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).
k12val(p, upto, by, marks)A list of class c("vads","k12val") with essentially the following components:
a vector of regularly spaced distances (seq(by,upto,by)).
a data frame with 2 components giving \((x,y)\) coordinates of type 1 points of the pattern.
a matrix of size \((length(xy),length(r))\) giving individual values of the bivariate pair density function \(g12(r)\).
a matrix of size \((length(xy),length(r))\) giving individual values of the bivariate neighbour density function \(n12(r)\).
a matrix of size \((length(xy),length(r))\) giving individual values of the intertype function \(K12(r)\).
a matrix of size \((length(xy),length(r))\) giving individual values the modified intertype function \(L12(r)\).
a "spp" object defining a multivariate spatial point pattern in a given sampling window (see spp).
maximum radius of the sample circles (see Details).
interval length between successive sample circles radii (see Details).
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.
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.
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.
plot.vads,
k12fun,
dval,
kval.