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

.

1 2 3 4 5 6 7 8 |

`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. |

The values of `par`

must be given in the argument `kerpar`

of `pairwise`

, they are shown here as examples.

`smark`

in `par`

indicates the location of the plant size variable in `marks`

. It can be a data frame column number, or a string id like "dbh".

Competition kernels seem to be limited only by the researchers imagination.
`powers.ker`

is a general form that includes many examples from the literature. If *Si* is the size of the subject plant, *Sj* the size of the competitor, and *R* is the distance between them, this kernel is *(Sj^pj / Si^pi) / R^pr*. 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.

`staebler.ker`

is the width of the overlap of zones of influence (ZOI), used by Staebler in 1951. Assumes that the ZOI radius is related to size *S* by *k S^p + c*.

`spurr.ker`

is an example of an index that depends on distance ranks: equations (9.5a), (9.5b) of Burkhart and Tomé (2012).

Vector of length equal to the length of `dists`

.

Oscar García.

http://forestgrowth.unbc.ca/siplab

Burkhart, H. E. and Tomé, M. (2012) *Modeling Forest Trees and Stands*. Springer.

García, O. “Siplab, a spatial individual-based plant modelling system”. Computational Ecology and Software 4(4), 215-222. 2014.

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