# Multiscale second-order neighbourhood analysis of a spatial phylogenetic or functional community pattern from fully mapped data 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). latin1 ```r 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 $\alpha = 0.01$. ## 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 $1$. ## Returns 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. ## 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. ## Author(s) Raphael.Pelissier@ird.fr ## Note There are printing and plotting methods for `"fads"` objects. ## See Also `plot.fads`, `spp`, `ksfun`, `krfun`, `divc`. ## Examples ```r 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) ```

kdfun function