List of distance-based competition indices

list of distance-based competition index functions for the use with compete_inv().

Usage

CI_Hegyi(target, neigh)

CI_Braathe(target, neigh)

CI_size(target, neigh)

CI_RK1(target, neigh)

CI_RK2(target, neigh)

CI_RK3(target, neigh)

CI_RK4(target, neigh)

Arguments

target: single row forest_inv class data.table object containing all the variables needed to calculate the corresponding competition index for the target tree (i.e. ´x´, ´y´, as well as ´dbh´, ´height´, ´size´ and/or other size-related attributes).
neigh: forest_inv class data.table object containing all the variables needed to calculate the corresponding competition index for all neighbor trees in the search radius of the target tree (i.e. ´x´, ´y´, as well as´dbh´, ´height´, ´size´ and/or other size-related attributes), that moreover includes their distance to the target tree in m (dist).

Value

A single numeric value (the competition index for the target tree).

Details

TreeCompR provides a number of distance-based competition indices for the use with compete_inv().

Available competition indices

The competition indices are computed according to the following equations, where $d_i$ and $h_i$ are the dbh and height of neighbor tree $i$, $d$ and $h$ are dbh and height of the target tree, and $dist_i$ is the distance from neighbor tree $i$ to the target tree.

Diameter-based competition indices

CI_Hegyi introduced by Hegyi (1974):
$CI_{Hegyi} = \sum_{i=1}^{n} d_{i} / (d \cdot dist_{i})$
CI_RK1 according to CI1 Rouvinen & Kuuluvainen (1997):
$CI_{RK1} = \sum_{i=1}^{n} \mathrm{arctan}(d_{i} / dist_{i})$
CI_RK2 according to CI3 in Rouvinen & Kuuluvainen (1997):
$CI_{RK2} =\sum_{i=1}^{n} (d_{i} / d) \cdot \mathrm{arctan}(d_{i} / dist_{i})$

Height-based competition indices

CI_Braathe according to Braathe (1980):
$CI_{Braathe} = \sum_{i=1}^{n} h_{i} / (h \cdot dist_{i})$
CI_RK3 according to CI5 in Rouvinen & Kuuluvainen (1997):
$CI_{RK3} = \sum_{i=1}^{n} \mathrm{arctan}(h_{i} / dist_{i})$ for all trees with $h_{i} > h$
CI_RK4 based on CI3 in Rouvinen & Kuuluvainen (1997) and Contreras et al. (2011):
$CI_{RK4} = \sum_{i=1}^{n} (h_{i} / h) \cdot \mathrm{arctan}(h_{i} / dist_{i})$

Generic size-based Hegyi-type competition index

CI_size based on Hegyi (1974), but with a user-specified size-related variable ($s_i$: size for neighbor tree $i$, $s$: size of the target tree): $$CI_{size} = \sum_{i=1}^{n} s_{i} / (s \cdot dist_{i})$

User-specified competition indices

The creation of new user-specified competition indices is easily possible, the only requirement is that they take two arguments, target (a single-row forest_inv class data.table with data for the target tree) and neigh (a multi-row forest_inv class data.table with data for the neighbor trees), and return a single numeric value. This function will then be called internally for each tree and its neighborhood inside compete_inv(). For example, a working implementation of the classical Hegyi index would look like this:

CI_Hegyi <- function(target, neigh) sum(neigh$dbh / (target$dbh * neigh$dist))

It is advisable to add checks to ensure the function does the right thing when it gets passed on empty datasets (e.g. because no trees are in the neighborhood of a tree) because sum(NULL) evaluates to 0 which may not always be intended.

Literature

Hegyi, F., 1974. A simulation model for managing jackpine stands. In: Fries, J. (Ed.), Proceedings of IUFRO meeting S4.01.04 on Growth models for tree and stand simulation, Royal College of Forestry, Stockholm.
Braathe, P., 1980. Height increment of young single trees in relation to height and distance of neighboring trees. Mitt. Forstl. VersAnst. 130, 43–48.
Rouvinen, S., Kuuluvainen, T., 1997. Structure and asymmetry of tree crowns in relation to local competition in a natural mature Scot pine forest. Can. J. For. Res. 27, 890–902.
Contreras, M.A., Affleck, D. & Chung, W., 2011. Evaluating tree competition indices as predictors of basal area increment in western Montana forests. Forest Ecology and Management, 262(11): 1939-1949.

Examples

if (FALSE) { # \dontrun{
  # read data from all trees in a plot
  data <- read_inv("path/to/data.csv")

  # compute the Hegyi for the first tree in the dataset, assuming that all
  # others were in its search radius
  CI_Hegyi(data[1,], data[-1, ])
} # }