siplab (version 1.6)

kernel: Competition Kernel Functions

Description

Functions representing the effect of a competitor on a subject plant, depending on distance and plant sizes (marks). For use in pairwise().

Note: In previous versions of siplab the function names had .ker in place of _ker.

Usage

powers_ker(imarks, jmarks, dists, dranks, par = list(pi=1, pj=1,
    pr=1, smark = 1))
staebler_ker(imarks, jmarks, dists, dranks, par = list(k=0.1, p=1,
    smark=1))
spurr_ker(imarks, jmarks, dists, dranks, par = list(type=1,
    smark=1))

Arguments

imarks

Marks for the subject plant, a 1-row data frame.

jmarks

Data frame with marks for competitors

dists

Vector of distances between the subject plant and the competitors.

dranks

Distance ranks.

par

List of parameters.

Value

Vector of length equal to the length of dists.

Details

The values of par are taken from the argument kerpar of pairwise(), if not NULL.

smark in par must be 1 or “mark” if there is only one mark. If the marks are a data frame, smark must be the number or name of the column with the plant size variable.

powers_ker() is a general form that includes many examples from the literature. If \(S_i\) is the size of the subject plant, \(S_j\) the size of the competitor, and \(R\) is the distance between them, then this kernel is \((S_j^{p_j} / S_i^{p_i}) / R^{p_r}\). For instance, the popular Hegyi's index corresponds to pi=1, pj=1, pr=1. This and other examples could be coded directly if computational efficiency is important, see the example below.

staebler_ker() is the width of the overlap of zones of influence (ZOI), used by Staebler in 1951. Assumes that the ZOI radius is \(k S^p\), where \(S\) is size.

spurr_ker() is an example of an index that depends on distance ranks: equations (9.5a), (9.5b) of Burkhart and Tom<U+00E9> (2012).

Competition kernels seem to be limited only by the researchers imagination. Others can be written following these examples.

References

https://github.com/ogarciav/siplab

Burkhart, H. E. and Tom<U+00E9>, M. (2012) Modeling Forest Trees and Stands. Springer.

Garc<U+00ED>a, O. “Siplab, a spatial individual-based plant modelling system”. Computational Ecology and Software 4(4), 215-222. 2014.

See Also

pairwise

Examples

# NOT RUN {
# Originally Hegyi added one foot to the distance:
hegyiorig_ker <- function(imarks, jmarks, dists, ...) {
# Assume coordinates in meters, and a single mark (dbh)
    (jmarks$mark / imarks$mark) / (dists + 0.30481)
}
# }