R/calcPrjMMB.R

In wStockhausen/rPIBKC: Package to run the PIBKC stock assessment

#'
#'@title Calculate projected MMMB at mating based on a fishing mortality rate.
#'
#'@description Function to calculate projected MMMB at mating based on a fishing mortality rate.
#'
#'@details MMB-at-mating is projected from survey MMB for a given directed fishing mortality using:
#'\enumerate{
#'  \item \eqn{MMB_f = MMB_s \cdot exp(-M \cdot t_{sf})}
#'  \item \eqn{M_r = MMB_f \cdot (1-exp(-F))}
#'  \item \eqn{M_d = \theta \cdot MMB_f}
#'  \item \eqn{MMB_m = [MMB_f - (M_r + M_d)] \cdot exp(-M \cdot t_{fm}) + R} 
#'}
#'where \eqn{MMB_s} is MMB at the time of the survey, \emph{M} is the rate of natural mortality, \eqn{t_{sf}}
#'is the time (as a fraction of the year) between the survey and fishery, \eqn{MMB_f} is MMB just before 
#'the fishery, \emph{F} is the retained mortality rate in the directed fishery, \eqn{M_r} is retained catch mortality,
#'\eqn{\theta} is the fraction of \eqn{MMB_f} killed as discards, \eqn{M_d} is discard catch mortality,
#'\eqn{t_{fm}} is the time (as fraction of the year) between the fishery and mating, and \eqn{R} is the assumed 
#'recruitment to the mature male component of the stock at mating.
#'
#'@param mmbSrvCurr - current MMB at time of survey
#'@param Fm         - assumed fishing mortality rate
#'@param theta      - \eqn{\theta}, the average ratio of mature male discard mortality to MMB at fishing
#'@param M    - assumed rate of natural mortality
#'@param t.sf - time from survey to fishery
#'@param t.fm - time from fishery to mating
#'@param rec  - assumed recruitment to MMB at mating (0 for PIBKC assessment)
#'@param verbose - flag (T/F) to print intermediate output
#'
#'@return list with elements:
#'\itemize{
#'  \item mmb  = \eqn{MMB_m} (t), MMB at time of mating (includes recruitment)
#'  \item retM = retained mortality (t)
#'  \item dscM = discard mortality on MMB (t) (**NOT** total discard mortality)
#'  \item mmbBF = projected MMB just before the fishery (t)
#'  \item mmbAF = projected MMB just after the fishery (t)
#'  \item mmbBM = projected MMB just before mating (t)
#'  \item rec = assumed recruitment to MMB at mating (t)
#'}
#'
#'@export
#'
calcPrjMMB<-function(mmbSrvCurr,
                     Fm,
                     theta,
                     M=0.18,
                     t.sf=3/12,
                     t.fm=4/12,
                     rec=0,
                     verbose=FALSE){
#NOTE: these calcs assume fishery occurs before mating/recruitment!!
    #projected MMB just before fishery
    mmbBF<-mmbSrvCurr*exp(-M*t.sf);

    #projected retained catch
    prjRet<-(1-exp(-Fm))*mmbBF;

    #projected discard mortality on MMB
    prjDsc<-theta*mmbBF;
    
    #projected MMB just after fishery
    mmbAF = mmbBF - (prjRet + prjDsc);
    
    #projected MMB just before mating
    mmbBM = mmbAF*exp(-M*t.fm);
    
    #projected MMB just after mating
    mmbAM<-mmbBM + rec;

    return(list(mmb=mmbAM,retM=prjRet,dscM=prjDsc,
                mmbBF=mmbBF,mmbAF=mmbAF,mmbBM=mmbBM,rec=rec));
}