correlog {ncf}

Uni- and multivariate spatial correlograms

Description

correlog is the function to estimate spatial (cross-)correlograms. Either univariate or multivariate (time seres) for each site can be used.

Usage

correlog(
  x,
  y,
  z,
  w = NULL,
  increment,
  resamp = 999,
  latlon = FALSE,
  na.rm = FALSE,
  quiet = FALSE
)

Arguments

x

vector of length n representing the x coordinates (or longitude; see latlon).

y

vector of length n representing the y coordinates (or latitude).

z

vector of length n or matrix of dimension n x p representing p observation at each location.

w

an optional second variable with identical dimension to z (to estimate cross-correlograms).

increment

increment for the uniformly distributed distance classes.

resamp

the number of permutations under the null to assess level of significance.

latlon

If TRUE, coordinates are latitude and longitude.

na.rm

If TRUE, NA's will be dealt with through pairwise deletion of missing values.

quiet

If TRUE, the counter is suppressed during execution.

Details

The spatial (cross-)correlogram and Mantel (cross-)correlogram estimates the spatial dependence at discrete distance classes.

The region-wide similarity forms the reference line (the zero-line); the x-intercept is thus the distance at which object are no more similar than that expected by-chance-alone across the region.

If the data are univariate, the spatial dependence is measured by Moran's I. If it is multivariate, it is measured by the centred Mantel statistic. (Use correlog.nc if the non-centered multivariate correlogram is desired).

Missing values are allowed – values are assumed missing at random.

Value

An object of class "correlog" is returned, consisting of the following components:

correlation

the value for the Moran (or Mantel) similarity.

mean.of.class

the actual average of the distances within each distance class.

nlok

the number of pairs within each distance class.

x.intercept

the interpolate x.intercept of Epperson (1993).

p

the permutation two-sided p-value for each distance-class.

corr0

If a cross-correlogram is calculated, corr0 gives the empirical cross-correlation at distance zero.

Author(s)

Ottar N. Bjornstad [e-mail]

References

Bjornstad, O.N., Ims, R.A. & Lambin, X. (1999) Spatial population dynamics: Analysing patterns and processes of population synchrony. Trends in Ecology and Evolution, 11, 427-431. <doi:10.1016/S0169-5347(99)01677-8>

Bjornstad, O.N. & Falck, W. (2001) Nonparametric spatial covariance functions: estimation and testing. Environmental and Ecological Statistics, 8:53-70. <doi:10.1023/A:1009601932481>

Epperson, B.K. (1993) Recent advances in correlation studies of spatial patterns of genetic variation. Evolutionary Biology, 27, 95-155. <doi:10.1007/978-1-4615-2878-4_4>

See Also

plot.correlog, spline.correlog, correlog.nc

Examples

# first generate some sample data
x <- expand.grid(1:20, 1:5)[, 1]
y <- expand.grid(1:20, 1:5)[, 2]

# z data from an exponential random field
z <- cbind(
  rmvn.spa(x = x, y = y, p = 2, method = "exp"), 
  rmvn.spa(x = x, y = y, p = 2, method = "exp")
  )

# w data from a gaussian random field
w <- cbind(
  rmvn.spa(x = x, y = y, p = 2, method = "gaus"), 
  rmvn.spa(x = x, y = y, p = 2, method = "gaus")
  )

# Spatial correlogram 
fit1 <- correlog(x = x, y = y, z = z[, 1], increment = 2, resamp = 0) 
## Not run: plot(fit1)

# Mantel correlogram 
fit2 <- correlog(x = x, y = y, z = z, increment = 2, resamp = 0) 
## Not run: plot(fit2)

# Mantel cross-correlogram 
fit3 <- correlog(x = x, y = y, z = z, w = w, increment = 2, resamp = 0) 
## Not run: plot(fit3)