ksfun {ads}  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 distancedependent measure of Simpson (1949) diversity can be estimated from Ripley (1977) Kfunction 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 Kfunctions 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 pvalues 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 
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, 142:215229.
Eckel, S., Fleisher, F., Grabarnik, P. and Schmidt V. 2008. An investigation of the spatial correlations for relative purchasing power in BadenWurttemberg. AstA  Advances in Statistical Analysis, 92:135152.
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 Kfunction. Journal of Vegetation Science, 10:433438.
Ripley B.D. 1977. Modelling spatial patterns. Journal of the Royal Statistical Society B, 39:172192.
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)