intgen.idw: Interpolation of genetic distances to a a grid of points.
In phylin: Spatial Interpolation of Genetic Data

Description Usage Arguments Details Value Author(s) References See Also Examples

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.

1	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 x and the sample points x_i, raised to the power p

w(x) = 1/d(x, xi)^p
Modified Shepard: distances are weighted with a search radius r to calculate the interpolation weights

w(x) = ((r-d(x, xi)) / (r*d(x, xi)))^p
Shepard with neighbours: A maximum ammount of N 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 <ptarroso@cibio.up.pt>

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

idw

    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)