R/01_npr.R

In mcsiple/mmrefpoints: Project Marine Mammal Populations and Calculate Reference Points

#' Calculate numbers per recruit
#'
#' @description Calculate numbers-per-recruit as a function of the bycatch rate assuming that 1+ animals are subject to bycatch  \emph{E}.
#'
#' @param S0 Calf/pup survival, a numeric value between 0 and 1
#' @param S1plus Adult survival, a numeric value between 0 and 1
#' @param nages Plus group age in years
#' @param AgeMat Age at maturity in years (must be equal to or less than nages)
#' @param E Bycatch mortality rate, a numeric value between 0 and 1
#'
#' @return A list of numbers per recruit (\code{npr}), 1+ numbers per recruit (\code{P1r}), and numbers at age per recruit (\code{nvec})
#'
#' @examples
#' (unpr <- npr(S0 = 0.9, S1plus = 0.9, 
#' AgeMat = 11, nages = 13, E = 0)) # unfished nums per recruit
#' (nprf <- npr(S0 = 0.9, S1plus = 0.9, 
#' AgeMat = 11, nages = 13, E = 0.8)) # nums per recruit at bycatch rate E
#' @export
npr <- function(S0, S1plus, nages, AgeMat, E = 0) {
  if(AgeMat > nages){warning("Age at maturity cannot be larger than plus group age. Change AgeMat or nages.")}
  if(S0 < 0 | S0 >= 1){stop("Calf/pup survival must be between 0 and 1.")}
  if(S1plus < 0 | S1plus >= 1){stop("Adult survival must be between 0 and 1.")}
  
  AgePart <- AgeMat + 1 # Age at first parturition

  N.vec <- vector(length = nages + 1) # Ages 0 thru nages --> vector 1:(nages+1)
  N.vec[1] <- 1 # Age 0
  N.vec[2] <- 1 * S0

  # Survival (due to natural and bycatch causes)
  OnePlusSurv <- (S1plus * (1 - E))

  # Calculate numbers-at-age
  for (a in 3:(nages)) {
    N.vec[a] <- S0 * (OnePlusSurv^(a - 2))
  }

  N.vec[nages + 1] <- (S0 * OnePlusSurv^(nages - 1)) / (1 - OnePlusSurv) # plus group age
  npr <- sum(N.vec[(AgePart + 1):(nages + 1)]) # *Reproducing* animals (AgeMat+1 = age at first parturition)
  P1r <- sum(N.vec[2:(nages + 1)]) # 1+ whales/pinnipeds
  Outs <- list()
  Outs$npr <- npr
  Outs$P1r <- P1r
  Outs$nvec <- N.vec
  return(Outs)
}