jabbamodel / jabba-select

Repository for JABBA-Select

JABBA-SELECT:Incorporating life history and fisheries’ selectivity into surplus production models

Henning Winker, Felipe Carvalho, James T. Thorson, Laurence T. Kell, Denham Parker, Maia Kapur, Rishi Sharma, Anthony J. Booth, Sven E. Kerwath.

The materials in this repository present the JABBA-Select stock assessment model (Winker et al. 2020). JABBA-Select textends the Bayesian state-space surplus production model JABBA (Winker et al. 2018) to account for selectivity-induced distortion of abundance indices and impacts on stock productivity. Like JABBA, JABBA-Select is implemented in JAGS, called from the statistical programming environment R. JABBA-Select retains the core features of a basic JABBA modelling framework (Winker et al., 2018), including its modular coding structure, a suite of options to fix or estimate process and observation variance components and inbuilt graphics to illustrate model fit diagnostics and stock status results.

Central to our approach is the integration of prior information from spawning biomass- and yield-per-recruit models with integrated Beverton-Holt spawner recruitment relationship (BH-SRR) into JABBA-Select, which we subsequently refer to as age-structured equilibrium model (ASEM).To directly link the generalized three parameter SPM by Pella and Tomlinson (1969) to the ASEM, we assume that surplus production is a function of spawning biomass and then express surplus production as a function of our formulation of H_MSY instead of the intrinsic rate of population increase, so that:

(Equation 1)

where SB₀ is the unfished biomass and m is a shape parameter that determines at which SB/SB₀ ratio maximum surplus production is attained. The functional links between the ASEM and Pella-Tomlinson SPM are illustrated in Fig. 1, which provides a means to translate typical input parameters of age-structured models into the key SPM parameters r and m.

Fig. 1. Schematic of functional relationships between the productivity parameter r and the shape parameter of the surplus production function and the Age-Structured Equilibrium Model (ASEM; i.e. yield- and spawning biomass-per-recruit models with integrated spawner recruitment relationship). Numbers in boxes denote the sequence of deriving deviates of r and m from life history and selectivity parameter inputs into the ASEM.

JABBA-Select has four novel elements compared to conventional Surplus Production Models:

1. The model uses the expression of harvest rate at MSY (H_MSY), which we define here as H_MSY = MSY /SB_MSY , as a reparameterization for the intrinsic rate of population increase r, and derives the shape parameter m of the surplus production curve as a function of SBMSY/SB0. This provides a means to generate prior distributions of likely values of H_MSY and m from the ASEM using life history parameters and fishery-selectivity inputs (Fig. 2a)
2. The parameter H_MSYs is specific to fishing operations that fish with selectivity function s and nd is used to estimate the mean annual sustainable harvest rate to account for selectivity-induced changes of the stock’s surplus production (Fig. 2b).
3. The model separates between exploitable biomass EB_s and spawning biomass SB; the former is used to fit indices given selectivity s, and the latter to predict surplus production. The parameters used to describe the ratio of EB_s,y and SB_y, as a function of spawning biomass depletion relative to average unfished levels are inferred from the ASEM (Fig. 2c)
4. The model accounts for the underlying correlation structure between generated values H_MSY and m through the formulation of a multivariate normal (MVN) prior, which allows for estimating both parameters jointly within the model (Fig. 2d).

Fig. 2. Illustration of the four novel elements of JABBA-Select based on the stock parameters for silver kob: (a) Comparison of the functional forms of the yield curves produced from the Age-Structured Equilibrium Model (ASEM) with the approximation by the JABBA-Select surplus production function (Eq. 1) as function spawning biomass depletion SB / SB₀, using the life history parameter input values and a range of length-at-50%-selectivity values; (b) JABBA-Select model estimates of time-varying varying average annual H_MSYy. The dashed line denotes an increase in minimum size limit; (c) ASEM-derived selectivity-dependent distortion in the exploitable biomass (EB) relative to the spawning biomass (SB) over a wide a range of SB₀ iterations, with the dashed line denoting the increase in minimum size limit for line-caught silver kob and the remainder of variations attributed to variations in the relative catch contribution the of inshore trawl; and (d) Multivariate normal (MVN) approximation of log⁡(H_MSYf,s,k and log(m_f,s,k) random deviates generated from the ASEM via Monte-Carlo simulations .

JABBA-Select is able to accommodate multiple catch time series, changes in selectivity within each fishery (e.g. due to gear regulations), and can be simultaneously fitted to multiple abundance indices with varying selectivity. JABBA-Select reduces to a conventional Pella-Tomlinson model (JABBA-PTM) if SB = EB and then estimates a single HMSY independent of selectivity. This JABBA-PTM can be evoked via an implemented “user option” that sets all selectivity functions associated with the catch time series and abundance indices equal to the asymptotic maturity curve parameterization.

JABBA-Select Basic User Guide

Written by Henning Winker
[email protected]

Getting started

A JABBA-Select model is designed to be set up in a R 'Prime' file, from which the JABBA-Select source code JABBA_SELECTv1.1.R via the source() function.

This tutorial explains the main segments of the Prime file setup using the simulation example for South African silver kob JABBA_SELECT_prime_KOBsim.R presented in Winker et al. (2020).

JABBA-Select requires the installation of R and JAGS and the following R packages that are installed within R if not available already.

##><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>
## Prime File for KOBsim JABBA-SELECT example
## written by Henning Winker - Cape Town
## [email protected]
##><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>

# Delete all objects
rm(list=ls())
gc()
# Install required packages if missing
list.of.packages <- c("gplots", "coda","rjags","R2jags","fitdistrplus","reshape","mvtnorm","scales")
new.packages <- list.of.packages[!(list.of.packages %in% installed.packages()[,"Package"])]
if(length(new.packages)) install.packages(new.packages)
# Load Packages
library(gplots);library(coda);library(rjags);library(R2jags);library("fitdistrplus");library(reshape);
library(mvtnorm);library(scales)

Simulation example of Silver Kob

The simulation example of Silver Kob is used to illustrate the basic steps of fitting a JABBA-Select model using the Prime file JABBA_SELECT_prime_KOBsim.R.

The population dynamics of silver kob are those assumed in Winker et al. (2020). The available data are catch and catch-per-unit effort (CPUE) time series over a period of 40 years. A simple logistic selectivity function is assumed, which is described by the lengths where 50% and 95% of fish are retained as catch. Length-at-50%-selectivity increased after year 25 to simulate an increase in minimum size limit regulations. Here, two CPUE indices are simulated, which are associated with different standard errors catchability q (different scale) to represent, for example, CPUE indices from two areas that are sampled with varying precision (Winker et al. 2020).

Input files

JABBA-Select requires four to five input comma-separated value files (.csv).
The four (or five) csv files are named such that the type classifier catch, cpue and se, selex and select is combined with the assessment name. In this example, we define assessment = "KOBSim", so that (i) catchKOBSim.csv, (ii) cpueKOBSim.csv, (iii) seKOBSim.csv, (iv) selexKOBSim.csv and (v) selectKOBSim.csv. All file must be located in the assessment folder, i.e. /KOBSim.

1. Catch

The catch.csv input file contains the time series of year and catch by weight, separated fisheries that operate with selectivity patterns. Missing catch years or catch values are not allowed. In this simple example of JABBA_SELECT_prime_KOBsim.R, fishing selectivity changed for the entire fleet between year 25 and 26.

In the more complex Atlantic Swordfish example SWOss3 the catches are separated into eleven fleets that are assumed to fish with different selectivity patterns (see below).

2. CPUE

JABBA-SELECT is formulated to accommodate abundance indices from multiple sources (i.e., fleets) in a single cpue.csv file, which contains all considered abundance indices. The first column of the cpue input is year, which must match the range of years provided in the catch.csv file. If a CPUE index is affected by a change selectivity, it has to be captured separately in two columns. In contrast to the catch.csv input, missing abundance index values are allowed, such that different abundance indices may correspond to smaller portions of the catch time series. Optionally, an additional se.csv input can be passed onto JABBA, containing standard error estimates associated with the abundance indices on a log scale. The se.csv input file is structurally identical to the cpue.csv input. Alternatively, this feature can be used to apply different weighting to individual abundance indices by assigning varying coefficients of variation (CV) to each time series. If such weighting is implemented, it is advised that the CV chosen for each indexed year approximates the observed standard error on the log scale, such that the data weights are congruent with expectations as to how well the model should fit these data (Winker et al. 2018).

3. Selectivity functions

JABBA-Select aims to account for the effects of different selectivity patterns on the stock's surplus production and arising distortions between spawning biomass (SB) and exploitable biomass (EB) when fitting the CPUE data. The selectivity functions under consideration are summarized in the selex .csv file. The JABBA SELEX function provides the option to specify a 2-parameter logistic as well as a 5-parameter piece-wise dome-shaped selectivity curve, with a logistic function for the ascending limb and the descending limb described by the mean and CV of a half-normal distribution (Huynh et al., 2018).


The KOBSim example only considers on the simple 2-parameter logistic function, which requires the lengths where 50% and 95% of fish are retained as catch. The early and recent selectivity functions are referenced a S1 and S2, respectively. The first column in the selex file lists the 5 parameters SL50, SL95 (ascending logistic), SL.desc (mean of double-normal), CV.desc (rate of descent) and min.desc. The next columns provide the parameter values. If the latter three parameters (SL.desc, CV.desc, min.desc) are left blank or provided as NA, the selex function automatically reduces to a logistic.

4. Assigning Selectivity to Catch and CPUE

JABBA-Select requires to assign a selection function to each Catch and CPUE time series provided in the form of columns in the catch and the cpue input files, respectively. The select input file is designed to facilitate this.

Column Fleet.ID specifies an index of unique numbers for each Catch and CPUE time series, where Catch series must be listed first, followed by CPUE indices. Column Fleet specifies the name labels for of each Catch and CPUE series corresponding column names chosen by the user in the catch and the cpue input files. The column Selectivity assigns the respective Fleet to a selectivity function provided in the selex file. In this example, the catches of fleet S1 and S2 are assigned to the first and second listed selectivity functions (S1 & S2) in in the selex by inputting 1 and 2, respectively. The CPUE indices (A1.S1, A1.S2, A2.S1, A2.S2) are then assigned in the same way. Column CPUE.units specify if CPUE is in weight = 1 or number = 0. Note that catch must be in weight. Column Catch specifies whether the time series represents catch, if TRUE, or cpue, if FALSE. Finally, column q assigns a estimable catchability coefficients each cpue index or 0 to catch.

#---------------------------------------------------------------------
# Set Working directory file where to store the results
#---------------------------------------------------------------------
File = "C:/Work/Research/GitHub/JABBA-SELECT/KOBsim_example"
# Set working directory for JABBA-Select R source code
JABBA.file = "C:/Work/Research/GitHub/JABBA-SELECT"
# JABBA-Select Version
version = "v1.1"
# Set Assessment file: assement folder within File that includes .csv input files
assessment = "KOBSim"

All input files have to be saved in a folder that is named after the assessment, here /KOBSim.

In the Prime file: File = requires the path where the assessment folder is located JABBA = requires the path where the JABBA model JABBA_SELECTv1.1.R is located version = determines the JABBA_SELECT version assessment = assignes the assessment folder name

#---------------------------------------------------------------------
# Set Working directory file where to store the results
#---------------------------------------------------------------------
File = "C:/Work/Research/GitHub/JABBA-SELECT/KOBsim_example"
# Set working directory for JABBA-Select R source code
JABBA.file = "C:/Work/Research/GitHub/JABBA-SELECT"
# JABBA-Select Version
version = "v1.1"
# Set Assessment file: assessment folder within File that includes .csv input files
assessment = "KOBSim"

Basic settings

JABBA-Select provides various Graphic, Output, Saving options that can be specified in the prime file. If not specified, JABBA will automatically use the default settings as specified on top of the JABBA-SELECTv1.1.R code.

#><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>
# Graphic, Output, Saving (.RData) settings 
#><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>
SELECT = TRUE
KOBE.plot = TRUE # Produces JABBA Kobe plot 
KOBE.type = c("ICCAT","IOTC")[2] # ICCAT uses 3 colors; IOTC 4 (incl. orange) 
Biplot= TRUE # Produces a "post-modern" biplot with buffer and target zones (Quinn & Collie 2005)
SP.plot = c("standard","phase")[2] # Produces standard or 'Kobe phase' SP plot  
save.trajectories =TRUE # saves posteriors of P=B/K, B/Bmsy and H/Hmsy as .RData object 
harvest.label = c("Hmsy","Fmsy")[2] # choose label preference H/Hmsy versus Fmsy
CPUE.plot= TRUE # Runs state-tool to produce "alligned" multi-CPUE plot  
meanCPUE = FALSE # Uses averaged CPUE from state-space tool instead of individual indices  
Projection = TRUE # Use Projections: requires to define TACs vectors 
save.projections = TRUE # saves projection posteriors as .RData object 
catch.metric = "(t)" # Define catch input metric e.g. (tons) "000 t" etc 
Reproduce.seed = FALSE # If FALSE a random seed assigned to each run, if TRUE set.seed(123)
runASEM=TRUE  
jabba2FRL = TRUE
# Save entire posterior as .RData object
save.all = FALSE # (if TRUE, a very large R object of entire posterior is saved)  
#><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>

Looping through scenarios

JABBA-Select makes it easy to run alternative scenarios in a loop. For this purpose, a unique name has to be assigned to each scenario. For example, a generic option to do this for 10 alternative scenarios is:

Scenarios = c(paste0("Scenario",1:10))

but individual names may be specified as well, e.g. Scenarios = c("Run_high_h","Run_medium_h","Run_low_h"). In this example the Prime file is set up to run the full SELECT model, followed by a reduced Pella-Tomlinson model, which does not account for selectivity by assuming that exploitable biomass equals spawning biomass (SB = EB).

Scenarios = c("SELECT","Pella")
s=1

for(s in 1:length(Scenarios)){
  Scenario = Scenarios[s] 
  if(s==2) SELECT = FALSE # Reduce JABBA-Select to a Bayesian Pella-Tomlinson

JABBA-Select automatically creates a folder for each scenario, including the Input and Output subfolders, where all default plots, .csv and .rdata files are saved automatically depending on the choices of Basic Settings (see above).

Read input data files

Here, the user can specify if the se file is available by setting `SE.I = TRUE'. We advice to always check if all csv files were correctly read-in.

  #--------------------------------------------------
  # Read csv files
  #--------------------------------------------------
  # Load assessment data
  catch = read.csv(paste0(File,"/",assessment,"/catch",assessment,".csv"))
  cpue = read.csv(paste0(File,"/",assessment,"/cpue",assessment,".csv"))#
  
  # Use SEs from csv file for abudance indices (TRUE/FALSE)
  SE.I = TRUE
  if(SE.I ==TRUE){
    se = read.csv(paste0(File,"/",assessment,"/se",assessment,".csv"))
  }
  names(cpue)
  names(catch)
  # Read select csv
  select = read.csv(paste0(File,"/",assessment,"/select",assessment,".csv"))
  
  # Read selex (selectivity) csv
  selex = read.csv(paste0(File,"/",assessment,"/selex",assessment,".csv"))
  

Biomass priors

JABBA-Select requires two priors relatated to Spawning Biomass (SB) levels. The first is a lognormal for the unfished SB₀, which should be typically specified as vaguely as possible around some most plausible "guess". To do this, we suggest a CV of 100%-200%. To minimize the influence of the choice and improve model performance, it adviced that the Posterior median should be always located to right of the highest density peak of the SB₀ prior distribution. A very small Prior-Posterior-Variance-Ratio (PPVR) is indicative for the estimate being minimally informed by the choice of prior.

The second is a prior to inform the the model about initial spawning biomass level at the start of the catch time series psi = SB_y=1/SB₀, which can be implemented as either lognormal psi.prior= c("lognormal","beta")[1] or beta psi.prior= c("lognormal","beta")[2] distribution by specifying the mean and CV of the respective distributions. Here we assumed that the inital SB at the start of the catch time series was varying around the unfished SB₀ by assuming a lognormal with a mean SB_y=1/SB₀ = 1 with a CV = 30% by setting mu.psi = 1; CV.psi = 0.3.

JABBA-Select provides imposes “soft” boundary penalty on SB if P_y = SB_y/SB₀, decreases below or is either equal to or greater than user-defined minimum and maximum values, respectively (default: min=0.02, max=1.3). The idea is that the likelihood is increasingly penalized the further that P_y diverges from the soft boundaries, thereby improving mixing behaviour of MCMC chains. These constraints can be manually relaxed by setting e.g. P_bound = c(0.0001,1.5) if the model runs sufficiently stable.

 #------------------------------------------------
  # mean and CV and sd for unfished biomass K (SB0)
  #------------------------------------------------
  mu.SB0 = 30000; CV.SB0 = 2; sd.SB0=sqrt(log(CV.SB0^2+1)) 
  SB0.pr = c(mu.SB0,sd.SB0)
    
  
  #-----------------------------------------------------------
  # mean and CV and sd for Initial depletion level P1= SB/SB0
  #-----------------------------------------------------------
  # Set the initial depletion prior SB/SB0 
  # To be converted into a lognormal prior (with upper bound at 1.1)
    
    psi.prior= c("lognormal","beta")[1]
    # specify as mean and CV 
    mu.psi = 1 
    CV.psi = 0.3 
  
 #--------------------------------------------
     
    # Soft Penalty to control lower and upper SB_t/SB0
    P_bound = c(0.0001,1.5) 

Life History Parameters

JABBA-Select requires basic life history parameters as input the [Age-Structured Equilibbrium Model (ASEM) function](link here), describing growth, weight-length, maturation, longevity, natural mortality and the spawning-recruitment relationship recruitment

    #---------------------------------------------------------------
    # STOCK PARAMETERS for prior generation Hmsy as a function of r
    #---------------------------------------------------------------
    # Age
    minage <- 0  																						
    maxage <- 20
    plusgroup = c(FALSE,TRUE)[1] 
    #Growth paramters (von Bertalnffy)
    Linf <- 1372
    kappa <- 0.115
    t0 <-  -0.815
    
    #Length-weight
    aW <- 0.000006 																						
    bW <- 3.07
    
    # Maturity 
    maturity = c(2.5,2.6,1) # knife edge age-3 # a single value is taken as age (knife-edge) 
    #c(Lm50,Lm95,0) # two values are taken as length-based: Lm50 and Lm95 
    
    # Natural mortality estimate (affects Hmsy)
    M = 0.18
    CV.M = 0.25 
    
    # steepness B&H SSR (effects Hmsy and determines SBmsy/SB0)
    h = 0.8
    CV.h = 0.15
    

Growth is described by the von Bertalnffy Growth Function (VBGF). The maximum age can be treated a plus group plusgroup = c(FALSE,TRUE)[2] or as de facto maximum age plusgroup = c(FALSE,TRUE)[1]. Maturity as logistic a logistic function that can be either specified by lengths where 50% (Lm50) and 95% (Lm95%) maturity is attained maturity = c(Lm50,Lm95,0) or the ages where 50% (Am50) and 95% (Am95%) maturity is attained maturity = c(Am50,Am95,1), which is selected by choosing 0 for length, and 1 for age as the third value when specifying maturity. Uncertainty can be admitted by specifying CVs for two key paramters natural mortality M (assumed to be age-independent) and the steepness parameter h of the Beverton and Holt Spawner-Recruitment Relationship.

The resulting relationships of length-at-age, weight-at-length, weight-at-age and maturity-at-length relative selectivity-at-length are shown in the StockFunctions_ plot that is saved in the Input folder.

In addition, JABBA-Select permits to specify growth and length-weight functions to be sex specific by adding nsexes = 2 (nsexes = 1 is default). This then requires specifying two values for each parameter: the first for females and the second for males (see our more complex worked example for North Atlantic swordfish SWOss3).

#---------------------------------------------------------------
# STOCK PARAMETERS for prior generation Hmsy as a fuction of r
#---------------------------------------------------------------
minage <- 0  																						
maxage <- 25
PlusGroup = TRUE
# Number of sexes order Female and Males (this model is sex-structured)
nsexes = 2
# VBGF parameters
Linf <- c(290.1,214.2)
kappa <- c(0.147,0.266)
t0 <- c(-1.163, -0.6)

If nsexes = 2, the maturity function and spawning biomass (SB) is specific to females.

Based on the Life History parameters and given uncertainty about M and h, JABBA-SELECT generates a Multivariate Normal (MVN) Prior for H_MSY and the shape m of the surplus production curve for selectivity function s.

Catchability, Observation Error and Process Error settings

Like JABBA, JABBA-SELECT allows the separation of the observation variance into three components: (1) the squared externally estimable observation error (SE), that is read-in via se csv file, (2) a fixed additional input variance denoted in the R code as fixed.obsE, and (3) estimable variance, which is invoked if sigma.est = TRUE, where the default prior option for assumes an uninformative inverse-gamma distribution with both gamma scaling parameters set to 0.001. This variance can be estimated individually for each abundance index i for groups of indices or as single quantity common to all indices. All three variance components are additive and can be switched on or off in any combination to provide flexible data-weighting options. Please also see section 2.3.2. Prior specification in Winker et al. (2018) for additional details.

The estimable observation variance σ_est, i² can be specified to be estimated: (1) for each CPUE index, (2) in groups or (3) as the same quantity for all indices. For (1), simply provide a vector of unique integer in order for each index, e.g. sets.var = select$q[select$CPUE]. For (2), set.var = can be specified by grouping similar indices, e.g. sets.var = c(1,1,2,2,3). For (3), simply provide the identifier 1 for all indices, e.g. sets.var = rep(1,ncol(cpue)-1). The exact same principles apply for changing the assigned q_i for index i. For example for option (1), one can simply specify sets.var = 1:length(select$q[select$CPUE]).

In this example index A1.S1 and A1.S2 are for example assumed to have a common q = 1, but different selectivity function due to the change in size limits, whereas A1.S1 and A2.S1, which were independently generated from e.g. two regions, are assigned common selectivity functions but different q's.

 #--------------------------------------------------------------
 # Determine estimation for catchability q and observation error 
 #--------------------------------------------------------------
    
    # Assign q to CPUE from select file
    sets.q = select$q[select$CPUE]
    if(SELECT==F) sets.q = 1:length(select$q[select$CPUE])
    
    # Assign additional observation variances to indices
    sets.var = select$q[select$CPUE] # assigns indices with same obervation variance 
    
    #To Estimate additional observation variance set sigma.est = TRUE
    sigma.est = c(TRUE,FALSE)[1]
    # As option for data-weighing
    # minimum additional observation error for each variance set (optional choose 1 value for both)
    fixed.obsE = 0.01

The process variation on log(SB) can be chosen to be estimable sigma.proc = TRUE or fixed sigma.proc = FALSE. If sigma.proc = TRUE, the user has the option to specify a prior for the estimable process variance as inverse-gamma distribution proc.type = c("igamma","lnorm")[1] (see Millar & Meyer 2000) or a process error prior (not variance) as lognormal distribution proc.type = c("igamma","lnorm")[1], which can be for example derived from simulation studies (Winker 2018). The default setting for inverse-gamma is an uninformative approximation of the Jeffrey's prior with pr.proc = c(0.001,0.001). It is probably more intuitive to formulate informative lognormal priors for the process error pr.proc = c(log(mu),CV), where range between 0.05 (long generation times) and 0.15 (short generation times) are thought to be within the expected ranges (see e.g. Winker 2018). A conservative starting value for an informative inverse-gamma prior would pr.proc = c(4,0.01) (c.f. Millar & Meyer 2000; (Winker et al. 2018)). The provided R code in this example Prime file includes some simple checks for approximating the mean and CV given the choice of scale and shape parameters pr.proc = c(shape,scale) for the inverse-gamma distribution.

If the choice is to fix the process error by setting sigma.proc = FALSE, the expected mean specified by e.g. sigma.proc = 0.1. Note that short and/or noisy CPUE time series may not permit to estimate the process error reliably due to lack of contrast and information in the data. In such cases, it is recommended to initially develop the JABBA-Select with fixed process error and possibly explore option to use prior once the model runs stable.

    #><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>>
    # Process Error
    #><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>>
    
    #------------------------------------------
    #Estimate set sigma.proc == True
    sigma.proc = TRUE
    proc.dev.all=1 # start process error in year 1
    #------------------------------------------
    if(sigma.proc == TRUE){
      proc.type = c("igamma","lnorm")[1] # choose 1: inverse-gamma or 2: lognormal
      
      if(proc.type=="lnorm"){
        pr.proc = c(log(0.08),0.2) # Option for lognormal process error
      }
      if(proc.type=="igamma"){
        #pr.proc = c(0.001,0.001) # Option for inverse-gamma prior
        #pr.proc = c(10,0.1)
        pr.proc = c(0.001,0.001)
        gamma.check = 1/rgamma(1000,pr.proc[1],pr.proc[2]) # Process error check
        # check mean process error + CV
        mu.proc = sqrt(mean(gamma.check)); CV.proc = sd(sqrt(gamma.check))/mean(sqrt(gamma.check))
        # check CV
        round(c(mu.proc,CV.proc),3)
        quantile(sqrt(gamma.check),c(0.1,0.9))
      }  
    }else{
      sigma.proc = 0.1 #IF Fixed (sigma.est = FALSE): typicallly 0.05-0.15 (see Ono et al. 2012)
      
    }

Biological Reference Points

By default the stock the stock status reference points are the harvest rate that is required to attain MSY, H_MSY and the corresponding spawning biomass at MSY, SB_MSY by using default SBmsy_SB0 = NULL.

In addition JABBA-Select provides the user option to specify a target SB/SB₀. In this example, we adopted SB₄₀40 = 0.4 × SB₀ and the corresponding H₄₀ as the target reference for SB, by setting SBmsy_SB0 = 0.4.

Projections under constant Total Allowable Catch (TAC)

JABBA-Select enables projections under a sequence of constant catch scenarios, where the weighted average of the annual sustainable harvest rate H_MSY,y (see Eq. 11 in Winker et al. (2020)) is determined by relative catch by fleet in the terminal year to account for selectivity induced changes of the stock’s surplus production during the projection phase. Note that projecting relative catch by fleet can be relatively easily customized by adding an additional year with values of to be projected catches by fleet to the catch input csv and another year with otherwise empty cells to the cpue and se input files.

JABBA-SELECT automatically compares the difference between the last assessment year and the quota implementation year imp.yr. The difference between these years is projected forward under the current catch. Alternative fixed catches can specified as TACs. In this, example, we project over a sequence from 50% to 120% of the current catch curC in steps of 10% increments. The TACsare implemented from from year 41 and the projection horizon is set to 10 years as pyrs = 10. The projected posteriors can be saved as _projections.Rdata object by setting save.projections = TRUE under the Basic settings section.

   #><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>>
   # Optional: Do TAC Projections
   #><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>>
    Projection = TRUE # Switch on by Projection = TRUE 
    
    # Check final year catch
    curC =  apply(catch[,-1],1,sum,na.rm=TRUE)[nrow(catch)]
    
    # Set range for alternative TAC projections
    TACs = ceiling(seq(0.5,1.2,0.1)*curC) #example
    
    # Set year of first TAC implementation
    imp.yr = 41
    
    # Set number of projections years
    pyrs = 10
    

MCMC setting and Model execution

  #><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>
  # Execute model and produce output
  #><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>><>
    # MCMC settings
    ni <- 14000 # Number of iterations
    nt <- 2 # Steps saved
    nb <- 4000 # Burn-in
    nc <- 3 # number of chains
    nsaved = (ni-nb)/nt*nc
    cat(paste0("\n","- Run Model","\n"))
    
    dir.create(paste0(File,"/",assessment),showWarnings = F)
    
    # RUN JABBA-SELECT
    source(paste0(JABBA.file,"/JABBA_SELECT",version,".r"))
 

Reference

Winker H., Carvalho F., Thorson J.T., Kell L.T., Parker D., Kapur M., Sharma R., Booth A.J., Kerwatha S.E. (2020) JABBA-Select: Incorporating life history and fisheries’ selectivity into surplus production models Fisheries Research *22: 105355

Winker, H., Carvalho, F., Kapur, M. (2018) JABBA: Just Another Bayesian Biomass Assessment. Fisheries Research 204: 275-288.