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Adapted Pair Correlation Function

Source: R/apcf-package.R
apcf-package.Rd

A faster implementation of the Adapted Pair Correlation Function presented in Nuske et al. (2009) in C++ using the library GEOS directly instead of through PostGIS.

Details

The Adapted Pair Correlation Function transfers the concept of the Pair Correlation Function from point patterns to patterns of objects of finite size and irregular shape (eg. lakes within a country). The main tasks are (i) the construction of null models by rondomizing the objects of the original pattern within the study area, (ii) the edge correction by determining the proportion of a buffer within the study area, and (iii) the calculation of the shortest distances between the objects.

This package mainly provides three functions:

  • pat2dists() creates null models and calculates distances and ratios,

  • dists2pcf() turns distances and ratios into an edge corrected PCF, and

  • plot() plots Pair Correlation Functions.

Pattern to Distances & Ratios

The task consists of two parts: creating null models / permutations and calculating distances between all objects of a pattern and determining the fraction of the perimeter a buffer inside the study area. Permutations of the original pattern are achieved by randomly rotating and randomly placing all objects within the study area without overlap.

The resulting collection of distances and ratios of each null model and the original pattern are returned as an object of class dists (a data.frame with some additional attributes).

The library GEOS (>= 3.4.0) is used for the geometrical analysis of the pattern. Geodata are converted to GEOS Geometries. The GEOS functions are called from C++ Functions which are integrated into R via Rcpp and wrapped in the R function pat2dists().

Create an edge corrected PCF

The dists objects are turned into fv_pcf objects by the function dists2pcf(). A C++ function finds all distances and ratios belonging to a null model or the original pattern (marked with index 0) and calculates a density function using the Epanechnikov kernel and Ripley's edge correction. Resulting in as many PCFs as null models were created plus a PCF for the original pattern. From the PCF of the null models a pointwise critical envelope is derived. The arithmetic mean of all PCF of the null models is employed for a bias correction of the empirical PCF and the upper and lower bound of the envelope.

Plot a PCF

plot.fv_pcf() is an S3 method of the plot function for the class fv_pcf. It provides a nice plot of the empirical PCF together with the pointwise critical envelope.

References

Nuske, R.S., Sprauer, S. and Saborowski, J. (2009): Adapting the pair-correlation function for analysing the spatial distribution of canopy gaps. Forest Ecology and Management, 259(1): 107–116. https://doi.org/10.1016/j.foreco.2009.09.050

See also

Useful links:

Author

Maintainer: Robert Nuske robert.nuske@mailbox.org (ORCID)