ads (version 1.5-5)

kdfun: Multiscale second-order neighbourhood analysis of a spatial phylogenetic or functional community pattern from fully mapped data

Description

Computes distance-dependent estimates of Shen et al. (2014) phylogenetic or functional mark correlation functions from a multivariate 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 species equivalence (see Details).

Usage

kdfun(p, upto, by, dis, nsim=0, alpha = 0.01)

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).

dis

a "dist" object defining Euclidean distances between species.

nsim

number of Monte Carlo simulations to estimate local confidence limits of the null hypothesis of a random allocation of species distances (species equivalence; 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 \(\alpha = 0.01\).

Value

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

r

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

gd

a data frame containing values of the function \(gd(r)\).

kd

a data frame containing values of the function \(Kd(r)\).

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 under the null hypothesis of species equivalence.

sup

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

inf

(optional) if nsim>0 a vector of the lower local confidence limits of a random distribution 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.

Details

Function kdfun computes Shen et al. (2014) \(Kd\) and gd-functions. For a multivariate point pattern consisting of \(S\) species with intensity \(\lambda\)p, such functions can be estimated from the bivariate \(Kpq\)-functions between each pair of different species \(p\) and \(q\). Function kdfun is thus a simple wrapper of k12fun (P?Pelissier & Goreaud 2014):

\(Kd(r) = D * Kr(r) / HD * Ks(r) = D * sum(\lambda p * \lambda q * Kpq(r) * dpq) / HD * sum(\lambda p * \lambda q * Kpq(r))\). \(gd(r) = D * g(r) / HD * gs(r) = D * sum(\lambda p * \lambda q * gpq(r) * dpq) / HD * sum(\lambda p * \lambda q * gpq(r))\).

where \(Ks(r)\) and \(gs(r)\) are distance-dependent versions of Simpson's diversity index, \(D\) (see ksfun), \(Kr(r)\) and \(gr(r)\) are distance-dependent versions of Rao's diversity coefficient (see krfun); \(dpq\) is the distance between species \(p\) and \(q\) defined by matrix dis, typically a taxonomic, phylogenetic or functional distance. The advantage here is that as the edge effects vanish between \(Kr(r)\) and \(Ks(r)\), implementation is fast for a sampling window of any shape. \(Kd(r)\) provides the expected phylogenetic or functional distance of two heterospecific individuals a distance less than r apart (Shen et al. 2014), while \(gd(r)\) provides the same within an annuli between two consecutive distances of r and r-by.

Theoretical values under the null hypothesis of species equivalence as well as local Monte Carlo confidence limits and p-values of departure from the null hypothesis (Besag & Diggle 1977) are estimated at each distance \(r\), by randomizing the between-species distances, keeping the point locations and distribution of species labels unchanged. The theoretical expectations of \(gd(r)\) and \(Kd(r)\) are thus \(1\).

References

Shen, G., Wiegand, T., Mi, X. & He, F. (2014). Quantifying spatial phylogenetic structures of fully stem-mapped plant communities. Methods in Ecology and Evolution, 4, 1132-1141.

P?Pelissier, R. & Goreaud, F. ads package for R: A fast unbiased implementation of the K-function family for studying spatial point patterns in irregular-shaped sampling windows. Journal of Statistical Software, in press.

See Also

plot.fads, spp, ksfun, krfun, divc.

Examples

# NOT RUN {
  data(Paracou15)
  P15<-Paracou15
  
# }
# NOT RUN {
spatial point pattern in a rectangle sampling window of size 125 x 125
# }
# NOT RUN {
  swmr <- spp(P15$trees, win = c(175, 175, 250, 250), marks = P15$species)
  
# }
# NOT RUN {
testing the species equivalence hypothesis
# }
# NOT RUN {
  kdswmr <- kdfun(swmr, dis = P15$spdist, 50, 2, 100)
  
# }
# NOT RUN {
running more simulations is slow
# }
# NOT RUN {
  
# }
# NOT RUN {
kdswmr <- kdfun(swmr, dis = P15$spdist, 50, 2, 500)
# }
# NOT RUN {
  plot(kdswmr)

 
# }
# NOT RUN {
spatial point pattern in a circle with radius 50 centred on (125,125)
# }
# NOT RUN {
  swmc <- spp(P15$trees, win = c(125,125,50), marks = P15$species)
  kdswmc <- kdfun(swmc, dis = P15$spdist, 50, 2, 100)
  
# }
# NOT RUN {
running more simulations is slow
# }
# NOT RUN {
  
# }
# NOT RUN {
kdswmc <- kdfun(swmc, dis = P15$spdist, 50, 2, 500)
# }
# NOT RUN {
  plot(kdswmc)
  
 
# }
# NOT RUN {
spatial point pattern in a complex sampling window
# }
# NOT RUN {
  swrt <- spp(P15$trees, win = c(125,125,250,250), tri = P15$tri, marks = P15$species)
  kdswrt <- kdfun(swrt, dis = P15$spdist, 50, 2, 100)
  
# }
# NOT RUN {
running simulations is slow
# }
# NOT RUN {
  
# }
# NOT RUN {
kdswrt <- kdfun(swrt, dis = P15$spdist, 50, 2, 500)
# }
# NOT RUN {
  plot(kdswrt)
# }