grid' column. |
sclab |
Scale label to plot under the scale bar. |
... |
Futher arguments to be passed to par. Most used is 'cex' to control the font size. |
This function may be used to produce a simple plot of the interpolated grid. It has some customizable features and it plots a scale bar of the Z values shown.
Does not work with multiple plots (e.g. with 'layout').
Pedro Tarroso <[email protected]>
data(vipers) data(d.gen) # create a grid of the sampled area for inteprolation grid <- expand.grid(x=seq(-9.5,3,0.25), y=seq(36, 43.75, 0.25)) # create a distance matrix between samples r.dist <- dist(vipers[,1:2]) # fit a model with defaults (shperical model) and estimation of range gv <- gen.variogram(r.dist, d.gen, 0.25) gv <- gv.model(gv) # interpolation of the distances to first sample with ordinary kriging int.krig <- krig(d.gen[,1], vipers[,1:2], grid, gv) #plot the interpolation results grid.image(int.krig, grid, main='Krigging Interpolation', xlab='Longitude',ylab = 'Latitude', sclab=paste('Genetic distance to sample', colnames(d.gen)[1])) # User can add extra elements to the main plot. points(vipers[,1:2], cex=d.gen[,1]*15+0.2)data(vipers) data(d.gen) # create a grid of the sampled area for inteprolation grid <- expand.grid(x=seq(-9.5,3,0.25), y=seq(36, 43.75, 0.25)) # create a distance matrix between samples r.dist <- dist(vipers[,1:2]) # fit a model with defaults (shperical model) and estimation of range gv <- gen.variogram(r.dist, d.gen, 0.25) gv <- gv.model(gv) # interpolation of the distances to first sample with ordinary kriging int.krig <- krig(d.gen[,1], vipers[,1:2], grid, gv) #plot the interpolation results grid.image(int.krig, grid, main='Krigging Interpolation', xlab='Longitude',ylab = 'Latitude', sclab=paste('Genetic distance to sample', colnames(d.gen)[1])) # User can add extra elements to the main plot. points(vipers[,1:2], cex=d.gen[,1]*15+0.2)
Fits a model to a semi-variogram contructed with
gen.variogram. Parameters for each model are estimated by
nonlinear least squares.
gv.model(gv, model='spherical', sill = NA, range=NA, nugget = 0, ctrl=nls.control())gv.model(gv, model='spherical', sill = NA, range=NA, nugget = 0, ctrl=nls.control())
gv |
'gv' object from the |
model |
Model to fit the data. Available models are spherical (default), gaussian, exponential or linear. See details. |
sill |
The heigth (semi-variance) of the model when it stabilizes. Defaults to NA. |
range |
The length (real distance) where stabilization occurs. Defaults to NA. |
nugget |
Intercept in the y-axis. Defaults to 0. |
ctrl |
Nls control object for the fitting procedure. (check ?nls.control for more details). |
This function fits a model to the data, either by estimating the model parameters using nonlinear least squares or by user provided values. Notice that parameters with NA will be estimated by the nls function and parameters with values given are not estimated (by default, the nugget is not estimated and set to zero). The variogram model can be plotted using 'plot' function or used to predict to a new set of values using 'predict'. It is used to define weights for the krigging interpolation.
The parameters of the semi-variogram model () are the
distance (), range (), sill (;
where is the partial sill), and nugget
().
The models available are:
gaussian:
exponential:
spherical:
pentaspherical:
cubic:
linear:
Returns a 'gv' object with the model, input data, and parameter values.
Pedro Tarroso <[email protected]>
Fortin, M. -J. and Dale, M. (2006) Spatial Analysis: A guide for Ecologists. Cambridge: Cambridge University Press.
Isaaks, E. H. and Srivastava, R. M. (1989) An Introduction to applied geostatistics. New York: Oxford University Press.
Legendre, P. and Legendre, L. (1998) Numerical ecology. 2nd english edition. Amesterdam: Elsevier
data(vipers) data(d.gen) # create a distance matrix between samples r.dist <- dist(vipers[,1:2]) # fit a variogram with defaults (shperical model) and estimation of range gv <- gen.variogram(r.dist, d.gen) gv <- gv.model(gv) # plot variogram plot(gv) # fit a new variogram with linear with sill model and range 8 gv2 <- gv.model(gv, model='linear', range=8) plot(gv2)data(vipers) data(d.gen) # create a distance matrix between samples r.dist <- dist(vipers[,1:2]) # fit a variogram with defaults (shperical model) and estimation of range gv <- gen.variogram(r.dist, d.gen) gv <- gv.model(gv) # plot variogram plot(gv) # fit a new variogram with linear with sill model and range 8 gv2 <- gv.model(gv, model='linear', range=8) plot(gv2)
This function interpolates a list of samples with location and a value to a table of coordinates, that generally represent a spatial grid. The interpolation is based on inverse distance weighting algoritm with three different methods available for weight calculation.
idw(values, coords, grid, method = "Shepard", p = 2, R = 2, N = 15, distFUN = geo.dist, ...)idw(values, coords, grid, method = "Shepard", p = 2, R = 2, N = 15, distFUN = geo.dist, ...)
values |
A table of points to be interpolated. Table must contain x and y locations, and a column of values to be interpolated. |
coords |
A table wit x and y coordinates of the samples. |
grid |
Coordinates of locations to interpolate. It is assumed to be in the same order as 'values' table. |
method |
Method to calculate weights for idw. Should be "Shepard" (default), "Modified", "Neighbours", or distinctive abreviations of each. See details section for additional help on each method. |
p |
The power to use in weight calculation. |
R |
Radius to use with Modified Shepard method. |
N |
Maximum number of neighbours to use with Shepard with neighbours. |
distFUN |
Distance function used to calculate distances between locations. The default is 'geo.dist' which calculates simple euclidean distances between the locations. This function must have a 'from' and a 'to' arguments to specify, respectively, the source and destination localities. |
... |
Other arguments to be passed to distFUN. |
The IDW interpolation algorithm is commonly used to interpolate genetic data over a spatial grid. This function provides a simple interface to interpolate such data with three methods:
Shepard:
weights are the inverse of the distance between the interpolation
location and the sample points , raised to the
power
Modified Shepard:
distances are weighted with a search radius to calculate the
interpolation weights
Shepard with neighbours:
A maximum ammount of neighbours is allowed to the weight
calculation following Shepard method.
It return a vector for each row of the 'coords' table with the respective interpolated value.
Pedro Tarroso <[email protected]>
Fortin, M. -J. and Dale, M. (2006) Spatial Analysis: A guide for Ecologists. Cambridge: Cambridge University Press.
Isaaks, E. H. and Srivastava, R. M. (1989) An Introduction to applied geostatistics. New York: Oxford University Press.
Legendre, P. and Legendre, L. (1998) Numerical ecology. 2nd english edition. Amesterdam: Elsevier
Vandergast, A. G.,Hathaway, S. A., Fisher, R. N., Boys, J., Bohonak, A. J., (2008) Are hotspots evolutionary potential adequately protected in southern California? Biological Conservation, 141, 1648-1664.
data(vipers) data(d.gen) data(grid) # interpolate and plot the genetic distances for sample s2 in the d.gen int <- idw(d.gen[,2], vipers[,1:2], grid) grid.image(int, grid, main='IDW interpolation', xlab='Longitude', ylab='Latitude', sclab="Genetic distance to sample s2") points(vipers[,1:2], cex=d.gen[,2]*15+0.2) # change idw power (i.e. points will have a larger influence in the # surroundings) int <- idw(d.gen[,2], vipers[,1:2], grid, p=5) result <- data.frame(grid, int) grid.image(int, grid, main='IDW interpolation', xlab='Longitude', ylab='Latitude', sclab="Genetic distance to sample s2") points(vipers[,1:2], cex=d.gen[,2]*15+0.2) # change idw method to "Modified Shepard" and define a maximum # neighbour distance int <- idw(d.gen[,2], vipers[,1:2], grid, 'Modified', R=10) grid.image(int, grid, main='IDW interpolation', xlab='Longitude', ylab='Latitude', sclab="Genetic distance to sample s2") points(vipers[,1:2], cex=d.gen[,2]*15+0.2) #-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-# # Example following methods in Vandergast et al. 2008 # # Fit a linear model and recover the residuals # # ATENTION: # # 1- Vandergast et al. (2008) suggests a RMA instead of a # # ordinary linear regression as in this example. Try package # # 'lmodel2' or or other similar for RMA linear regression. # # 2- This example tests if the package 'geometry' is installed # # to compute midpoints. If TRUE, a Delaunay triangulation is # # used, similarly to Vandergast et al. (2008). Otherwise, # # midpoints are computed for the combination of all pairs of # # samples. # # # # the d.gen and d.real matrices in this example have the same # # column and row order! # #-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-# if (is.element('geometry', installed.packages()[,1])) all=FALSE else all=TRUE mp <- midpoints(vipers[,1:2], all=all) d.real <- as.matrix(dist(vipers[,1:2])) fit <- lm(as.vector(d.gen) ~ as.vector(d.real)) resid <- matrix(fit$residuals, nrow(vipers), nrow(vipers)) dimnames(resid) <- dimnames(d.gen) mp$z <- extract.val(resid, mp[,1:2]) int <- idw(mp[,5], mp[,3:4], grid) grid.image(int, grid, main='IDW interpolation', xlab='Longitude', ylab='Latitude', sclab="Residuals of genetic vs. real distances") # plot samples connecting lines for (i in 1:nrow(mp)) { pair <- as.character(unlist(mp[i,1:2])) x <- c(vipers[pair[1],1], vipers[pair[2],1]) y <- c(vipers[pair[1],2], vipers[pair[2],2]) lines(x, y, lty=2) } points(vipers[,1:2], pch=16) # plot samples points in black points(mp[,3:4], pch=16, col='gray') # plot midpoints in graydata(vipers) data(d.gen) data(grid) # interpolate and plot the genetic distances for sample s2 in the d.gen int <- idw(d.gen[,2], vipers[,1:2], grid) grid.image(int, grid, main='IDW interpolation', xlab='Longitude', ylab='Latitude', sclab="Genetic distance to sample s2") points(vipers[,1:2], cex=d.gen[,2]*15+0.2) # change idw power (i.e. points will have a larger influence in the # surroundings) int <- idw(d.gen[,2], vipers[,1:2], grid, p=5) result <- data.frame(grid, int) grid.image(int, grid, main='IDW interpolation', xlab='Longitude', ylab='Latitude', sclab="Genetic distance to sample s2") points(vipers[,1:2], cex=d.gen[,2]*15+0.2) # change idw method to "Modified Shepard" and define a maximum # neighbour distance int <- idw(d.gen[,2], vipers[,1:2], grid, 'Modified', R=10) grid.image(int, grid, main='IDW interpolation', xlab='Longitude', ylab='Latitude', sclab="Genetic distance to sample s2") points(vipers[,1:2], cex=d.gen[,2]*15+0.2) #-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-# # Example following methods in Vandergast et al. 2008 # # Fit a linear model and recover the residuals # # ATENTION: # # 1- Vandergast et al. (2008) suggests a RMA instead of a # # ordinary linear regression as in this example. Try package # # 'lmodel2' or or other similar for RMA linear regression. # # 2- This example tests if the package 'geometry' is installed # # to compute midpoints. If TRUE, a Delaunay triangulation is # # used, similarly to Vandergast et al. (2008). Otherwise, # # midpoints are computed for the combination of all pairs of # # samples. # # # # the d.gen and d.real matrices in this example have the same # # column and row order! # #-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-# if (is.element('geometry', installed.packages()[,1])) all=FALSE else all=TRUE mp <- midpoints(vipers[,1:2], all=all) d.real <- as.matrix(dist(vipers[,1:2])) fit <- lm(as.vector(d.gen) ~ as.vector(d.real)) resid <- matrix(fit$residuals, nrow(vipers), nrow(vipers)) dimnames(resid) <- dimnames(d.gen) mp$z <- extract.val(resid, mp[,1:2]) int <- idw(mp[,5], mp[,3:4], grid) grid.image(int, grid, main='IDW interpolation', xlab='Longitude', ylab='Latitude', sclab="Residuals of genetic vs. real distances") # plot samples connecting lines for (i in 1:nrow(mp)) { pair <- as.character(unlist(mp[i,1:2])) x <- c(vipers[pair[1],1], vipers[pair[2],1]) y <- c(vipers[pair[1],2], vipers[pair[2],2]) lines(x, y, lty=2) } points(vipers[,1:2], pch=16) # plot samples points in black points(mp[,3:4], pch=16, col='gray') # plot midpoints in gray
Interpolations of a matrix containing genetic distances using the Inverse Distance Weighting (IDW) algorithm. It generates a matrix of interpolated values for each grid cell and for each sample.
intgen.idw(d.real, d.gen, method = "Shepard", p = 2, R = 2, N = 15)intgen.idw(d.real, d.gen, method = "Shepard", p = 2, R = 2, N = 15)
d.real |
distance matrix between sampled locals (columns) and locals where interpolation is to be executed (rows). Names should correspond to genetic distances matrix. |
d.gen |
genetic distances matrix. Names should correspond to real distances matrix, but not necessarily in the same order. |
method |
Method to calculate weights for idw. Should be "Shepard" (default), "Modified", "Neighbours", or distinctive abreviations of each. See details section for additional help on each method. |
p |
The power to use in weight calculation. |
R |
Radius to use with Modified Shepard method. |
N |
Maximum number of neighbours to use with Shepard with neighbours. |
The IDW interpolation algorithm is commonly used to interpolate genetic data over a spatial grid. This function provides a simple interface to interpolate such data with three methods:
Shepard:
weights are the inverse of the distance between the interpolation
location and the sample points , raised to the
power
Modified Shepard:
distances are weighted with a search radius to calculate the
interpolation weights
Shepard with neighbours:
A maximum ammount of neighbours is allowed to the weight
calculation following Shepard method.
The functions 'intgen.idw' and 'idw' are similar but whereas the first interpolate all samples to a grid-based coordinates, the second interpolates a single set of values. Although 'idw' can be used to generate the same results, the 'intgen.idw' should be faster (see the examples).
This function returns a matrix containing all interpolated values for each locality (rows) and for each sample (columns)
Pedro Tarroso <[email protected]>
Fortin, M. -J. and Dale, M. (2006) Spatial Analysis: A guide for Ecologists. Cambridge: Cambridge University Press.
Isaaks, E. H. and Srivastava, R. M. (1989) An Introduction to applied geostatistics. New York: Oxford University Press.
Legendre, P. and Legendre, L. (1998) Numerical ecology. 2nd english edition. Amesterdam: Elsevier
data(vipers) data(d.gen) data(grid) # create a matrix of distances from sample points (columns) to all # grid pixels rd <- geo.dist(grid, vipers[,1:2]) #interpolate with idw result <- intgen.idw(rd, d.gen) #plot the 12 random interpolations layout(matrix(c(1:12), 4,3)) for (i in sample(1:nrow(vipers), 12)) { dt <- data.frame(grid, int=result[,i]) # when samples are given with real coordinates, aspect of image # should be maintained with asp=1 to plot properly. image(sort(unique(grid[,1])), sort(unique(grid[,2])), xtabs(int~x+y, dt), xlab='Longitude', ylab='Latitude', main=colnames(result)[i]) cex <- (d.gen[,i]-min(d.gen[,i]))/(max(d.gen[,i])-min(d.gen[,i])) points(vipers[,1:2], cex=cex+0.5) } ## Not run: # Compare 'idw' with 'intgen.idw' to generate the same results. # NOTE: it may take a few minutes to run. result2 <- matrix(NA, nrow=nrow(grid), ncol=nrow(vipers)) for (i in 1:nrow(vipers)) { values <- d.gen[i,] intpl <- idw(values, vipers[,1:2], grid) result2[,i] <- intpl[,1] } colnames(result2) <- rownames(vipers) # compare all items in the two matrices to check equality: all(result == result2) ## End(Not run)data(vipers) data(d.gen) data(grid) # create a matrix of distances from sample points (columns) to all # grid pixels rd <- geo.dist(grid, vipers[,1:2]) #interpolate with idw result <- intgen.idw(rd, d.gen) #plot the 12 random interpolations layout(matrix(c(1:12), 4,3)) for (i in sample(1:nrow(vipers), 12)) { dt <- data.frame(grid, int=result[,i]) # when samples are given with real coordinates, aspect of image # should be maintained with asp=1 to plot properly. image(sort(unique(grid[,1])), sort(unique(grid[,2])), xtabs(int~x+y, dt), xlab='Longitude', ylab='Latitude', main=colnames(result)[i]) cex <- (d.gen[,i]-min(d.gen[,i]))/(max(d.gen[,i])-min(d.gen[,i])) points(vipers[,1:2], cex=cex+0.5) } ## Not run: # Compare 'idw' with 'intgen.idw' to generate the same results. # NOTE: it may take a few minutes to run. result2 <- matrix(NA, nrow=nrow(grid), ncol=nrow(vipers)) for (i in 1:nrow(vipers)) { values <- d.gen[i,] intpl <- idw(values, vipers[,1:2], grid) result2[,i] <- intpl[,1] } colnames(result2) <- rownames(vipers) # compare all items in the two matrices to check equality: all(result == result2) ## End(Not run)
Computes simple or ordinary kringing using a list of sampled locations. The interpolation is executed to the table of coordinates given.
krig(values, coords, grid, gv, distFUN = geo.dist, ..., m=NA, cv=FALSE, neg.weights = TRUE, clamp = FALSE, verbose = TRUE)krig(values, coords, grid, gv, distFUN = geo.dist, ..., m=NA, cv=FALSE, neg.weights = TRUE, clamp = FALSE, verbose = TRUE)
values |
A vector of values per sampled location. |
coords |
A table containing longitude and latitude of sample locations for each value. |
grid |
A table containing the coordinates of locations to interpolate |
gv |
A fitted model to variogram as given by 'gv.model' function. |
distFUN |
Distance function used to calculate distances between locations. The default is 'geo.dist' which calculates simple euclidean distances between the locations. This function must have a 'from' and a 'to' arguments to specify, respectively, the source and destination localities. Other functions can be given to include, for instance, a landscape resistance (see examples and vignette). |
... |
Other arguments to be passed to distFUN. |
m |
A value for the mean. When the mean is known and given, a simple kriging is used for the interpolation. If m = NA (default) then the mean is estimated using ordinary kriging. |
cv |
A logical value to perform cross validation of the interpolation. |
neg.weights |
A logical value indicating if negative weights are allowed in the calculation. If FALSE, negative weights are corrected and eliminating the need for clamping. See details. |
clamp |
A logical value indicating if Z values will be adjusted to the interval [0,1]. |
verbose |
A logical indicating if the function should be verbose. |
This function interpolates the probability of lineage occurrence to all locations given in 'coords'. Usually 'coords' stores coordinates of pixel centroids representing the study area with a user-defined spatial resolution. The variogram with a fitted model describes the autocorrelation structure of the genetic data. This is used by kriging to determine the weight of the sampled points on the location to predict a value.
The most usual kriging is performed with geographical distances between localities (samples and grid). The default function is the 'geo.dist' that calculate simple euclidean distances. However, the 'krig' function allows to provide user-defined distance functions to calculate other kind of distances. A landscape resistance, for instance, may be used to calculate cost distances between points and to be used in the interpolation process. The same distance function provided here has to be used before, to produce the variogram. The function 'distFUN' has to have the arguments 'from' and 'to' to use as source and destination coordinates, respectively. It may have other arguments that can be passed to the function. See the vignette for a exhaustive example on how to use this functionality.
The kriging algorithm often produce negative weights for the interpolation. This results in predictions outside the original range between zero and one. Correcting negative weights allows to maintain predictions in this range and to preserve kriging proprieties. Correction of negative weights is done following Deutsch (1996): negative weights and small positive weights (within the variation of the negative weights) are set to zero and the sum of the resulting weights rescaled to one.
Cross-validation is computed by leaving each of the observation in 'values' out of kriging and predict for the same location. A mean squared error (MSE) is computed using the original observation and the predicted value.
Returns a vector of interpolated values and respective variance for each location in 'coords'.
If cross-validation is performed (cv=TRUE) than a list of interpolation and variance values is given with a cross-validation matrix (original observation and predicted value) and a mean squared error (MSE).
Pedro Tarroso <[email protected]>
Deutsch C. V. (1996) Correcting for negative weights in ordinary kriging. Computers and Geosciences, 22(7), 765-773.
Fortin, M. -J. and Dale, M. (2006) Spatial Analysis: A guide for Ecologists. Cambridge: Cambridge University Press.
Isaaks, E. H. and Srivastava, R. M. (1989) An Introduction to applied geostatistics. New York: Oxford University Press.
Legendre, P. and Legendre, L. (1998) Numerical ecology. 2nd english edition. Amesterdam: Elsevier
gen.variogram
plot.gv
predict.gv
idw
intgen.idw
data(vipers) data(d.gen) data(grid) # In this example we want to create the probable distribution of a # lineage based on the genetic distance. We need a vector defining if # each sample belongs or not to the lineage lin <- as.integer(vipers$lin == 1) # create a distance matrix between samples r.dist <- dist(vipers[,1:2]) # fit a model with defaults (spherical model) and estimation of range gv <- gen.variogram(r.dist, d.gen) gv <- gv.model(gv) # perform interpolation with ordinary kriging int.krig <- krig(lin, vipers[,1:2], grid, gv) #plot the interpolation results grid.image(int.krig, grid, main='Kriging with genetic distances', xlab='Longitude', ylab='Latitude', sclab='Lineage interpolation') points(vipers[,1:2], pch=lin+1) # plot the interpolation standard variance grid.image(int.krig, grid, ic='sd', main='Kriging with genetic distances', xlab='Longitude', ylab='Latitude', sclab='Standard deviation') points(vipers[,1:2], pch=lin+1) #plot only pixels higher than 0.95 lin.krig <- as.integer(int.krig$Z>0.95) grid.image(lin.krig, grid, main='Kriging with genetic distances', xlab='Longitude', ylab='Latitude', sclab='Lineage') points(vipers[,1:2], pch=lin+1) ## Not run: #-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-# # The following code is an example to combine the possible clusters # # of a tree in a single map. It samples the tree at different length # # and combines the probabilities. # # # # NOTE: it may take some time to run! # #-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-# # A phylogenetic tree is sampled at different lengths. An appropriate # package (e.g. ape) should be used to process the tree. To avoid extra # dependencies we convert the genetic distances to an hclust. hc <- hclust(as.dist(d.gen)) hs = seq(0.01, 0.08, 0.005) # tree length sampling # Another options for tree sampling can be using the nodes position, # avoiding the root and tip levels: # hs <- hc$height[hc$height > 0.0 & hc$height < max(hc$height)] # # Or a single threshold: # hs <- 0.06 contact = rep(0, nrow(grid)) # Sums all probabilities for (h in hs) { lins <- cutree(hc, h=h) print(paste("height =", h, ":", max(lins), "lineages")) #keep track ct = rep(1, nrow(grid)) # Product of individual cluster/lineage map for (i in unique(lins)) { lin <- as.integer(lins == i) krg <- krig(lin, vipers[,1:2], grid, gv, clamp = TRUE, verbose=FALSE) # Probability of NOT belonging to a cluster. ct <- ct * (1 - krg$Z) # Probab. of NOT belonging to a cluster } contact = contact + ct } krg$Z <- contact / length(hs) # Recycle krg with contact zones #plot the interpolation results grid.image(krg, grid, xlab='Longitude', ylab='Latitude', main='Uncertainty in cluster classification / contact zones') points(vipers[,1:2], pch=16, cex=0.5) ## End(Not run)data(vipers) data(d.gen) data(grid) # In this example we want to create the probable distribution of a # lineage based on the genetic distance. We need a vector defining if # each sample belongs or not to the lineage lin <- as.integer(vipers$lin == 1) # create a distance matrix between samples r.dist <- dist(vipers[,1:2]) # fit a model with defaults (spherical model) and estimation of range gv <- gen.variogram(r.dist, d.gen) gv <- gv.model(gv) # perform interpolation with ordinary kriging int.krig <- krig(lin, vipers[,1:2], grid, gv) #plot the interpolation results grid.image(int.krig, grid, main='Kriging with genetic distances', xlab='Longitude', ylab='Latitude', sclab='Lineage interpolation') points(vipers[,1:2], pch=lin+1) # plot the interpolation standard variance grid.image(int.krig, grid, ic='sd', main='Kriging with genetic distances', xlab='Longitude', ylab='Latitude', sclab='Standard deviation') points(vipers[,1:2], pch=lin+1) #plot only pixels higher than 0.95 lin.krig <- as.integer(int.krig$Z>0.95) grid.image(lin.krig, grid, main='Kriging with genetic distances', xlab='Longitude', ylab='Latitude', sclab='Lineage') points(vipers[,1:2], pch=lin+1) ## Not run: #-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-# # The following code is an example to combine the possible clusters # # of a tree in a single map. It samples the tree at different length # # and combines the probabilities. # # # # NOTE: it may take some time to run! # #-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-# # A phylogenetic tree is sampled at different lengths. An appropriate # package (e.g. ape) should be used to process the tree. To avoid extra # dependencies we convert the genetic distances to an hclust. hc <- hclust(as.dist(d.gen)) hs = seq(0.01, 0.08, 0.005) # tree length sampling # Another options for tree sampling can be using the nodes position, # avoiding the root and tip levels: # hs <- hc$height[hc$height > 0.0 & hc$height < max(hc$height)] # # Or a single threshold: # hs <- 0.06 contact = rep(0, nrow(grid)) # Sums all probabilities for (h in hs) { lins <- cutree(hc, h=h) print(paste("height =", h, ":", max(lins), "lineages")) #keep track ct = rep(1, nrow(grid)) # Product of individual cluster/lineage map for (i in unique(lins)) { lin <- as.integer(lins == i) krg <- krig(lin, vipers[,1:2], grid, gv, clamp = TRUE, verbose=FALSE) # Probability of NOT belonging to a cluster. ct <- ct * (1 - krg$Z) # Probab. of NOT belonging to a cluster } contact = contact + ct } krg$Z <- contact / length(hs) # Recycle krg with contact zones #plot the interpolation results grid.image(krg, grid, xlab='Longitude', ylab='Latitude', main='Uncertainty in cluster classification / contact zones') points(vipers[,1:2], pch=16, cex=0.5) ## End(Not run)
Computes the midpoints for a table of sample points with coordinates.
midpoints(samples, x=1, y=2, sp.name=row.names(samples), all=FALSE)midpoints(samples, x=1, y=2, sp.name=row.names(samples), all=FALSE)
samples |
Table with coordinates for each sample point. |
x |
Column index or name of longitudes (x) in samples table (default is first column). |
y |
Column index or name of latitudes (y) in samples table (default is second column). |
sp.name |
Name for each sample point (defaults to row names of samples). |
all |
If TRUE computes midpoints between all sample points. If FALSE (default) computes a Delaunay triangulation and the midpoints of the resulting connected samples. |
This function computes the coordinates of the middle points between samples. The connecting network can be between all points or between neighbours with non-overlaping edges after a Delaunay triangulation.
Returns a data frame with 4 columns referring the source and target samples (ss and ts, respectively) and the coordinates of the midpoints.
Depends on package 'geometry' for Delaunay triangulation.
Pedro Tarroso <[email protected]>
data(vipers) mp <- midpoints(vipers[,1:2], all=TRUE) # With 'all=FALSE' (Delaunay triang.), package 'geometry' is mandatory.data(vipers) mp <- midpoints(vipers[,1:2], all=TRUE) # With 'all=FALSE' (Delaunay triang.), package 'geometry' is mandatory.
Computes the generalized inverse of a matrix using singular-value decomposition.
mpinv(A, eps = 1e-13)mpinv(A, eps = 1e-13)
A |
Matrix to be inverted. |
eps |
Minimum value threshold. |
Returns a matrix containing the inverse of matrix A.
Pedro Tarroso <[email protected]>
m <- matrix(rnorm(16), 4, 4) mi <- mpinv(m)m <- matrix(rnorm(16), 4, 4) mi <- mpinv(m)
Tests if the semi-variogram in the 'gv' object has a model fitted.
mtest.gv(gv)mtest.gv(gv)
gv |
An object with class 'gv'. |
This function is usefull to test if a model for the semi-variogram in 'gv' is already built.
logical
It is not exported.
Pedro Tarroso <[email protected]>
This function may be used to summarize data from different species or similar (e.g. different lineages, etc). By default, it summarizes with the mean and standard deviation, but different functions may be used.
multispecies(..., FUN=list(mean=mean, sd=sd), na.rm=FALSE)multispecies(..., FUN=list(mean=mean, sd=sd), na.rm=FALSE)
... |
Input data to be summarized. It must be numeric and it can be multiple vectors of the same size and order, or more simply a matrix with all data to be summarised. The matrix must have the different species/data in columns. |
FUN |
This is a list of functions to be applied to summarize the data. By default it uses the mean and sd, but it can be any other function that returns a number from a vector (e.g. max, min) or a user-defined function. If the objects are named in the FUN list, than those names will be given to the resulting columns. Otherwise, function are applied in the same order as given. |
na.rm |
A logical indicating whether missing values should be removed. Will only work if the functions in FUN accept it. |
This function is a simple wrapper with some error checking for the native R function 'apply'.
Returns a matrix with functions applied in the same order as FUN.
Pedro Tarroso <[email protected]>
data(vipers) data(d.gen) data(grid) # create a matrix of distances from sample points (columns) to all # grid pixels rd <- geo.dist(grid, vipers[,1:2]) #interpolate with idw result <- intgen.idw(rd, d.gen) ms <- multispecies(result) # plot the mean grid.image(ms, grid, main = "Mean") # plot the standard deviation grid.image(ms, grid, ic=2, main = "Standard Deviation")data(vipers) data(d.gen) data(grid) # create a matrix of distances from sample points (columns) to all # grid pixels rd <- geo.dist(grid, vipers[,1:2]) #interpolate with idw result <- intgen.idw(rd, d.gen) ms <- multispecies(result) # plot the mean grid.image(ms, grid, main = "Mean") # plot the standard deviation grid.image(ms, grid, ic=2, main = "Standard Deviation")
Plot the semi-variogram in a gv object. If a multiple genetic distances are found, it plots the median value and the 95% confidence interval for the median.
## S3 method for class 'gv' plot(x, line.res = 100, pch=1, legend=TRUE, leg.x=NA, leg.y=NA, leg.cex=1, bar.length=0.1, bar.col="gray", bar.lty=par("lty"), xlab='Distance', ylab='Semivariance', x.line=3, y.line=3, ncol=1, main=NULL, leg.label = expression(italic('n')*' size'), ...)## S3 method for class 'gv' plot(x, line.res = 100, pch=1, legend=TRUE, leg.x=NA, leg.y=NA, leg.cex=1, bar.length=0.1, bar.col="gray", bar.lty=par("lty"), xlab='Distance', ylab='Semivariance', x.line=3, y.line=3, ncol=1, main=NULL, leg.label = expression(italic('n')*' size'), ...)
x |
'gv' object as given by 'gen.variogram'. |
line.res |
Number of points in the model line. |
pch |
Symbol to be used in the plot. |
legend |
Boolean indicating if a legend showing n size should be printed. |
leg.x |
The x position for the legend. The legend will be placed at the right side of the plot if this value is set to NA. |
leg.y |
The y position for the legned. The legend will be placed at the bottom of the plot if this value is set to NA. |
leg.cex |
Multiplication factor for the legend symbol size. |
bar.length |
If multiple trees are given, confidence interval bars are ploted. The horizontal length of the line at both bar tips is defined with this parameter (defaults to 0.1). |
bar.col |
The color of the bars when multiple trees are given. |
bar.lty |
The line type for the bars when multiple tree are given. |
xlab |
The label for x axis. |
ylab |
The label for y axis. |
x.line |
Position of x label in lines. |
y.line |
Position of y label in lines. |
ncol |
Number of legend columns. |
main |
Main title of the plot. |
leg.label |
Legend title. |
... |
Further plotting arguments to be passed. |
Simple plot of the semi-variogram contained in a 'gv' object. If the object has a model, the model line is also plotted.
Plot.
Pedro Tarroso <[email protected]>
data(vipers) data(d.gen) # create a distance matrix between samples r.dist <- dist(vipers[,1:2]) # fit a variogram with defaults (shperical model) and estimation of range gv <- gen.variogram(r.dist, d.gen, 0.25) #plot semi-variogram plot(gv) # plot semi-variogram with model gv <- gv.model(gv) plot(gv)data(vipers) data(d.gen) # create a distance matrix between samples r.dist <- dist(vipers[,1:2]) # fit a variogram with defaults (shperical model) and estimation of range gv <- gen.variogram(r.dist, d.gen, 0.25) #plot semi-variogram plot(gv) # plot semi-variogram with model gv <- gv.model(gv) plot(gv)
Predicts values based on a fitted gen.variogram model.
## S3 method for class 'gv' predict(object, newdata, ...)## S3 method for class 'gv' predict(object, newdata, ...)
object |
'gv' fitted model (see 'gen.variogram'). |
newdata |
Real distances matrix to predict genetic distance by the fitted model. |
... |
Further arguments to be passed. |
Returns the matrix of predicted genetic distances.
Pedro Tarroso <[email protected]>
data(vipers) data(d.gen) # create a grid of the sampled area for interpolation grid <- expand.grid(x=seq(-10,10,0.5), y=seq(30, 50, 0.5)) # create a distance matrix between samples r.dist <- dist(vipers[,1:2]) # fit a variogram with defaults (spherical model) and estimation of range gv <- gen.variogram(r.dist, d.gen) gv <- gv.model(gv) all.dist <- as.matrix(dist(grid)) result <- predict(gv, all.dist)data(vipers) data(d.gen) # create a grid of the sampled area for interpolation grid <- expand.grid(x=seq(-10,10,0.5), y=seq(30, 50, 0.5)) # create a distance matrix between samples r.dist <- dist(vipers[,1:2]) # fit a variogram with defaults (spherical model) and estimation of range gv <- gen.variogram(r.dist, d.gen) gv <- gv.model(gv) all.dist <- as.matrix(dist(grid)) result <- predict(gv, all.dist)
The function is used when a 'gv' object is called.
## S3 method for class 'gv' print(x, ...)## S3 method for class 'gv' print(x, ...)
x |
'gv' object as given by 'gen.variogram'. |
... |
Further plotting arguments to be passed. |
This prints the details of a 'gv' object including number of observations and other variogram creation parameters used. It will also display model details if a model was fitted to the empirical variogram.
Pedro Tarroso <[email protected]>
data(vipers) data(d.gen) # create a distance matrix between samples r.dist <- dist(vipers[,1:2]) # fit a variogram with defaults (shperical model) and estimation of range gv <- gen.variogram(r.dist, d.gen, 0.25) # print variogram details gv # add a model to variogram gv <- gv.model(gv) # print variogram with model details gvdata(vipers) data(d.gen) # create a distance matrix between samples r.dist <- dist(vipers[,1:2]) # fit a variogram with defaults (shperical model) and estimation of range gv <- gen.variogram(r.dist, d.gen, 0.25) # print variogram details gv # add a model to variogram gv <- gv.model(gv) # print variogram with model details gv
A table with two gridded simulation environments.
data(simulations)data(simulations)
'simul.env' is a data frame with 1849 rows and 4 columns. Each row is a cell in the gridded surface. The column one and two are the x and y centroid coordinates of each cell, respectively. The third and fourth columns are the two simulates environments.
Tarroso, P., Carvalho, S.B. & Velo-Anton, G. (2019). PHYLIN 2.0: Extending the phylogeographic interpolation method to include uncertainty and user-defined distance metrics. Molecular Ecology Resources, in press.
data(simulations) # Plot the second environmental surface: negative values as open circles and # positive as solid black circles. Size proportional to absolute value plot(simul.env[,1:2], pch=1, cex=simul.env[,4]/5) points(simul.env[,1:2], pch=16, cex=-simul.env[,4]/5)data(simulations) # Plot the second environmental surface: negative values as open circles and # positive as solid black circles. Size proportional to absolute value plot(simul.env[,1:2], pch=1, cex=simul.env[,4]/5) points(simul.env[,1:2], pch=16, cex=-simul.env[,4]/5)
A 'dist' class object with simulated genetic distances.
data(simulations)data(simulations)
'simul.gen.dist' is an object with 'dist' class containing the simulated genetic distances of 200 samples.
Tarroso, P., Carvalho, S.B. & Velo-Anton, G. (2019). PHYLIN 2.0: Extending the phylogeographic interpolation method to include uncertainty and user-defined distance metrics. Molecular Ecology Resources, in press.
data(simulations) hc <- hclust(as.dist(simul.gen.dist)) plot(hc, main="Simulated gentic distances", xlab="Samples", cex=0.7)data(simulations) hc <- hclust(as.dist(simul.gen.dist)) plot(hc, main="Simulated gentic distances", xlab="Samples", cex=0.7)
A table with x and y coordinates of 200 random samples in the simulated grid and a lineage information.
data(simulations)data(simulations)
'simul.sample' is a data frame with 200 rows and 3 columns. Each row is a sample in the simulated grid. The column one and two are the x and y coordinates of each sample, respectively. The lineage to which each sample belongs is given in the third column.
Tarroso, P., Carvalho, S.B. & Velo-Anton, G. (2019). PHYLIN 2.0: Extending the phylogeographic interpolation method to include uncertainty and user-defined distance metrics. Molecular Ecology Resources, in press.
data(simulations) # Plot all the samples with different symbols for each lineage. plot(simul.sample[,1:2], pch=simul.sample[,3])data(simulations) # Plot all the samples with different symbols for each lineage. plot(simul.sample[,1:2], pch=simul.sample[,3])
Displays general information about the 'gv' object.
## S3 method for class 'gv' summary(object, ...)## S3 method for class 'gv' summary(object, ...)
object |
'gv' object as given by 'gen.variogram' or 'gv.model'. |
... |
Further plotting arguments to be passed. |
Print summary table.
Pedro Tarroso <[email protected]>
data(vipers) data(d.gen) # create a distance matrix between samples r.dist <- dist(vipers[,1:2]) # fit a variogram with defaults (shperical model) and estimation of range gv <- gen.variogram(r.dist, d.gen) #plot semi-variogram summary(gv) # plot semi-variogram with model gv <- gv.model(gv) summary(gv)data(vipers) data(d.gen) # create a distance matrix between samples r.dist <- dist(vipers[,1:2]) # fit a variogram with defaults (shperical model) and estimation of range gv <- gen.variogram(r.dist, d.gen) #plot semi-variogram summary(gv) # plot semi-variogram with model gv <- gv.model(gv) summary(gv)
This dataset contains the x and y coordinates of 58 Vipera latastei samples with corresponding lineages.
data(vipers)data(vipers)
A data frame with 3 columns (x/Longitude, y/Latitude and lineage) and 58 rows.
Velo-Anton G., Godinho R., Harris D. J. et al. (2012) Deep evolutionary lineages in a Western Mediterranean snake (Vipera latastei/monticola group) and high genetic structuring in Southern Iberian populations. Molecular phylogenetics and evolution, 65, 965–973.
data(vipers) data(grid) plot(grid, cex=0.5, col='lightgrey', asp=1, main="Vipers data", xlab="Longitude", ylab="Latitude") points(vipers[,1:2], pch=vipers$lin) legend(1, 38, legend=c("West", "South", "East"), pch=1:3, title="Lineages")data(vipers) data(grid) plot(grid, cex=0.5, col='lightgrey', asp=1, main="Vipers data", xlab="Longitude", ylab="Latitude") points(vipers[,1:2], pch=vipers$lin) legend(1, 38, legend=c("West", "South", "East"), pch=1:3, title="Lineages")