Essential Statistical Concepts, Definitions, and Terminology - Sampling Spatial Units for Agricultural Surveys - page 33

K -function to account for edge effects. The most commonly used was proposed by
Ripley ( 1977 ). However, in Besag s paper, he showed

that this correction gave excessive weight to the most distant neighbors.
The R package for spatial point pattern analysis is spatstat. Here, we have
used the redwood data set, which represents the locations of 62 California red-
wood tree seedlings and saplings in a square sampling region. They are available in
the spatstat package. The routine to estimate Ripley

s( 1977 ) discussion of Ripley

' '

s K -function is Kest. '

> library(spatstat)
> data(redwood)
> K < - Kest(redwood)
> par(mfrow ¼ c(1,2),mar ¼ c(1,1,1,1))
> plot(redwood$x,redwood$y,cex ¼ 1,pch ¼ 19,axes ¼ F)
> box()
> plot(K$r,K$iso,type ¼ "l",lty ¼ 1,axes ¼ F)
> box()
> lines(K$r,K$trans,lty¼2)
> lines(K$r,K$border,lty¼3)
> lines(K$r,K$theo,lty¼4)
> legend(0,0.2,c("iso","trans","border","theo"),lty¼c(1,2,3,4))

The second graph of Fig. 1.4 shows the estimates of the K -function obtained with
different methods for edge correction (border, isotropic, and translate) and the
theoretical value (theo) for a stationary Poisson process (Ripley 1988 ).
Interested readers can find further details of the spatstat package in the
reference manual at http://cran.r-project.org/web/packages/spatstat/spatstat.pdf .

Fig. 1.4 Point pattern ( left ) and K -function estimates ( right )