NOAA Technical Memorandum NMFS-SEFSC-616

CALCULATING ACCEPTABLE BIOLOGICAL CATCH

FOR STOCKS THAT HAVE RELIABLE CATCH DATA ONLY

(Only Reliable Catch Stocks – ORCS)

By:

Jim Berkson, NMFS SEFSC

Luiz Barbieri, Florida FWC

Steve Cadrin, University of Massachusetts at Dartmouth

Shannon Cass-Calay, NMFS SEFSC

Paul Crone, NMFS SWFSC

Martin Dorn, NMFS AFSC

Claudia Friess, Ocean Conservancy

Donald Kobayashi, NMFS PIFSC

Thomas J. Miller, U. Maryland Ctr Environmental Science

Wesley S. Patrick, NMFS OSF

Sarah Pautzke, Western Pacific Fishery Management Council

Stephen Ralston, NMFS SWFSC

Michael Trianni, CNMI Division of Fish and Wildlife

U.S. DEPARTMENT OF COMMERCE

National Oceanic and Atmospheric Administration

National Marine Fisheries Service

Southeast Fisheries Science Center

75 Virginia Beach Drive

Miami, Florida 33149

May 2011

NOAA Technical Memorandum NMFS-SEFSC-616

CALCULATING ACCEPTABLE BIOLOGICAL CATCH

FOR STOCKS THAT HAVE RELIABLE CATCH DATA ONLY

(Only Reliable Catch Stocks – ORCS)

By:

Jim Berkson, NMFS SEFSC

Luiz Barbieri, Florida FWC

Steve Cadrin, University of Massachusetts at Dartmouth

Shannon Cass-Calay, NMFS SEFSC

Paul Crone, NMFS SWFSC

Martin Dorn, NMFS AFSC

Claudia Friess, Ocean Conservancy

Donald Kobayashi, NMFS PIFSC

Thomas J. Miller, U MD Ctr Environmental Science

Wesley S. Patrick, NMFS OSF

Sarah Pautzke, Western Pacific Fishery Management Council

Stephen Ralston, NMFS SWFSC

Michael Trianni, CNMI Division of Fish and Wildlife

U.S. DEPARTMENT OF COMMERCE

Gary Locke, Secretary

NATIONAL OCEANANIC AND ATMOSPHERIC ADMINISTRATION

Jane Lubchenco, Under Secretary for Oceans and Atmosphere

NATIONAL MARINE FISHERIES SERVICE

Eric Schwaab, Assistant Administrator for Fisheries

May 2011

This Technical Memorandum series is used for documentation and timely communication of 

preliminary results, interim reports, or similar special-purpose information. Although the 

memoranda are not subject to complete formal review, editorial control, or detailed editing, they 

are expected to reflect sound professional work.
ii

NOTICE

The National Marine Fisheries Service (NMFS) does not approve, recommend or endorse any 

proprietary product or material mentioned in this publication. No reference shall be made to 

NMFS or to this publication furnished by NMFS, in any advertising or sales promotion which 

would imply that NMFS approves, recommends, or endorses any proprietary product or 

proprietary material mentioned herein which has as its purpose any intent to cause directly or 

indirectly the advertised product to be used or purchased because of this NMFS publication.

This report should be cited as follows: 

Berkson, J., L. Barbieri, S. Cadrin, S. L. Cass-Calay, P. Crone, M. Dorn, C. Friess, D. 

Kobayashi, T. J. Miller, W. S. Patrick, S. Pautzke, S. Ralston, M. Trianni. 2011. Calculating 

Acceptable Biological Catch for Stocks That Have Reliable Catch Data Only (Only Reliable 

Catch Stocks – ORCS). NOAA Technical Memorandum NMFS-SEFSC-616, 56 P. 

Copies of this report can be obtained from:

National Marine Fisheries Service

Southeast Fisheries Science Center

75 Virginia Beach Drive

Miami, FL 33149

or

National Technical Information Service

5825 Port Royal

Springfield, VA 22161

(703) 605-6000 or (800) 553-6847

http://www.ntis.gov/numbers.htm
iii

EXECUTIVE(SUMMARY

In response to the 2006 reauthorization of the Magnuson-Stevens Act (MSA), the National 

Marine Fisheries Service established National Standard 1 (NS1) Guidelines, which included a 

requirement to set an acceptable biological catch (ABC) that accounts for scientific uncertainty 

in the estimate of a stock’s overfishing limit (OFL). This is an exceedingly difficult task for the 

large number of stocks for which reliable catch data are the only information available, as these 

stocks cannot be assessed with traditional stock assessment methods. For the purpose of this 

document, these stocks will be called “only reliable catch stocks” (ORCS). Despite the inherent 

problem of setting ABCs for ORCS, the MSA requirement remains.

At the second National SSC meeting November 10-13, 2009 in St. Thomas, USVI, an ad-hoc 

Working Group was established to identify, suggest, and evaluate alternative approaches for the 

setting of ABCs for ORCS. Working Group members represent seven of the eight SSCs, five of 

the six NMFS Science Centers, NMFS Headquarters, as well as a regional fishery management 

council, academic institutions, a state agency, and an NGO. The goal of the Working Group was 

to develop an approach for addressing ABCs in ORCS that could potentially be applied in all 

jurisdictions under a flexible framework.

This report reviews existing methods for setting catch limits for ORCS. Each approach is briefly 

summarized followed by a description of the required data, the major assumptions and 

consequent cautionary advice in utilizing the particular approach, its potential for use in a riskbased decision-making framework, the status of the approach along with examples of its 

implementation, and the pros and cons of using the approach as viewed by the Working Group.

The Working Group also presents its own approach, designed to build on existing approaches, 

while strengthening the biological and population dynamics underpinnings. The method 

provides additional flexibility and allows policymakers to set risk levels, as required under the 

NS1 guidelines.

Ultimately, the Working Group recommends that the following tiered approach be used when 

setting ABCs for ORCS:

• Apply depletion-based stock reduction analysis (DB-SRA) to a stock, if possible. The 

main limitation here is the requirement for a complete time series of historical catches, 

which is often not available.

• If it is not possible to apply DB-SRA, apply depletion-corrected average catch (DCAC)

to a stock. DCAC’s main limitation is that it is only appropriate for stocks with moderate 

to low natural mortality rates (≤ 0.20 yr-1).
iv

• If DB-SRA and DCAC are not appropriate, apply the ORCS Working Group’s Approach. 

The main limitation with this approach is that a number of critical decisions are required 

before it can be made operational. Some would also view this as an advantage, as it 

provides flexibility in its establishment. 

• Finally, in some cases none of the above methods are practical for setting ABCs for an 

individual stock, as specific ORCS may not be capable of being effectively managed or 

monitored. In these cases, it may be best to use a stock complex approach. There are 

many limitations of applying a stock complex approach as described in this report, and 

the ORCS Working Group cautions against overusing or misusing this approach, as it 

may result in the converse of precautionary management, exactly what MSA was 

designed to avoid. 

It is important to note that the methods for setting ABCs for ORCS are in various stages of 

development and will be better understood and improved upon over time. For that reason, a list 

of research recommendations is included in the report that highlights the most important 

activities that must be supported to make substantive progress in the future.

The Working Group emphasizes that none of the methods discussed in this report are a substitute 

for additional data and monitoring. Therefore, all of the methods impose a certain risk and 

imprecision that fisheries managers must acknowledge when using the results of these methods.
v

Table(of(Contents

I.##BACKGROUND ................................................................................................................................... 1

A.##Requirement#for#ABC#specifications#and#ACLs................................................................................ 1

B.##History#of#dealing#with#ORCS ................................................................................................................ 1

C.##Unique#problem#for#ORCS....................................................................................................................... 2

D.##Catch#vs.#landings...................................................................................................................................... 3

E.##Formation#of#the#ORCS#working#group .............................................................................................. 3

F.##Scientific#and#management#uncertainty#in#ORCS ........................................................................... 3

G.##Incorporating#risk .................................................................................................................................... 4

H.##Report#outline............................................................................................................................................ 4

II.##REVIEW#OF#METHODS .................................................................................................................. 5

A.##Scalar#approaches..................................................................................................................................... 5

1.!!Summary!of!approach .............................................................................................................................................5

2.!!Data!needs ....................................................................................................................................................................5

3.!!Informed!judgment...................................................................................................................................................6

4.!!Caveats ...........................................................................................................................................................................6

5.!!Risk!assignment.........................................................................................................................................................7

6.!!Status!of!approach ....................................................................................................................................................7

7.!!Pluses/minuses!of!approach!as!viewed!by!Working!Group...................................................................8

B.##Scalar#multiplied#by#the#ABC#of#the#target#species,#when#ORCS#are#bycatch#species......... 8

1.!!Summary!of!approach .............................................................................................................................................8

2.!!Data!needs ....................................................................................................................................................................8

3.!!Informed!judgment...................................................................................................................................................8

4.!!Caveats ...........................................................................................................................................................................9

5.!!Risk!assignment.........................................................................................................................................................9

6.!!Status!of!approach ....................................................................................................................................................9

7.!!Pluses/minuses!of!approach!as!viewed!by!Working!Group...................................................................9

C.##Natural#mortalityUbased#approach...................................................................................................... 9

1.!!Summary!of!approach .............................................................................................................................................9

2.!!Data!needs ................................................................................................................................................................. 10

3.!!Informed!judgment................................................................................................................................................ 10

4.!!Caveats ........................................................................................................................................................................ 10

5.!!Risk!assignment...................................................................................................................................................... 11

6.!!Status!of!approach ................................................................................................................................................. 11

7.!!Pluses/minuses!of!approach!as!viewed!by!Working!Group................................................................ 11

D.##DepletionUCorrected#Average#Catch#(DCAC)..................................................................................11

1.!!Summary!of!Approach ......................................................................................................................................... 11

2.!!Data!needs ................................................................................................................................................................. 12

3.!!Informed!judgment................................................................................................................................................ 12

4.!!Caveats ........................................................................................................................................................................ 12
vi

5.!!Risk!assignment...................................................................................................................................................... 12

6.!!Status!of!the!approach.......................................................................................................................................... 12

7.!!Pluses/minuses!of!approach!as!viewed!by!Working!Group................................................................ 13

E.##DepletionUBased#Stock#Reduction#Analysis#(DBUSRA) ................................................................13

1.!!Summary!of!Approach ......................................................................................................................................... 13

2.!!Data!needs ................................................................................................................................................................. 13

3.!!Informed!judgment................................................................................................................................................ 14

4.!!Caveats ........................................................................................................................................................................ 14

5.!!Risk!assignment...................................................................................................................................................... 15

6.!!Status!of!the!approach.......................................................................................................................................... 15

7.!!Pluses/minuses!of!approach!as!viewed!by!Working!Group................................................................ 16

F.##The#Methot#Table#Conceptual#Framework .....................................................................................16

1.!!Summary!of!approach .......................................................................................................................................... 16

2.!!Data!needs ................................................................................................................................................................. 17

3.!!Informed!judgments ............................................................................................................................................. 17

4.!!Caveats ........................................................................................................................................................................ 17

5.!!Risk!assignment...................................................................................................................................................... 18

6.!!Status!of!approach ................................................................................................................................................. 18

7.!!Pluses/minuses!of!approach!as!viewed!by!Working!Group................................................................ 18

III.##The#ORCS#Working#Group#Approach....................................................................................19

A.##Introduction..............................................................................................................................................19

B.##Assigning#stocks#to#exploitation#categories...................................................................................20

1.!!Background............................................................................................................................................................... 20

2.!!Guidelines!for!assigning!stock!status............................................................................................................. 21

C.##Determining#an#appropriate#catch#statistic#for#an#OFL#calculation.......................................23

1.!!Outliers ....................................................................................................................................................................... 24

2.!!Avoiding!a!ratchet!effect ..................................................................................................................................... 24

3.!!Recent!trends ........................................................................................................................................................... 25

D.##Obtaining#OFL#scalars#for#different#exploitation#categories....................................................25

E.##Obtain#an#ABC#as#a#proportion#of#the#OFL.......................................................................................26

IV.##STOCK#COMPLEXES.....................................................................................................................26

V.##DISCUSSION ....................................................................................................................................29

VI.##RESEARCH#RECOMMENDATIONS...........................................................................................30

VII.##CONCLUSIONS .............................................................................................................................31

VIII.##LITERATURE#CITED.................................................................................................................32
vii

List(of(Tables

TABLE!1.!!THE!METHOT!TABLE!SHOWING!POSSIBLE!ACTIONS!FOR DETERMINING!ABC BASED!ON!DIFFERENT!FISHERY!IMPACT!

CATEGORIES!AND!EXPERT!OPINION. TAKEN!FROM!THE!WORKSHOP!REPORT!OF!THE!2ND NATIONAL!SSC MEETING. ........... 35

TABLE!2.!!THE!NATURAL!VARIABILITY!FACTOR, C, USED!IN!THE!NEW!ZEALAND!APPROACH, AS!DETERMINED!BY!THE VALUE!OF!

THE!NATURAL!MORTALITY!RATE, M................................................................................................................................................... 35

TABLE!3.!!POTENTIAL!MANAGEMENT!OBJECTIVES!DEPENDING ON!STOCK!STATUS!FOR!ORCS WORKING!GROUP!APPROACH. ..... 36

TABLE!4.!!TABLE!OF!ATTRIBUTES!FOR!ASSIGNING!STOCK!STATUS!FOR!HISTORICAL CATCH_ONLY!ASSESSMENTS............................. 37

TABLE!5.!!RECOMMENDED!OFLS!USING!ORCS WORKING!GROUP APPROACH...................................................................................... 38

TABLE!6. EXAMPLE!ABC OPTIONS!FOR!CATCH_ONLY!STOCKS!USING!THE!ORCS WORKING!GROUP!APPROACH. ............................ 38
viii

List(of(Figures

FIGURE!1.!!THE!RELATIONSHIP!OF!CATCH!REFERENCE!POINTS!UNDER!NATIONAL!STANDARD!1........................................................ 39

FIGURE!2. DISTRIBUTION!OF!1989 WIDOW!ROCKFISH!YIELDS!FROM!DCAC ANALYSIS!(TAKEN!FROM!MACCALL!2009).!!THE!

MEDIAN!OF!THE!SUSTAINABLE!YIELD!DISTRIBUTION!IS!6,849 MT, WHICH!COMPARES!WITH!MSY THAT!WAS!ESTIMATED!TO!

BE!8,300 MT.......................................................................................................................................................................................... 40

FIGURE!3.!!GRAPHICAL!REPRESENTATION!OF!ONE!ITERATION OF!THE!DB_SRA METHOD, SHOWN!ON!RESCALED!BIOMASS!(B0 =

1.0). ........................................................................................................................................................................................................ 41

FIGURE!4.!!DB_SRA OUTPUT!FOR!BROWN!ROCKFISH. THE!UPPER!PANEL!SHOWS A!TIME!SERIES!OF!THE PROBABILITY!THAT!

OVERFISHING!OCCURRED IN!ANY!PARTICULAR!YEAR.!!THE!LOWER!PANEL!PROVIDES!THE!POSTERIOR!DISTRIBUTION!OF!OFL

IN!2011 (VERTICAL!DOTTED!LINE = MEDIAN!OF!DISTRIBUTION)................................................................................................. 42

FIGURE!5.!!EQUILIBRIUM!YIELD!AS!A!FUNCTION!OF!BIOMASS!FOR!THE!PELLA_TOMLINSON!MODEL!WITH!N!= 1.2.......................... 43

FIGURE!6.!!MULTIPLIER!FOR!FISHING!MORTALITY!TO!REDUCE!OR!INCREASE!FISHING!MORTALITY!TO!FMSY FOR THE!PELLA_

TOMLINSON!MODEL!WITH!N!= 1.2. .................................................................................................................................................... 44

FIGURE!7.!!!MULTIPLIER!FOR!YIELD!TO!REDUCE!OR!INCREASE!YIELD!TO!MSY FOR THE!PELLA_TOMLINSON!MODEL!WITH!N!= 1.2.

................................................................................................................................................................................................................. 44
ix

Symbols(and(Abbreviations(used(in(this(Document

Δ The expected proportional change in stock biomass from the first to the last year 

of the catch series in DCAC; the proportional reduction in biomass relative to K 

in DB-SRA

ABC Acceptable biological catch

ACL Annual catch limit

ACT Annual catch target

AM Accountability measure

B* Equilibrium biomass at some level of fishing mortality F* in the Pella-Tomlinson 

production model

B0 Virgin biomass

B20% Biomass level that corresponds to 20% of the unfished biomass

BMSY Biomass that would produce MSY

Bpeak The ratio of BMSY / K as used in DB-SRA

c Natural variability factor used in natural mortality-based approach

CCAMLR Convention on the Conservation of Antarctic Marine Living Resources

CFMC Caribbean Fishery Management Council

CPUE Catch per unit effort

DB-SRA Depletion-based stock reduction analysis

DCAC Depletion-corrected average catch

EC Ecosystem Component

FMSY The fishing mortality that produces MSY

GMFMC Gulf of Mexico Fishery Management Council

h Steepness of the Beverton-Holt stock recruitment relationship

ICCAT International Commission for the Conservation of Atlantic Tunas

K Carrying capacity

M Natural mortality

m Maximum productivity (MSY) in the Pella-Tomlinson production model

MAY Maximum average yield

MCY Maximum constant yield

MFMT Maximum fishing mortality threshold

MSST Minimum stock size threshold

MSA Magnuson-Stevens Act

MSE Management strategy evaluation

MSY Maximum sustainable yield

NEFMC New England Fishery Management Council

NGO Non-governmental organization

NMFS National Marine Fisheries Service

NOAA National Oceanographic and Atmospheric Administration
x

NPFMC North Pacific Fishery Management Council

NS1 National Standard 1

OFL Overfishing limit

ORCS Only reliable catch stocks

OY Optimum yield

P* Risk level; Probability of overfishing

PFMC Pacific Fishery Management Council

PGY Pretty good yield

PSA Productivity Susceptibility Analysis

r Intrinsic rate of increase

R0 Virgin recruitment

SAFMC South Atlantic Fishery Management Council

SD Standard deviation

SSC Scientific and Statistical Committee

TAC Total allowable catch

YAV Average catch used in natural mortality-based approach

Y* Annual equilibrium yield for the Pella-Tomlinson production model

Acknowledgements

Extremely helpful comments on an earlier draft were provided by E. J. Dick, Rick Methot, Joe 

Powers, and Erik Williams. 
1

I.((BACKGROUND

A.##Requirement#for#ABC#specifications#and#ACLs

The Magnuson-Stevens Fishery Conservation and Management Act (MSA) of 1996 required 

Regional Fishery Management Councils (Councils) to end overfishing and rebuild overfished 

stocks. It strengthened US fisheries law by putting in place firm timelines for rebuilding and 

specified requirements for rebuilding plans. In 2006, however, the majority of overfished stocks 

were still not rebuilt and overfishing continued to be a widespread problem because fishery 

management plans failed to sufficiently reduce exploitation rates (Rosenberg et al. 2006). As a 

result, Congress amended the MSA during the 2006 reauthorization with requirements for annual 

catch limits (ACLs) and accountability measures (AMs) for each managed fishery by fishing 

year 2010 for all stocks experiencing overfishing and by fishing year 2011 for all other stocks in 

the fishery (DOC, 2007). The reauthorized MSA further strengthened the role of science in the 

fishery management process by requiring that ACLs set by Councils may not exceed the fishing 

level recommendations of the Councils’ Scientific and Statistical Committees (SSCs). 

In the 2009 National Standard 1 (NS1) guidelines, the National Marine Fisheries Service 

(NMFS) provided specific guidance on how to comply with the new requirements of the MSA, 

including limit and target reference points for fisheries (NMFS, 2009) (Figure 1). The OFL is 

the annual estimate of the catch that would be obtained if a stock were fished at a rate producing 

the long-term maximum sustainable yield (MSY); overfishing occurs when catch exceeds the 

OFL. The ABC is the upper limit at which Councils can set the ACL. The SSCs were 

designated with the responsibility to set the acceptable biological catch (ABC), which is the 

catch level that accounts for scientific uncertainty in the estimate of the overfishing limit (OFL) 

and other sources of scientific uncertainty. The NS1 guidelines further require each Council, in 

conjunction with its SSC, to establish an ABC control rule that specifies how ABC is calculated 

based on the scientific uncertainty in the OFL estimate and the Council’s risk policy. These 

requirements apply to data-rich stocks that can be assessed through quantitative stock assessment 

models, as well as data-poor stocks that cannot be assessed with traditional stock assessment 

methods. This report focuses on the ABC requirements for stocks that have only catch history 

data available for estimating harvest limits. We refer to these stocks here as “Only Reliable 

Catch Stocks” (ORCS).

B.##History#of#dealing#with#ORCS

The 1998 NS1 technical guidelines (Restrepo et al. 1998) recommended that Councils “adopt a 

precautionary approach to specification of [optimum yield] OY,” stemming from the 1996 MSA 

requirement to end overfishing and rebuild depleted fishery resources. The precautionary 

approach was implemented to reduce the risk of overfishing in circumstances where scientific 

evidence of overfishing was not available (Restrepo et al. 1998). As it was recognized that all 
2

regions possessed data of varying states of quality for stock assessment and management 

purposes, subsequent guidance provided an array of precautionary control rules that could be 

used to set exploitation targets below the risk-neutral limits based on MSY-related benchmarks,

such as the maximum fishing mortality threshold (MFMT) and minimum stock size threshold 

(MSST) or reasonable proxies for one or both of these status determination criteria (Restrepo et 

al., 1998; Restrepo and Powers, 1999). 

In the absence of biomass and fishing mortality reference points, the 1998 Technical Guidance 

(Restrepo et al., 1998) for implementing the NS1 guidelines suggested using the historical 

average catch from a period during which there was no evidence of declining abundance as a 

proxy for MSY. This recent catch would be multiplied by a scalar (ranging from 25% to 75%) 

based on “informed judgment” regarding the qualitative estimate of stock size relative to BMSY

(stock biomass at maximum sustainable yield) and MSST to obtain the limit catch, but the 

performance of this recommendation was never investigated (Restrepo and Powers, 1999). From 

discussions among members of this Working Group, however, it appears that many Councils 

have used a constant scalar (e.g., 50%, 75%) as their precautionary approach regardless of the 

stock’s size relative to BMSY and MSST. 

C.##Unique#problem#for#ORCS

The 2009 NS1 guidelines state that the ABC should be based, when possible, on the probability 

of overfishing, which cannot exceed and should be less than 50 percent. The guidelines further 

require that “the ABC control rule must articulate how ABC will be set compared to the OFL 

based on the scientific knowledge about the stock or stock complex and the scientific uncertainty 

in the estimate of OFL and any other scientific uncertainty. The ABC control rule should 

consider uncertainty in factors such as stock assessment results, time lags in updating 

assessments, the degree of retrospective revision of assessment results, and projections”. Thus, 

the NS1 guidance for setting ABCs is clearly directed towards stocks that can be assessed 

through traditional stock assessment methods. Many stocks under US federal management, 

however, lack current stock assessments and are not likely to be assessed in the near future, due 

to substantial data limitations. For example, the 2009 Report to Congress on the Status of U.S. 

Fisheries reported that "272 stocks or stock complexes have overfishing thresholds not defined or 

applicable, or are unknown with respect to their overfishing status".1 In these data-limited 

situations, the guidelines are vague with respect to factors that could be considered for setting 

ABCs and simply suggest the use of reasonable proxies.

Many of the ABC control rules that are currently being developed in the regions follow a tiered 

approach in which the size of the buffer between the OFL and ABC increases as the level of 

 1 NMFS 2009 Report to Congress on U.S. Fisheries, May 2010. Available online at 

http://www.nmfs.noaa.gov/sfa/statusoffisheries/sos_full28_press.pdf
3

scientific uncertainty increases (Witherell, 2010). Since uncertainty is expected to increase with 

decreasing availability of reliable data, it follows that data-poor stocks should generally have 

larger buffers than data-rich stocks for the same desired risk of overfishing. Without a system in 

place that monitors key fishery indicators and responds to changes in these indicators, scientists 

and managers have no means of evaluating whether any newly established catch limits for ORCS 

are too conservative or too liberal. 

D.##Catch#vs.#landings##

These two terms are not synonymous, since catch is considered the landed catch plus the total 

amount of dead discard (i.e., bycatch). Too often an evaluation of historical catch becomes an 

examination of historical landings. Bycatch levels in other fisheries, as well as discard rates and 

discard mortality levels, should be discussed and factored into the evaluation of historical catch. 

Anecdotal information, fishermen’s knowledge, and local expertise should be considered in such 

cases.

E.##Formation#of#the#ORCS#working#group

At the second National SSC meeting November 10-13, 2009 in St. Thomas, USVI, an ad-hoc

Working Group was established to address the question of how to develop ABCs for data-poor 

fisheries under the jurisdiction of Regional Councils, where traditional stock assessment 

techniques cannot be applied due to data deficiencies. 

The Working Group was established to identify, suggest, and evaluate alternative approaches for 

the setting of ABCs for ORCS. Working Group members represent seven of the eight SSCs, five 

of the six NMFS Science Centers, NMFS Headquarters, as well as a regional fishery 

management council, academic institutions, a state agency, and an NGO. The Working Group 

has communicated general process-related comments, as well as stock assessment and 

management ideas through email and teleconference. 

The overriding goal of the Working Group was to develop an approach for addressing ABCs in 

ORCS that could potentially be applied in all jurisdictions under a flexible framework process. 

To this end, the Working Group reviewed existing methods that have been used both nationally 

and internationally to address data-deficient fisheries, and developed a hierarchy of 

recommended models or techniques for use in a particular fishery, given only that the fishery 

possesses a time-series of reliable catch data. 

F.##Scientific#and#management#uncertainty#in#ORCS

Unlike the 1998 NS1 guidelines, the 2009 guidelines make the distinction between two types of 

uncertainty that are to be considered in the catch-setting process: management and scientific. 

Management uncertainty arises from uncertainty in quantifying the true catch amount and 

uncertainty in the ability of managers to limit actual catches to the ACL. Councils have the 
4

flexibility to account for management uncertainty by setting an annual catch target (ACT) at or 

below ACL. Scientific uncertainty has been discussed earlier, and deals with the estimate of the 

OFL and ABC.

While the two types of uncertainty are distinct, they are not independent because the realized

catch affects abundance and consequently, future OFLs, which then feed back into ACLs 

(Shertzer et al. 2008). It is not always possible to distinguish between scientific and 

management uncertainty, especially in the case of ORCS, where total catches may be highly 

uncertain because of missing information regarding bycatch and discard mortality, affecting both 

scientific and management uncertainty. The NS1 guidelines allow for both scientific and 

management uncertainty to be incorporated into a single control rule, but ABCs by definition 

address only scientific uncertainty, which is the scope of this report.

G.##Incorporating#risk

It is the responsibility of stock assessment scientists and the SSCs to determine the level of 

scientific uncertainty that exists in an assessment or estimated level of sustainable yield, but it is 

the role of the Councils to determine the acceptable risk of overfishing given the scientific 

uncertainty. When the probability distribution around the OFL estimate can be computed and 

characterized, the median estimate of the OFL implies a risk level of 50 percent, which is the 

level of risk the NS1 guidelines state is not to be exceeded in setting ABC. When the OFL and 

its statistical distribution can be estimated, probability-based methods can be used to compute the 

ABC that corresponds to the Council-desired risk of overfishing (e.g., Prager and Shertzer 2010). 

In the case of most ORCS, quantitative estimates of reference points from assessment models are 

unavailable, and formal risk statements cannot be made because the uncertainty is often not 

quantifiable. In those cases, an adaptive approach to developing ABCs that involves monitoring 

key fishery indicators may need to be adopted. 

H.##Report#outline

The report is divided into seven primary sections:

• Section I, which you are currently reading, provides background on ORCS, the need to 

set ABCs, and the difficulties specific to ORCS.

• Section II reviews existing national and international methods that are currently in use or 

in the process of being further developed. Each approach is briefly summarized followed 

by a description of the required data, the major assumptions and consequent cautionary 

advice in utilizing the particular approach, its potential for use in a risk-based decisionmaking framework, the status of the approach along with examples of its implementation, 

and finally, the pros and cons of using the approach as viewed by the Working Group. 
5

• Section III introduces a new approach for setting ABCs for ORCS developed by the 

authors of this paper. 

• Section IV examines the suitability of the previously described methods for setting ABCs 

for stock complexes and presents any necessary modifications, additional assumptions, or 

important caveats that need be considered prior to applying each approach to stock 

complexes. 

• Section V provides a discussion of the topics raised in this paper. 

• Section VI provides research recommendations to further our ability to understand, set 

ABCs for, and manage ORCS. 

• The final section, Section VII, puts forth a set of recommendations to Councils and SSCs 

for moving forward in addressing the 2006 MSA mandate, under the 2009 NS1 

guidelines, for ORCS.

II.( REVIEW(OF(METHODS

A.##Scalar#approaches

1.((Summary(of(approach

Scalar approaches involve specification of future catch by using simple scalar multipliers applied 

to current or historical catch patterns. The primary reference for this approach is Restrepo et al. 

(1998) who formalized the concept in their Technical Guidance document for the 1998 National 

Standard 1. Scalar approaches were presented in the sections of the document specifying catch 

targets and catch limits in data-poor situations (this is henceforth termed the Restrepo approach). 

Although Restrepo et al. (1998) is the primary citation for this particular set of scalar tiers, it is 

quite likely that the concept was widely used historically in fishery management. The Restrepo 

approach proposed scalar multipliers for catch targets ranging from 0.25 to 0.75, depending on 

the estimated stock status at the time. For example, if the stock was overfished and hence below 

the MSST, then the catch multiplier for the Restrepo approach was 0.25 with the intent to reduce

fishing effort and allow the stock to rebuild. If the stock was above BMSY, the multiplier was 

0.75, which reflected the precautionary buffer between the catch target and catch limit, with the 

catch limit being status-quo catch levels in a presumed healthy fishery. For intermediate stock 

conditions the multiplier was 0.5. 

2.((Data(needs

The Restrepo approach uses an average catch. In the original document this was defined as the 

average catch during a time period, not necessarily the most recent, for which there is evidence 
6

of stable abundance. Ideally, there should be no quantitative or qualitative evidence of declining 

or increasing abundance trends in the selected time period. We note that approaches for deriving 

catch recommendations for stocks with decreasing trends are developed in sections II.E and F of 

this report. In an optimal situation there is an adequate catch data stream to objectively identify 

such a time period, and may vary temporally in location and span for particular stocks and 

fisheries. Since it was realized that stock status information is not available in many data-poor 

cases, it was suggested to explore several definitions of recent catch such as the mean or median 

catch during the last 5, 10, or 15 years. In minimal data situations, the Restrepo approach could 

be applied to a single year of fishery catch data, but this is obviously a tenuous application unless 

the single year of data was highly significant for some reason. A logical extension of the 

variable scalar multiplier would be to similarly reduce the value for shorter catch data streams 

owing to likely greater uncertainty.

3.((Informed(judgment

Some type of expert or otherwise informed judgment is required for the Restrepo approach if 

stock status information is lacking, which would likely be the case for any potential application 

of the approach. This judgment is critical because an overfished determination can result in 

catch limits that are adjusted downward to a third of what could conceivably be taken if stock 

status was not judged to be in an overfished condition. Such a declaration of stock status is 

generally difficult even with strong quantitative support. Scientific judgments should be 

supported with as much objective analysis as possible. Careful examination of all available 

biological and fishery indicators is warranted. Even if a formal stock assessment is lacking, a 

diverse assemblage of data (including qualitative and anecdotal information) can be evaluated in 

a meta-framework to infer stock status (e.g., Porch et al., 2006). The Restrepo et al. document 

mentions a variety of similar alternative approaches such as informed judgments, Delphi 

approaches, qualitative approaches, expert opinions, and consensus-building methods. In 

addition, Bayesian statistical methodology is an appropriate tool for heterogeneous data and 

variable prior knowledge.

4.((Caveats

The primary assumptions of the Restrepo approach are that the fishery is at or near a sustainable 

equilibrium, the stock is stable, and some qualitative determination of stock status is possible. 

However, without adequate information, it can be difficult to judge stock status, and, likewise,

without a protracted period of near-constant and/or sustainable fishing effort and catches, it can 

be difficult to verify stability. If fishing effort is highly variable or if a fishery is in development 

or experiencing overfishing, then the catch data stream will be problematic for the Restrepo 

approach. 
7

5.((Risk(assignment

Restrepo et al. (1998) conducted simulation modeling to explore what an appropriate default 

target catch control rule for data-adequate stocks might look like and found that fishing at 75% 

FMSY resulted in equilibrium yields of 94% MSY or higher and equilibrium biomass levels 

between 125% and 131% of BMSY while reducing the probability that the stock would decline to 

1⁄2 BMSY. Based on these results, the recommended default target control rule became fishing at 

75% FMSY. The data-poor proxy of this default rule for stocks judged to be above BMSY thus 

became 75% of recent catch. Additional risk can be built into the approach by simply reducing

the scalar multipliers. This is analogous to the catch limit and catch target differential multipliers 

in the 1998 technical guidance document. Biological and/or fishery information can be 

incorporated into the approach by using natural mortality rate or risk assessments like the PSA 

(productivity susceptibility analysis; Patrick et al., 2009; 2010) inputs to the scalar specification. 

These potential improvements will be discussed in forthcoming sections of text. 

6.((Status(of(approach

The Restrepo approach and variants thereof are used in the management of many fisheries across 

the nation. Scalar multipliers range from 0.25 to 0.75 consistent with the original guidance.

There is considerable variability in the time window of recent catch ranging from 1 year to 18 

years. The location of this recent catch time window also varies considerably from recent years 

to over 30 years into the past. As pointed out earlier, these parameters for the recent catch 

specification will have to be tailored to individual stocks and fisheries on a case-by-case basis. 

Some examples of current use for ORCS:

• The Pacific Fishery Management Council (PFMC) coastal pelagics ABC is specified 

using a scalar multiplier of 0.25 applied to average catch and scaled by proportion of 

stock available in U.S. waters.

• The International Commission for the Conservation of Atlantic Tunas (ICCAT) specifies 

total allowable catch (TAC) to be no more than the product of scalars of 0.33 for white 

marlin and 0.50 for blue marlin applied to 1996 or 1999 landings, whichever is greater. 

These reference years were chosen because they were thought to be particularly reliable. 

The scalars reflect the understanding of the recent level of overfishing, particularly for 

white marlin.

• OY for some PFMC groundfish stocks is specified using a scalar multiplier of 0.50 

applied to average catch.

• The North Pacific Fishery Management Council (NPFMC) specifies ABC using a scalar 

multiplier of 0.75 applied to average catch from 1978-1995.

• The Caribbean Fishery Management Council (CFMC) specifies ABC and ACL using a 

scalar multiplier of 0.85 applied to average catch from 1999-2005 or 2000-2005 

depending on the management area.
8

• The New England Fishery Management Council (NEFMC) used a scalar of 1.0 for ABC 

of Atlantic herring because a provisional analysis suggested that the stock was not 

overfished and overfishing was not occurring.

• The NEFMC also used a scalar of 1.0 for ABC of red crab because there was no evidence 

of depletion since the beginning of the fishery. 

7.( Pluses/minuses(of(approach(as(viewed(by(Working(Group

Some advantages of the Restrepo approach are that it a) is straightforward and therefore easily 

explained and understood by scientists, policymakers and stakeholders, b) can easily be applied 

even by those not specifically trained in stock assessment procedures, and c) is broadly 

applicable across species with different biological characteristics. Some of the disadvantages are 

that a) the appropriateness and performance of the recommended multipliers has not been 

evaluated, b) the assumptions of a stable stock which is at or near sustainable equilibrium can 

often not be verified, c) it is not suitable for application to an ORCS stock that is very lightly 

exploited since it does not allow for a catch limit larger than recent average catch, d) it does not 

explicitly account for species differences in productivity, and e) continued application could 

ratchet catch downwards as the recent average catch was forced to decline. The method was 

intended to be used as a short-term fix, until either additional data could be collected or an 

improved method could be developed. 

B.##Scalar#multiplied#by#the#ABC#of#the#target#species,#when#ORCS#are#bycatch#

species#

1.((Summary(of(approach

In one international arena, ORCS species believed to be exploited well below MSY levels and 

caught incidentally in directed fisheries are regulated in concert with the targeted species, based 

on a proportion (or harvest cap) associated with the targeted stock's quota. In those cases, the 

targeted stock’s ABC is multiplied by a scalar, for example 5%, to obtain the ABC of the 

bycatch species. Management for these bycatch species focuses on collecting additional 

information to elevate these fisheries to a formal assessment status as soon as possible and 

thereby allow what may have started as an exploratory fishery to safely expand to a targeted 

fishery.

2.((Data(needs

The only data required to carry out this management approach is a catch limit for the targeted 

species of the exploited assemblage.

3.((Informed(judgment

Judgment is needed for deciding what the proportion of the targeted species’ catch limit should 

be that serves as the scalar for determining the ABC of the bycatch species which requires expert 
9

opinion regarding the abundance of the bycatch stock relative to the target stock. The choice of 

scalars should be guided by the precautionary principle to avoid overfishing but should also 

allow for data collection and potential fishery expansion. Where this method has been applied, 

quotas have ranged from 5-16% of the targeted species’ catch limit.

4.((Caveats

The appropriateness of the chosen scalar cannot be known initially, and therefore, ongoing 

monitoring programs are imperative to the application of this general approach. Precise estimates 

of species composition from the landings, as well as observer data and fishery-independent 

survey data are necessary to ensure current proportional allocations for bycatch species are 

representative of recent resource/fishery dynamics and are ultimately sustainable.

5.((Risk(assignment

Although formal risk cannot be explicitly assigned in this straightforward method, the risk of 

overfishing bycatch species is considered to be relatively low by the management body

implementing the approach. Higher landings caps imply higher risk of overfishing.

6.((Status(of(approach

This approach is being implemented by the Convention on the Conservation of Antarctic Marine 

Living Resources (CCAMLR). In most cases, all bycatch species associated with the directed 

fisheries have recommended harvest levels that are defined in accordance with the CCAMLR. 

7.((Pluses/minuses(of(approach(as(viewed(by(Working(Group

The approach is very simple to apply, as it involves multiplying a scalar by the quota of a 

targeted species. Given species are selected because they are believed to be underutilized, it is 

assumed that there is a relatively low risk of overfishing using this method, but ultimately, there 

is little information to inform the initial choice of any particular scalar. Since this method sets an 

ABC for a group of species rather than an individual stock, it is a special case of a stock complex 

approach, which is discussed in Section IV of this report. If implemented correctly, the method 

allows for fishery expansion to occur slowly and in a coordinated fashion. 

C.##Natural#mortalityJbased#approach

1.((Summary(of(approach

The natural mortality-based approach (Anon 2009) is another variant of a scalar approach. It is 

based on the formula: 

MCY = c YAV
10

Where MCY is the maximum constant yield, c is the natural variability factor (defined below) 

and YAV is the average catch over an appropriate period. 

If the catch data are from a period when the stock was fully exploited (i.e., fishing mortality near 

the level that would produce MAY [= Maximum Average Yield]), then the method should 

provide a good estimate of MCY. In this case, YAV = MAY. If the population was underexploited, the method gives a conservative estimate of MCY.

The natural variability factor is defined as in Table 2. It is assumed that because a stock with a 

higher mortality rate will have fewer age-classes, it will also suffer greater fluctuations in 

biomass. The deviations from values of c in the table are for stocks where there is evidence that 

recruitment variability is unusually high or low.

2.((Data(needs

Familiarity with stock demographics and the history of the fishery is necessary for the 

determination of an appropriate period on which to base estimates of YAV. The period chosen to 

perform the averaging will depend on the behavior of the fishing mortality or fishing effort time 

series, the prevailing management regime, the behavior of the catch time series, and the lifespan 

of the species.

The period should be selected so that it contains no systematic changes in fishing mortality (or 

fishing effort, if this can be assumed to be proportional to fishing mortality). The period chosen 

should also contain no systematic changes in catch. If the period shows a systematic upward (or 

downward) trend in catches then the MCY will be under-estimated (or over-estimated). It is 

desirable that the period be equal to at least half the exploited life span of the fish. 

An estimate of natural morality is required to obtain the value of c, the natural variability factor. 

Knowledge of recruitment variability levels is needed to modify the natural variability factor, if 

necessary.

3.((Informed(judgment

In many cases informed judgment will be needed to select the period chosen to perform the 

averaging, as all of the information required to adequately select the period may not be available. 

4.((Caveats

The primary assumptions of the natural mortality-based approach are that the fishery is at or near 

a sustainable equilibrium and the stock is stable. However, it can be difficult to estimate stability 

without a protracted period of near-constant and/or sustainable fishing effort and catches. If 

fishing effort is highly variable or if a fishery is in development or experiencing overfishing, then 

the catch data stream will be problematic for this approach. 
11

5.((Risk(assignment

Risk is incorporated through the use of the natural variability factor, which takes into account the 

natural mortality of the stock. It is assumed that because a stock with a higher mortality rate will 

have fewer age-classes it will also suffer greater fluctuations in biomass. In addition this can be 

modified where there is evidence that recruitment variability is unusually high or low.

6.((Status(of(approach

The approach is currently being implemented for ORCS in New Zealand.

7.((Pluses/minuses(of(approach(as(viewed(by(Working(Group

The natural mortality-based approach has limited potential for application in the U.S. It is not 

designed for stocks that are currently in an overfished state. It is designed for stocks that have 

either been fully exploited or under exploited. It does not take into account cases where stocks 

have been over-exploited (overfished). Further, it requires a time period of stable catch, which 

may not be available for all stocks. Shorter life spans are viewed as inherently more risk prone 

and difficult to manage effectively, given they exhibit greater population fluctuations, requiring a 

smaller scalar to account for the increased risk. Other factors affecting risk are not incorporated 

into the method. The method has not been evaluated 

D.##DepletionJCorrected#Average#Catch#(DCAC)

1.( Summary(of(Approach((

Restrepo et al. (1998) provide guidance on estimating sustainable catch in situations where only 

a catch time series is available, suggesting that a sequence of relatively constant catches is 

evidence that the average annual harvest is sustainable. Although this approach can be useful for 

providing catch advice for data-poor stocks, the inference of sustainability is only true if both 

fishing mortality and stock abundance are stable during the period in question. A constant catch 

could be produced during a period of increasing fishing mortality and decreasing stock 

abundance, in which case the catch may not be sustainable. Nonetheless, Restrepo et al. (1998) 

argued that an average catch taken from a time period of stable harvest is a useful proxy estimate 

of sustainable yield.

MacCall (2009) developed an approach that allows for changing population abundance during 

the period when catches are obtained. He described the method as “depletion-corrected average 

catch” (DCAC) because it accounts for the windfall augmentation of catch that occurs due to a 

one-time reduction in standing stock, also known as “fishing up.” Conveniently, the method 

works just as well if a stock is increasing in abundance during the time interval. Fundamentally, 

DCAC is based on the premise that knowledge of natural mortality (M) is informative of FMSY, a 

reasonable prior for relative BMSY (BMSY / B0; B0 = virgin biomass) is available, and some view 

of relative stock depletion can be obtained.
12

2.((Data(needs

The basic DCAC calculation requires: a) an average catch calculated over some period of years, 

b) an estimate of natural mortality, which may be obtained from the relationship between 

longevity and M developed by Hoenig (1983) or other indirect methods, c) an estimate of the 

ratio of FMSY to M, which MacCall (2009) argues is typically in the range of 0.6−1.0, and d) an 

idea of how much stock abundance may have changed during the time period when catch 

statistics are summarized. This last input value is termed Δ and represents the relative decline 

(or increase) in stock size, with a larger value representing a greater decrement to the stock. In 

addition, the method has recently been generalized to include a prior distribution for relative 

BMSY (Stock Assessment Toolbox; http://nft.nefsc.noaa.gov/index.html).

3.((Informed(judgment

The DCAC method is a generalization of the average catch approach because an adjustment is 

made for changes in stock size (Δ). This is, however, a quantity that is difficult to obtain, and 

expert opinion must be used to decide on relative stock status. Likewise, informed judgment 

may be helpful in deciding on the ratio of FMSY to M and BMSY to B0. Prior distributions for Δ, 

ratio of FMSY to M and BMSY to B0 could be based on meta-analysis for related stocks, rather than 

expert opinion.

4.((Caveats((

DCAC assumes that the catch statistics used in the calculation are unbiased. Also, the method is 

only appropriate for stocks with moderate to low natural mortality rates (≤ 0.20 yr-1) because the 

depletion correction becomes negligible at higher values of M. Moreover, in its initial 

implementation the calculation assumed that relative BMSY occurs at 0.40. While this is a robust 

proxy supported by the simulations conducted by Clark (1991), the newest version of the 

calculation (i.e., the NOAA Fisheries Stock Assessment Toolbox) allows the user to specify a 

prior distribution for this quantity. 

5.((Risk(assignment((

Propagation of uncertainty is a strong point of the DCAC method, which is accomplished by 

Monte Carlo simulation based on draws from distributions of the key input quantities. In 

particular, the principal inputs (M, FMSY/ M, BMSY/ B0, and Δ) are specified as distributions. 

Importantly, MacCall (2009) provides a variance statistic for M based on reanalysis of the data 

summarized in Hoenig (1983). The result of the algorithm is an output distribution of catch that 

would have been sustainable over the specified timeframe, conditional on the input distributions, 

which can be used as a basis for risk assessment (Figure 2).

6.((Status(of(the(approach

The NEFMC and its SSC evaluated an application of DCAC to deep-sea red crab and concluded 

that because it provides an estimate of a sustainable yield and not MSY, it was inappropriate to 
13

use in calculating OFLs. Moreover, because survey information did not indicate that the 

population abundance of red crab had changed between 1974 and 2005, no depletion correction 

was required and an ABC was set based simply on average landings during that time period.

Because the DCAC calculation utilizes a sum of catches calculated over a period of years, the 

PFMC endorsed its use in developing OFLs for seven groundfish stocks that are characterized by 

erratic and/or incomplete catch histories. Those stocks included six rockfishes (Sebastes spp.) 

and one elasmobranch (i.e., blue rockfish, blackgill rockfish, gopher rockfish, honeycomb 

rockfish, Mexican rockfish, squarespot rockfish, and soupfin shark). 

7.((Pluses/minuses(of(approach(as(viewed(by(Working(Group

There are a number of appealing features of the DCAC method, including: a) it is based 

principally on catch statistics and basic life history information, b) the catch time series need not 

be comprehensive, c) stock abundance is explicitly allowed to vary, d) the method’s inputs are 

approximate and are specified as distributions as opposed to point estimates, and e) uncertainty is 

propagated to produce a distribution of sustainable yield. Some of the disadvantages of the 

approach are: a) the estimated yield is typically sustainable, but not maximal, b) expert opinion 

is required to characterize stock depletion, and c) the estimated yield may not be sustainable if 

the stock at the end of the time series is not representative of the production that occurred during 

the time series (i.e., it is severely depleted).

E.##DepletionJBased#Stock#Reduction#Analysis#(DBJSRA)

1.((Summary(of(Approach

Depletion-Based Stock Reduction Analysis (DB-SRA) is an extension of DCAC that 

incorporates full stock dynamics (Dick and MacCall, In press). At a basic level stock production 

is the product of per capita production (= productivity) scaled by the total size of the population. 

For example, under Beverton-Holt spawner-recruit dynamics these quantities are represented by 

steepness (h) and virgin recruitment (R0), respectively. Likewise, under a Schaefer surplus 

production model they are equal to the intrinsic rate of increase (r) and the carrying capacity (K). 

The DB-SRA method relies on specifying a plausible range of “scaled” production parameters 

and depletion levels in the form of prior distributions. Then, given the availability of a 

comprehensive catch history to scale the problem, virgin biomass can be uniquely calculated, 

conditional on each draw from the input distributions.

2.((Data(needs

Because the DB-SRA method is fully dynamic, a complete history of removals is required, i.e., 

annual catches from the beginning of the fishery are needed. Moreover, the method, at least in 

its current form, has been implemented as a delay-difference production model (Quinn and 

Deriso, 1999) and age-at-maturity is used to lag recruitment relative to production. Beyond 
14

those fixed inputs, the technique depends on the same four “prior” input distributions as DCAC, 

including: a) natural mortality (M), b) the ratio of FMSY to M, c) the ratio of BMSY to B0, and d) 

stock depletion (Δ). The DB-SRA method is also formulated in a way that provides considerable 

independence between FMSY and BMSY by implementation of a generalized production function 

(Fletcher 1978; McAllister et al. 2000; Dick and MacCall, In press).

As with DCAC, FMSY is scaled relative to the natural mortality rate, and the product of the scalar 

and M provides an estimate of FMSY. By also drawing an estimate of relative BMSY from its input 

distribution, production is then completely specified on a relative biomass basis. Next, the time 

series of catches and a random draw from the depletion distribution (Δ) are used to scale biomass 

and solve for the unique value of B0 and current biomass that satisfy all conditions (Figure 3). 

Of course in some instances the time series of catches is impossible with the random draws from 

the input distributions and the population trajectory goes negative. Those realizations are 

considered biologically implausible and are dropped from the collection of feasible outcomes 

(see also Walters et al. 2006). The process is repeated numerous times and posterior 

distributions of B0, Bcurrent, MSY (FMSY×BMSY) and OFL (FMSY×Bcurrent) are summarized from the 

individual results.

3.((Informed(judgment((

The DB-SRA method further generalizes DCAC and, like that method, requires expert opinion to 

provide a general idea of stock depletion at some point in the catch time series. However, the 

depletion distribution can be somewhat vague and/or uninformative without great loss in 

performance. Likewise, informed biological judgment is needed to provide the initial input 

distributions for the ratios of FMSY to M and BMSY to B0. However uncertainty in those 

distributions can be captured explicitly in their variances and they are biological characteristics 

that can reasonably be informed by conventional scientific wisdom.

4.((Caveats

Other than assumptions associated with generating the four key input distributions, the DB-SRA 

method is very general. In particular, the implementation of a generalized production function 

that uncouples FMSY from Bpeak allows a broad range of models to be explored. Also, the method 

is robust to stochastic variation in stock recruitment, as long as recruitment is not highly episodic 

or strongly autocorrelated. Nonetheless, the method requires the user to provide four 

distributional inputs, which can be difficult to specify. No doubt the most troubling of these is

the depletion (Δ) distribution, which is perhaps the main output statistic obtained in a data-rich 

stock assessment; requiring it as an input would seem to undermine the utility of the DB-SRA 

approach. In practice, however, the same type of inference is required of all ORCS methods (see 

above), but with DB-SRA it is expressed quantitatively as a distribution. The obvious benefit of 

this is that the prior distribution of Δ can be vaguely specified, which is to say the variance about 

the mean of the distribution implies that not much is actually known about depletion. Also, 
15

given that the approach incorporates depletion as an input, it is not an appropriate method for 

determining relative stock status; rather its strength is in yield estimation (MSY and OFL). 

Finally, the method requires a complete time series of total catch (landings + discards) to 

implement. To the extent that discards are underreported or not accounted for the method will 

produce biased results.

5.((Risk(assignment

Expression and depiction of uncertainty is a major goal of the DB-SRA method and is 

accomplished by Monte Carlo simulation of four input distributions through to the output 

distributions of management concern, i.e., current biomass, FMSY, unfished biomass, and OFL. 

An example of how uncertainty and risk are characterized within the DB-SRA framework is 

given in Figure 4, which shows the probability of overfishing for brown rockfish (Sebastes 

auriculatus) from 1920 to the present, as well as the posterior distribution of OFL values for 

2011 (Dick and MacCall, 2010). Given a distribution of OFL, it is possible to develop a control 

rule that maps ABC onto the probability of overfishing, a direct expression of scientific 

uncertainty.

6.((Status(of(the(approach

In 2010, the PFMC SSC endorsed the use of DB-SRA to estimate OFLs for 42 groundfish 

stocks, including 34 rockfishes (Sebastes sp.), four flatfishes (Pacific sanddab, rex sole, rock 

sole, and sand sole), one roundfish (kelp greenling), two elasmobranches (leopard shark and 

dogfish), and one complex (grenadiers). All data-poor rockfish stocks are managed within 

assemblages that are defined based on: a) distribution north or south of Cape Mendocino (lat. 

40°10’N), and b) cross-shelf distribution (nearshore, shelf, or slope). These 42 stocks include 

approximately half of the species listed in the PFMC Groundfish Fishery Management Plan and 

the development of OFL estimates for these species represents a significant improvement in the 

scientific information used to manage these stocks.

The medians of the bias-corrected posterior distributions of OFL were used by the PFMC as 

stock-specific point estimates of OFL. These were aggregated into single OFLs for each 

assemblage, and a semi-quantitative estimate of scientific uncertainty was endorsed for the 

DCAC and DB-SRA methods by the Council’s SSC (i.e., quadrupling the uncertainty of Tier 1, 

data-rich assessments). The Council also established a policy on buffering all groundfish ABCs 

below their OFLs by limiting the probability of overfishing (P*) to ≤ 0.45. Harvest 

specifications for the 2011-2012 biennial fishing cycle are being developed under this general 

paradigm.

The DB-SRA method has been coded in R (R Development Core Team, 2009) and is 

documented in two manuscripts. The first of these describes application of the method to 31 

different Tier 1 stocks and compares estimates of OFL, MSY, and B0 from DB-SRA to those 
16

obtained from a full data-rich stock assessment, which have typically been conducted using the 

maximum likelihood based, integrated Stock Synthesis model (Dick and MacCall, In press). The 

second publication describes and documents the application of the DB-SRA method to the 42 

data-poor, Tier 3 groundfish stocks listed above, including development of bias-corrections 

based on PSA and performance relative to data-rich stock assessments (Dick and MacCall, 

2010).

7.((Pluses/minuses(of(approach(as(viewed(by(Working(Group

Like DCAC, DB-SRA is based principally on catch statistics and basic life history information, 

uses inputs that are approximate and are specified as distributions as opposed to point estimates, 

and allows for the propagation of uncertainty to produce a distribution of sustainable yield. The 

method was evaluated by comparison of OFL estimates from DB-SRA to those from 31 data-rich 

stock assessments. Results of that comparison showed that DB-SRA sometimes underestimates 

and sometimes overestimates OFL for individual stocks. As might be expected, the bias in OFL 

depended on PSA scores associated with each of the stocks. In particular, DB-SRA applied to 

flatfish generally underestimated OFL by a factor of 0.55. For high vulnerability non-flatfish 

stocks DB-SRA was largely unbiased, whereas for low vulnerability non-flatfish stocks the 

method underestimated OFL by a factor of 0.83. These biases were quantified and applied as an 

adjustment in estimating OFL for the 42 data-poor stocks by the PFMC. A primary disadvantage 

is that this method is rather time and resource-extensive and requires application by trained stock 

assessment scientists. In addition, for many ORCS species, it may not be possible to fully 

reconstruct catch history. 

F.##The#Methot#Table#Conceptual#Framework

1.( Summary(of(approach

During the second National SSC meeting, NMFS’s Rick Methot gave a presentation on the 2009 

NS1 guidance regarding ACLs and the treatment of scientific uncertainty. In that presentation, a 

table was provided that showed an example of how ABCs might be set in catch-only situations. 

The original purpose of this conceptual framework was to generate discussion and inspire 

thought. The structured approach that it offered has since been used in discussions in different 

parts of the country to base ABC recommendations on, and the working group therefore deemed 

it appropriate to review the method here. The table, which we refer to here as “the Methot table 

conceptual framework”, is based on the same basic concept as the Restrepo approach and 

requires an expert evaluation of fishery impact. The Methot table generates four fishery impact 

categories of historic catch: trivial, small, moderate, and moderately high and proposes a possible 

action for ABC determination for each (Table 1). The first impact category highlights the fact 

that trivial catches of non-targeted species are unlikely to affect the species population status and 

under these circumstances the Council should consider listing these species as “Ecosystem 

Components” (EC species) within their fishery management plan. EC species are not required to 
17

specify OFL, ABC, or ACL thresholds; however, their catch levels should be monitored to 

ensure they are not targeted by the fishery in the future. If historic catches are judged to be small 

(the second impact category), it is assumed that the stock is not overfished and that the target 

catch could be set at the historic level while setting ABC and ACL above that. If historic catches 

are moderate, the fishery should be capped because any increase in catches might mean the stock 

could become overfished. If historic catches are moderately high, the stock might be overfished 

and recent catches should be considered as the limit. In that case, ABC would be set below 

recent catch levels to allow the stock to rebuild. The approach is fairly qualitative in that it does

not provide specific methods for calculating the degree to which catch should be set above or 

below historic levels. Methot does suggest that a stock’s vulnerability should be a consideration.

2.( Data(needs

The data needs for this method are similar to the Restrepo approach. Catch history is required 

along with any information that may help to determine stock status from the catch data. In 

addition, vulnerability information is recommended. Vulnerability can be determined through 

risk assessments such as the PSA analysis that evaluates a stock’s productivity and susceptibility 

to the fishery (Patrick et al. 2009, 2010). The final vulnerability score could be a factor in the 

setting of a scalar used to multiply recent catch; the scalar would be lowest for the most 

vulnerable species and highest for the least vulnerable species, scaled to fit within some 

predetermined range. This relates the level of allowable catch directly to the biology of the 

species.

3.((Informed(judgments

At the onset, expert judgment is needed in order to assign species to one of the four impact 

categories, analogous to the judgment call needed for the Restrepo method for determining stock 

status with respect to MSST and BMSY. In addition, informed judgment is needed to determine

how much the ABC should be set above or below historic catch levels, and a judgment call is 

also needed to determine what the appropriate period of recent or historic catch is relative to 

which ABCs should be set.

4.((Caveats

Although the Methot method does not make any explicit assumptions about stock stability or 

fishery equilibrium, the period of historic or recent catch used to determine future ABCs could 

have potentially large impacts on the final ABC that is calculated. Moreover, this method in its

current state of development provides only qualitative statements about relative catch. 

Establishing absolute values or formulas for how much to increase or decrease OFL from historic 

catch in the case of low or moderately high impact, respectively, and how vulnerability is used as 

a relative scalar would still need to be fleshed out.
18

5.((Risk(assignment

Risk for this method could be assigned by setting boundaries on how much ABC can be 

increased or decreased from historic catch. For example, in the case of low historic catch, it 

would be less risk-prone to specify that ABC can be maximally 50% higher than historic catch 

instead of 100% higher. Similarly, in the case of moderately high historic catch, higher 

reductions in ABC translate into a higher probability that the stock will rebuild quickly than low 

reductions. Risk could also be assigned by deciding how much weight should be given to 

vulnerability. The PSA risk categories of low, medium and high could be converted into discrete 

scalars, and how much these scalars differ is a reflection of how much more risk one is willing to 

take for less vulnerable species. 

6.((Status(of(approach

A variation of this approach is currently being developed by the SSC of the Gulf of Mexico 

Fishery Management Council (GMFMC). The current Gulf ABC control rule consists of three 

tiers, the lowest of which contains the ORCS. The Gulf SSC is considering only two of the four 

dimensions from the Methot Table Conceptual Framework: small and moderately high impact 

(tier 3a and 3b, respectively). In the case of small impact, recent average catch over a stable 

period would be designated as the target catch, ABC would be set at either 0.5, 1, or 1.5 standard 

deviations (SDs) above the target, and OFL will be set at 2 SDs above that target. The rationale 

for setting OFL at 2 SDs above the mean is that this will result in only a 2.5% probability of 

catches in any given year exceeding and OFL so defined. The choice of SD level for ABC 

reflects a choice of risk because even though the SSC would recommend that target catch be set 

at the mean of recent average catch, the ultimate setting of ACT and ACL rests with the Council, 

and the Council could choose to set both equal to ABC, in which case an ABC of 0.5 SDs above 

the mean would constitute a less risk-prone upper limit than an ABC set at 1.5 SDs above the 

mean. In the case of moderately high impact, the GMFMC SSC approach would set OFL equal 

to the recent average catch and ABC would be set at 65%, 75%, 85%, or 100% of the OFL. 

Neither GMFMC tier 3a nor 3b currently use species vulnerability as part of their ABC 

considerations.

7.((Pluses/minuses(of(approach(as(viewed(by(Working(Group

The Methot Table Conceptual Framework represents a general approach for addressing ORCS 

and offers only qualitative advice for adjusting the magnitude of future catch limits with respect 

to recent catches. This can be advantageous in that it allows flexibility in regional application 

but it is also a drawback in its lack of specificity because it could result in potentially 

inappropriate application of the concept. As the GMFMC SSC has found out, the expression 

“the devil is in the details” seems to hold true, in taking an intuitive concept and making it 

operational. Like the Restrepo approach, the Methot Table Conceptual Framework is intuitive 

and easy to explain and therefore extremely useful for scientists, policymakers and stakeholders. 

Another advantage is that it takes into account species vulnerability, thereby acknowledging the 
19

differences in resource response to exploitation. It can also be applied to stocks for which there is 

evidence that exploitation levels can be increased safely, and time and resources needed to apply 

this method are minimal because data needs are small and it does not require application by 

highly trained stock assessment scientists. The method’s performance has not yet been tested in 

either simulations or application. 

III.((The(ORCS(Working(Group(Approach

A.##Introduction

While this report has already summarized several control rules based on average catch scalars,

the Working Group felt that the existing scalar approaches lacked a solid technical basis and that 

inadequate guidance had been provided for their application, leading to widespread misuse. 

Therefore, the Working Group developed a new control rule for the managers and scientists to

address these issues. The proposed control rule for catch-only stocks builds on methods in 

Restrepo et al. (1998) and the Methot Table Conceptual Framework (summarized in Witherell 

2010 and reviewed in section II F of this report). The Restrepo et al. (1998) approach assigns 

stocks to one of three status categories (less than MSST, between MSST and BMSY, and above 

BMSY) and uses a different average catch scalar for stocks in each category. The scalars are 

intended to be precautionary, so it would be difficult to use the Restrepo et al. (1998) approach in 

the new OFL/ABC framework where scientific uncertainty is explicitly taken into account. The 

new approach presented here also uses different scalars for three stock status categories, but 

defines the categories differently, and develops a scoring procedure for assigning stocks to these 

categories. Alternative buffers are proposed to account for scientific uncertainty in setting ABCs, 

since this is regarded as a policy decision.

The Working Group is fully aware that these methods rely heavily on assumptions and expert 

judgment, and are not intended to be a substitute for quantitative information on stock status and 

trend. Nevertheless there is a need for robust methods that provide useful scientific advice in 

less than ideal situations. Our goal is to improve on existing methods and provide a structured 

and transparent approach, but we recognize that further improvements are probably needed. 

With these caveats in mind, the basic approach is the following:

1. Assign stocks to one of three exploitation categories using an evidence-based scoring 

procedure;

2. Obtain an OFL by multiplying a statistical measure of historical catch (e.g., mean, 

median, maximum, minimum, percentile, etc.) by a scalar that depends on the 

exploitation category; and

3. Obtain an ABC as a proportion (< 1) of the OFL to reflect a policy decision on acceptable 

risk, which may depend on productivity of the stock (see Patrick et al., 2009; 2010). 
20

B.##Assigning#stocks#to#exploitation#categories

Stocks can be grouped into three broad exploitation categories for which different management 

objectives apply (Table 3): 1) lightly exploited; 2) moderately exploited; and 3) heavily 

exploited. For stocks that are considered lightly exploited, catches could generally be increased 

without harm to the stock. For stocks that are considered moderately exploited, management 

objectives will focus on maintaining status quo catch levels, and preventing non-sustainable 

increases. For stocks that are considered heavily exploited and possibly overfished, the 

management objective is to end overfishing and rebuild the stock to BMSY levels as mandated by 

the MSA. 

1.((Background

The concept of 'pretty good' yield (PGY) provides a theoretical basis for broadly classifying 

stocks into exploitation categories. This concept, proposed by Alec MacCall and developed 

further by Hilborn (2010), is based on the observation that a large percentage of maximum 

sustainable yield (>80%) can be produced on a long-term basis over a broad range of stock sizes. 

This concept is particularly meaningful in data-limited situations, since it implies that successful 

management outcomes are possible even if stock status is not known precisely. To illustrate the 

PGY concept and to develop a technical basis for catch multipliers, a Pella-Tomlinson 

production model was used. The Pella-Tomlinson model duplicates the results of the more 

complex age-structured model used by Hilborn (2010), but allows equilibrium yield to be 

calculated directly for any percentage of unfished stock size.

Annual equilibrium yield (Y*) for the Pella-Tomlinson production model is: 

where:

m is maximum productivity (MSY), B0 is unfished biomass, and B* is equilibrium biomass at 

some level of fishing mortality F*, with Y* = F* B* (Quinn and Deriso 1999). Setting n = 1.2 

results in a BMSY that occurs at 40% of the unfished stock size, which is often considered a 

reasonable default value (Clark, 1991). For these assumptions, equilibrium stock abundance in a 

range from B19% to B65% of the unfished biomass provides at least 80% of the MSY yield on a 

, *

0

*

0

*

n

n B

B

m B

B

m Y γ γ = −

! = nn /(n!1)

n !1 ,
21

sustainable basis (Figure 5). Stocks above this range would be considered lightly exploited, 

while stocks below this range would be considered heavily exploited (i.e., overfished). These 

results are comparable to those obtained by Hilborn (2010) for an age-structured population. 

Special cases of the Pella-Tomlinson model are n=2, which becomes the Graham-Schaefer 

production model where BMSY is 50% of unfished biomass, and n→1, which translates to the Fox 

production model where BMSY is approximately 37% of unfished biomass.

2.((Guidelines(for(assigning(stock(status

Status assignments based on historical catches will not have the benefit of a stock assessment, 

but will instead need to rely on ‘expert’ judgment. Experts in this context are those with 

experience conducting research, working on management issues, or participating in a fishery, 

and may include scientists, fishery managers, fishermen, and other involved parties. It will be 

important to be as comprehensive as possible when making status assignments and evaluate 

multiple lines of evidence. Given the absence of definitive information, the effort to generate 

these assignments may not be straightforward. It is important to note that that the overriding 

goal here is simply to assign stocks to very broad status categories with acceptable accuracy 

(e.g., say greater than a 70% success rate), recognizing that some inappropriate assignments will 

be inevitable.

An evidence-based scoring procedure (Table 4) has been developed to help assign stocks to the 

different status categories. This table incorporates some of the susceptibility elements in a PSA 

analysis (Patrick et al., 2010), as well as several new elements. The susceptibility scores in PSA 

evaluate the likelihood that a stock is captured in a fishery and the probable levels of fishing 

mortality, but PSA also includes productivity scores as a second dimension that takes into 

account the consequences of stock becoming overfished. In the framework we develop, 

productivity is considered separately when setting a buffer between OFL and ABC. While 

scoring procedures are a relatively recent development in fishery management, multi-attribute 

scoring algorithms have been used to evaluate the risk of species extinction (see Musick, 1999 

and Dulvy et al., 2003). Multi-attribute scoring algorithms are also used in the medical field for 

making diagnoses and deciding treatment plans (Ebell, 2001). Elements of the evidence-based 

scoring procedure are described below.

Overall fishery exploitation based on assessed stocks. In general, the characteristics of the 

fishery in which the stock is caught are the most important factor to consider when assigning 

stocks to exploitation categories. If there are assessed stocks in the fishery, are they mostly 

overfished, moderately exploited, or are most lightly exploited? Unless there are reasons to think 

that the stock is more or less vulnerable than assessed stocks, it may be reasonable to assign it 

the same status as an associated stock that has been assessed. Certain habitats may have an 

overall level of exploitation that can be used to infer the status of unassessed stocks that live in 

that habitat.
22

Presence of natural or managed refugia. A stock that is fished throughout its range is more 

likely to be impacted by fishing than a stock that is fished only in a portion of its range. Species 

with extensive natural or managed refugia are unlikely to become severely depleted. This 

consideration would only apply to species that are not highly mobile as adults in relation to size 

of the refugia.

Schooling, aggregation, or other behavior responses affecting capture. This element 

encompasses both the behavioral response of individual fish to fishing gear and group behaviors 

that affect capture such as schooling or aggregating for spawning in known locations. Individual 

responses may include, for example, herding or gear avoidance behavior that would affect 

catchability. 

Morphological characteristics affecting capture. This element pertains to the ability of the 

fishing gear to capture fish based on their morphological characteristics. For example, are there 

aspects of morphological characteristics affecting capture (i.e., large spines) that could make the 

fish more or less susceptible to capture? Because gear selectivity varies with size and age, this 

measure should be based on the age or size classes most representative of the entire stock.

Targeted species or Bycatch; and rarity. Targeting behavior by the fishery may help inform 

stock status assignments. Targeting may be inferred if a species has high commercial value or is 

considered highly desirable in a recreational fishery. Stocks that are caught primarily as bycatch 

in fisheries that target other stocks are likely to be lightly exploited relative to the targeted stock. 

However a non-targeted stock may still become overfished if it is much less productive than the 

targeted stock. Some stocks are simply too rare to be targeted, and would tend have low fishing 

impacts. 

Natural mortality compared to targeted species in the fishery. This element provides a relative 

gauge of the stock’s productivity compared to the dominant or targeted species in the fishery. 

Generally, for stocks subject to similar fishing mortality rates, those with low natural mortality 

have a higher likelihood of becoming overfished than those with higher natural mortality.

Value or desirability. Highly valued fish stocks are more susceptible to overfishing or becoming 

overfished by the recreational or commercial fishery due to targeting behavior with the goal of 

maximizing profits or non-market value. To identify the value of the fish, we suggest using the 

approach of Patrick et al. (2010) who used price per pound, or retention rates for recreational 

fisheries.

Trend in catches and effort. Finally, trends in historical catches may also be informative under 

some circumstances. If fishing effort is stable, a declining trend in catches may be an indicator 
23

of stock depletion. Again, if effort is not increasing, stable or increasing catches are an 

indication that the stock is exhibiting resiliency and not likely being severely impacted by 

fishing, but caution is warranted when interpreting catch patterns in the absence of other 

indicators and sources of data. Qualitative measures of effort, such as the number of active 

vessels or employment in the fishery, are likely to be all that are available for data-poor stocks, 

but may be misleading if there are technological advancements in the fishery. Increasing catches 

could also be an indication of fishery expansion, i.e., a stock that is transitioning from lightly 

exploited to moderately or heavily exploited status. 

The evidence-based scoring procedure provided (Table 4) includes default-scoring thresholds; 

however, we realize that revisions to the scoring procedure will likely be needed in different 

regional ecosystems and recommend that the scoring table be used flexibly. A starting point 

would be to assign status using the arithmetic mean of all attributes that can be scored, but 

weighting factors could be considered, or taking the geometric mean rather than the arithmetic 

mean. Careful consideration should be given to the logistics of scoring stocks. One possibility 

would be to assemble a core group of scientific experts that draws on information from formally 

appointed advisors that may include fishery managers, fishermen, and other knowledgeable 

individuals. Through trial and error techniques, it may also be useful to separate the scoring 

process into two steps by first ranking stocks along a continuum from lightly exploited to heavily 

exploited, and then identifying the break points between the lightly exploited, moderately 

exploited, and heavily exploited categories. Given management implications of identifying the 

break points, a higher-level science advisory body, such as the Regional Council’s SSC, may be 

more appropriate for this task. 

C.##Determining#an#appropriate#catch#statistic#for#an#OFL#calculation

Calculating the OFL using the ORC methodology is based on two terms: a scalar (or multiplier) 

that is based on the stock status category (described above), and a catch statistic derived from a 

time series of historical catches. Ideally, historical catches should represent a period with a 

stable harvest rate, i.e., a harvest rate where fishing removals are balanced by stock production 

and the stock can be assumed to be in a steady state condition or at its long term equilibrium. 

Stability in catches should be considered relative to the longevity of the stock. Catches of a 

long-lived species can be stable over a long period even though the stock is declining during this 

period. Although historical catches can be very stable with low variability, more often they are 

highly variable, sometimes with large outliers, or could be characterized by alternate periods of 

stability and periods of high variability or strong trends. Catches of relatively uncommon stocks 

can vary for a number of reasons unrelated to increases or decreases in abundance. These stocks 

may be incidental catches in fisheries that target other stocks or are minor members in a 

multispecies complex. The greater or lesser occurrence of a stock in the catch could be a chance 

event, caused by changes in the spatial or ecological overlap between that stock and other stocks 

that are more actively targeted in the fishery. Furthermore, fishery sampling programs can 
24

produce imprecise estimates of catches of stocks that are relatively uncommon. Evaluation of 

historical catch should include discussion of data quality and potential bias of catch estimates. If 

landings are highly variable, an attempt should be made to identify the reason for the variation 

and evaluate implications on the sustainability of historical catches. Other potential reasons for 

high fluctuations or outliers could be species misidentification, underreporting, effort variability, 

gear changes, or changes to the regulations for targeted species.

Although in many cases taking the arithmetic mean of historical catches is appropriate for an 

OFL calculation, the use of an alternative catch statistic may be needed in some situations to 

provide useful results. Several issues are described below, and suggestions presented for dealing 

with them are provided.

1.((Outliers((

In some cases, catch time series include extreme outliers that cannot be fully supported or 

rejected with available information. Several approaches to handling outliers are possible. First, 

a trimmed mean can be used (i.e., the inter-quartile mean) when the extreme values are 

considered unreliable. A similar approach would be to use the Winsorized mean, which is 

obtained by replacing all the values greater than or less than some quantile of catches by the 

largest (or smallest) of the remaining values. Usually 10 or 25 percent of the tails of the 

distribution are replaced. This approach would be appropriate when the extreme values are 

thought to carry some information about the catch quantity, but their actual values are considered 

unreliable.

2.((Avoiding(a(ratchet(effect(((

If catches are highly variable, the use of average catch as an OFL may be more constraining than 

is necessary, particularly when stocks are considered lightly or moderately exploited. When the 

management objective is to maintain current catch levels, setting the OFL equal to average catch 

could have the negative effect of depressing the mean level of the catch in the future, since 

presumably the management measures will need to prevent catches from exceeding the OFL, 

thereby truncating half of the distribution that was used to calculate the historical average. One 

possibility is to define the OFL to be some upper percentile of the historical catch, e.g., the 75% 

percentile of historical catch, with the rationale being that such a value would be exceeded on 

average one year in four if the fishery was prosecuted similar to historical patterns. Using the 

maximum catch is another alternative to average catch, but this should only be considered for 

non-target species with compelling evidence that they are lightly exploited. A similar approach 

has been proposed by the GMFMC SSC to, in some situations, base OFL on average catch plus 

two standard deviations (97.5 percentile), but it is unclear whether this approach provides 

sufficient constraint to prevent stocks from becoming depleted.
25

3.((Recent(trends

The theoretical development of average catch multipliers assumes that stocks are in equilibrium 

at some level of biomass, but this is necessarily an approximation to the real world, and in some 

cases it may be an inappropriate assumption from which to proceed. When there are downward 

trends in the landings, the safest approach (i.e., the most precautionary approach) would be to 

use an average based on the more recent lower values. However, if the downward trend in 

catches can be clearly linked to a reduction in effort, as when management restrictions are 

implemented for other species in a multi-species fishery, average catches from an earlier period 

may be more appropriate. If catches are trending upwards, using an average over all years may 

be the most reasonable approach.

D.##Obtaining#OFL#scalars#for#different#exploitation#categories

When catch trends are stable and the stock is considered to be moderately exploited, setting the 

OFL to current catch levels is an appropriate action. For these stocks, a multiplier of 1.0 is 

recommended for the OFL. 

For stocks that are considered to be heavily exploited, fishing mortality will need to be reduced 

to at least FMSY to end overfishing and begin rebuilding the stock to levels closer to BMSY. Since 

catch is proportional to fishing mortality for the Pella-Tomlinson model, a proportional reduction 

in catch will result in the same proportional reduction in fishing mortality for a given stock size. 

There is a time-dependency implicit in this recommendation, since a stock will immediately start 

to increase when fishing mortality is reduced to FMSY. The Pella-Tomlinson model suggests that 

multipliers on average catch that reduce fishing mortality to FMSY range from 0.17 when the 

stock is close to zero to 0.61 when the stock is at B20% (Figure 6) The average of multipliers 

from B5% to B20% is 0.48. Stock levels below B5% were excluded because it is unlikely that 

fishing mortality could be high enough to reduce stock size to such low levels. These results 

suggest that a multiplier of 0.5 is appropriate for the OFL when the stock is considered to be 

heavily exploited. Since increased yields should be possible once the stock rebuilds, use of a 0.5 

multiplier for the OFL should be considered a temporary measure that will be re-evaluated 

periodically.

When the stock is considered lightly exploited, fishing mortality is lower than FMSY and thus 

could potentially be increased. However a multiplier on catch would result in an immediate 

decrease in biomass so that that FMSY would quickly be exceeded. An alternative multiplier 

when the stock is lightly exploited is a multiplier that would increase yield to MSY, so that 

annual catches of this amount would move the stock into the moderately exploited category

without overfishing. The average of yield multipliers from B66% to B90% is 1.98 (Figure 7). 

Stock levels above B90% were excluded because these stocks would likely be classified as 

ecosystem component species. These results indicate that a multiplier of 2.0 is appropriate for 

the OFL when the stock is lightly exploited. Comparisons between the Pella-Tomlinson model 
26

with n = 1.2, the Graham-Schaefer model, and Fox model indicate that the recommended 

multipliers are reasonably robust to the shape of the production function. Due to the simple 

modeling approach used to derive these multipliers, we suggest using Table 5 as a starting point 

in discussions regarding appropriate OFLs. 

Although three categories have been broadly defined in the above analysis, distinguishing 

between lightly exploited and moderately exploited stocks may be difficult in some 

circumstances (e.g., widely varying catch data). Under such circumstances, it may be more 

practical to combine these two categories and use a 1.0 scalar for both; however this would 

imply a decision to constrain the catch of stocks that may be lightly exploited.

E.##Obtain#an#ABC#as#a#proportion#of#the#OFL

The last step in the control rule is determining the appropriate buffer between OFL and the ABC, 

which is based on the scientific knowledge about the stock and the uncertainty in the estimate of 

OFL (i.e., historical catch analysis). Since both risk policy and scientific uncertainty are 

involved in the choice of an ABC multiplier, input will be required from managers (i.e., Regional 

Fishery Management Councils) and science advisors (i.e., SSCs). Technical approaches to 

characterizing uncertainty are not yet possible for data-poor stocks, but it is clear that uncertainty 

is greater for these stocks than for data-rich assessed stocks. The size of the ABC multipliers 

derived from data-rich stocks provides a starting point for considering ABC multipliers for datapoor stocks. In developing ABCs, managers should consider distinguishing between high 

productivity stocks and low productivity stocks, the latter of which can be considered higher risk 

because they are more prone to becoming overfished and have long recovery times if they do 

become overfished. Assigning stocks to productivity categories is largely a scientific task, and 

can be done using productivity scores from a PSA analysis (Patrick et al., 2010) or other 

approaches. The degree to which different ABC multipliers are used for the productivity 

categories is more of a policy issue that should be decided by managers.

Table 6 lists some ABC options we developed as examples, but these are not meant to preclude 

managers from developing their own alternatives based on their risk preference. The alternatives 

in Table 6 have a greater or lesser degree of risk aversion, and contrast policy decisions to be 

more risk averse for low productivity stocks with those that do not. The most productive stocks 

tend to be coastal pelagic species such as anchovy and sardine, which have characteristics other 

than productivity that may be taken into account in setting the ABCs (or ACLs), such as decadal 

variability or importance as forage species. Other ways of grouping stocks into risk categories 

by productivity scores or some other characteristic are possible and should be considered.

IV.((STOCK(COMPLEXES

The National Standard One Guidelines (NMFS, 2009) describe the concept of a stock complex 

management, which is defined as a group of stocks that are managed as a single unit. Stock 
27

complexes are considered an approach to deal with stocks that are harvested together and cannot 

be assessed separately because of insufficient data or resources. Stock complexes can include 

similar species (e.g., southeastern U.S. reef fishes) or distinct populations of the same species 

that support mixed-stock fisheries (e.g., the Georges Bank-Gulf of Maine stock complex of 

Atlantic herring). In all fishery management systems, priority is given to assessing and 

monitoring stocks with the highest economic value or ecological importance. Nevertheless, 

marine ecosystems are diverse, and become increasingly so at lower latitudes. Although there is 

a general need for additional stock assessments, the cost of monitoring and assessing some 

stocks could potentially exceed the value of landings, suggesting that there is a limit to how 

many stocks should be individually assessed and managed. Management of stock complexes is 

an approach to addressing complexity by managing stocks at a higher level than an individual 

stock. Whether management by stock complexes is considered successful depends on how well 

the approach achieves management objectives, which can be evaluated like any other 

management strategy. Stock complexes are likely to be useful in the same data-poor situations 

as average catch assessments. This section discusses the issues that should be considered when 

these two approaches are used together.

The formation of stock complexes should take into account life history, geographic distribution, 

depth distribution, and vulnerability to the fishery (NMFS, 2009). When stock complexes are 

formed using these criteria, it is assumed that 1) a single catch limit will be sustainable for all 

members of the stock complex, and 2) fishery impacts are relatively uniform across the members 

of stock complex (i.e., there is no targeting of individual stocks in the complex). NMFS (2009) 

also recommends the use of indicator stocks, which is a stock selected as being representative of 

the complex, and is assessed periodically as a proxy for the other members of the complex. 

Indicator stocks have been used in various fisheries (e.g., Hawaii Seamount and Bottomfish 

Fishery, Alaska Salmon Fishery, North Pacific Groundfish Fishery, etc.) and have shown various 

levels of success. Shertzer and Williams (2008) evaluated the utility of stock complexes and 

indicator stocks as a proxy of status for reef fisheries off the southeast United States coast. Two 

difficulties were encountered: 1) species did not group naturally into well-defined complexes 

based on a cluster analysis of catch data, and, 2) fishery CPUE trends of member stocks within 

complexes showed little synchrony, suggesting that a single stock could not be used as an 

indicator for the complex. This study did not distinguish between the utility of using stock 

complexes and indicator stocks to prevent overfishing, as opposed to being simply used for 

status determination. At this point, it is not possible to conclude that Shertzer and Williams 

(2008) results generally apply to other stock complexes, and the indicator stock approach 

warrants further evaluation (see Branton and Richardson, 2011). Preliminary work with Pacific 

Coast groundfish using the results of a PSA as well as geographic distribution in a clustering 

algorithm to define stock complexes shows promising results, but is not expected to be 

implemented until the next management cycle (Cope et al., In press).
28

A stock complex can be managed in-season by monitoring the aggregate landings of the complex 

relative to an annual catch limit as a way to control the fishing mortality experienced by the 

stock complex in its entirety. Determination of stock status relative to target or limit stock size 

could be done for the complex as whole, or for an indicator stock that is a member of the group. 

Determining stock status may be difficult or impossible for data-poor stocks, but a management 

system that successfully limits catch to sustainable levels would be expected to prevent any stock 

from becoming overfished. While an inability to determine whether stocks are below a critical 

threshold is a weakness of average catch assessments, a management system that is designed to 

be precautionary should accommodate this uncertainty with an appropriate response. 

It is difficult to find examples where stock complexes have been implemented following the 

principles in NMFS (2009), most likely because the guidance is relatively new (earlier versions 

of the NS1 guidelines did not provide guidance on the formation of stock complexes). Stock 

complexes have often been established based on broad taxonomic groupings. For example, in 

the North Pacific, stock complexes have been established for squids and sculpins, while in New 

England, skates are managed as a complex despite large differences in productivity and 

susceptibility for members of the complex. In other cases, stock complexes are treated as a kind 

of warehouse for stocks that have not been dealt with using other assessment and management 

approaches. For an example, the “Other fish” complex used by PFMC includes several skate, 

shark, deepwater (e.g., finescale codling and Pacific rattail), and nearshore species (e.g., cabezon 

and kelp greenling). A more appropriate use of stock complexes is the PFMC management of 

minor rockfish species, which are grouped into complexes based on geographic distribution 

(north and south of 40°10” lat. N.), and depth distribution (nearshore, shelf, and slope). Another 

example is the “Shelf Demersal Rockfish” stock complex in the Gulf of Alaska, consisting of an 

assessed stock, yelloweye rockfish, and a number of other rockfish stocks occupying similar 

habitats that are not assessed. ABCs and OFLs are based on the assessed stock with an 

adjustment to account for the percent of the total catch of the stock complex consisting of other 

members of the complex.

Reef fishes in the Gulf of Mexico and U.S. Southeastern Atlantic Ocean were grouped into 

assemblages for management purposes based on multivariate statistical analyses conducted by 

the NMFS Southeast Regional Office. The analysis was based on landings associations, life 

history, and PSA. In the Gulf of Mexico, depth was the most important factor influencing 

assemblage composition. In the U.S. Southeastern Atlantic Ocean, depth and latitude were both 

important factors. Each identified assemblage contained at least one targeted, assessed species. 

OFLs and ABCs for stock complexes can be specified for indicator stock(s) of the complex or set 

for the complex as a whole. When indicator species is not a feasible option, and OFLs and 

ABCs need to be set for the complex as a whole, average catches can be compiled for the 

complex and the OFL and ABC calculations can be done for the entire complex. This is because 
29

the average catch of a complex is simply the sum of the average catches of the individual 

members of the complex. This approach would also be useful for stock complexes when 

estimates of the catch by species are unavailable, however some level of catch sampling is 

necessary to track the relative landings of stocks in a complex. Although the OFL and ABC of a 

stock complex can be the sum of the OFLs and ABCs for its individual stocks, the best scientific 

information available may not support the definition of stock-specific reference points. In the 

most data-poor situations, OFL and ABC may need to be based on the time series of aggregate 

stock catch.

The ABCs established for the indicator stocks for a complex as a whole should reflect the risk 

policy adopted by the Council. It is recommended by NMFS (2009) that indicator stocks be 

representative of the stocks within the complex with respect to their vulnerability to the fishery; 

otherwise the indicator stock should be chosen to represent the more vulnerable stocks in the 

complex. Similar rationale should be used when setting ABCs for the complex as a whole, 

which should take into account more vulnerable stocks within the complex. An important 

consideration in the use of stock complexes for management of data-poor species is that the 

catch of individual species within the complex is not monitored or controlled in-season. 

Consequently there is additional uncertainty associated with management by stock complexes 

that is not present when stocks are managed independently. If the objective is precautionary 

management, it may be necessary to build some additional conservatism into the system to 

account for the additional uncertainty associated with management using stock complexes. One 

approach would be to set an ACT for the stock complex that is less than ACL to account for 

management uncertainty.

V.((DISCUSSION

This review of methods covers a wide range of scientific approaches to confront the challenges 

associated with recommending appropriate catch recommendations for data-poor stocks. Unlike 

previous guidance on data-poor stocks, we view the range of methods as a hierarchy, from the 

most informative to the most data-limited approaches, with the scalar approach recommended by 

Restrepo et al. (1998) for the bottom tier. A hierarchical approach to catch advice can be used 

for determining the most appropriate method for each stock in the short-term, depending on 

stock properties and data availability, as well as a broader perspective on how fishery and 

resource monitoring information can be improved to advance the catch advice to a more 

informative tier of methodology (e.g., Cadrin et al., 2004). The ORCS Working Group 

recognized these method-based tiers and developed an adaptive approach in which the 

appropriate method is hierarchical with the goal to eventually improve the scientific basis of 

catch limits.

The adaptive approach to determining appropriate methods for setting ABC accepts that lowerlevel approaches for the most data-poor stocks do not meet all of the needs of the mandated 
30

management system or the desires of fishery stakeholders. Although it is beyond the scope of 

this report, the top-tier of scientific support is a stock assessment that incorporates and fully 

accounts for key sources of uncertainty to yield an estimate of the distribution of the OFL. 

Given this information on OFL and its statistical distribution, Fishery Management Councils can 

develop ABC control rules in which ABC is derived from an evaluation of scientific uncertainty 

and their acceptable probability of overfishing (see for example Ralston et al., In press). Several 

intermediate-tier methods (e.g., DB-SRA) support such a probabilistic approach to ABC and 

fully comply with NS1 guidelines. By contrast, lower tier methods (e.g., scalars of average 

catch) are not explicitly based on the Council’s desired risk tolerance.

Lower tier methods are designed to provide catch advice so that the fishery will be sustainable, 

but the optimality of the derived catch and the probability of overfishing are not known. These 

deficiencies of the lower tier approaches can impose substantial costs in the form of larger 

uncertainty buffers and substantial foregone yield. The hierarchical and adaptive approach to 

data-poor methods for determining ABC provides incentives for improving the scientific 

information.

Ideally, the performance of each method in the tiered system should be evaluated for avoidance 

of overfishing and maintaining optimum yield (and any other potential benefits identified as 

management objectives) through simulation of an operating model that is tailored to the stock of 

interest. Furthermore, the entire tier system could be evaluated through management strategy 

evaluation if a decision rule is simulated for improving data and moving from lower to higher 

tiers.

While it is important to improve methods used to set ABCs for ORCS, even improved methods 

will never take the place of data and monitoring. Informed judgment plays a critical part in 

every ORCS approach. It cannot be avoided or assumed away. Data collection through research 

and monitoring are needed to eliminate the need for informed judgment. 

VI.((RESEARCH(RECOMMENDATIONS

Due to the new requirements of the reauthorized Magnuson-Stevens Act (2006), development of 

methods to evaluate the status of data-poor stocks, including ORCS, is an active area of research. 

In particular, status determination and characterization of uncertainty are two focal study areas 

where significant advances are being achieved. In this regard, we believe that continued 

progress could be accomplished if additional research is conducted along the following lines:

 

 • Develop and accept formal methods to elicit expert opinion from scientists, stakeholders, 

and managers.
31

 • Conduct Management Strategy Evaluations (MSEs) to evaluate the robustness of 

methods used to characterize data-poor stocks and control rules for their management.

 • Collect basic life history information on data-poor stocks, especially maximum age, to 

better inform estimation of natural mortality.

• Conduct stock delineation for fish species that occur over extensive ranges and/or 

overlapping jurisdictions.

• Improve the coverage and accuracy of catch sampling programs. 

 • As a basis for risk assessment, complete Productivity-Susceptibility Analyses (Patrick et 

al. 2009) for all stocks that are currently under fishery management plans.

 • Increase the study of data-rich stocks within a meta-analytic framework to develop priors 

and proxies for application to data-poor stocks.

 • Coordinate efforts to assemble regional landings statistics into databases in a 

comprehensive, thorough way.

 • Monitor fishery indicators to provide additional information on sustainability of datapoor catch limits.

VII.((CONCLUSIONS

The problem of setting appropriate catch levels (now called ABCs) for ORCS is not new, is not 

going away, and doesn’t have an ideal solution. As discussed earlier, methods to deal with 

ORCS go back to the Restrepo et al. (1998) technical guidance. It is not realistic to assume that 

all, the majority of, or even many of these “data-limited” ORCS stocks will become “data-rich,” 

allowing for comprehensive stock assessments. Past, present, and proposed methods all require 

the incorporation of “informed judgment” and major assumptions in critical steps of the process. 

Given this situation and all of the information presented in this report, the ORCS Working Group 

recommends the following tiered approach to setting ABCs for ORCS:

• Apply DB-SRA to a stock, if possible. The main limitation here is the availability of a 

complete time series of historical catch, which is often not available.

• If it is not possible to apply DB-SRA, apply DCAC to a stock. DCAC’s main limitation 

is that it is only appropriate for stocks with moderate to low natural mortality rates (≤

0.20 yr-1).
32

• If DB-SRA and DCAC are not possible, apply the ORCS Working Group’s Approach. 

The main limitation with this approach is that a number of critical decisions are required 

before it can be made operational. Some would also view this as an advantage, as it 

provides flexibility in its establishment. 

• Finally, in some cases none of the above methods are practical for setting ABCs for an 

individual stock, as specific ORCS stocks may not have the capability to be effectively 

managed or monitored. In these cases, it may be best to use a stock complex approach. 

There are many limitations of applying a stock complex approach as described above, 

and the ORCS Working Group cautions against overusing or misusing this approach, as it 

may result in converse of precautionary management, exactly what MSA was designed to 

avoid. 

Finally, we recommend moving forward with the research recommendations listed above, given 

the methods for setting ABCs for ORCS are in various stages of development and necessarily 

depend on adequate attention and funding in the future. 

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35

Table 1. The Methot table showing possible actions for determining ABC based on different 

fishery impact categories and expert opinion. Taken from the workshop report of the 2nd National 

SSC meeting. 

Historical Catch Expert Judgment Possible Action 

Nil, not targeted Inconceivable that catch could be 

affecting stock 

Not in fishery; Ecosystem 

Component;

SDC not required 

Small Catch is enough to warrant 

including stock in the fishery and 

tracking, but not enough to be of 

concern 

Set ABC and ACL above 

historical catch; 

Set ACT at historical catch level. 

Allow increase in ACT if 

accompanied by cooperative 

research and close monitoring. 

Moderate Possible that any increase in catch 

could be overfishing 

ABC/ACL = f(catch, 

vulnerability)

So caps current fishery 

Moderately high Overfishing or overfished may 

already be occurring, but no 

assessment to quantify 

Set provisional OFL = f(catch, 

vulnerability);

Set ABC/ACL below OFL to 

begin stock rebuilding 

Table 2. The natural variability factor, c, used in the New Zealand approach, as determined by 

the value of the natural mortality rate, M.

M c

< 0.05 1.0

0.05-0.15 0.9

0.16-0.25 0.8

0.26-0.35 0.7

> 0.35 0.6
36

Table 3. Potential management objectives depending on stock status for ORCS Working Group 

Approach.

Stock status Potential management objectives

Lightly exploited Maintain current catch levels or allow for 

limited increases in catch

Moderately exploited Maintain current catch levels 

Heavily exploited, possibly overfished Reduce catches to end overfishing
37

Table 4. Table of attributes for assigning stock status for historical catch-only assessments. 

Overall scores are obtained by an unweighted average of the attributes for which scoring is possible, although alternative weighting 

schemes could also be considered. An initial assignment to a stock status category is: mean scores>2.5—heavily exploited; stocks with 

mean scores 1.5-2.5--moderately exploited; and stocks with mean scores<1.5--lightly exploited. When the attribute does not apply or 

is unknown it can be left unscored.

Stock status

Attribute Lightly exploited (1) Moderately exploited (2) Heavily exploited (3)

Overall fishery exploitation 

based on assessed stocks

All known stocks are either moderately or 

lightly exploited. No overfished stocks

Most stocks are moderately exploited. No 

more than a few overfished stocks

Many stocks are overfished 

Presence of natural or 

managed refugia

Less than 50% of habitat is accessible to fishing 50%-75% of habitat is accessible to fishing >75% of habitat is

accessible to fishing

Schooling, aggregation, or 

other behavior responses 

affecting capture

Low susceptibility to capture (specific behaviors 

depend on gear type)

Average susceptibility to capture (specific 

behaviors depend on gear type)

High susceptibility to 

capture (specific behaviors 

depend on gear type)

Morphological characteristics 

affecting capture

Low susceptibility to capture (specific 

characteristics depend on gear type)

Average susceptibility to capture (specific 

characteristics depend on gear type)

High susceptibility to 

capture (specific 

characteristics depend on 

gear type)

Bycatch or actively targeted 

by the fishery

No targeted fishery Occasionally targeted, but occurs in a mix 

with other species in catches

Actively targeted

Natural mortality compared 

to dominant species in the 

fishery

Natural mortality higher or approximately equal 

to dominant species ( M ≥ M )

Natural mortality equal to dominant species 

( M ≈ M )

Natural mortality less than 

dominant species (

M < M )

Rarity Sporadic occurrence in catch Not uncommon, mostly pure catches are 

possible with targeting

Frequent occurrence in 

catch

Value or desirability Low value (< $1.00/lb, often not retained (< 

33% of the time)

Moderate value ($1.00 - $2.25), usually 

retained (34-66% of the time)

Very valuable or desirable 

(e.g., > $2.25/lb ), almost 

always retained (>66% of 

the time).

Trend in catches (use only 

when effort is stable)

Catch trend increasing or stable (assign score of 

1.5)

Catch trend increasing or stable (assign 

score of 1.5)

Decreasing catches 
Table 5. Recommended OFLs using ORCS Working Group Approach.

Stock category

Lightly exploited 

(B > B65%)

Moderately exploited 

(B ~ BMSY)

Heavily exploited

(B < B20%)

2.0 x catch statistic 1.0 x catch statistic 0.50 x catch statistic

Table 6. Example ABC options for catch-only stocks using the ORCS Working Group 

Approach. 

Risk level Alternative 

A

Alternative 

B

Alternative 

C

Alternative 

D

Low risk 

(high productivity) 0.75 x OFL 0.75 x OFL 0.90 x OFL 0.90 x OFL

Moderate risk

(moderate productivity) 0.75 x OFL 0.75 x OFL 0.75 x OFL 0.80 x OFL

High risk 

(low productivity) 0.75 x OFL 0.50 x OFL 0.50 x OFL 0.70 x OFL
39

Figure 1. The relationship of catch reference points under National Standard 1.
40

Figure 2. Distribution of 1989 widow rockfish yields from DCAC analysis (taken from MacCall 

2009). The median of the sustainable yield distribution is 6,849 mt, which compares with MSY 

that was estimated to be 8,300 mt.
41

0 10 20 30 40 50 60 70 80 90 100

Percentage)of)Unfished)Biomass

Yield

Yield

FMSY3x3Biomass

BMSY3/3K

MSY

Stock3Status

MSY

Figure 3. Graphical representation of one iteration of the DB-SRA method, shown on rescaled

biomass (B0 = 1.0). 

The slope of the diagonal solid line is determined by the current value of FMSY, which is the 

product of draws from the M and FMSY ÷ M distributions. The relative biomass that generates 

maximum sustainable yield (BMSY/B0) is also drawn from its distribution (value shown = 0.4). 

Lastly, stock status relative to unfished biomass is determined by a draw from the distribution of 

relative biomass depletion (∆, value shown = 0.5). For each set of draws from the four input 

distributions, the catch time series determines the unique value of unfished biomass (B0) that 

satisfies the current estimate of stock status. Figure courtesy of E.J. Dick.
42

Figure 4. DB-SRA output for brown rockfish. The upper panel shows a time series of the 

probability that overfishing occurred in any particular year. The lower panel provides the 

posterior distribution of OFL in 2011 (vertical dotted line = median of distribution). 
43

Figure 5. Equilibrium yield as a function of biomass for the Pella-Tomlinson model with n = 

1.2. 
44

F Multipliers

0

1

2

3

4

5

0 20 40 60 80 100

Percent unfished biomass

Multipliers

Figure 6. Multiplier for fishing mortality to reduce or increase fishing mortality to FMSY for the 

Pella-Tomlinson model with n = 1.2. 

Yield Multipliers

0

1

2

3

4

5

0 20 40 60 80 100

Percent unfished biomass

Multipliers

Figure 7. Multiplier for yield to reduce or increase yield to MSY for the Pella-Tomlinson model 

with n = 1.2.