k12val: 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

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).

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.

Value

A list of class c("vads","k12val") with essentially the following components:
ra vector of regularly spaced distances (seq(by,upto,by)).
xya data frame with 2 components giving $(x,y)$ coordinates of type 1 points of the pattern.
g12vala matrix of size $(length(xy),length(r))$ giving individual values of the bivariate pair density function $g12(r)$.
n12vala matrix of size $(length(xy),length(r))$ giving individual values of the bivariate neighbour density function $n12(r)$.
k12vala matrix of size $(length(xy),length(r))$ giving individual values of the intertype function $K12(r)$.
l12vala matrix of size $(length(xy),length(r))$ giving individual values the modified intertype function $L12(r)$.

encoding

latin1

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�lissier & Goreaud 2001.

References

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

Examples

Run this code

data(BPoirier)
  BP <- BPoirier
  # 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)
 
  # 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)
  
  # 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)

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