#' Equation 13: Pairing in sink (k) habitat of good-good pairs (P.kgg)
#'
#'
#'
#' @param W2 population vector
#' @param K.bc Carrying capacity during breeding season in source habitat
#' @param K.bk Carrying capacity during breeding season in sink habitat
#' @param B.mk Males (m) allocated to sink (k)
#' @param B.fk Females allocated to sink
#' @param ... Additional parameters
#'
#' @references Runge, MC and PP Marra. 2004. Modeling seasonal interactions in the population dynamics of migratory birds. In Greenberg, R and PP Marra, eds. Birds of two worlds. Johns Hopkins University Press, Baltimore.
#'
#' @examples
#' #Trivial example
#' W2. <- c(10,10,10,10)
#' names(W2.) <- c("mg","fg","mp","fp")
#' eq13_Pkgg(W2 = W2., K.bc = 0, K.bk = 10, B.mk = 5, B.fk =5)
#'
#'
#'
#' @return P.kgg Proportion of pairs in sink (k) habitat where both male and female originated from good winter habitat (gg)
#'
#' @export
eq13_Pkgg <- function(W2,
K.bc,
K.bk,
B.mk,
B.fk,
...){
#condition 3: if other conditions fails
num <- (min(W2["mg"], W2["fg"]) - K.bc)
denom <- min(B.mk, B.fk)
P.kgg <- num/denom
# Condition 1
if(W2["mg"] >= (K.bc+K.bk)){
if(W2["fg"] >= (K.bc+K.bk)){
P.kgg <- 1}
}
# Condition 2
## 2a
if(W2["mg"] <= K.bc){
P.kgg<-0}
## 2b
if(W2["fg"] <= K.bc) {
P.kgg<-0}
## error check
if(P.kgg > 1| P.kgg < 0){
warning("Equation produces invalied value")
}
return(P.kgg)
}
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