# o.ring

##### Inhomogeneous O-ring

Calculates the inhomogeneous O-ring point pattern statistic (Wiegand & Maloney 2004)

The function K(r) is the expected number of points in a circle of radius r centered at an arbitrary point (which is not counted), divided by the intensity l of the pattern. The alternative pair correlation function g(r), which arises if the circles of Ripley's K-function are replaced by rings, gives the expected number of points at distance r from an arbitrary point, divided by the intensity of the pattern. Of special interest is to determine whether a pattern is random, clumped, or regular.

Using rings instead of circles has the advantage that one can isolate specific distance classes, whereas the cumulative K-function confounds effects at larger distances with effects at shorter distances. Note that the K-function and the O-ring statistic respond to slightly different biological questions. The accumulative K-function can detect aggregation or dispersion up to a given distance r and is therefore appropriate if the process in question (e.g., the negative effect of competition) may work only up to a certain distance, whereas the O-ring statistic can detect aggregation or dispersion at a given distance r. The O-ring statistic has the additional advantage that it is a probability density function (or a conditioned probability spectrum) with the interpretation of a neighborhood density, which is more intuitive than an accumulative measure.

##### Usage

`o.ring(x, inhomogeneous = FALSE, ...)`

##### Arguments

- x
spatstat ppp object

- inhomogeneous
(FALSE/TRUE) Run homogeneous (pcf) or inhomogeneous (pcfinhom)

- ...
additional arguments passed to pcf or pcfinhom

##### Value

plot of o-ring and data.frame with plot labels and descriptions

##### References

Wiegand T., and K. A. Moloney (2004) Rings, circles and null-models for point pattern analysis in ecology. Oikos 104:209-229

##### Examples

```
# NOT RUN {
library(spatstat)
data(lansing)
x <- spatstat::unmark(split(lansing)$maple)
o.ring(x)
# }
```

*Documentation reproduced from package spatialEco, version 1.3-2, License: GPL-3*