vario {synchrony}

vario

Description

Compute the empirical variogram and determine its significance via Monte Carlo randomizations

Usage

vario (n.bins = 20, size.bins = NULL, extent = 0.5, data, data2 = NULL, 
                  is.latlon = TRUE, is.centered = FALSE, nrands = 0, 
                  type = c("semivar", "cov", "pearson", 
                  "spearman", "kendall", "moran", "geary"),
                  alternative = c("one.tailed", "two.tailed"),
                  mult.test.corr = c("none", "holm", "hochberg", "bonferroni"),
                  regional = c("all", "extent"),
                  quiet = FALSE)

Arguments

n.bins

Number of bins or lag distances. This argument is only used when size.bins=NULL

size.bins

Size of bins in units of distance (e.g., km). When specified, this argument overrides n.bins. Default is NULL

extent

Proportion of the spatial extent of the data over which to compute the variogram. Default is 0.5 to limit potentially spurious results due to the limited number of data points at large lag distances.

data

n x m matrix containing y-coordinates (or latitude), x-coordinates (or longitude), and values. The values can either be a single column of observations at each site for univariate variograms or a matrix of observations at each site for multivariate variograms (e.g., to compute spatial synchrony).

data2

n x m matrix containing y-coordinates (or latitude), x-coordinates (or longitude), and values for second variable. The values can either be a single column of observations at each site for univariate variograms or a matrix of observations at each site for multivariate variograms (e.g., to compute spatial synchrony).

is.latlon

Are coordinates latitudes/longitudes? Default is TRUE

is.centered

Should the variogram be centered by subtracting the regional mean from each value? If so, the zero-line represents the regional mean. Default is FALSE

nrands

Number of randomizations to determine statistical significance of variogram. Default is 0.

type

Type of variogram to compute. Default is semivar for semivariance. Other options include cov for covariance, pearson for Pearson correlation, spearman for Spearman correlation, kendall for Kendall correlation, moran for Moran's I, and geary for Geary's C

alternative

Conduct a one-tailed or a two-tailed test? Note that the statistical test is to determine whether the local value within each lag distance is different from the regional mean. If the variogram is centered, the null hypothesis is that the local values are equal to zero. If the variogram is not centered, the null hypothesis is that the local values are equal to the regional mean. Default is one.tailed

mult.test.corr

Correct for multiple tests? Default is "none". Other options include holm, hochberg and bonferroni

regional

Should the regional average be computed for the entire dataset (all) or just the extent specified (extent). Default is the entire dataset (all)

quiet

Suppress progress bar when set to TRUE. Default is FALSE

Details

This function can be used to compute univariate correlograms using Moran's I, Geary's C, and the covariance function or variograms using the semivariance function. Multivariate (Mantel) correlograms can also be computed using the covariance function, Pearson's, Spearman's or Kendall's correlation coefficients. Cross-correlograms/variograms between data1 and data2 can be computed with the covariance function, Pearson's, Spearman's or Kendall's correlation coefficients for multivariate variograms and Moran's I, Geary's C, the covariance function, or semivariance for univariate variograms.

Value

Returns a named list containing the following variables:

bins

Center of each lag/bin

mean.bin.dist

Mean distance of each lag/bin

vario

Variogram values in each lag/bin

npoints

Number of pairs of points in each lag/bin

metric

Type of variogram computed

is.centered

Is the variogram centered?

regional.mean

Regional mean value

pvals

p-value for each lag/bin. This variable is only returned if nrands > 0.

rands

nrands x n.bins matrix of randomizations. This variable is only returned if nrands > 0.

alternative

One-tailed or two-tailed test? This variable is only returned if nrands > 0.

mult.test.corr

Correct for multiple tests? This variable is only returned if nrands > 0.

is.multivar

Was the analysis performed on multivariate data?

Author(s)

Tarik C. Gouhier ([e-mail])

References

Bjornstad, O. N., and W. Falck. 2001. Nonparametric spatial covariance functions: Estimation and testing. Environmental and Ecological Statistics 8:53-70.

Bjornstad, O. N., R. A. Ims, and X. Lambin. 1999. Spatial population dynamics: analyzing patterns and processes of population synchrony. Trends in Ecology & Evolution 14:427-432.

Fortin, M. J., and M. R. T. Dale. 2005. Spatial Analysis: A Guide for Ecologists. Cambridge University Press.

See Also

vario.func

Examples

data(pisco.data)
d=subset(pisco.data, subset=year==2000, select=c("latitude", "longitude", "sst"))
semiv=vario(data=d)
moran=vario(data=d, type="moran", nrands=100)
par(mfrow=c(2,1), mar=c(4.2, 4, 1, 1))
plot(semiv$mean.bin.dist, semiv$vario, xlab="Lag distance (km)", ylab="Semivariance")
plot(moran$mean.bin.dist, moran$vario, xlab="Lag distance (km)", ylab="Moran's I", t="l")
points(moran$mean.bin.dist[moran$pvals >= 0.05], moran$vario[moran$pvals >= 0.05], 
       bg="white", pch=21)
points(moran$mean.bin.dist[moran$pvals < 0.05], moran$vario[moran$pvals < 0.05], 
       bg="black", pch=21)
abline(h=0, lty=2)

# Compute spatial synchrony
d.upw=subset(pisco.data, select=c("latitude", "longitude", "year", "upwelling"))
d.cov=subset(pisco.data, select=c("latitude", "longitude", "year", "mussel_abund"))
# Reshape the data
d.upw.wide=reshape(data=d.upw, idvar=c("latitude", "longitude"), timevar=c("year"), 
                   direction="wide")
d.cov.wide=reshape(data=d.cov, idvar=c("latitude", "longitude"), timevar=c("year"), 
                   direction="wide")
# Generate variograms
v.upw=vario(n.bins=12, data=d.upw.wide, type="pearson", extent=1, nrands=999)
v.cov=vario(n.bins=12, data=d.cov.wide, type="pearson", extent=1, nrands=999)
## Fit variograms
v.cov.per=vario.fit(v.cov$vario, v.cov$mean.bin.dist, type="period", 
                    start.vals=list(a=1, b=3, c=0))
v.upw.lin=vario.fit(v.upw$vario, v.upw$mean.bin.dist, type="linear")

par(mfrow=c(2,1))
plot(v.cov, xlab="Lag distance (km)", bg.sig="red", col.nonsig="red", 
     main="Mussel cover", 
     rug=TRUE, ylim=c(-0.3, 0.3))
lines(v.cov$mean.bin.dist, v.cov.per$fit, col="red")
plot(v.upw, xlab="Lag distance (km)", bg.sig="blue", col.nonsig="blue", 
     main="Upwelling", rug=TRUE)
lines(v.upw$mean.bin.dist, v.upw.lin$fit, col="blue")