kmfun {ads}

Multiscale second-order neighbourhood analysis of a marked spatial point pattern

Description

Computes estimates of the mark correlation Km-function and associated neighbourhood functions from a marked spatial point pattern in a simple (rectangular or circular) or complex sampling window. Computes optionally local confidence limits of the functions under the null hypothesis of no correlation between marks (see Details).

Usage

kmfun(p, upto, by, nsim=0, alpha=0.01)

Arguments

p

a "spp" object defining a marked 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).

nsim

number of Monte Carlo simulations to estimate local confidence limits of the null hypothesis of no correlation between marks (see Details). By default nsim=0, so that no confidence limits are computed.

alpha

if nsim>0, significant level of the confidence limits. By default \alpha=0.01.

Details

Function kmfun computes the mark correlation function Km(r) and the associated function gm(r).

It is defined from a general definition of spatial autocorrelation (Goreaud 2000) as:

Km(r) = (COV(Xi,Xj)|d(i,j)<r) / VAR(X)

where X is a quantitative random variable attached to each point of the pattern.

Km(r) has a very similar interpretation than more classical correlation functions, such as Moran's I: it takes values between -1 and 1, with an expectation of 0 under the null hypothesis of no spatial correlation between the values of X, becomes positive when values of X at distance r are positively correlated and negative when values of X at distance r are negatively correlated.

gm(r) is the derivative of Km(r) or pair mark correlation function, which gives the correlation of marks within an annuli between two successive circles with radii r and r-by).

The program introduces an edge effect correction term according to the method proposed by Ripley (1977) and extended to circular and complex sampling windows by Goreaud & P?Pelissier (1999).

Local Monte Carlo confidence limits and p-values of departure from the null hypothesis of no correlation are estimated at each distance r, after reallocating at random the values of X over all points of the pattern, the location of trees being kept unchanged.

Value

A list of class "fads" with essentially the following components:

r

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

gm

a data frame containing values of the pair mark correlation function gm(r).

km

a data frame containing values of the mark correlation function Km(r).

Each component except r is a data frame with the following variables:

obs

a vector of estimated values for the observed point pattern.

theo

a vector of theoretical values expected for the null hypothesis of no correlation between marks.

sup

(optional) if nsim>0 a vector of the upper local confidence limits of the null hypothesis at a significant level \alpha.

inf

(optional) if nsim>0 a vector of the lower local confidence limits of the null hypothesis at a significant level \alpha.

pval

(optional) if nsim>0 a vector of local p-values of departure from the null hypothesis.

Note

Applications of this function can be found in Oddou-Muratorio et al. (2004) and Madelaine et al. (submitted).

Author(s)

[e-mail]

References

Goreaud, F. 2000. Apports de l'analyse de la structure spatiale en foret tempere a l'etude et la modelisation des peuplements complexes. These de doctorat, ENGREF, Nancy, France.

Goreaud F. & P?Pelissier R. 1999. On explicit formulas of edge effect correction for Ripley's K-function. Journal of Vegetation Science, 10:433-438.

Madelaine, C., Pelissier, R., Vincent, G., Molino, J.-F., Sabatier, D., Prevost, M.-F. & de Namur, C. 2007. Mortality and recruitment in a lowland tropical rainforest of French Guiana: effects of soil type and species guild. Journal of Tropical Ecology, 23:277-287.

Oddou-Muratorio, S., Demesure-Musch, B., Pelissier, R. & Gouyon, P.-H. 2004. Impacts of gene flow and logging history on the local genetic structure of a scattered tree species, Sorbus torminalis L. Molecular Ecology, 13:3689-3702.

Ripley B.D. 1977. Modelling spatial patterns. Journal of the Royal Statistical Society B, 39:172-192.

See Also

plot.fads, spp, kfun, k12fun, kijfun, ki.fun.

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$dbh)
  kmswrm <- kmfun(swrm, 25, 2, 500)
  plot(kmswrm)
  
  ## Not run: spatial point pattern in a circle with radius 50 centred on (55,45)
  swc <- spp(BP$trees, win=c(55,45,45), marks=BP$dbh)
  kmswc <- kmfun(swc, 25, 2, 500)
  plot(kmswc)

  ## Not run: spatial point pattern in a complex sampling window
  swrt <- spp(BP$trees, win=BP$rect, tri=BP$tri2, marks=BP$dbh)
  kmswrt <- kmfun(swrt, 25, 2, 500)
  plot(kmswrt)