kdfun | R Documentation |
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).
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 gd-functions. For a multivariate point pattern consisting of S species with intensity λp, 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(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 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.
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 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 |
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 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.
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)
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