ksfun | R Documentation |
Computes estimates of Shimatani alpha and beta functions of Simpson diversity 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 a random allocation of species labels (see Details).
ksfun(p, upto, by, 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). |
nsim |
number of Monte Carlo simulations to estimate local confidence limits of the null hypothesis of a random allocation of species labels (see Details).
By default |
alpha |
if |
Function ksfun
computes Shimatani α(r) and β(r) functions of Simpson diversity, called here Ks(r) and gs(r), respectively.
For a multivariate point pattern consisting of S species with intensity λp, Shimatani (2001) showed that
a distance-dependent measure of Simpson (1949) diversity can be estimated from Ripley (1977) K-function computed for each species separately and for all the points grouped together (see also Eckel et al. 2008).
Function ksfun
is thus a simple wrapper function of kfun
, standardized by Simpson diversity coefficient:
Ks(r) = 1 - sum(λ p * λ p * Kp(r)) / (λ * λ * K(r) * D) which is a standardized estimator of α(r) in Shimatani (2001).
gs(r) = 1 - sum(λ p * λ p * gp(r)) / (λ * λ * g(r) * D) corresponding to a standardized version of β(r) in Shimatani (2001).
Kp(r) and K(r) (resp. gp(r) and g(r)) are univariate K-functions computed for species p and for all species together; D = 1 - sum(Np * (Np - 1) / (N*(N - 1))) is the unbiased version of Simpson diversity, with Np the number of individuals of species p in the sample and N = sum(Np).
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).
The theoretical values of gr(r) and Kr(r) under the null hypothesis of random labelling is 1 for all r. Local Monte Carlo confidence limits and p-values of departure from this hypothesis are estimated at each distance r by reallocating at random the species labels among points of the pattern, keeping the point locations unchanged.
A list of class "fads"
with essentially the following components:
r |
a vector of regularly spaced out distances ( |
gs |
a data frame containing values of the function gs(r). |
ks |
a data frame containing values of the function Ks(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 random labelling, i.e. 1 for all r. |
sup |
(optional) if |
inf |
(optional) if |
pval |
(optional) if |
There are printing and plotting methods for "fads"
objects.
Shimatani K. 2001. Multivariate point processes and spatial variation in species diversity. Forest Ecology and Management, 142:215-229.
Eckel, S., Fleisher, F., Grabarnik, P. and Schmidt V. 2008. An investigation of the spatial correlations for relative purchasing power in Baden-Wurttemberg. AstA - Advances in Statistical Analysis, 92:135-152.
Simpson, E.H. 1949. Measurement of diversity. Nature, 688:163.
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.
Ripley B.D. 1977. Modelling spatial patterns. Journal of the Royal Statistical Society B, 39:172-192.
plot.fads
,
spp
,
kfun
,
kpqfun
,
kp.fun
,
krfun
.
data(Paracou15) P15<-Paracou15 ## Not run: spatial point pattern in a rectangle sampling window of size 125 x 125 swmr <- spp(P15$trees, win = c(125, 125, 250, 250), marks = P15$species) kswmr <- ksfun(swmr, 50, 5, 500) plot(kswmr) ## 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) kswmc <- ksfun(swmc, 50, 5, 500) plot(kswmc) ## 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) kswrt <- ksfun(swrt, 50, 5, 500) plot(kswrt)
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