## Multiscale second-order neighbourhood analysis of a multivariate spatial point pattern

### Description

(Formerly `ki.fun`) Computes a set of K12-functions between all possible marks p and the other marks in a multivariate spatial point pattern defined in a simple (rectangular or circular) or complex sampling window (see Details).

### Usage

```kp.fun(p, upto, by)
```

### Arguments

 `p ` a `"spp"` object defining a multivariate 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).

### Details

Function `kp.fun` is simply a wrapper to `k12fun`, which computes K12(r) between each mark p of the pattern and all other marks grouped together (the j points).

### Value

A list of class `"fads"` with essentially the following components:

 `r ` a vector of regularly spaced distances (`seq(by,upto,by)`). `labp ` a vector containing the levels i of `p\$marks`. `gp. ` a data frame containing values of the pair density function g12(r). `np. ` a data frame containing values of the local neighbour density function n12(r). `kp. ` a data frame containing values of the K12(r) function. `lp. ` a data frame containing values of the modified L12(r) function. ` ` 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 population independence (see `k12fun`).

### Note

There are printing and plotting methods for `"fads"` objects.

### Author(s)

Raphael.Pelissier@ird.fr

`plot.fads`, `spp`, `kfun`, `k12fun`, `kpqfun`.

### Examples

```  data(BPoirier)
BP <- BPoirier
## Not run: multivariate spatial point pattern in a rectangle sampling window
swrm <- spp(BP\$trees, win=BP\$rect, marks=BP\$species)
kp.swrm <- kp.fun(swrm, 25, 1)
plot(kp.swrm)

## Not run: multivariate spatial point pattern in a circle with radius 50 centred on (55,45)
swcm <- spp(BP\$trees, win=c(55,45,45), marks=BP\$species)
kp.swcm <- kp.fun(swcm, 25, 1)
plot(kp.swcm)

## Not run: multivariate spatial point pattern in a complex sampling window
swrtm <- spp(BP\$trees, win=BP\$rect, tri=BP\$tri2, marks=BP\$species)
kp.swrtm <- kp.fun(swrtm, 25, 1)
plot(kp.swrtm)
```