kdfun {ads}  R Documentation 
Computes distancedependent 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).
kdfun(p, upto, by, dis, nsim=0, alpha = 0.01)
p 
a 
upto 
maximum radius of the sample circles (see Details). 
by 
interval length between successive sample circles radii (see Details). 
dis 
a 
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 
alpha 
if 
Function kdfun
computes Shen et al. (2014) Kd and gdfunctions. For a multivariate point pattern consisting of S species with intensity λp, such functions can be estimated from the bivariate Kpqfunctions 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(λ p * λ q * Kpq(r) * dpq) / HD * sum(λ p * λ q * Kpq(r)).
gd(r) = D * g(r) / HD * gs(r) = D * sum(λ p * λ q * gpq(r) * dpq) / HD * sum(λ p * λ q * gpq(r)).
where Ks(r) and gs(r) are distancedependent versions of Simpson's diversity index, D (see ksfun
), Kr(r) and gr(r) are distancedependent 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 rby.
Theoretical values under the null hypothesis of species equivalence as well as local Monte Carlo confidence limits and pvalues of departure from the null hypothesis (Besag & Diggle 1977) are estimated at each distance r, by randomizing the betweenspecies distances, keeping the point locations and distribution of species labels unchanged. The theoretical expectations of gd(r) and Kd(r) are thus 1.
A list of class "fads"
with essentially the following components:
r 
a vector of regularly spaced out distances ( 
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 
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 
inf 
(optional) if 
pval 
(optional) if 
There are printing and plotting methods for "fads"
objects.
Shen, G., Wiegand, T., Mi, X. & He, F. (2014). Quantifying spatial phylogenetic structures of fully stemmapped plant communities. Methods in Ecology and Evolution, 4, 11321141.
P?Pelissier, R. & Goreaud, F. ads package for R: A fast unbiased implementation of the Kfunction family for studying spatial point patterns in irregularshaped sampling windows. Journal of Statistical Software, in press.
plot.fads
,
spp
,
ksfun
,
krfun
,
divc
.
data(Paracou15) P15<Paracou15 ## Not run: spatial point pattern in a rectangle sampling window of size 125 x 125 swmr < spp(P15$trees, win = c(175, 175, 250, 250), marks = P15$species) ## Not run: testing the species equivalence hypothesis kdswmr < kdfun(swmr, dis = P15$spdist, 50, 2, 100) ## Not run: running more simulations is slow kdswmr < kdfun(swmr, dis = P15$spdist, 50, 2, 500) plot(kdswmr) ## Not run: spatial point pattern in a circle with radius 50 centred on (125,125) swmc < spp(P15$trees, win = c(125,125,50), marks = P15$species) kdswmc < kdfun(swmc, dis = P15$spdist, 50, 2, 100) ## Not run: running more simulations is slow kdswmc < kdfun(swmc, dis = P15$spdist, 50, 2, 500) plot(kdswmc) ## Not run: spatial point pattern in a complex sampling window 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 kdswrt < kdfun(swrt, dis = P15$spdist, 50, 2, 500) plot(kdswrt)