gen.variogram {phylin}

Semi-variogram with the genetic distance matrix

Description

Computes the semi-variance with the real and genetic distances, and with user defined lag parameters.

Usage

gen.variogram(x, y, lag = quantile(as.matrix(x), 0.05), tol=lag/2, lmax = NA,
              bootstraps = 999, verbose = FALSE)

Arguments

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.

Details

This function produces a table with real lag centers and semi-variance. The formula to calculate semi-variance, \gamma(h), is:

\gamma(h) = {\frac{1}{2 n(h)}} \sum_{i=1}^{n}[z(x_i + h) - z(x_i)]^2

where n(h) is the number of pairs with the lag distance h between them, and z is the value of the sample x at the the location i. The difference between sample z(x_i+h) and sample z(x_i) 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.

Value

Returns a 'gv' object with the input data, lag centers and semi-variance.

Note

It is assumed that the order of samples in x corresponds to the same in y.

Author(s)

Pedro Tarroso <[e-mail]>

References

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

See Also

plot.gv predict.gv gv.model

Examples

    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)