setwd("~/Desktop/gitTest/erp_mac/rmd")

Introduction

The Operating Model is based on the ICES stock assessment, where natural mortality is split into predation (M2) and background (M1) mortality, based on hypotheses from the Ecosystem Models. The assessment is then refitted, and a stock recruitment relationship estimated using priors from FishLife (Thorson et al. 2017).

A Reference Case Operating Model is conditioned first, then to evaluate robustness a range of plausible scenarios are used to condition a Robustness Set. These are a limited set of scenarios which are likely to to have major impacts on the performance of the management strategies.

All coding is done using R (R Core Team 2021) and FLR (Kell et al. 2007) in Rmarkdown (Xie, Allaire, and Grolemund 2018), and summarised in as vignettes. The information (data, files, etc.) required to re-do the analysis, is available at ???, including the ICES assessment data set, and the inputs and outputs from the ecosystem models.

Code for cleaning the input data, and R libraries used for the analysis, are contained in the ‘Rmd’ files such as this one. Only Key steps in the analysis are shown in the documents generated, code used for plotting are not echoed in the output but can be found in the ‘Rmd’ file.

This vignette is divided into sections for Installation of the required libraries, sourcing bespoke functions, and loading the data, before the Operating Condition is conducted. Hypotheses about Natural Mortality and Stock Rcruitment are then fitted.

Details on Funding, Software Versions andReferences can be found at the end of the document.

Installation

Libraries (i.e. packages) can be installed from gihtub using the remotes package:

install.packages("remotes")

library(remotes)

install.packages("ggplot2")
install.packages("plyr")
install.packages("dplyr")
install.packages("reshape")

remotes::install_github("flr/FLCore")
remotes::install_github("flr/ggplotFL")
remotes::install_github("flr/FLBRP")
remotes::install_github("flr/FLasher")
remotes::install_github("flr/FLAssess")
remotes::install_github("flr/FLife")
remotes::install_github("flr/mydas")
remotes::install_github("flr/FLCandy")

remotes::install_github("flr/FLSRTMB")

install.packages("patchwork")

remotes::install_github("james-thorson/FishLife")

remotes::install_github('fishfollower/SAM/stockassessment', ref='components')
remotes::install_github("flr/FLfse/FLfse")
library(FLCore) 
library(ggplotFL)
library(FLBRP)
library(FLasher)
library(FLAssess)

library(plyr)
library(dplyr)
library(reshape)

library(FLife)
library(FLBRP)
library(FLCandy)

library(FLSRTMB)
library(patchwork)

library(stockassessment)
library(FLfse)

library(FishLife)

theme_set(theme_bw(16))

Data

The data are the ICES inputs and historical estimates (ICES 2023) generated by “10_ICES” which runs the ICES assessment

load("../data/om/icesAssessment.RData")

Bespoke functions

Functions are used to run key parts of the analysis, this makes it easier to document and debug code, and replicate key steps. The ICES assessment is run uisng the function ‘runSam’, this means that the assessment can be redone in a comparable way when new data become available or based on alternative hypotheses, and steps are documented.

source("../source/runSam.R")

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Natural Mortality

In the ICES assessment natural mortality (\(M\)) is assumed to be 0.15 for a ll ages in all year. However, mass-at-age of mackerel has varied over time.

Figure1 Predation mortality (M2) estimates for Mackerel from ecosystem models of the Northern Barents Sea (NorBar), West Coast of Scotand (WCofS) and North Sea. The dashed horizontal line at M=0.15 represents the assumed M in the ICES stock assessment for North Atlantic mackerel.”}

Natural mortality (M) has been shown to be a function of size-at-age (Lorenzen 2022), e.g. \(M=aW^b\),

In this study \(a\) was chosen so that M at age-at-maturity (\(A_{50}\)) is a given value (e.g. 0.15) then M1 (0.025) is subtracted to derive M2. Based on the stock weights-at-age M-at-age was then re-estimated

ddM<-function(wt,par){ 
  par["m1"]%*%(wt%^%par["m2"])}

M1Fn=function(x,y=0.025) FLQuant(y,dimnames=dimnames(m(x))) 
M2Fn=function(x) m(x) - M1Fn(x)

par=FLPar(m1=c(0.15/(0.300^-0.288)),
          m2= -0.288)

Assume that M is a function of mass-at-age and has varied over time, and model M-at-age in the ICES assessment as a function of mass-at-age, there are no values for th 0-group in the stock so replace with the catch values.

load("../data/om/icesAssessment.RData")

om=ices 

stock.wt(om)["0"]=catch.wt(om)["0"]

m(om)=ddM(stock.wt(om),par)

Figure2 Time series of mass-at-age.

Figure3 Time series of natural mortality at age.

Check the relationship between mass and M-at-age

Figure4 Plot of mass verse M.

Figure5 Time series of natural mortality at age based on Norwegian and Barents Seas predation mortalities.

Change M

Change M and then rerun the assessment the ICES catch numbers-at-age (using ‘runSam()’) to re-estimate numbers and fishing mortality-at-age.

There are four scenarios, the ICES assessment (M=0.15), the case where M is a function of mass-at0age (Reference), and two sensitivity tests where M varied based on the Barents Sea data (Environmental Driver) and where M was increased (High M).

m=t(m(om)[drop=T])
m=rbind(m,m[rep(41,2),])

cat(c("Natural Mortality", 
      "1 5",
      "1980 2022",
      "0 12", 
      "1"), sep="\n",file="../data/inputs/ices/nm-1.dat")
write(t(m),file="../data/inputs/ices/nm-1.dat",ncol=13,append=T)

m=t(m(oms[["Environmental\nDriver"]])[drop=T])
m=rbind(m,m[rep(41,2),])

cat(c("Natural Mortality",
      "1 5",
      "1980 2022",
      "0 12", 
      "1"), sep="\n",file="../data/inputs/ices/nm-2.dat")
write(t(m),file="../data/inputs/ices/nm-2.dat",ncol=13,append=T)

m=t(m(om)[drop=T])
m=rbind(m,m[rep(41,2),])*1.25

cat(c("Natural Mortality",
      "1 5",
      "1980 2022",
      "0 12", 
      "1"), sep="\n",file="../data/inputs/ices/nm-3.dat")
write(t(m),file="../data/inputs/ices/nm-3.dat",ncol=13,append=T)
res=list("M=0.15"               =runSam("nm"  ,dir="../data/inputs/ices"),
         "Reference"            =runSam("nm-1",dir="../data/inputs/ices"),
         "Environmental\nDriver"=runSam("nm-2",dir="../data/inputs/ices"),
         "High M"               =runSam("nm-3",dir="../data/inputs/ices")) 

## function returns both assessment outputs and an FLStock object
## FLStock object is used for running the MSE
oms =FLStocks(llply(res, function(x) x[[1]]))
sams=llply(res, function(x) x[[2]])

save(oms, file="../data/om/oms.RData")  
save(sams,file="../data/om/sams.RData")

Figure6 SAMs

Stock recruitment relationship

  • Prior for steepness
  • Steepness = 0.9, i.e. recruitment environmentally driven
  • Depensation

Prior for steepness

     [,1]           [,2]         
[1,] "K"            "M"          
[2,] "Winfinity"    "Loo"        
[3,] "tmax"         "tm"         
[4,] "Lm"           "Temperature"
[5,] "ln_margsd"    "rho"        
[6,] "logitbound_h" "ln_r"

Figure 7 Priors from FishBase

  0:     34.465065:  15.3876 -0.916291 0.218005
  1:     31.658899:  15.4851 -0.834069 0.244373
  2:     29.992221:  15.5759 -0.758716 0.189164
  3:     25.862006:  15.6747 -0.681923 0.225442
  4:     25.627391:  15.7335 -0.660245 0.214782
  5:     25.483474:  15.7529 -0.720645 0.218443
  6:     25.481076:  15.7467 -0.719491 0.217788
  7:     25.478268:  15.7466 -0.713176 0.218493
  8:     25.478189:  15.7476 -0.711280 0.217747
  9:     25.477559:  15.7467 -0.710682 0.218134
 10:     25.477546:  15.7456 -0.711104 0.218119
 11:     25.477541:  15.7459 -0.710707 0.218129
 12:     25.477540:  15.7460 -0.710829 0.218136
 13:     25.477540:  15.7460 -0.710882 0.218133
 14:     25.477540:  15.7460 -0.710877 0.218133

Figure 8 Stock recruitment relationship fits

Figure 9 Recruitment residuals, with regimes indicated by box.

Based on the residuals increase the expected recruitment

source("../source/eqFn.R")

eqs=eqFn(oms[["Reference"]],s=hpar[1,1],sd=hpar[1,2])
  0:     40.286159:  15.5488 -0.916291 0.218005
  1:     36.839968:  15.6328 -0.837746 0.247229
  2:     32.745959:  15.7110 -0.766192 0.194020
  3:     28.281545:  15.7979 -0.692163 0.226382
  4:     27.288552:  15.8984 -0.631085 0.210558
  5:     26.611207:  15.9991 -0.692100 0.224744
  6:     26.520052:  16.0219 -0.722870 0.214341
  7:     26.404487:  16.0315 -0.684425 0.216996
  8:     26.398284:  16.0316 -0.684468 0.218266
  9:     26.394886:  16.0364 -0.686127 0.217724
 10:     26.391516:  16.0407 -0.688826 0.218586
 11:     26.388264:  16.0509 -0.687452 0.218277
 12:     26.388165:  16.0512 -0.688848 0.218196
 13:     26.388156:  16.0518 -0.688648 0.218182
 14:     26.388156:  16.0517 -0.688670 0.218186
 15:     26.388156:  16.0517 -0.688669 0.218185

Figure 10 M-at-age 4

Figure 11 Stock Recruitment Relationship

Equilibrium relationships and reference points

Initial Conditions

Hindcast Projections

Figure 12 Simulations

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Software Version

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Funding

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References

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ICES. 2023. “Mackerel (Scomber scombrus) in subareas 1–8 and 14, and in Division 9.a (Northeast Atlantic and adjacent waters),” September. https://doi.org/10.17895/ices.advice.21856533.v1.
Kell, L.T., I. Mosqueira, P. Grosjean, J.M. Fromentin, D. Garcia, R. Hillary, E. Jardim, et al. 2007. “FLR: An Open-Source Framework for the Evaluation and Development of Management Strategies.” ICES J. Mar. Sci. 64 (4): 640.
Lorenzen, Kai. 2022. “Size-and Age-Dependent Natural Mortality in Fish Populations: Biology, Models, Implications, and a Generalized Length-Inverse Mortality Paradigm.” Fisheries Research 255: 106454.
R Core Team. 2021. R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing. https://www.R-project.org/.
Thorson, James T, Stephan B Munch, Jason M Cope, and Jin Gao. 2017. “Predicting Life History Parameters for All Fishes Worldwide.” Ecological Applications 27 (8): 2262–76.
Xie, Yihui, J. J. Allaire, and Garrett Grolemund. 2018. R Markdown: The Definitive Guide. Boca Raton, Florida: Chapman; Hall/CRC. https://bookdown.org/yihui/rmarkdown.