R/martinEk.R

In johngodlee/compInd: Forest tree-tree competition indices

#' Martin and Ek 1984
#' 
#' @param dbh vector of DBH (diameter at breast height) measurements of 
#'     competitor trees
#' @param dist vector of distances from focal tree to competitor trees
#' @param focal_dbh DBH of focal tree
#'
#' @return value of competition index for focal tree
#' 
#' @details Gives the sum of ratios of competitor to focal tree DBHs, multiplied 
#' by the exponential of distances divided by competitor DBH plus focal DBH. 
#' Given by the equation:
#' \deqn{\sum_{j\neq{}i}^{n} (d_{j} / d_{i}) exp((16l_{ij}) / (d_{i} + d_{j}))}
#' 
#' @references Martin G. L., Ek A. R. (1984). A Comparison of Competition 
#' Measures and Growth Models for Predicting Plantation Red Pine Diameter and 
#' Height Growth. Forest Science. Volume 30. Pages 731-743.
#' 
#' @examples 
#' data(bicuar)
#' nb <- nearNeighb(bicuar$x, bicuar$y, bicuar$stem_id, k = 4) 
#' lapply(nb, function(x) {
#'   nb <- merge(x, bicuar, by.x = "nb", by.y = "stem_id")
#'   focal_diam <- unique(bicuar[bicuar$stem_id == nb$focal,"diam"])
#'   martinEk(nb$diam, nb$nb_dist, focal_diam)
#'   })
#' 
#' @export
#'
martinEk <- function(dbh, dist, focal_dbh) {
	eq1 <- dbh / focal_dbh
	eq2 <- (16 * dist) / (dbh + focal_dbh)
	eq3 <- eq1 * exp(-eq2)
	sum(eq3)
}