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Assessments of 48 simulated and 159 real stocks with a Monte Carlo
and Bayesian Implementation of a Surplus Production Model
Rainer Froese, Nazli Demirel, Gianpaolo Coro, Kristin M. Kleisner and Henning Winker
Corresponding Author: Rainer Froese, GEOMAR, Kiel, Germany, rfroese@geomar.de
Version of June 23, 2016
Supplement for Froese, R., Demirel, N., Coro, G. Kleisner, K.M., Winker, H., Estimating fisheries
reference points from catch and resilience, accepted by Fish and Fisheries in July 2016.
Available from http://oceanrep.geomar.de/33076/
Table of contents
Introduction…………………………………………………………………………………………………………………………………3
Material and Methods…………………………………………………………………………………………………………………3
Selection of real stocks ………………………………………………………………………………………………….4
Generation of simulated stocks………………………………..…………………………………………………....4
Default rules for biomass priors………………………………………………………………………………………6
General settings………………………………………………………………………………………………….6
Rules for the initial prior biomass range…………………..…………………………………………6
Rules for the intermediate prior biomass range…….….………………………………………..6
Rules for the final prior biomass range………………….….…………………………………………7
CMSY analysis………………………………………………………………………………………………………………….7
BSM analysis …………………………………………………………………………………………………………………..8
Explanation of graphical CMSY and BSM output………………………………………………………………8
Results………………………………………………………………………………………………………………………………………..13
CMSY and BSM results compared with “true” values from simulated data…………………….13
Comparison of CMSY and BSM parameter estimates for 128 fully assessed stocks…………16
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CMSY and BSM results compared with “true” values from simulated CPUE data…………..28
Comparison of CMSY and BSM parameter estimates for 31 data-limited stocks…….………30
References………………………………………………………………………………………………………………………………….32
Appendix I: Simulated stocks with catch and biomass ..………………………………………………………………33
Appendix II: Fully assessed stocks……………………………………………………………………………………………….57
Region: Alaska…………………………………………….………………………………………………………………….57
Region: Pacific………………………………………………………………………………………………………………..77
Region: Northwest Atlantic…………………………………………………………………………………………….92
Region: Caribbean / Gulf of Mexico……………………………………………………………………………….105
Region: Northeast Atlantic, ICES Area……………………………………………………………………………108
Region: Mediterranean…………………………………………………………………………………………………170
Region: Black Sea………………………………………………………………………………………………………….173
Region: South Africa……………………………………………………………………………………………………..176
Appendix III. Simulated CPUE stocks………………………………………………………………………………………….185
Appendix IV. Data-limited stocks with catch or landings and CPUE……………………………………………209
Appendix V: Landings vs catches………………………………………………………………………………………………..271
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Introduction
This Supplement details the results of applying a Monte Carlo algorithm (CMSY) and a Bayesian
state-space implementation of the Schaefer surplus production model (BSM) to 48 simulated and
159 real stocks. The respective R-code and the data files are available as online material. The
selection of the real stocks, the generation of the simulated stocks, and the settings used in the
CMSY analysis are detailed below. The graphical output of the CMSY and BSM analyses is explained
in general before the results are presented in summary tables and in detail in Appendices I to IV.
Material and Methods
Table S1 contains the names and a short description of the content of the files that were used in the
context of this study. All files are available for download at http://oceanrep.geomar.de/
33076/.
Table S1. List of files that were used in the context of this study, with indication of file name and description of content.
File name
Content
AllStocks_ID20.csv
Stock descriptions, priors, official reference points
AllStocks_Catch16.csv
Time series of catch and biomass or CPUE
AllStocksResults_6.xlsx
Spreadsheet behind the results in Table S5 and S6
CMSY_45y.R
R-code implementing CMSY and BSM for simulated stocks
CMSY_46e.R
R-code implementing CMSY and BSM for real stocks
CMSY_46eFig1.R
R-code used to create Figure 1 in the main text
CMSY_46eFig2.R
R-code used to create Figure 2 in the main text
CMSY_46eFig3.R
R-code used to create Figure 3 in the main text
CMSY_46eFig4.R
R-code used to create Figure 4 in the main text
CMSY_46eFig5-6.R
R-code used to create Figures 5 and 6 in the main text
CPUEStocks_Results_6.xlsx
Spreadsheet behind the results in Table S9 and S10
SimCatch_6.csv
Time series of simulated catch and biomass
SimCatchResults_6.xlsx
Spreadsheet behind the results in Table S3 and S4
SimCatchCPUE_6.csv
Time series of simulated catch and CPUE
SimCatchCPUE_Results_6.xlsx
Spreadsheet behind the results in Table S7 and S8
SimSpec_6.csv
Priors and “true” parameters for simulated stocks with biomass
SimSpecCPUE_6.csv
Priors, “true” parameters for simulated stocks with biomass and CPUE
SimCatchGenerator_6.xlsx
Spreadsheet with algorithm to create simulated stocks with biomass
SimCatchCPUEGenerator_6.xlsx
Spreadsheet with algorithm to create simulated stocks with CPUE
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Selection of real stocks
Altogether 128 fully assessed stocks with biomass estimates, 29 data-limited stocks with CPUE data,
and two stocks without abundance data were used for the evaluation of the CMSY method. Catch
and biomass data were extracted from stock assessment documents that are available online or
were provided by the respective assessment bodies. Sixty-two fully assessed stocks from the
Northeast Atlantic were obtained from the ICES Stock Summary database and from ICES Advice
reports published in 2015 at http://ices.dk
. U.S.-managed stocks from the East Pacific and West
Atlantic had assessment reports with catch and total biomass estimates available online and were
included in the analysis (AFSC 2011; 2012; www.st.nmfs.noaa.gov/sisPortal/sisPortalMain.jsp). Data
for six stocks were obtained from working group reports for the Mediterranean and Black Sea (FAO-
GFCM, ICES 2014c; JRC 2012). Data for fifteen stocks from the Pacific Ocean were found (BillfishWG–
ISC, ISC 2015; www.st.nmfs.noaa.gov/sisPortal/sisPortalMain.jsp) and nine stocks from South Africa
(Winker et al., 2012; ICCAT 2015) were made available and included in the analysis. Catch and CPUE
for data-limited stocks from the Northeast Atlantic were obtained from ICES advice reports and from
the WKLIFE IV workshop held on 27-31 October 2014 in Lisbon, Portugal (ICES 2014a). Files
containing the time series data for these stocks and the respective meta-data and priors are
available as part of the online material (see Table S1).
Generation of simulated stocks
In order to compare parameter estimates of CMSY and BSM with “true” values, stocks with catch
and biomass or catch and CPUE were simulated with a time range of 50 years and a fixed k value of
1000. The values for r were drawn randomly from a normal distribution with mean and standard
deviation as shown in Table S2. A parameter estimate was considered as “good” if it contained the
respective “true” value within its confidence limits (Hedderich and Sachs 2015).
Table S2. Means and standard deviations used for generating normal distributions from which r values were selected
randomly for use in simulations.
Resilience
r range
mean
sd
High
0.6 – 1.5
1.05
0.15
Medium
0.2 – 0.8
0.5
0.1
Low
0.05 – 0.5
0.275
0.075
Very Low
0.015 – 0.1
0.0575
0.0142
The goal was to create a range of biomass scenarios, including strongly as well as lightly depleted
stocks, with monotone stable or monotone changing (i.e., steadily decreasing or increasing) or with
alternating biomass trajectories: patterns of high-high (HH), high-low (HL), high-low-high (HLH), low-
low (LL), low-high (LH), and low-high-low (LHL) biomass trends. Simulated stocks have names that
indicate the combination of biomass trajectory and intrinsic growth rate, e.g., HH_L signifies a stock
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with monotone high biomass and low resilience. Resilience categories were translated into r ranges
as shown in Table S2. The biomass trajectories were created by using the fixed k value, a randomly
selected r value (see Table S2), and an initial biomass. The biomass in subsequent years was then
generated from a Schaefer model according to Equation S1.
=
+ 1
(S1)
where B
t+1
is the exploited biomass in the year t+1, B
t
is the biomass in the current year t, C
t
is the
catch in year t, and e
s1
and e
s2
are bias-corrected lognormal errors. Note that the error term s
1
was
assigned to the estimation of the surplus production, i.e., to the interaction process of B
t
, r and k,
and the second error term s
2
was assigned to the catch, representing observation error for the
purpose of creating simulated data and for the purpose of CMSY analysis, where abundance is not
observed.
If biomass falls below 0.25 k, a linear decline in recruitment towards zero at zero k is assumed and a
respective multiplier 4 B
t
/k resulting in 1 at 0.25 k to zero at zero k is applied to the surplus
production term as shown in Equation S2.
=
+ 4
1
(S2)
This consideration of reduced recruitment at low biomass is visible in the indented equilibrium curve
at low biomass in Figure 1. It makes the simulated data more realistic and also fixes a bias in CMSY,
which otherwise would assume average productivity at severely depleted stock sizes with reduced
recruitment and would consequently overestimate surplus production in such cases.
The desired simulated biomass patterns were achieved by manually setting a time series of F/F
msy
values, with error terms set initially to zero. Once the desired pattern was achieved, the standard
deviation of the process error was set to 0.2 and of the observation error to 0.1. To avoid
subjectivity, the first time series of catch and biomass produced by the random process and
observation errors was selected for analysis, even if it was not a good representation of the intended
biomass pattern. The time series and the corresponding parameters were then stored for processing
by CMSY and BSM.
For the generation of simulated data for data-limited stocks where only catch and CPUE are
available, the simulated catch and biomass data described above were used as a starting point to
