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

Description

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

Usage

kval(p, upto, by)

Arguments

p

a "spp" object defining a 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).

Value

• A list of class c("vads","kval") with essentially the following components:
• r
  a vector of regularly spaced out distances (seq(by,upto,by)).
• xy
  a data frame with 2 components giving $(x,y)$ coordinates of points of the pattern.
• gval
  a matrix of size $(length(xy),length(r))$ giving individual values of the pair density function $g(r)$.
• nval
  a matrix of size $(length(xy),length(r))$ giving individual values of the neighbour density function $n(r)$.
• kval
  a matrix of size $(length(xy),length(r))$ giving individual values of Ripley's function $K(r)$.
• lval
  a matrix of size $(length(xy),length(r))$ giving individual values the modified Ripley's function $L(r)$.

encoding

latin1

Warning

Function kval ignores the marks of multivariate and marked point patterns (they are all considered to be univariate patterns).

Details

Function kval returns indivdiual values of K(r) and associated functions (see kfun) estimated for each point of the pattern. For a given distance r, these values can be mapped within the sampling window (Getis & Franklin 1987, 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.

See Also

plot.vads, kfun, dval, k12val.

Examples

data(BPoirier)
  BP <- BPoirier
  # spatial point pattern in a rectangle sampling window of size [0,110] x [0,90]
  swr <- spp(BP$trees, win=BP$rect)
  kvswr <- kval(swr, 25, 1)
  summary(kvswr)
  plot(kvswr)

  # spatial point pattern in a circle with radius 50 centred on (55,45)
  swc <- spp(BP$trees, win=c(55,45,45))
  kvswc <- kval(swc, 25, 1)
  summary(kvswc)
  plot(kvswc)
  
  # spatial point pattern in a complex sampling window
  swrt <- spp(BP$trees, win=BP$rect, tri=BP$tri1)
  kvswrt <- kval(swrt, 25, 1)
  summary(kvswrt)
  plot(kvswrt)