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RESULTS OF PRELIMINARY RUNS OF THE CMSY-METHOD AGAINST DATA
LIMITED ICCAT STOCKS
Rainer Froese1
SUMMARY
CMSY is a new method for estimating maximum sustainable yield (MSY) and related fisheries
reference points (Bmsy, Fmsy) from catch data and resilience, to help with preliminary stock
assessment in data-limited stocks. CMSY was applied to 18 stocks of data-limited ICCAT
species using default settings. The preliminary results are meant to be discussed by ICCAT
experts and a rerun with more realistic priors is expected to provide results that may be deemed
fit-for-use for at least some of the species.
KEYWORDS
Data-limited stocks, Catch MSY, Reference points
1. Introduction
CMSY is a method for estimating maximum sustainable yield (MSY) and related fisheries reference points (Bmsy,
Fmsy) from catch data and resilience. It is an advanced implementation of the Catch-MSY method of Martell &
Froese (2013), which was tested and found satisfactory at the WKLIVE IV workshop in Lisbon, October 2014
(ICES 2014). If managers, experts or stakeholders have a perception about the depletion history and the current
status of a given stock, then CMSY can test such hypotheses against observed catches and the known resilience
of the species. If combinations of productivity and stock size are found that are compatible with catches and
resilience, then the stock status and exploitation rate are presented in an MSY-framework. CMSY has been
tested against simulated data, where the “true” parameter values were known, and against over one hundred fully
assessed stocks, with good agreement between CMSY predictions and “true” or observed data. The respective
publication (Froese et al. submitted) is under review as of this writing. Appendix I contains three examples of
ICCAT stocks (ALB, BET, SWO) from this publication, assessed with CMSY as well as with a Bayesian statespace implementation of the Schaefer model analyzing catch and biomass data.
With the CMSY method, prior parameter ranges for the maximum intrinsic range of population increase (r) and
for unexploited population size or carrying capacity (k) are filtered with a Monte Carlo approach to detect
‘viable’ r-k pairs. A parameter pair is ‘viable’ if the corresponding biomass trajectories calculated with a
Schaefer model are compatible with the observed catches, in the sense that predicted biomass does not overshoot
carrying capacity nor crash the stock. Also, predicted biomass shall be compatible with prior estimates of
relative biomass ranges for the beginning and the end of the respective time series. Optionally, a third
intermediate prior biomass range can be provided to reflect extraordinary year classes or stock depletions. Also
optionally, an indication whether the stock is likely to crash within three years if current catches continue can be
given. This will improve the estimation of biomass in the final years.
A plot of viable r-k pairs typically results in a triangular-shaped cloud in log r-k space. A special algorithm is
applied to select the most probable r-k pair from near the tip of the triangle and to establish approximate
confidence limits.
2. Material and Methods
CMSY is written in R and the version used for this working paper was CMSY_44_ICCAT_5.R.
The CMSY method requires prior information about the range of possible r-values for the considered species. As
a proxy for r-ranges, the resilience of the species as stated in FishBase (www.fishbase.org) can be used as shown
1
GEOMAR, Helmholtz Centre for Ocean Research , Duesternbrooker Weg 20, D-24105 Kiel, Germany. Email address of lead author:
rfroese@geomar.de.
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in Table 1. In a real CMSY application for stock assessment, experts are of course encouraged to use more
specific prior ranges for r.
The CMSY method requires prior estimates of relative biomass at the beginning and end of the time series, and
optional also in the middle. For example, the relative biomass ranges shown in Table 2 can be used for low or
strong biomass depletion. Experts are of course free to use more suitable prior ranges for relative biomass.
CMSY input data are contained in two files, here SmallTuna_Catch.csv and SmallTuna_ID.csv. The first file
contains time series of catch and, if available, total biomass or CPUE, with mandatory headers for the stock ID
“stock” (e.g. “FRI”), a column for the years with available data “yr” (e.g. 1950…2013), a column for catches
“ct” (e.g. 581760…511416) and an optional column for total (=exploited) biomass or CPUE “TB” (e.g.
7053207…3937277). The second file contains information about the stock and the priors to be used for r, k,
initial relative biomass and final relative biomass, and the “FutureCrash” indicator with options “Possible” or
“No”. A column with header “Btype” classifies available total biomass data as “observed”, “simulated”,
“CPUE”, or “None”, i.e., CMSY can also be used if no biomass or CPUE data are available.
If total biomass or CPUE data are available, CMSY also fits a full Schaefer model (BSM) using a state-space
Bayesian approach for estimating the most probable r-k pair from biomass and catch trends. The state-space
approach explicitly assigns process and observation errors to improve posterior distributions of the wanted
parameters. The full Schaefer model is used to obtain “similar” types of reference points with which the results
of CMSY can be compared (rather than using MSY, Fmsy and Bmsy estimated with other methods). Examples for
three ICCAT stocks from Froese et al. (submitted) are shown in Appendix I. In addition BSM is applied to catch
and biomass and catch and CPUE data for Bluefin tuna (BFT) (Appendix III).
3. Results
CMSY was applied to altogether 18 stocks of data-limited ICCAT species. The results are detailed in the
Appendix II. For every analyzed stock, CMSY produces a screen printout describing the analyzed data, the
priors, the results of the full Schaefer analysis (if any), and the results of CMSY. For visual examination, CMSY
also produces standardized graphs. Figure 1 shows such graph for West African Spanish mackerel
Scomberomorus tritor (MAW).
The “[stock] catch” graph in the upper left indicates the acronym used for the stock by the assessment working
group (here: MAW), and shows the time series of catch data used by CMSY. The red circles indicated the
highest and the lowest catch, respectively. If the user does not provide prior information on biomass ranges,
simple prior rules are applied to catch relative to maximum and minimum catch, and are used to establish likely
relative biomass ranges for the beginning and the end of the time series, as well as for an intermediate year (blue
vertical lines in in the “Pred. biomass vs observed” graph).
The “Finding viable r-k” graph shows the filtered log-r-k-space, with viable r-k pairs in grey. While CMSY is
executed, this graphs shows progress by adding grey dots as viable r-k pairs are found. This search for viable r-k
pairs is the most time-demanding part of CMSY.
The “Analysis of viable r-k” graph shows the result of the CMSY-analysis, with viable pairs in grey and the
predicted most probable r-k pair in blue, with 95% confidence limits. r-k pairs to the left of the vertical dashed
line are excluded from the analysis, as this section of the viable r-k space is not expected to contain the
maximum intrinsic rate of population increase.
The “Pred. biomass vs None” graph shows in bold the median relative biomass trajectory predicted by CMSY,
with 2.5th and 97.5th percentiles. The dashed horizontal line at 0.5 k indicates Bmsy and the horizontal dotted line
at 0.25 k indicates half Bmsy and thus the border to stock sizes that may result in reduced recruitment. The blue
vertical lines show the prior biomass ranges set by the user or by prior rules applied to the catch pattern. The
purple point in the final year indicates the 25th percentile of predicted biomass, which could be used as
precautionary starting point for harvest control rules.
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The “Equilibrium curve” graph shows the Schaefer parabola with catch expressed relative to MSY on the Y-axis
and biomass relative to k on the X-axis. Grey dots are catch over biomass predicted by the CMSY method. Dots
falling on the parabola indicate catches that will maintain the corresponding biomass. Dots above the parabola
will shrink the biomass; dots below the parabola allow the biomass to increase.
The “Exploitation rate” graph shows the time series of the catch/biomass ratio (u) relative to the ratio
corresponding to MSY. It can be understood as depicting F/Fmsy. The black curve is the exploitation rate resulting
from catch relative to biomass predicted by CMSY. The dashed horizontal line indicates the maximum
sustainable exploitation rate.
4. Discussion
4.1. Warning about reduced recruitment at low stock
Productivity models such as used by CMSY assume average recruitment across all stock sizes, including stock
sizes below half of Bmsy, where fisheries textbooks predict an increased risk of reduced recruitment. In other
words, if recruitment is indeed reduced, then production models such as CMSY will overestimate production of
new biomass and will underestimate exploitation rates. Thus, if the final biomass predicted by CMSY is close to
half of Bmsy, then extra precaution should be applied if CMSY is used for management. For example, instead of
the median a lower percentile of predicted biomass could be used, such as the 25th percentile or even less. Stock
recovery predicted by CMSY from low biomass should always be confirmed by independent data, such as
CPUE.
4.2. Impact of using landings instead of catch
Whenever possible, stock assessment is based on true removals from the stock, i.e., including discards and other
unallocated removals. But for data-limited stocks, estimates of discard are typically not available and only the
reported landings can be used as indicator of removals. The effect of using landings instead of catch for CMSY
assessment was explored previously for cases where the landings underestimated true catches by about 30%. As
a result, the estimate of r remained practically unaffected, but the estimates of MSY, k and biomass were reduced
by also about 30%. However, the relative estimates of B/k and c/B remained unchanged. Thus, the CMSY
method seems capable of providing reliable relative assessments for stocks for which only landing data are
available.
4.3. Preliminary CMSY evaluation of data-limited ICCAT stocks
CMSY was successfully fitted to all data-limited ICCAT stocks. Results differ greatly in their confidence limits
for the desired reference points. Not surprisingly, long time-series with contrast in the catch data gave much
narrower confidence limits than short or monotonic ones. For several stocks it cannot be excluded that biomass
is below half of Bmsy and thus recruitment may be impaired and predicted recovery of biomass based on average
recruitment may be too optimistic. In these cases (e.g. BOP) it would be prudent to use not the median but the
25th or 5th percentile of predicted biomass for precautionary management purposes.
4.4. Improving CMSY evaluation of data-limited ICCAT stocks
This preliminary investigation used default settings for prior ranges of r, k, and relative biomass. Serious
application would start with gathering best available expert knowledge on these priors. Also, any independent
indication of abundance, which can even be annual catches in a single fishers logbook (assuming same gears and
similar effort), should be added, to build confidence in the CMSY analysis of available catch data. Questions to
be put to experts are exemplified in Table 3. Preliminary results of using more realistic priors and CPUE data for
some of the stocks are shown in Appendix IV.
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References
Froese, R., Demirel, D., Coro, G., Kleisner, K.M., Winker, H. Estimating fisheries reference points from catch
and resilience. Submitted to Fish and Fisheries on 28 February 2015
ICES, 2014. Report of the Workshop on the Development of Quantitative Assessment Methodologies based on
LIFE-history traits, exploitation characteristics, and other relevant parameters for data-limited stocks
(WKLIFE IV), 27–31 October 2014, Lisbon, Portugal. ICES CM 2014/ACOM:54. 241 pp.
Martell, S. and R. Froese, 2013. A simple method for estimating MSY from catch and resilience. Fish and
Fisheries 14: 504-514
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Table 1. Prior ranges for parameter r, based on classification of resilience.
Resilience
prior r range
High
Medium
Low
Very low
0.6 – 1.5
0.2 – 0.8
0.05 – 0.5
0.015 – 0.1
Table 2. Prior relative biomass ranges B/k used by CMSY for analyzing the simulated data.
Point in time series
Beginning
Intermediate
End
Strong depletion
0.1 – 0.5
0.01 – 0.4
0.01 – 0.4
Low depletion
0.5 – 0.9
0.3 – 0.9
0.4 – 0.8
Table 3. Example of questions to be put to experts to establish priors for CMSY analysis.
Prior
Question to experts
Start year for catch time series
From what year onward are catch data deemed
reliable?
Relative start- and end biomass
What was the most likely exploitation level at the
B/B0
beginning and end of that time series: light, full, or
overfishing?
Relative intermediate biomass
Is there an intermediate year where, e.g., exploitation
B/B0
changed from light to full, or where an extraordinary
large year class entered the fishery?
2M≈r
What is your best guess for the range of values
including natural mortality of adults (M)?
2 Fmsy ≈ r
What is your best guess for the range of values
including maximum sustainable fishing mortality
(Fmsy)?
B/B0 < 0.2 : Possible / No
If current catches continue, is it likely that the stock
will be outside of safe biological limits within the next 3
years?
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Figure 1. Graphical output of CMSY applied to West African Spanish mackerel Scomberomorus tritor (MAW).
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Appendix I
A.I.1. Results of applying CMSY to 3 fully assessed ICCAT stocks
The following three pages contain a comparison of CMSY analysis of catch and resilience with a Bayesian statespace analysis (BSM) of catch and biomass data for three ICCAT stocks (ALB, BET and SWO). These three
pages were copied from the Appendix of the submitted CMSY paper (Froese et al. submitted). The interpretation
of the Figures for CMSY is as explained above. In addition, the upper middle panel shows a cloud of black
points, which are viable r-k pairs as estimated by BSM, with the green cross indicating the most probable r-k pair
with its confidence limits. The upper right panel shows as black dots the observed catch and biomass data
relative to MSY and k as estimated by BSM. The lower middle panel shows as red curve the time series of
observed biomass relative to k as estimated by BSM, with dotted indications of the 2.5th and 97.5th percentile.
The lower right panel shows as red curve the observed exploitation rate, relative to the catch/biomass ratio that
would be compatible with MSY as estimated by BSM.
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Species: Thunnus alalunga , stock: Albacore_NA, ALB
Name and region: Albacore , Albacore - North Atlantic
Catch data used from years 1930 - 2011 , biomass = observed
Prior initial relative biomass = 0.5 - 0.9
Prior intermediate rel. biomass= 0.3 - 0.9 in year 1963
Prior final relative biomass = 0.01 - 0.4
If current catches continue, is the stock likely to crash within 3 years? No
Prior range for r = 0.2 - 0.8 , prior range for k = 75.8 - 910
Results from Bayesian Schaefer model using catch & observed biomass
r = 0.355 , 95% CL = 0.322 - 0.392 , k = 461 , 95% CL = 428 - 497
MSY = 40.9 , 95% CL = 37.8 - 44.3
Biomass in last year = 175 or 0.38 k
Results of CMSY analysis with altogether 1334 viable trajectories for 735 r-k pairs
397 r-k pairs above r = 0.242 and 494 trajectories within r-k CLs were analyzed
r = 0.377 , 95% CL = 0.246 - 0.578 , k = 458 , 95% CL = 286 - 734
MSY = 43.2 , 95% CL = 39.7 - 47.1
Predicted biomass last year= 0.265 , 2.5th = 0.0742 , 25th = 0.167 , 97.5th = 0.394
Predicted biomass next year= 0.292 , 2.5th = 0.063 , 25th = 0.179 , 97.5th = 0.439
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Species: Thunnus obesus , stock: BETuna_A , BET
Name and region: Bigeye Tuna , Bigeye tuna - Atlantic
Catch data used from years 1950 - 2009 , biomass = observed
Prior initial relative biomass = 0.5 - 0.9
Prior intermediate rel. biomass= 0.3 - 0.9 in year 1993
Prior final relative biomass = 0.01 - 0.4
If current catches continue, is the stock likely to crash within 3 years? No
Prior range for r = 0.2 - 0.8 , prior range for k = 160 - 1925
Results from Bayesian Schaefer model using catch & observed biomass
r = 0.467 , 95% CL = 0.418 - 0.521 , k = 847 , 95% CL = 809 - 886
MSY = 98.8 , 95% CL = 89.4 - 109
Biomass in last year = 406 or 0.48 k
Results of CMSY analysis with altogether 3484 viable trajectories for 540 r-k pairs
263 r-k pairs above r = 0.321 and 1334 trajectories within r-k CLs were analyzed
r = 0.509 , 95% CL = 0.332 - 0.781 , k = 705 , 95% CL = 433 - 1149
MSY = 89.8 , 95% CL = 79.9 - 101
Predicted biomass last year= 0.309 , 2.5th = 0.173 , 25th = 0.246 , 97.5th = 0.397
Predicted biomass next year= 0.306 , 2.5th = 0.137 , 25th = 0.23 , 97.5th = 0.413
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Species: Xiphias gladius , stock: Swordfish_NA , SWO
Name and region: Swordfish , Swordfish - North Atlantic
Catch data used from years 1950 - 2011 , biomass = observed
Prior initial relative biomass = 0.5 - 0.9
Prior intermediate rel. biomass= 0.01 - 0.4 in year 1995
Prior final relative biomass = 0.4 - 0.8
If current catches continue, is the stock likely to crash within 3 years? No
Prior range for r = 0.2 - 0.8 , prior range for k = 48.8 - 390
Results from Bayesian Schaefer model using catch & observed biomass
r = 0.462 , 95% CL = 0.415 - 0.514 , k = 127 , 95% CL = 120 - 134
MSY = 14.6 , 95% CL = 13.4 - 16
Biomass in last year = 72 or 0.569 k
Results of CMSY analysis with altogether 2189 viable trajectories for 844 r-k pairs
337 r-k pairs above r = 0.597 and 1128 trajectories within r-k CLs were analyzed
r = 0.691 , 95% CL = 0.602 - 0.793 , k = 85.7 , 95% CL = 73.1 - 101
MSY = 14.8 , 95% CL = 14.2 - 15.4
Predicted biomass last year= 0.635 , 2.5th = 0.423 , 25th = 0.55 , 97.5th = 0.736
Predicted biomass next year= 0.652 , 2.5th = 0.449 , 25th = 0.582 , 97.5th = 0.742
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Appendix II
A.II.1. Results of applying CMSY to 18 data-limited ICCAT stocks
Species: Thunnus atlanticus , stock: BLF
Name and region: Blackfin tuna , A+M
Catch data used from years 1950 - 2013 , biomass = None
Prior initial relative biomass = 0.4 - 0.8
Prior intermediate rel. biomass= 0.4 - 0.8 in year 1960
Prior final relative biomass = 0.01 - 0.4
If current catches continue, is the stock likely to crash within 3 years? Possible
Prior range for r = 0.2 - 0.8 , prior range for k = 5.61 - 67.3
Results of CMSY analysis with altogether 308 viable trajectories for 296 r-k pairs
144 r-k pairs above r = 0.206 and 128 trajectories within r-k CLs were analyzed
r = 0.217 , 95% CL = 0.207 - 0.229 , k = 42.7 , 95% CL = 39.5 - 45.8
MSY = 2.32 , 95% CL = 2.21 - 2.43
Predicted biomass last year= 0.239 , 2.5th = 0.0195 , 25th = 0.111 , 97.5th = 0.392
Predicted biomass next year= 0.244 , 2.5th = -0.00996 , 25th = 0.0984 , 97.5th = 0.411
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Species: Auxis rochei , stock: BLT
Name and region: Bullet tuna , A+M
Catch data used from years 1950 - 2013 , biomass = None
Prior initial relative biomass = 0.4 - 0.8
Prior intermediate rel. biomass= 0.4 - 0.8 in year 1955
Prior final relative biomass = 0.4 - 0.8
If current catches continue, is the stock likely to crash within 3 years? Possible
Prior range for r = 0.2 - 0.8 , prior range for k = 21.9 - 176
Results of CMSY analysis with altogether 9649 viable trajectories for 4724 r-k pairs
4134 r-k pairs above r = 0.257 and 6517 trajectories within r-k CLs were analyzed
r = 0.343 , 95% CL = 0.258 - 0.456 , k = 81 , 95% CL = 50.4 - 130
MSY = 6.95 , 95% CL = 4.78 - 10.1
Predicted biomass last year= 0.673 , 2.5th = 0.426 , 25th = 0.586 , 97.5th = 0.795
Predicted biomass next year= 0.656 , 2.5th = 0.39 , 25th = 0.563 , 97.5th = 0.786
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Species: Sarda sarda , stock: BON_ATL
Name and region: Atlantic bonito , ATL
Catch data used from years 1950 - 2013 , biomass = None
Prior initial relative biomass = 0.4 - 0.8
Prior intermediate rel. biomass= 0.4 - 0.8 in year 1953
Prior final relative biomass = 0.01 - 0.4
If current catches continue, is the stock likely to crash within 3 years? Possible
Prior range for r = 0.2 - 0.8 , prior range for k = 22.1 - 265
Results of CMSY analysis with altogether 1558 viable trajectories for 608 r-k pairs
489 r-k pairs above r = 0.266 and 823 trajectories within r-k CLs were analyzed
r = 0.449 , 95% CL = 0.273 - 0.74 , k = 78.6 , 95% CL = 46.2 - 134
MSY = 8.83 , 95% CL = 8.28 - 9.41
Predicted biomass last year= 0.278 , 2.5th = 0.0237 , 25th = 0.167 , 97.5th = 0.395
Predicted biomass next year= 0.274 , 2.5th = -0.0536 , 25th = 0.138 , 97.5th = 0.41
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Species: Sarda sarda , stock: BON_MED
Name and region: Atlantic bonito , MED
Catch data used from years 1950 - 2013 , biomass = None
Prior initial relative biomass = 0.4 - 0.8
Prior intermediate rel. biomass= 0.4 - 0.8 in year 1953
Prior final relative biomass = 0.01 - 0.4
If current catches continue, is the stock likely to crash within 3 years? Possible
Prior range for r = 0.2 - 0.8 , prior range for k = 72.7 - 873
Results of CMSY analysis with altogether 1975 viable trajectories for 1319 r-k pairs
631 r-k pairs above r = 0.236 and 664 trajectories within r-k CLs were analyzed
r = 0.341 , 95% CL = 0.245 - 0.476 , k = 263 , 95% CL = 182 - 381
MSY = 22.5 , 95% CL = 20.8 - 24.2
Predicted biomass last year= 0.276 , 2.5th = 0.0295 , 25th = 0.189 , 97.5th = 0.397
Predicted biomass next year= 0.261 , 2.5th = -0.0309 , 25th = 0.158 , 97.5th = 0.392
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Species: Orcynopsis unicolor , stock: BOP
Name and region: Plain bonito , A+M
Catch data used from years 1950 - 2013 , biomass = None
Prior initial relative biomass = 0.4 - 0.8
Prior intermediate rel. biomass= 0.4 - 0.8 in year 1957
Prior final relative biomass = 0.01 - 0.4
If current catches continue, is the stock likely to crash within 3 years? Possible
Prior range for r = 0.2 - 0.8 , prior range for k = 3.75 - 45
Results of CMSY analysis with altogether 463 viable trajectories for 414 r-k pairs
194 r-k pairs above r = 0.221 and 194 trajectories within r-k CLs were analyzed
r = 0.262 , 95% CL = 0.223 - 0.311 , k = 13.9 , 95% CL = 11.2 - 17
MSY = 0.909 , 95% CL = 0.842 - 0.982
Predicted biomass last year= 0.261 , 2.5th = 0.0246 , 25th = 0.141 , 97.5th = 0.392
Predicted biomass next year= 0.268 , 2.5th = -0.00856 , 25th = 0.132 , 97.5th = 0.412
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Species: Scomberomorus brasiliensis , stock: BRS
Name and region: Serra Spanish mackerel , A+M
Catch data used from years 1950 - 2013 , biomass = None
Prior initial relative biomass = 0.4 - 0.8
Prior intermediate rel. biomass= 0.4 - 0.8 in year 1960
Prior final relative biomass = 0.01 - 0.4
If current catches continue, is the stock likely to crash within 3 years? Possible
Prior range for r = 0.2 - 0.8 , prior range for k = 11.9 - 143
Results of CMSY analysis with altogether 1607 viable trajectories for 555 r-k pairs
455 r-k pairs above r = 0.25 and 920 trajectories within r-k CLs were analyzed
r = 0.333 , 95% CL = 0.253 - 0.438 , k = 71.9 , 95% CL = 52.9 - 97.7
MSY = 5.99 , 95% CL = 5.63 - 6.36
Predicted biomass last year= 0.237 , 2.5th = 0.0211 , 25th = 0.133 , 97.5th = 0.396
Predicted biomass next year= 0.278 , 2.5th = 0.00836 , 25th = 0.151 , 97.5th = 0.458
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Species: Prionace glauca , stock: BSH
Name and region: Blue shark , A+M
Catch data used from years 1954 - 2013 , biomass = None
Prior initial relative biomass = 0.7 - 1
Prior intermediate rel. biomass= 0.5 - 1 in year 1990
Prior final relative biomass = 0.4 - 0.8
If current catches continue, is the stock likely to crash within 3 years? Possible
Prior range for r = 0.015 - 0.1 , prior range for k = 652 - 13466
Results of CMSY analysis with altogether 80596 viable trajectories for 9749 r-k pairs
3864 r-k pairs above r = 0.0346 and 35549 trajectories within r-k CLs were analyzed
r = 0.0578 , 95% CL = 0.0351 - 0.0953 , k = 1720 , 95% CL = 728 - 4066
MSY = 24.9 , 95% CL = 12.2 - 50.5
Predicted biomass last year= 0.685 , 2.5th = 0.423 , 25th = 0.601 , 97.5th = 0.796
Predicted biomass next year= 0.66 , 2.5th = 0.372 , 25th = 0.568 , 97.5th = 0.782
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Species: Scomberomorus regalis , stock: CER
Name and region: Cero , A+M
Catch data used from years 1968 - 2013 , biomass = None
Prior initial relative biomass = 0.4 - 0.8
Prior intermediate rel. biomass= 0.01 - 0.4 in year 1998
Prior final relative biomass = 0.01 - 0.4
If current catches continue, is the stock likely to crash within 3 years? Possible
Prior range for r = 0.2 - 0.8 , prior range for k = 1 - 12
Results of CMSY analysis with altogether 1047 viable trajectories for 941 r-k pairs
430 r-k pairs above r = 0.234 and 408 trajectories within r-k CLs were analyzed
r = 0.307 , 95% CL = 0.238 - 0.397 , k = 6.11 , 95% CL = 4.46 - 8.36
MSY = 0.469 , 95% CL = 0.418 - 0.526
Predicted biomass last year= 0.3 , 2.5th = 0.14 , 25th = 0.228 , 97.5th = 0.395
Predicted biomass next year= 0.357 , 2.5th = 0.17 , 25th = 0.276 , 97.5th = 0.466
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Species: Coryphaena hippurus , stock: DOL
Name and region: Common dolphinfish , A+M
Catch data used from years 1954 - 2013 , biomass = None
Prior initial relative biomass = 0.7 - 1
Prior intermediate rel. biomass= 0.5 - 1 in year 2003
Prior final relative biomass = 0.01 - 0.4
If current catches continue, is the stock likely to crash within 3 years? Possible
Prior range for r = 0.6 - 1.5 , prior range for k = 3.63 - 34.5
Results of CMSY analysis with altogether 13892 viable trajectories for 1465 r-k pairs
754 r-k pairs above r = 0.94 and 6756 trajectories within r-k CLs were analyzed
r = 1.19 , 95% CL = 0.944 - 1.49 , k = 13.2 , 95% CL = 9.51 - 18.4
MSY = 3.92 , 95% CL = 3.21 - 4.79
Predicted biomass last year= 0.247 , 2.5th = 0.0185 , 25th = 0.128 , 97.5th = 0.395
Predicted biomass next year= 0.227 , 2.5th = -0.235 , 25th = 0.00217 , 97.5th = 0.474
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Species: Auxis thazard , stock: FRI
Name and region: Frigate tuna , ATL
Catch data used from years 1950 - 2013 , biomass = None
Prior initial relative biomass = 0.5 - 0.9
Prior intermediate rel. biomass= 0.3 - 0.9 in year 1986
Prior final relative biomass = 0.4 - 0.8
If current catches continue, is the stock likely to crash within 3 years? No
Prior range for r = 0.2 - 0.8 , prior range for k = 51.4 - 411
Results of CMSY analysis with altogether 9464 viable trajectories for 1032 r-k pairs
474 r-k pairs above r = 0.329 and 3721 trajectories within r-k CLs were analyzed
r = 0.509 , 95% CL = 0.332 - 0.781 , k = 113 , 95% CL = 68.6 - 186
MSY = 14.4 , 95% CL = 12.5 - 16.5
Predicted biomass last year= 0.785 , 2.5th = 0.54 , 25th = 0.759 , 97.5th = 0.799
Predicted biomass next year= 0.76 , 2.5th = 0.544 , 25th = 0.74 , 97.5th = 0.782
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Species: Scomberomorus cavalla , stock: KGM
Name and region: King mackerel , A+M
Catch data used from years 1950 - 2013 , biomass = None
Prior initial relative biomass = 0.4 - 0.8
Prior intermediate rel. biomass= 0.4 - 0.8 in year 1955
Prior final relative biomass = 0.4 - 0.8
If current catches continue, is the stock likely to crash within 3 years? Possible
Prior range for r = 0.05 - 0.5 , prior range for k = 74.1 - 937
Results of CMSY analysis with altogether 31210 viable trajectories for 9194 r-k pairs
8322 r-k pairs above r = 0.112 and 23480 trajectories within r-k CLs were analyzed
r = 0.223 , 95% CL = 0.118 - 0.424 , k = 285 , 95% CL = 132 - 617
MSY = 15.9 , 95% CL = 12.3 - 20.6
Predicted biomass last year= 0.705 , 2.5th = 0.421 , 25th = 0.602 , 97.5th = 0.797
Predicted biomass next year= 0.711 , 2.5th = 0.424 , 25th = 0.61 , 97.5th = 0.8
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Species: Euthynnus alletteratus , stock: LTA_ATL
Name and region: Little tunny , ATL
Catch data used from years 1950 - 2013 , biomass = None
Prior initial relative biomass = 0.4 - 0.8
Prior intermediate rel. biomass= 0.4 - 0.8 in year 1955
Prior final relative biomass = 0.4 - 0.8
If current catches continue, is the stock likely to crash within 3 years? Possible
Prior range for r = 0.2 - 0.8 , prior range for k = 59 - 472
Results of CMSY analysis with altogether 9004 viable trajectories for 4170 r-k pairs
3691 r-k pairs above r = 0.264 and 6038 trajectories within r-k CLs were analyzed
r = 0.364 , 95% CL = 0.269 - 0.494 , k = 186 , 95% CL = 121 - 285
MSY = 16.9 , 95% CL = 13.3 - 21.6
Predicted biomass last year= 0.707 , 2.5th = 0.434 , 25th = 0.637 , 97.5th = 0.796
Predicted biomass next year= 0.701 , 2.5th = 0.426 , 25th = 0.631 , 97.5th = 0.791
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Species: Euthynnus alletteratus , stock: LTA_MED
Name and region: Little tunny , MED
Catch data used from years 1950 - 2013 , biomass = None
Prior initial relative biomass = 0.4 - 0.8
Prior intermediate rel. biomass= 0.4 - 0.8 in year 1955
Prior final relative biomass = 0.4 - 0.8
If current catches continue, is the stock likely to crash within 3 years? Possible
Prior range for r = 0.2 - 0.8 , prior range for k = 8.46 - 67.7
Results of CMSY analysis with altogether 7325 viable trajectories for 3651 r-k pairs
3126 r-k pairs above r = 0.25 and 4670 trajectories within r-k CLs were analyzed
r = 0.326 , 95% CL = 0.252 - 0.422 , k = 31.3 , 95% CL = 20.5 - 47.9
MSY = 2.55 , 95% CL = 1.84 - 3.55
Predicted biomass last year= 0.695 , 2.5th = 0.431 , 25th = 0.614 , 97.5th = 0.796
Predicted biomass next year= 0.656 , 2.5th = 0.375 , 25th = 0.57 , 97.5th = 0.768
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Species: Scomberomorus tritor , stock: MAW
Name and region: West African Spanish mackerel , A+M
Catch data used from years 1968 - 2013 , biomass = None
Prior initial relative biomass = 0.4 - 0.8
Prior intermediate rel. biomass= 0.3 - 0.9 in year 1977
Prior final relative biomass = 0.01 - 0.4
If current catches continue, is the stock likely to crash within 3 years? Possible
Prior range for r = 0.2 - 0.8 , prior range for k = 8.29 - 99.4
Results of CMSY analysis with altogether 1395 viable trajectories for 928 r-k pairs
457 r-k pairs above r = 0.251 and 554 trajectories within r-k CLs were analyzed
r = 0.417 , 95% CL = 0.259 - 0.67 , k = 28.9 , 95% CL = 16.8 - 49.4
MSY = 3.01 , 95% CL = 2.66 - 3.41
Predicted biomass last year= 0.256 , 2.5th = 0.0332 , 25th = 0.158 , 97.5th = 0.395
Predicted biomass next year= 0.271 , 2.5th = -0.00616 , 25th = 0.157 , 97.5th = 0.434
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Species: Lamna nasus , stock: POR
Name and region: Porbeagle , A+M
Catch data used from years 1961 - 2013 , biomass = None
Prior initial relative biomass = 0.4 - 0.8
Prior intermediate rel. biomass= 0 - 1 in year 1987
Prior final relative biomass = 0.01 - 0.4
If current catches continue, is the stock likely to crash within 3 years? Possible
Prior range for r = 0.015 - 0.1 , prior range for k = 32.8 - 1017
Results of CMSY analysis with altogether 22745 viable trajectories for 6297 r-k pairs
3262 r-k pairs above r = 0.0281 and 9290 trajectories within r-k CLs were analyzed
r = 0.0523 , 95% CL = 0.0289 - 0.0948 , k = 89.9 , 95% CL = 36.9 - 219
MSY = 1.18 , 95% CL = 0.658 - 2.1
Predicted biomass last year= 0.249 , 2.5th = 0.0191 , 25th = 0.141 , 97.5th = 0.396
Predicted biomass next year= 0.255 , 2.5th = 0.0184 , 25th = 0.145 , 97.5th = 0.406
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Species: Isurus oxyrinchus , stock: SMA
Name and region: Shortfin mako , A+M
Catch data used from years 1971 - 2013 , biomass = None
Prior initial relative biomass = 0.4 - 0.8
Prior intermediate rel. biomass= 0.4 - 0.8 in year 1980
Prior final relative biomass = 0.4 - 0.8
If current catches continue, is the stock likely to crash within 3 years? Possible
Prior range for r = 0.015 - 0.1 , prior range for k = 147 - 1518
Results of CMSY analysis with altogether 53221 viable trajectories for 7593 r-k pairs
4064 r-k pairs above r = 0.0346 and 23662 trajectories within r-k CLs were analyzed
r = 0.0578 , 95% CL = 0.0351 - 0.0953 , k = 396 , 95% CL = 139 - 1124
MSY = 5.72 , 95% CL = 1.96 - 16.7
Predicted biomass last year= 0.66 , 2.5th = 0.418 , 25th = 0.555 , 97.5th = 0.795
Predicted biomass next year= 0.654 , 2.5th = 0.398 , 25th = 0.543 , 97.5th = 0.794
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Species: Scomberomorus maculatus , stock: SSM
Name and region: Atlantic Spanish mackerel , A+M
Catch data used from years 1950 - 2013 , biomass = None
Prior initial relative biomass = 0.4 - 0.8
Prior intermediate rel. biomass= 0.4 - 0.8 in year 1960
Prior final relative biomass = 0.01 - 0.4
If current catches continue, is the stock likely to crash within 3 years? Possible
Prior range for r = 0.2 - 0.8 , prior range for k = 20.4 - 245
Results of CMSY analysis with altogether 1940 viable trajectories for 959 r-k pairs
588 r-k pairs above r = 0.223 and 843 trajectories within r-k CLs were analyzed
r = 0.257 , 95% CL = 0.226 - 0.292 , k = 169 , 95% CL = 146 - 196
MSY = 10.9 , 95% CL = 10.5 - 11.3
Predicted biomass last year= 0.243 , 2.5th = 0.0243 , 25th = 0.137 , 97.5th = 0.395
Predicted biomass next year= 0.257 , 2.5th = -0.000169 , 25th = 0.136 , 97.5th = 0.423
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Species: Acanthocybium solandri , stock: WAH
Name and region: Wahoo , A+M
Catch data used from years 1970 - 2013 , biomass = None
Prior initial relative biomass = 0.4 - 0.8
Prior intermediate rel. biomass= 0.4 - 0.8 in year 1980
Prior final relative biomass = 0.4 - 0.8
If current catches continue, is the stock likely to crash within 3 years? Possible
Prior range for r = 0.2 - 0.8 , prior range for k = 7.39 - 59.1
Results of CMSY analysis with altogether 1428 viable trajectories for 1166 r-k pairs
584 r-k pairs above r = 0.212 and 537 trajectories within r-k CLs were analyzed
r = 0.233 , 95% CL = 0.212 - 0.258 , k = 37.9 , 95% CL = 30.1 - 47.3
MSY = 2.21 , 95% CL = 1.72 - 2.84
Predicted biomass last year= 0.528 , 2.5th = 0.405 , 25th = 0.467 , 97.5th = 0.681
Predicted biomass next year= 0.517 , 2.5th = 0.388 , 25th = 0.454 , 97.5th = 0.675
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Appendix III
A.III.1, Application of CMSY and BSM to BFT, first with biomass, then with CPUE
Species: Thunnus thynnus , stock: BFT
Name and region: Bluefin Tuna , North Atlantic
Catch data used from years 1950 - 2013 , biomass = observed
Prior initial relative biomass = 0.5 - 1
Prior intermediate rel. biomass= 0.5 - 1 in year 1960
Prior final relative biomass = 0.2 - 0.6
If current catches continue, is the stock likely to crash within 3 years? Possible
Prior range for r = 0.15 - 0.4 , prior range for k = 35.4 - 347
Results from Bayesian Schaefer model using catch & observed biomass
r = 0.144 , 95% CL = 0.121 - 0.172 , k = 87.8 , 95% CL = 74.3 - 105
MSY = 3.16 , 95% CL = 2.75 - 3.65
Biomass in last year = 45.7 or 0.52 k
Results of CMSY analysis with altogether 1997 viable trajectories for 993 r-k pairs
765 r-k pairs above r = 0.185 and 1069 trajectories within r-k CLs were analyzed
r = 0.273 , 95% CL = 0.191 - 0.389 , k = 72.5 , 95% CL = 47.2 - 111
MSY = 4.94 , 95% CL = 4.29 - 5.69
Predicted biomass last year= 0.482 , 2.5th = 0.222 , 25th = 0.38 , 97.5th = 0.594
Predicted biomass next year= 0.523 , 2.5th = 0.244 , 25th = 0.415 , 97.5th = 0.635
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Species: Thunnus thynnus , stock: BFT
Name and region: Bluefin Tuna , North Atlantic
Catch data used from years 1950 - 2013 , biomass = CPUE
Prior initial relative biomass = 0.5 - 1
Prior intermediate rel. biomass= 0.5 - 1 in year 1960
Prior final relative biomass = 0.2 - 0.6
If current catches continue, is the stock likely to crash within 3 years? No
Prior range for r = 0.15 - 0.4 , prior range for k = 35.4 - 347
Prior range of q = 4.16e-05 - 0.000136
Results from Bayesian Schaefer model using catch & CPUE biomass
r = 0.322 , 95% CL = 0.248 - 0.512 , k = 86.3 , 95% CL = 49.3 - 154
MSY = 7.13 , 95% CL = 3.99 - 13
q = 4.08e-05 , lcl = 3.35e-05 , ucl = 4.89e-05
Biomass in last year from q*CPUE = 55.7 or 0.645 k
Results of CMSY analysis with altogether 1879 viable trajectories for 926 r-k pairs
714 r-k pairs above r = 0.179 and 1075 trajectories within r-k CLs were analyzed
r = 0.266 , 95% CL = 0.182 - 0.389 , k = 74.3 , 95% CL = 47.2 - 117
MSY = 4.94 , 95% CL = 4.28 - 5.7
Predicted biomass last year= 0.48 , 2.5th = 0.221 , 25th = 0.377 , 97.5th = 0.596
Predicted biomass next year= 0.519 , 2.5th = 0.242 , 25th = 0.412 , 97.5th = 0.637
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Graphical output of CMSY analysis and BSM analysis based on catch and CPUE (here: combined Atlantic
longline indices LL_ind for Bluefin tuna, ATUN) (red curve in lower middle panel). The red curve in the lower
right panel is the catch/biomass ratio relative to the ratio compatible with MSY as estimated by BSM.
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CMSY management graph for BFT (ATUN), showing in the upper left panel catches relative to MSY and its
lower 95% confidence limit. The upper right graph shows estimated biomass with 2.5th and 97.5th percentiles
relative to Bmsy and half of Bmsy; the circle indicates the 25th percentile of predicted biomass in the last year; the
red dashed curve shows reported CPUE relative to Bmsy estimated by BSM. The lower left panel shows the
exploitation rate relative to the one compatible with MSY; the red dashed curve shows results from the BSM
analysis of catch and CPUE data. The lower right panel shows the trajectory of relative biomass over relative
exploitation, for CMSY (black) and BSM (red).
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Appendix 4. Stocks updated with expert input and CPUE
Start year was changed and longline CPUE combined from Table 2 was added
Species: Thunnus atlanticus , stock: BLF
Name and region: Blackfin tuna , A+M
Catch data used from years 1980 - 2013 , biomass = CPUE
Prior initial relative biomass = 0.4 - 0.8
Prior intermediate rel. biomass= 0.3 - 0.9 in year 1990
Prior final relative biomass = 0.01 - 0.4
If current catches continue, is the stock likely to crash within 3 years? Possible
Prior range for r = 0.2 - 0.8 , prior range for k = 5.61 - 67.3
Prior range of q = 0.0447 - 0.179
Results from Bayesian Schaefer model using catch & CPUE biomass
r = 0.51 , 95% CL = 0.461 - 0.607 , k = 23.8 , 95% CL = 20.3 - 27.4
MSY = 3.06 , 95% CL = 2.69 - 3.49
q = 0.055 , lcl = 0.0422 , ucl = 0.0724
Biomass in last year from q*CPUE = 8.7 or 0.366 k
Results of CMSY analysis with altogether 1456 viable trajectories for 389 r-k pairs
164 r-k pairs above r = 0.29 and 531 trajectories within r-k CLs were analyzed
r = 0.484 , 95% CL = 0.301 - 0.779 , k = 23.8 , 95% CL = 13.9 - 40.5
MSY = 2.88 , 95% CL = 2.56 - 3.23
Predicted biomass last year= 0.243 , 2.5th = 0.0243 , 25th = 0.134 , 97.5th = 0.394
Predicted biomass next year= 0.267 , 2.5th = -0.0169 , 25th = 0.131 , 97.5th = 0.448
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Start year and prior for r were changed
Species: Scomberomorus cavalla , stock: KGM
Name and region: King mackerel , A+M
Catch data used from years 1970 - 2013 , biomass = None
Prior initial relative biomass = 0.4 - 0.8
Prior intermediate rel. biomass= 0.3 - 0.9 in year 1996
Prior final relative biomass = 0.4 - 0.8
If current catches continue, is the stock likely to crash within 3 years? Possible
Prior range for r = 0.2 - 0.6 , prior range for k = 61.7 - 428
Results of CMSY analysis with altogether 21847 viable trajectories for 2190 r-k pairs
1041 r-k pairs above r = 0.325 and 9691 trajectories within r-k CLs were analyzed
r = 0.44 , 95% CL = 0.328 - 0.591 , k = 147 , 95% CL = 98.2 - 220
MSY = 16.2 , 95% CL = 13.1 - 20
Predicted biomass last year= 0.738 , 2.5th = 0.437 , 25th = 0.649 , 97.5th = 0.798
Predicted biomass next year= 0.742 , 2.5th = 0.449 , 25th = 0.661 , 97.5th = 0.8
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Set new starting year and added CPUE from Brazil
Species: Acanthocybium solandri , stock: WAH
Name and region: Wahoo , A+M
Catch data used from years 1985 - 2013 , biomass = CPUE
Prior initial relative biomass = 0.3 - 0.7
Prior intermediate rel. biomass= 0.3 - 0.9 in year 1996
Prior final relative biomass = 0.4 - 0.8
If current catches continue, is the stock likely to crash within 3 years? Possible
Prior range for r = 0.5 - 1 , prior range for k = 5.91 - 33.5
Less than 10 years with abundance data available, shown on second axis
Results of CMSY analysis with altogether 32576 viable trajectories for 3232 r-k pairs
1632 r-k pairs above r = 0.704 and 14735 trajectories within r-k CLs were analyzed
r = 0.835 , 95% CL = 0.707 - 0.986 , k = 13.8 , 95% CL = 10 - 19
MSY = 2.88 , 95% CL = 2.13 - 3.88
Predicted biomass last year= 0.73 , 2.5th = 0.468 , 25th = 0.668 , 97.5th = 0.798
Predicted biomass next year= 0.718 , 2.5th = 0.454 , 25th = 0.654 , 97.5th = 0.793
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Start year was changed to 1970
Species: Scomberomorus brasiliensis , stock: BRS
Name and region: Serra Spanish mackerel , A+M
Catch data used from years 1970 - 2013 , biomass = None
Prior initial relative biomass = 0.4 - 0.8
Prior intermediate rel. biomass= 0.3 - 0.9 in year 1988
Prior final relative biomass = 0.01 - 0.4
If current catches continue, is the stock likely to crash within 3 years? Possible
Prior range for r = 0.2 - 0.8 , prior range for k = 11.9 - 143
Results of CMSY analysis with altogether 2190 viable trajectories for 602 r-k pairs
282 r-k pairs above r = 0.288 and 864 trajectories within r-k CLs were analyzed
r = 0.484 , 95% CL = 0.301 - 0.779 , k = 51.5 , 95% CL = 30.4 - 87.2
MSY = 6.23 , 95% CL = 5.63 - 6.91
Predicted biomass last year= 0.246 , 2.5th = 0.0216 , 25th = 0.136 , 97.5th = 0.396
Predicted biomass next year= 0.297 , 2.5th = 0.00718 , 25th = 0.16 , 97.5th = 0.473
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