k12val {ads}

Multiscale local second-order neighbour density of a bivariate spatial point pattern

Description

Computes local second-order neighbour density estimates for a bivariate spatial point pattern, i.e. the number of neighbours of type 2 per unit area within sample circles of regularly increasing radii r, centred at each type 1 point of the pattern (see Details).

Usage

 k12val(p, upto, by, marks)

Arguments

p

a "spp" object defining a multivariate spatial point pattern in a given sampling window (see spp).

upto

maximum radius of the sample circles (see Details).

by

interval length between successive sample circles radii (see Details).

marks

by default c(1,2), otherwise a vector of two numbers or character strings identifying the types (the p$marks levels) of points of type 1 and 2, respectively.

Details

Function K12val returns individual values of K12(r) and associated functions (see k12fun) estimated at each type 1 point of the pattern. For a given distance r, these values can be mapped within the sampling window, as in Getis & Franklin 1987 or P?Pelissier & Goreaud 2001.

Value

A list of class c("vads","k12val") with essentially the following components:

r

a vector of regularly spaced distances (seq(by,upto,by)).

xy

a data frame with 2 components giving (x,y) coordinates of type 1 points of the pattern.

g12val

a matrix of size (length(xy),length(r)) giving individual values of the bivariate pair density function g12(r).

n12val

a matrix of size (length(xy),length(r)) giving individual values of the bivariate neighbour density function n12(r).

k12val

a matrix of size (length(xy),length(r)) giving individual values of the intertype function K12(r).

l12val

a matrix of size (length(xy),length(r)) giving individual values the modified intertype function L12(r).

Note

There are printing, summary and plotting methods for "vads" objects.

Author(s)

[e-mail]

References

Getis, A. and Franklin, J. 1987. Second-order neighborhood analysis of mapped point patterns. Ecology, 68:473-477.

P?Pelissier, R. and Goreaud, F. 2001. A practical approach to the study of spatial structure in simple cases of heterogeneous vegetation. Journal of Vegetation Science, 12:99-108.

See Also

plot.vads, k12fun, dval, kval.

Examples

  data(BPoirier)
  BP <- BPoirier
  ## Not run: spatial point pattern in a rectangle sampling window of size [0,110] x [0,90]
  swrm <- spp(BP$trees, win=BP$rect, marks=BP$species)
  k12vswrm <- k12val(swrm, 25, 1, marks=c("beech","oak"))
  summary(k12vswrm)
  plot(k12vswrm)
 
  ## Not run: spatial point pattern in a circle with radius 50 centred on (55,45)
  swc <- spp(BP$trees, win=c(55,45,45), marks=BP$species)
  k12vswc <- k12val(swc, 25, 1, marks=c("beech","oak"))
  summary(k12vswc)
  plot(k12vswc)
  
  ## Not run: spatial point pattern in a complex sampling window
  swrt <- spp(BP$trees, win=BP$rect, tri=BP$tri2, marks=BP$species)
  k12vswrt <- k12val(swrt, 25, 1, marks=c("beech","oak"))
  summary(k12vswrt)
  plot(k12vswrt)