Age-Structured Length-Based Model

The LBSPR model described by Hordyk et al. (2015a, b), and tested in a MSE framework (Hordyk et al. 2015c), use a conventional age-structured equilibrium population model. An inherent assumption of this model structure is that selectivity is age-based not length-based.

Length-Structured Growth-Type-Group Model

Hordyk et al. (2016) describe a length-structured version of the LBSPR model that uses growth-type-groups (GTG) to account for size-based selectivity. The GTG-LBSPR model also has the ability to include variable M at size (by default M is assumed to be constant). The GTG-LBSPR model typically estimates a lower fishing mortality rate for a given size structure compared to the earlier age-structured model. This is because the age-structured model has a ‘regeneration assumption’, where, because of the age-based selectivity assumption, large individuals are expected even at high fishing mortality (large, young fish).

The default setting for the LBSPR package is to use the GTG-LBSPR model for all simulation and estimation. Control options in the simulation and estimation functions can be used to switch to the age-structured LBSPR model.

Only the life history parameters need to be specified for the estimation model. The exploitation parameters will be estimated.

First Steps

Installing the LBSPR Package

# install.packages("LBSPR")

## Load the Package

library(LBSPR)

#Setup the working directory

** You will need to create your workshop directory on your computer. Example of suggested directory name “C:/…User…/ICCAT_DL_WS/LBSPR”

datdir <- DataDir()
datdir <- "C:/Users/demersais/Dropbox/_ICCAT_Data_limited workshop/Scripts/LBSPR/Example data files"

The available example files can be printed out using list.files:

list.files(datdir, pattern=".csv")

## [1] "LFreq_MultiYr.csv"     "LFreq_MultiYrHead.csv" "LFreq_SingYr.csv"     
## [4] "LFreq_SingYrHead.csv"  "LRaw_MultiYr.csv"      "LRaw_MultiYrHead.csv" 
## [7] "LRaw_SingYr.csv"       "LRaw_SingYrHead.csv"

Creating a LB_pars object

A valid LB_pars object must be first created (see sections above):

MyPars <- new("LB_pars")

## A blank LB_pars object created

## Default values have been set for some parameters

MyPars@Species <- "Example"
MyPars@Linf <- 110       # Von Bertalanffy asymptotic length
MyPars@L50 <- 50          # Size at first maturity
MyPars@L95 <- 75          # Size at 95% of maturity
MyPars@MK <- 1.6          # Relationship between natural mortality "M" and individual growth coefficient "K"
MyPars@BinMax <- 127.5       # Máximum length bin which must be larger than Linf and the larger sampled individual
MyPars@BinMin <- 2.5        # Minimum length bin which must be smaller than the smaller sampled individual
MyPars@BinWidth <- 5      # Length bin width
MyPars@SPR <- 1            # Target SPR

Creating a LB_lengths object

Specifications of files containing length data:

** The length data can be either raw data, that is, individual length measurements, or length frequency data, where the first column of the data set must contain the mid-points of the length bins, and the remaining columns contain the counts for each length class.

** The data type (freq or raw) must be specified in the call to the new function.

** A LB_lengths object can be created by reading from a CSV file with the data to be used:

** See the different CSV files configurations contained in the workshop directory “…/ICCAT_DL_WS/Example data files”

–> A length frequency data set with multiple years:

Len1 <- new("LB_lengths", LB_pars=MyPars, file=paste0(datdir, "/LFreq_MultiYr.csv"), dataType="freq")

–> A length frequency data set with multiple years and a header row (identical to Len1 data, but with a header row):

Len2 <- new("LB_lengths", LB_pars=MyPars, file=paste0(datdir, "/LFreq_MultiYrHead.csv"), dataType="freq", header=TRUE)

–> A raw length data set with multiple years:

Len3 <- new("LB_lengths", LB_pars=MyPars, file=paste0(datdir, "/LRaw_MultiYr.csv"), dataType="raw")

–> A raw length data set with multiple years and a header row (identical to Len3 data, but with a header row):

Len4 <- new("LB_lengths", LB_pars=MyPars, file=paste0(datdir, "/LRaw_MultiYrHead.csv"), dataType="raw", header=TRUE)

** Notice that for raw length measurements you must specify the parameters for the length bins (maximum, minimum, and width of length classes) in the LB_pars object. If these are left blank, default values are used.

Plotting Length Data

The plotSize function can be used to plot the imported length data. This is usually a good idea to do before proceeding with fitting the model, to confirm that everything has been read in correctly:

plotSize(Len1)

plotSize(Len2)

plotSize(Len3)

plotSize(Len4)

Fit the Model

The LBSPR model is fitted using the LBSPRfit function:

myFit1 <- LBSPRfit(MyPars, Len1)
myFit2 <- LBSPRfit(MyPars, Len2)

Note that the Control argument can be used to modify the additional parameters or LBSPR model type (see description in the “Control” section below).

Examine and Plot Results

The LBSPR package uses a Kalman filter and the Rauch-Tung-Striebel smoother function (see FilterSmooth) to smooth out the multi-year estimates of SPR, F/M, and selectivity parameters.

The smoother parameter estimates can be accessed from the myFit object (which is an object of class LB_obj [see earlier section for details]):

myFit1@Ests

##       SL50  SL95   FM  SPR
## [1,] 50.16 65.12 0.98 0.36
## [2,] 50.16 65.15 0.98 0.36
## [3,] 50.13 65.02 0.98 0.37
## [4,] 50.13 65.02 0.98 0.37
## [5,] 50.04 64.81 0.98 0.37
## [6,] 49.85 64.59 0.96 0.37

myFit2@Ests

##       SL50  SL95   FM  SPR
## [1,] 52.97 70.02 1.26 0.33
## [2,] 52.91 69.90 1.26 0.33
## [3,] 52.74 69.72 1.24 0.33
## [4,] 52.86 70.18 1.25 0.33
## [5,] 52.90 70.30 1.25 0.33
## [6,] 52.91 70.15 1.24 0.33

Note that by default the smoothed estimates are used in the plotting routines.

The individual point estimates for each year can be accessed from the LB_obj object:

data.frame(rawSL50=myFit1@SL50, rawSL95=myFit1@SL95, rawFM=myFit1@FM, rawSPR=myFit1@SPR)

##   rawSL50 rawSL95 rawFM    rawSPR
## 1   50.68   65.46  1.01 0.3610884
## 2   50.41   66.78  0.99 0.3621779
## 3   49.85   63.72  0.98 0.3599764
## 4   51.01   67.12  0.92 0.3865039
## 5   51.05   64.84  1.22 0.3185321
## 6   47.97   62.45  0.76 0.4133589

The plotSize function can also be used to show the model fit to the data:

plotSize(myFit1)

plotSize(myFit2)

Similarly, the plotMat function can be used to show the specified maturity-at-length curve, and the estimated selectivity-at-length curve:

plotMat(myFit1)

plotMat(myFit2)

Finally, the plotEsts function can be used to visually display the estimated parameters. Note that this works for all data sets, but only makes sense when there are several years of data:

plotEsts(myFit1)

plotEsts(myFit2)

Obs. Estimates of SPR for any given year are independent of every other year because LBSPR is an equilibrium calculation. So it does not provide a time series of SPR, and the smoothing is not a time series, but an average response over the many years. An alternative treatment to the smoothing would be to combine length comps over years to get an average SPR over those multiple samples.

Comparing Observed Length Data to Target Size Structure

You can compare the observed size data against an expected size composition at a target SPR using the plotTarg function.

Here we have set the target SPR at 100%, by the function MyPars@SPR <- 1

But we can set SPR at 75% by setting MyPars@SPR <- 0.75

Then import your prefeered length data. Here we will use the Frequency type with multiple years.

LenDat <- new("LB_lengths", LB_pars=MyPars, file=paste0(datdir, "/LFreq_MultiYr.csv"), dataType="freq")

Finally, you must set the selectivity parameters for the simulated size data. You may be able to estimate these from the data:

Mod <- LBSPRfit(MyPars, LenDat)

## Fitting model

## Year:

## 1

## 2

## 3

## 4

## 5

## 6

yr <- 1 # first year of data

MyPars@SL50 <- Mod@SL50[yr] # Length at first selectivity estimated from the fitted model
MyPars@SL95 <- Mod@SL95[yr] # Length at 95% selectivity estimated from the fitted model


plotTarg(MyPars, LenDat, yr=yr)

yr <- 6 # last year of data

MyPars@SL50 <- Mod@SL50[yr] # Length at first selectivity estimated from the fitted model
MyPars@SL95 <- Mod@SL95[yr] # Length at 95% selectivity estimated from the fitted model


plotTarg(MyPars, LenDat, yr=yr)

MyPars@Linf <- 100 
MyPars@SL50 <- 50
MyPars@SL95 <- 55 
MyPars@FM <- numeric()
MyPars@SPR <- 0.4
MySim <- LBSPRsim(MyPars, Control=list(modtype="absel"))
MySim@FM

## [1] 0.95

MySim <- LBSPRsim(MyPars, Control=list(modtype="GTG"))
MySim@FM  # lower F/M for the GTG model

## [1] 0.95