An Economic Perspective on 

National Standard 1 

Mike Dalton

Daniel S. Holland

Dale Squires

Joe Terry

David Tomberlin

U.S. Department of Commerce

National Oceanic and Atmospheric Administration

National Marine Fisheries Service

NOAA Technical Memorandum NMFS-F/SPO-180

April 2018

An Economic Perspective on National Standard 1 

Mike Dalton, Alaska Fisheries Science Center 

Daniel S. Holland, Northwest Fisheries Science Center 

Dale Squires, Southwest Fisheries Science Center 

Joe Terry, Office of Science and Technology 

David Tomberlin, Office of Science and Technology

NOAA Technical Memorandum NMFS-F/SPO-180

April 2018

U.S. Department of Commerce

Wilbur L. Ross, Jr., Secretary 

National Oceanic and Atmospheric Administration

RDML Tim Gallaudet, Ph.D., USN Ret., Acting NOAA Administrator

National Marine Fisheries Service

Chris Oliver, Assistant Administrator for Fisheries
Recommended citation: 

Dalton, M., D. Holland, D. Squires, J. Terry, and D Tomberlin. 2018. An Economic Perspective on 

National Standard 1. NOAA Tech. Memo. NMFS-F/SPO-180, 70 p. 

Copies of this report may be obtained from: 

Office of Science and Technology 

National Oceanic and Atmospheric Administration 

1315 East-West Highway 

Silver Spring, MD 20910 

Or online at: 

http://spo.nmfs.noaa.gov/tech-memos/

ii
iii

Table of Contents

Figures and Tables................................................................................................................................... iv

ABSTRACT................................................................................................................................................ v

ACKNOWLEDGMENTS ............................................................................................................................. vi

EXECUTIVE SUMMARY ........................................................................................................................... vii

ACRONYMS, ABBREVIATIONS, AND VARIABLES......................................................................................... x

1. Introduction......................................................................................................................................... 1

1.1 Purpose and Organization of the Paper....................................................................................................1

1.2 National Standard 1 and Key Elements of the NS1 Guidelines................................................................2

1.3 Key Economic Ideas Relevant to NS1........................................................................................................4

2. Applying Economic Principles to NS1 in a Simple Setting ........................................................................ 7

2.1 Economics and Preventing Overfishing ....................................................................................................7

2.2 The Economics of OY: Why MSY Is Not OY ...............................................................................................8

2.2.1 Defining OSY and Net Benefit to the Nation.....................................................................................9

2.2.2 Using a Simple Model to Depict OSY and Compare It to MSY........................................................10

2.2.3 Using OSY as an Additional Management Reference Point ...........................................................12

3. Applying Economic Principles to NS1 in a More Realistic Setting that Addresses the Complications of 

Dynamics, Uncertainty, and Stock Interactions........................................................................................ 15

3.1 Dynamics: Discounting and Optimum Yield Trajectory..........................................................................15

3.2 Uncertainty and Fishery Management under NS1 .................................................................................19

3.3 Additional Trade-Offs in a Fishery with Stock Interactions....................................................................20

3.3.1 MSY in a Fishery with Stock Interactions........................................................................................20

3.3.2 OSY in a Fishery with Stock Interactions.........................................................................................22

3.3.3 OYT in a Fishery with Stock Interactions.........................................................................................23

3.3.4 Concluding Remarks Concerning an Aggregate MSY, OSY and OYT for a Fishery as a Whole ......24

4. Conclusions........................................................................................................................................ 29

4.1 Key Points ................................................................................................................................................29

4.2 Important Topics for Future Work...........................................................................................................30

APPENDIX 1. A More Comprehensive Model of OSY ................................................................................ 33

APPENDIX 2. The Management Approach and Its Effects on OSY.............................................................. 39

APPENDIX 3. Dynamics and Discounting.................................................................................................. 43

APPENDIX 4. Modeling Uncertainty ........................................................................................................ 47

APPENDIX 5. Numerical Examples of Aggregate MSY and OSY in a Two-Stock Fishery with a Technical 

Interaction............................................................................................................................................. 51

APPENDIX 6. Catchability: A Critical Parameter in Stock Assessment and Bioeconomic Models................. 61

LITERATURE CITED.................................................................................................................................. 63
iv

Figures and Tables

Figure 1. MSY on a sustainable yield curve, where levels of sustainable yield and biomass are functions 

of the level of fishing effort............................................................................................................9

Figure 2. A simple model of OSY and comparison of the MSY and OSY levels of sustainable yield, 

biomass, and effort, where the simple model includes a narrowly defined measure of overall net 

benefit, a linear cost curve, a constant ex-vessel price, and logistic growth ...................................11

Figure 3. Sustainable revenue, total cost, and optimum sustainable yield with increasing prices and 

decreasing costs...........................................................................................................................42

Figure 4. MSY for a two-stock fishery as a whole when both stocks are caught together....................53

Figure 5. MSY and OSY for a two-stock fishery as a whole when the two stocks are caught together, 

the price of stock 2 is substantially greater than that of stock 1 (i.e., $5,000 versus $100 per metric 

ton), the cost of a unit of effort is $100,000, and overall net benefit is narrowly defined (Case 1)...56

Figure 6. MSY and OSY for a two-stock fishery as a whole when the two stocks are caught together, 

the price of stock 1 is greater than that of stock 2 (i.e., $300 versus $100 per metric ton), and the 

cost of a unit of effort is $100,000 (Case 2) ...................................................................................58

Figure 7. MSY and OSY for a two stock fishery as a whole when the two stocks are caught together, 

the price of stock 1 is greater than that of stock 2 (i.e., $300 vs. $100 per metric ton), and the cost of 

a unit of effort is reduced to $75,000 (Case 3)...............................................................................60

Table 1. Sustainable yield when MSY1, MSY2, and MSYF levels of effort are jointly applied to both 

stocks in a two-stock fishery with a technical interaction that results in the stocks being caught 

together ......................................................................................................................................53

Table 2. Sustainable yield, revenue, and cost, as well as a narrowly defined measure of overall net 

benefit, for Case 1 when MSY1, MSY2, MSYF, MSRevF, and OSYF levels of effort are jointly applied 

to both stocks in a two-stock fishery ............................................................................................55

Table 3. Sustainable yield, revenue, and cost, as well as a narrowly defined measure of overall net 

benefit, for Case 2 when MSY1, MSY2, MSYF, MSRevF, and OSYF levels of effort are applied jointly 

to both stock in a two-stock fishery..............................................................................................57

Table 4. Sustainable yield, revenue, and cost, as well as a narrowly defined measure of overall net 

benefit, for Case 3 when MSY1, MSY2, MSYF, MSRevF, and OSYF levels of effort are applied jointly 

to both stock in a two-stock fishery..............................................................................................59
v

ABSTRACT

This paper provides an economic perspective on the Magnuson-Stevens Fishery Conservation and 

Management Act (MSA) National Standard 1 (NS1) requirement to prevent overfishing while achieving 

the optimum yield (OY) from each fishery. Section 1 introduces NS1, key elements of the NS1 

Guidelines, and some relevant economic concepts. Section 2 relates these economic concepts to the 

goals of preventing overfishing and achieving OY. In that Section, OY is defined as a stable long-term 

average amount of desired sustainable yield, and a simple deterministic long-term sustainable economic 

yield model is used to determine OY. Section 3 extends the discussion to address important issues not 

captured in the simpler setting in Section 2, namely dynamics, uncertainty, and stock interactions. 

Several appendices further develop these ideas and their application to NS1. The core message of the 

paper is that NS1 requires considering costs and benefits, uncertainty, fishery dynamics, stock 

interactions, and the structure of the fishery management regime. The intent is to frame economic 

considerations in interpreting and implementing NS1 for agency staff, regional Fishery Management 

Council members and staff, and others in the broader US marine fishery management community.
vi

ACKNOWLEDGMENTS

We wish to thank Rick Methot and Rita Curtis for encouraging us to write this paper. We have benefited 

from extensive review comments by Lee Anderson and from discussions with or review comments by 

Steve Freese, Debra Lambert, Doug Lipton, Wesley Patrick, Lew Queirolo, Steve Stohs, Eric Thunberg, 

Mike Travis, and participants at the 2009 national meeting of Scientific and Statistical Committee 

members from the eight Regional Fishery Management Councils. In addition, Dan Lew and Amber 

Himes-Cornell provided assistance in drafting Sections A1.3 and A1.4, respectively. Any remaining errors 

are the authors’ alone. The views expressed herein are those of the authors and do not necessarily 

reflect the current views of the National Oceanic and Atmospheric Administration’s National Marine 

Fisheries Service. 
vii

EXECUTIVE SUMMARY

The Magnuson-Stevens Fishery Conservation and Management Act (MSA) includes ten national 

standards to be met by all fishery management plans and associated regulations. National Standard 1 

(NS1) requires that management “prevent overfishing while achieving, on a continuing basis, the 

optimum yield from each fishery for the United States fishing industry.” This paper demonstrates the 

relevance of economic concepts and analyses to NS1. The paper is intended primarily to be of use to 

agency staff, regional Fishery Management Council members and staff, and others in the broader US 

marine fishery management community who are involved in interpreting and implementing NS1.

Section 1 introduces NS1, key elements of the NS1 Guidelines, and key relevant economic concepts (see 

Box 1). Section 2 then explains how these economic concepts inform the goals of preventing 

overfishing and achieving optimum yield (OY). The main point regarding prevention of overfishing is 

that it generally entails a foregone value, or opportunity cost. The main point regarding OY is that

maximum sustainable yield (MSY) is in general not a compelling proxy for OY because MSY provides only 

a crude and incomplete measure of the overall benefit to the Nation. Introducing economic value in the 

context of current NS1 Guidelines, which describe OY as a long-term average amount of desired 

sustainable yield, leads to an OY proxy we call optimum sustainable yield (OSY). OSY is normally a more 

conservative reference point than MSY—that is, it requires higher biomass and lower catch and effort—

while resulting in greater overall net benefit to the Nation. In other words, more conservative 

management often promotes both of the NS1’s goals.

The goals of preventing overfishing and achieving optimum yield are linked in other ways. First, the 

opportunity cost of preventing overfishing affects net benefits and should therefore figure into OY 

discussions. Second, any yield that does not prevent overfishing is inconsistent with the MSA definition 

of OY. Third, preventing overfishing does not guarantee that OY is achieved, because low yields may 

prevent overfishing while failing to achieve OY. Taken together, these ideas suggest that joint treatment 

of preventing overfishing and achieving OY is likely to lead to better management.

Section 3 takes up three important factors not treated in the simple setting of Section 2: dynamics (i.e., 

changes in the fishery system over time), uncertainty, and stock interactions. Most, if not all, fisheries 

change over time and seldom if ever attain an idealized long-term biological or economic optimum such 

as MSY or OSY. As a result, yield targets are generally best thought of as trajectories rather than single 

values, an idea formalized as optimum yield trajectory (OYT) in Section 3.1. Section 3.2 treats the 

subject of uncertainty in fisheries management. The main points here are that preventing overfishing is 

best thought of in probabilistic terms (similar to insurance) and that a fully formulated notion of OSY or 

OYT explicitly captures decision makers’ attitude toward uncertainty in both scientific information and 

the application of management measures. Section 3.3 addresses the topic of ecological and economic 

interactions among stocks. Selecting yield targets given these interactions entails managing trade-offs 

that reflect a key tenet of ecosystem-based fisheries management (EBFM): MSY cannot be achieved 

simultaneously for all harvested stocks in an ecosystem. Froese et al. (2015) note that this is one of the 

few currently uncontested tenets of EBFM. Economics can contribute to a framework for assessing such 

trade-offs, consistent with NS1 and statements in the Ecosystem-Based Fisheries Management Policy of 

the National Marine Fisheries Service (National Marine Fisheries Service 2016).

Section 4 summarizes the connections made between economics and NS1 and offers recommendations 

for future work.
viii

The most important points we make in this paper are as follows:

1. Economic concepts and analyses can contribute to understanding of the trade-offs inherent in 

fisheries management decisions that aim to prevent overfishing while achieving OY. For example, 

understanding how fishermen and others involved in the fisheries are likely to respond to 

alternative management actions is critical to determining or modifying those trade-offs.

2. Because uncertainty is inherent in fisheries, preventing overfishing is meaningful only in probabilistic 

terms. A greater probability of preventing overfishing generally comes at greater cost, in terms of 

forgone yield. In other words, reducing yield is a form of payment to insure against overfishing.

3. Optimum yield is defined by the MSA in terms of benefits to the Nation. Including economic 

benefits generally leads to harvest policies that imply higher levels of biomass and overall net 

benefit and lower levels of effort and catch. For example, OSY is normally a more conservative 

reference point than MSY and it results in greater overall net benefit to the Nation.

4. Measures to achieve the joint goals of preventing overfishing and attaining OY are more likely to 

succeed if they account for system dynamics, uncertainty, stock interactions, and the effects of 

alternative management regimes.

Economics is well-suited to exploring trade-offs inherent in fisheries management decisions that aim to 

prevent overfishing while achieving OY for each stock, as well as trade-offs between what is best for 

each stock and what is best for the fishery as a whole given stock interactions or other ecosystem 

factors. We therefore believe economics has an important role to play in both meeting NS1 and 

implementing EBFM.
ix

Box 1. Key Economic Concepts

Value matters more than quantity. The value or net benefit of a fishery is a more appropriate 

guide to fishery conservation and management than is the quantity harvested alone. This is true 

because OY is defined in terms of the yield from a fishery that provides the greatest overall 

benefit to the Nation. Quantity harvested (i.e., weight or number of fish) is typically a limited 

measure of overall net benefit from a fishery. For example, catch weight is a poor measure of the 

benefits fishermen, consumers, and others receive from a fishery and it accounts for few of the 

costs associated with providing those benefits.

Every choice has an opportunity cost. The opportunity cost of using resources, including living 

marine resources, in a particular way is the forgone value of the best alternative use of those 

resources, which is determined by estimating the values of likely alternative uses.

Timing matters. Timing is important because most people prefer current benefits (e.g., income or 

consumption) to the same level of benefits in the future. A discount rate that reflects society’s 

time preference is required to make useful comparisons among benefits and costs that occur in 

different periods.

Risk is unavoidable and there are trade-offs among risks. Because of inherent variability and the 

difficulty of fully understanding and observing fisheries systems, fisheries management decisions 

inevitably involve various risks, such as the risk of overfishing, the risk of underfishing (i.e., 

catching less than OY), the risk of unexpected system effects (e.g., through food-web effects), and 

the risk of economic and/or social welfare loss. Such risks often compete, meaning that there are 

trade-offs among them; often, one risk can be reduced only through actions that require taking on 

more of a different risk. 
x

ACRONYMS, ABBREVIATIONS, AND VARIABLES

ABC Acceptable biological catch

ACL Annual catch limit

ACT Annual catch target

AM Accountability measures

BMEY Biomass at maximum economic yield (MEY)

BMSRev1

Independently determined maximum sustainable revenue (MSRev) level 

of biomass for stock 1

BMSRevF1 Biomass for stock 1 at MSRev for the fishery as a whole 

BMSY Biomass at maximum sustainable yield (MSY)

BMSY1 Independently determined MSY level of biomass for stock 1 

BMSYF1 Biomass for stock 1 at MSY for the fishery as a whole

BOSY Biomass at OSY

CGE model Computable general equilibrium model

CPUE Catch per unit of effort

EBFM Ecosystem-based fisheries management

EMSRev1 Effort at MSRev for stock 1

EMSRevF Effort at MSRev for the fishery as a whole

EMSY Effort at MSY

EMSY1 Independently determined MSY level of fishing effort for stock 1

EMSYF Effort at MSY for the fishery as a whole

EO 12866 Executive Order 12866

EOSY

EOSYF

Effort at optimum sustainable yield (OSY)

Effort at OSY for the fishery as a whole

FMSY Fishing mortality at MSY

FOSY Fishing mortality at OSY

Frebuild Fishing mortality associated with achieving Ttarget

IFQ Individual fishing quota

IVQ Individual vessel quota

LME Large marine ecosystem

MDP Markov decision process

MEY Maximum economic yield

MFMT Maximum Fishing Mortality Threshold

MSA or 

MSFCMA Magnuson-Stevens Fishery Conservation and Management Act

MSRev Maximum sustainable revenue

MSRevF Maximum sustainable revenue for the fishery as a whole

MSST Minimum stock size threshold

MSY Maximum sustainable yield

MSY1 Independently determined MSY for stock 1

MSYF MSY for the fishery as a whole
xi

MSYF1 MSY for stock 1 at MSY for the fishery as a whole

NMFS National Marine Fisheries Service

NOAA National Oceanic and Atmospheric Administration

NS1 National Standard 1

OECD Organisation for Economic Co-operation and Development

OFL Overfishing limit

OSY Optimum sustainable yield

OSYF OSY for the fishery as a whole

OSYF1 OSY for stock 1 at OSY for the fishery as a whole

OY Optimum yield

OYT Optimum yield trajectory

POMDP Partially observable Markov decision process

SDC Status determination criteria

SSC Scientific and Statistical Committee

TAC Total allowable catch

Tmax

The maximum allowable rebuilding time prescribed in the NS1 

Guidelines

Tmin

The amount of time the stock or stock complex is expected to take to rebuild to 

its MSY biomass level in the absence of any fishing mortality

Ttarget Target rebuilding period 
xii
1

1. Introduction 

The Magnuson-Stevens Fishery Conservation and Management Act (MSA)1requires that fishery 

management plans and regulations implemented under its authority be consistent with ten National

Standards. National Standard 1 (NS1) states that “conservation and management measures shall 

prevent overfishing while achieving, on a continuing basis, the optimum yield from each fishery for the 

United States fishing industry” (Sec. 301(a)(1)). 

Economics is relevant to NS1 for two related reasons. First, optimum yield (OY) includes in principle 

considerations of employment, nonmarket and recreational values, the profitability of fishing and 

processing firms, and benefits to seafood consumers. Second, from an economic perspective, ending 

overfishing or rebuilding a fishery is an investment undertaken with the expectation that benefits to 

society will exceed costs over time; and economic analysis can aid in evaluating those benefits and costs. 

Therefore, the NS1 Guidelines2suggest that the specifications of acceptable biological catches (ABCs), 

annual catch limits (ACLs), and accountability measures (AMs), which may include annual catch targets 

(ACTs), can be refined through the use of economic analysis of costs, benefits, distributional impacts, 

and risks. In fact, the MSA and other applicable laws (e.g., the National Environmental Policy Act, the 

Regulatory Flexibility Act, and Executive Order 12866 [EO 12866]) require economic analysis of those 

specifications and all other management actions.

1.1 Purpose and Organization of the Paper

The purpose of this paper is to demonstrate the relevance of economic concepts and analyses to NS1. 

The paper is intended primarily to be of use to agency staff, regional Fishery Management Council 

members and staff, and others in the broader US marine fishery management community who are 

involved in interpreting and implementing NS1 and exploring the trade-offs inherent in meeting NS1. 

Economic information is particularly useful since these trade-offs cannot be addressed adequately in 

terms of differences in levels of sustainable yield and biomass. For example, economic analyses are 

valuable when assessing trade-offs that require understanding how fishermen and others involved in 

fisheries are likely to respond to alternative management actions. More generally, economic analysis 

can support more informed decision-making as fishery managers face the joint problem of preventing 

overfishing and achieving OY. 

The remainder of Section 1 describes NS1, key elements of the NS1 Guidelines, and some relevant 

economic concepts. Section 2 relates these economic concepts to the goals of preventing overfishing

and achieving optimum yield. After discussing the economics of preventing overfishing, we examine 

economics’ relevance to achieving optimum yield by: 1) introducing the concept of optimum sustainable 

yield (OSY); 2) comparing OSY to maximum sustainable yield (MSY); and 3) exploring the use of OSY as 

an OY-related reference point. Section 3 then explores the important complications of dynamics (i.e., 

changes in the fishery system over time and the timing of those changes), uncertainty, and stock 

interactions. 

 

1 https://www.fisheries.noaa.gov/resource/document/magnuson-stevens-fishery-conservation-and-managementact

2 The NS1 Guidelines are in the Federal Register at: https://www.gpo.gov/fdsys/pkg/FR-2016-10-18/pdf/2016-

24500.pdf).
2

NOTE: This paper demonstrates how economics is relevant to understanding and implementing NS1; it 

is not intended to serve as a guide for the practice of economic analysis in support of NS1.

1.2 National Standard 1 and Key Elements of the NS1 Guidelines

Several changes to the MSA enacted in January 2007 were designed to prevent overfishing. Those 

changes included the addition of requirements for ACLs and AMs, where the ACLs established by a 

Council for its fisheries may not exceed the ABC recommendations of its Scientific and Statistical 

Committee (SSC) or a comparable MSA-approved peer review process. NOAA’s National Marine 

Fisheries Service (NMFS) revised the NS1 Guidelines in 2009 to provide guidance for implementing the 

requirements in MSA for ACLs and AMs to end and prevent overfishing (74 FR 3178; 1/16/2009). NMFS 

revised the NS1 guidelines again in 2016 to improve and clarify the guidance and address experiences 

gained during the implementation of ACLs and AMs (81 FR 71858; 10/18/2016). The NS1 Guidelines 

define and provide guidance on the terms ACL, AM, and ABC (used but not defined in the MSA), and 

provide separate definitions of “overfished”3 and “overfishing.”4 The NS1 Guidelines also explain the 

relationships between ACTs, ACLs, ABCs, and OFLs (overfishing limits) and how those reference points 

and the use of AMs play key roles in addressing scientific and management uncertainty.

The MSA provides the following definitions of the terms “optimum yield,” “overfishing,” and 

“overfished” (Sec. 3(33 and 34)). These definitions establish the importance of the concept of MSY for 

NS1 and the MSA as a whole. Specifically, they prohibit OY from exceeding MSY, define overfishing and 

overfished in terms of MSY, and require overfished fisheries to be rebuilt to a level consistent with 

producing MSY.

The term optimum, with respect to the yield from a fishery, means the amount of fish that: 

 Will provide the greatest overall benefit to the Nation, particularly regarding food 

production and recreational opportunities and taking into account the protection of marine 

ecosystems. 

 Is prescribed as such on the basis of the MSY from the fishery, as reduced by any relevant 

economic, social, or ecological factor. 

 In the case of an overfished fishery, provides rebuilding to a level consistent with producing 

the MSY in such a fishery. 

The terms overfishing and overfished mean a rate or level of fishing mortality that jeopardizes the 

capacity of a fishery to produce the MSY on a continuing basis.

NMFS and the Councils typically implement the concept of MSY using single-species biological models. 

MSY-based stock size limits and targets, and fishing mortality or catch limits, are fundamental features 

of the NS1 Guidelines. The NS1 Guidelines require each Council to establish a minimum stock size 

threshold (MSST) and other status determination criteria (SDC) based on MSY or MSY proxies for each 

stock or stock complex5in need of conservation and management unless data are not available to 

 

3 A stock or stock complex is considered ‘‘overfished’’ when its biomass has declined below the minimum stock size 

threshold (MSST), where MSST is the level of biomass below which the capacity of the stock or stock complex to 

produce MSY on a continuing basis has been jeopardized.

4 Overfishing occurs whenever a stock or stock complex is subjected to a level of fishing mortality or total catch 

that jeopardizes its capacity to produce MSY on a continuing basis.

5 The NS1 Guidelines define “stock complex” as a tool to manage a group of stocks within a FMP.
3

specify MSY-based SDC. In that case, alternative types of SDC can be used. The NS1 Guidelines do not 

address the use of alternative types of SDC when the rationale for using MSY-based SDC is in doubt.

However, the NS1 Guidelines recognize that MSY can be estimated for an aggregate group of stocks 

(including stock complexes and the fishery as a whole). If an aggregate MSY is used, it is conceivable 

that the SDC should be based on the aggregate MSY and the corresponding MSYs for individual stocks as 

opposed to the independently estimated MSYs for the individual stocks. NMFS has advised that the use 

of aggregate MSY estimates does not negate the need to use individual stock SDC (based on the best 

scientific information available), ACLs, and related reference points to ensure that individual stocks do 

not become overfished or experience overfishing. NMFS needs to determine whether the best scientific 

information available actually supports the use of SDC for the individual stocks that are based on 

independently determined MSYs, which ignore stock interactions and which cannot be achieved 

simultaneously for all harvested stocks in an ecosystem according to EBFM (e.g., Froese et al. 

2015). The use of SDC based on aggregate MSYs and the associated MSYs for individual stocks that do 

account for those interactions is discussed further in Section 3.3.4.

The NS1 Guidelines define an overfished stock or stock complex as one that is below its MSST, which 

should be between 1⁄2 Bmsy and Bmsy. Although the NS1 Guidelines allow MSSTs to be set for stocks or 

stock complexes, they recommend that where practicable, stock complexes should include one or more 

indicator stocks (each of which has SDC and ACLs). The NS1 Guidelines also stipulate that the rebuilding 

stock size target for an overfished stock is BMSY, and that the target rebuilding period (Ttarget) must not 

exceed Tmax

6 and shall be as short as possible, taking into account: the status and biology of any 

overfished stock, the needs of fishing communities, recommendations by international organizations in 

which the U.S. participates, and interaction of the stock within the marine ecosystem. The fishing 

mortality associated with achieving Ttarget is referred to as Frebuild.

Fishing mortality limits and catch limits are intended to prevent or end overfishing and to ensure that 

overfished stocks are rebuilt to BMSY as quickly as required by the NS1 Guidelines. The NS1 Guidelines 

require each Council to evaluate and describe MSY-based7 OFLs, ABCs, ACLs, and OYs, as well as AMs, 

for all the stocks and stock complexes in need of conservation and management that are not subject to 

at least one of two exceptions.8 The NS1 Guidelines require Councils to take an approach that considers 

uncertainty in scientific information and management control of the fishery.9

 

6

If Tmin for the stock or stock complex is 10 years or less, then Tmax is 10 years, where Tmin is the amount of time the 

stock or stock complex is expected to take to rebuild to its MSY biomass level in the absence of any fishing 

mortality. If Tmin for the stock or stock complex exceeds 10 years, then one of the following methods can be used 

to determine Tmax: Tmin plus the length of time associated with one generation time for that stock or stock complex; 

the amount of time the stock or stock complex is expected to take to rebuild to Bmsy if fished at 75 percent of 

maximum fishing mortality threshold (MFMT); or Tmin multiplied by two.

7 As noted above, alternative types of SDC can be used when data are not available to specify SDC based on MSY or 

MSY proxies but not when the rationale for using MSY-based SDC is in doubt.

8 The exceptions are for species with a life cycle of approximately 1 year, unless subject to overfishing, and for 

stocks managed under an international agreement to which the U.S. is party. 

9 The term “fishery” is defined in the MSA as one or more stocks of fish that can be treated as a unit for purposes 

of conservation and management and that are identified on the basis of geographical, scientific, technical, 

recreational, and economic characteristics; and any fishing for such stocks. Therefore, “fishery” refers to 

commercial, recreational, and subsistence fishing. 
4

Five key elements of the ACL-setting process described in the NS1 Guidelines are as follows:

1. ACL may not exceed ABC.

2. For overfished stocks and stock complexes, a rebuilding ABC must be set to reflect the annual 

catch that is consistent with the schedule of fishing mortality rates (i.e., Frebuild) in the rebuilding 

plan.

3. ABC may not exceed OFL.

4. The difference between OFL and ABC depends on how scientific uncertainty and the Council’s 

risk policy are accounted for in the ABC control rule.

5. The MSA requires that ABC be provided by the Council’s SSC or a comparable peer review 

process.

The NS1 Guidelines also suggest that Councils adopt an explicit risk policy as part of their ABC control 

rules, and go on to define acceptable probabilities of overfishing:

The Council’s risk policy could be based on an acceptable probability (at least 50 percent) that 

catch equal to the stock’s ABC will not result in overfishing, but other appropriate methods can 

be used. When determining the risk policy, Councils could consider the economic, social, and 

ecological trade-offs between being more or less risk adverse.

The NS1 Guidelines encourage Councils to address management uncertainty through a range of ACLs 

and AMs. Examples of management uncertainty include uncertainty in fishery managers’ ability to 

constrain catch so that the ACL is not exceeded and uncertainty in quantifying true catch amounts (i.e., 

estimation errors). AMs are intended to prevent ACLs from being exceeded and to correct or mitigate 

overages if they occur. The NS1 Guidelines also recommend that management uncertainty be accounted 

for in the ACL if an ACT is not used.

For fisheries without in-season management control to prevent ACLs from being exceeded, the NS1 

Guidelines note that AMs should include ACTs that are set below ACLs so that catches do not exceed the 

ACLs. If catches do exceed ACLs, AMs must be implemented as soon as possible to correct the 

operational issue that caused the ACL overage, as well as to mitigate the biological consequences to the 

stock, if any.

Although the goals of NS1 are to prevent overfishing while achieving OY, which includes rebuilding 

overfished fisheries, the NS1 Guidelines and the 2007 changes to the MSA discussed previously focus on 

preventing overfishing and rebuilding overfished stocks. Unfortunately, preventing overfishing and 

rebuilding overfished stocks do not ensure that OY will be attained. Indeed, with the exception of 

rebuilding overfished stocks, the guidance on developing and applying OY has been minimal, and 

practices have varied widely. In the remainder of this paper, we explore how economics can contribute 

to achieving both NS1 goals, in part by giving more attention to OY and the trade-offs faced when 

addressing overfishing and optimum yield simultaneously.

1.3 Key Economic Ideas Relevant to NS1

As suggested above, preventing overfishing while achieving OY is in part an economic problem. Here, 

we introduce some key ideas from economics that we will use in later sections to examine the economic 

content of NS1. 
5

Value matters more than quantity. The value or net benefit of a fishery is a more appropriate guide to 

fishery conservation and management than is the quantity harvested alone. This is true because OY is 

defined in terms of the yield from a fishery that provides the greatest overall benefit to the Nation. 

Quantity harvested (i.e., weight or number of fish) is typically a limited measure of overall net benefit

from a fishery. For example, catch weight is a poor measure of the benefits fishermen, consumers, and 

others receive from a fishery and it accounts for few of the costs associated with providing those 

benefits.

Every choice has an opportunity cost. The opportunity cost of using resources in a particular way is the 

forgone value of the best alternative use of those resources, which is determined by estimating the 

values of likely alternative uses. Consider the following examples: 

 Preventing a decline in future harvests or allowing an increase in future harvests may require a 

reduction in current harvest. 

 An increase in recreational harvest may require a reduction in commercial harvest, or vice versa. 

 Because of the complex interactions among the stocks in a fishery, higher levels of sustainable 

yield for some stocks may require lower levels for other stocks. 

 A reduction in fishing activity and catch may be required to provide additional protection for an 

endangered species and its habitat. 

Timing matters. Timing is important because most people prefer current benefits (e.g., income or 

consumption) to the same level of benefits in the future. A discount rate that reflects society’s time 

preference is required to make useful comparisons among benefits and costs that occur in different 

periods.

Risk is unavoidable and there are trade-offs among risks. Because of inherent variability and the 

difficulty of fully understanding and observing fisheries systems, fisheries management decisions 

inevitably involve various risks, such as the risk of overfishing, the risk of underfishing (i.e., catching less 

than OY), the risk of unexpected system effects (e.g., through food-web effects), and the risk of 

economic and/or social welfare loss. Such risks often compete, meaning that there are trade-offs among 

them; often, one risk can be reduced only through actions that require taking on more of a different risk. 

In the following sections, we will first explore the implications of these ideas in a very simple setting, and 

then consider more complicated and realistic settings.
6
7

2. Applying Economic Principles to NS1 in a Simple Setting

In this section, we first briefly consider the economic aspects of the requirement to prevent overfishing. 

Then, we use a single-species, long-term sustainable economic yield model of OSY to explore the 

application of economics to OY in a simple setting. Including economic measures of benefits and costs 

leads to a measure of greatest overall net benefit to the Nation, which we call OSY. OSY is a welldefined and useful—if, in practice, necessarily an incomplete—benchmark of management 

performance.

OSY is relevant to NS1 because it provides a measure of a well-managed fishery’s potential net benefit, 

as well as a reference point for estimating the forgone net benefit of pursuing particular harvest policies. 

OSY is derived from a more meaningful measure of net benefits to society than is MSY and can be kept 

consistent with the MSA’s conservation goals by defining it such that it satisfies all appropriate biological 

constraints, including MSY itself. 

2.1 Economics and Preventing Overfishing

The NS1 requirement to prevent overfishing, a fundamentally biological constraint, has important 

economic implications. First, the most obvious implication is that the yield forgone to account for 

uncertainty and decrease the probability of overfishing represents an opportunity cost that should be 

compared to the benefit of decreasing the probability of overfishing. 

Second, because uncertainty is inherent in fisheries, preventing overfishing is meaningful only in 

probabilistic terms, and a greater probability of preventing overfishing generally comes at greater cost in 

terms of forgone short-term yield and long-term average sustainable yield. In other words, reducing 

yield is a form of insurance against overfishing. 

Third, preventing overfishing is required to achieve OY but does not ensure that OY will be achieved. 

That is, preventing overfishing is necessary but not sufficient to achieve OY.

Fourth, management actions intended to prevent overfishing will have economic implications because: 

 Economic incentives resulting from those management actions may encourage or discourage 

accurate and timely reporting and compliance with fishery regulations; 

 Accurate and timely reporting and compliance may affect managers’ ability to move toward 

optimum yield while preventing overfishing; and 

 The monitoring, reporting, and enforcement components affect fishery management costs.

Fifth, preventing overfishing should involve institutional design that promotes efficiency in a fishery. 

National Standards 5 and 7 include requirements to consider efficiency.10 Overfishing may be prevented 

in various ways, and the identification of the costs and benefits of alternative measures to prevent 

overfishing requires economic information.

 

10 National Standards 5 and 7 are as follows:

(5) Conservation and management measures shall, where practicable, consider efficiency in the utilization of 

fishery resources; except that no such measure shall have economic allocation as its sole purpose. 

(7) Conservation and management measures shall, where practicable, minimize costs and avoid unnecessary 

duplication. 
8

Finally, efforts to prevent overfishing may have differential impacts among individuals, communities, 

fleets, and sectors. These impacts often involve market and nonmarket effects that make economics 

relevant to discussions of equity in relation to preventing overfishing.

2.2 The Economics of OY: Why MSY Is Not OY 

In this section, we apply economic principles to show that MSY is in general not a compelling proxy for 

OY. Specifically, we use a simple deterministic long-term sustainable economic yield model to develop

the concept of OSY, compare OSY to MSY, and explore the use of OSY as an OY-related reference point. 

Appendix 1 describes extensions to our simple model that more effectively capture the full range of net 

benefits from alternative levels of sustainable catch, biomass, and effort. 

Because the MSA does not define MSY, the NS1 Guidelines provide the following definition: 

MSY is the largest long-term average catch or yield that can be taken from a stock or stock 

complex under prevailing ecological, environmental conditions and fishery technological 

characteristics (e.g., gear selectivity), and the distribution of catch among fleets.11

The prevailing ecological and environmental conditions and fishery technological characteristics, and the 

distribution of catch among fleets are, in part, determined by regulatory and market conditions. 

Therefore, each MSY is defined for a specific set of regulatory and market conditions, and as those 

conditions change, the MSY can change. For example, a change in the fishery management regime, the 

price of fuel, gear selectivity, or the distribution of catch among fleets can affect MSY. This 

characteristic of MSY is discussed more fully in Section 2.2.3.

MSY for a stock of fish is usually determined using a biological model in which sustainable levels of yield 

(catch) and biomass, as well as the associated sustainable age, size, or stage structure (when an age-, 

size-, or stage-structured model is used12), are functions of the level of fishing effort. Typically, 

relationships among sustainable levels of effort, yield, and biomass are depicted by a sustainable yield 

curve, such as that in Figure 1. As effort increases, the sustainable level of biomass decreases, and 

sustainable yield increases, reaches a maximum at MSY, and then decreases as the actual level of effort 

exceeds the MSY level of effort (EMSY) by a larger amount, and actual biomass decreases farther below 

the MSY biomass level (BMSY).

 

11 The term "user groups" may be more appropriate than “fleets” in this context to clarify that this definition 

includes the distribution of catch among user groups in or among commercial, recreational, and subsistence 

fisheries.

12 When such a model is used, the reference to the associated sustainable age, size, or stage structure is implied 

but not made explicit in the rest of this paper.
9

Figure 1. MSY on a sustainable yield curve, where levels of sustainable yield and biomass are functions 

of the level of fishing effort.

MSY (measured as numbers or weight of fish) is not a sound proxy for OY because it is a poor measure of 

the benefits of catching and consuming fish and because it doesn’t account for most of the associated 

costs. There are many trade-offs when selecting among the sustainable sets of effort, biomass, and 

yield, and those trade-offs cannot be adequately addressed in terms of differences in levels of 

sustainable yield and biomass. Therefore, a reference point based on a more inclusive measure of 

overall net benefit would be useful for implementing NS1; OSY is such a reference point.

2.2.1 Defining OSY and Net Benefit to the Nation

Neither the MSA nor the NS1 Guidelines refer to OSY. The definition of OSY, which we derived from that 

of MSY on the previous page, is as follows:

OSY is the catch associated with the largest long-term average overall net benefit to the Nation 

that can be provided by a stock or stock complex under prevailing ecological, environmental, 

and economic conditions; fishery technological characteristics (e.g., gear selectivity); and the 

distribution of catch among user groups (e.g., fleets), where the sustainable levels of effort and 

biomass associated with each sustainable level of catch are among the determinants of the 

overall net benefit of that sustainable level of catch.13

To avoid the implication that we are referring to a narrowly defined set of net benefits, we use the term 

“OSY” instead of the more common term “MEY” (maximum economic yield). We define OSY in a way 

that, in principle, accounts for all the determinants of overall net benefit to the Nation for each 

sustainable level of yield and associated sustainable levels of biomass and effort. However, we recognize 

that data and model limitations will determine the extent to which OSY is, in practice, a more inclusive 

concept than MEY has often been.

 

13 In the definitions of MSY and OSY and throughout this paper, the terms “yield” and “catch” are used 

interchangeably.

MSY

Effort

0

0 EMSY 

BMSY

Yield

Biomass 
10

As with MSY, OSY is, in part, determined by regulatory and market conditions. Therefore, each OSY is 

defined for a specific set of regulatory and market conditions, and OSY will change as those conditions 

change. This characteristic of OSY is discussed more fully in Section 2.2.3 and Appendix 2.

There are various ways to define overall net benefit to the Nation. Executive Order 12866 provides a 

broad definition in its guidance concerning the requirement that NMFS and other federal agencies 

assess the costs and benefits of proposed regulations and alternative regulations. Specifically, it 

indicates that net benefit includes “potential economic, environmental, public health and safety, and 

other advantages; distributive impacts; and equity” (see Federal Register, 58(190), October 4, 1993 at 

http://cdn.loc.gov/service/ll/fedreg/fr058/fr058190/fr058190.pdf).

2.2.2 Using a Simple Model to Depict OSY and Compare It to MSY 

Figure 2 depicts a simple model of OSY in which: 1) Net benefit is measured narrowly as the difference 

between total revenue and total cost; 2) Total revenue is the product of sustainable catch and a 

constant ex-vessel price; 3) Total cost, which includes only the cost of labor, capital, and other inputs 

fishermen pay for, is the product of the level of effort and a fixed cost per unit of effort; 4) The stock of 

fish is caught exclusively in one commercial fishery and not in any recreational or subsistence fisheries; 

and 5) There are no ecological or economic interactions between this stock and any other living marine 

resources. With these simplifications, OSY and MEY are equivalent. A more comprehensive model of 

OSY, which eliminates this equivalency by including a much broader range of benefits and costs and by 

addressing recreational and subsistence fisheries, is discussed in Appendix 1. Appendix 2 shows how a 

change in the fishery management regime will affect OSY through its effects on the ex-vessel price and 

the marginal cost of effort. Section 3.3 discusses extension of the concepts of MSY, OSY and optimum 

yield trajectory (OYT) to a fishery with significant ecological or economic stock interactions. That 

discussion is based in part on the numerical examples in Appendix 5 for a two-stock fishery in which the 

economic interactions is that both stocks are caught together.

Figure 2 is based on the Gordon-Schaefer model (Gordon, 1954). This figure includes a standard 

sustainable yield curve for a surplus production model. The curve doubles as a sustainable revenue 

curve with the addition of a vertical axis with a scale that reflects a constant ex-vessel price (e.g., dollars 

per ton). In addition, the figure includes a linear cost curve. In Figure 2, the difference between the 

revenue curve and the linear total cost curve is maximized when the slope of the cost curve (the 

marginal cost of effort) is equal to the slope of the revenue curve (marginal revenue, or the additional 

revenue resulting from an additional unit of effort). Clark (1990) calls this outcome “maximization of 

sustainable economic rent.”
11

Figure 2. A simple model of OSY and comparison of MSY and OSY levels of sustainable yield, biomass, 

and effort, where the simple model includes a narrowly defined measure of overall net benefit, a 

linear cost curve, a constant ex-vessel price, and logistic growth.

With this simple model, sustainable levels of yield, biomass, and revenue, as well as cost, and the 

narrowly defined measure of overall net benefit, are functions of the level of fishing effort. The 

following occur as effort increases: 

 The sustainable level of biomass decreases. 

 The sustainable levels of yield and revenue increase, reach a maximum at MSY, and then 

decrease because effort exceeds EMSY by a larger amount, and biomass falls farther below BMSY. 

 Cost increases continuously.

 The sustainable level of net benefit increases, reaches a maximum at OSY, and then decreases 

because cost is increasing more rapidly than revenue (i.e., marginal cost becomes greater than 

marginal revenue); the OSY level of effort (EOSY) is exceeded by larger amounts; and biomass falls 

farther below the level that supports OSY (BOSY).

In this simple model, OSY is a more conservative reference point than MSY and provides greater overall 

net benefit to the Nation. It is more conservative because it is associated with a higher sustainable level 

of biomass (BOSY > BMSY) and lower sustainable levels of effort (EOSY < EMSY) and catch (OSY < MSY). 

Therefore, use of OSY as a reference point for OY is consistent with the MSA requirement that OY is to 

be less than MSY based on “any relevant economic, social, or ecological factor.” Although achieving a 

stock size of Bosy (which is higher than Bmsy) would be a higher standard than in the NS1 Guidelines, the 

following description of OY in the NS1 Guidelines indicates that a higher standard can be used:

Effort

Total Cost

Total 

Revenue

EOSY and 

BOSY

0

0 EMSY and 

BMSY

Yield Revenue

Biomass

Marginal Cost =

Marginal Revenue

MSY

OSY
12

In NS1, the phrase “achieving, on a continuing basis, the OY from each fishery” means: 

producing, from each stock, stock complex, or fishery, an amount of catch that is, on average, 

equal to the Council’s specified OY; prevents overfishing; maintains the long-term average 

biomass near or above Bmsy; and rebuilds overfished stocks and stock complexes consistent with 

timing and other requirements of section 304(e)(4)(j) of the MSA and paragraph 50 CFR 

600.310(j) of the National Standard 1 Guidelines.

2.2.3 Using OSY as an Additional Management Reference Point

As defined previously, MSY and OSY are complementary, stable long-term management reference 

points that are similar in the following ways: 

 They are based on biological models that estimate long-term sustainable levels of catch and 

associated sustainable levels of biomass and effort for a stock of fish. 

 Because MSY is constrained by “prevailing ecological, environmental conditions and fishery 

technological characteristics (e.g., gear selectivity), and the distribution of catch among fleets,” 

and because OSY is additionally constrained by prevailing economic conditions, the numeric 

values of MSY and OSY depend on variables that can fluctuate frequently and significantly. 

Examples of such variables include: 1) the conditions of other stocks in a fishery or large marine 

ecosystem that have ecological interactions (predation and competition) with the stock for 

which MSY or OSY is being assessed; 2) fleet-specific costs and ex-vessel prices and fishery 

regulations that change over time and affect gear selectivity and the distribution of catch among 

fleets, which in turn affect MSY and OSY through their effects on catch size composition; 3) 

variables that define the climate or environmental regime and affect recruitment, growth rates, 

and natural mortality; and 4) variables that affect time-varying catchability, gear selectivity, 

areas and depths fished, and even choice of gear and equipment.

 Changes in fishery management measures can change these constraints, which in turn lead to 

changes in MSY and OSY for a stock. For example, a fishery management action that changes the 

distribution of catch among fleets or the spatial or temporal distribution of catch could change 

the size composition of catch in a way that increases MSY and OSY. Similarly, a management 

action that decreases the marginal cost of effort would increase OSY. For example, by 

eliminating the race for fish, a well-designed catch share program can decrease fishing costs by 

decreasing fishing capacity, allocating catch to the most efficient fishing operations, and 

allowing each remaining fishing operation to fish more efficiently (e.g., reduce the amount of 

fuel and labor, bycatch, and fishing accidents for a given amount of catch). In addition, a welldesigned catch share program can increase ex-vessel revenue by increasing ex-vessel prices and 

catch utilization rates. 

 The actual biomass of a stock of fish is often not equal to BMSY or BOSY. 

However, because OSY maximizes sustainable overall net benefit rather than sustainable catch for a 

given set of ecological, environmental, regulatory, and market conditions, these two complementary 

reference points (i.e., OSY and MSY) have the following important differences: 
13

 OSY is or should be derived subject to various biological, ecological, oceanographic, climatic, 

economic, and social constraints or conditions that often interact with each other. Thus, OSY is 

fundamentally based on human values, consistent with the MSA requirement to manage 

fisheries to achieve the “greatest overall benefit to the Nation.” 

 In order to estimate an OSY that accounts for all the determinants of the overall net benefit to 

the Nation of alternative levels of sustainable catch, we need economic, biological, and 

ecological data and models in addition to the biological data and models used to estimate MSY.

 The uncertainty concerning numerical value, and the frequency and magnitude of fluctuations in 

that value, may be greater for OSY than for MSY because more variables determine OSY. For 

example, changes in fuel costs and ex-vessel prices have more direct and often larger effects on 

OSY than on MSY. Their effects on MSY are less direct; they result from effects on gear 

selectivity and the distribution of catch among fleets, which are among the determinants of MSY 

as it is defined in the NS1 Guidelines.

 OSY is a more conservative reference point (i.e., OSY < MSY, BOSY > BMSY, and EOSY < EMSY). This is 

not necessarily (or exclusively) due to precautionary considerations. For example, though OSY is 

smaller than MSY in the model discussed earlier, it is not appropriate to think of OSY in terms of 

a precautionary buffer for MSY. Rather, the difference between MSY and OSY in the long-term 

sustainable yield models is the result of their different objectives (maximizing catch weight 

versus maximizing a measure of the net benefit of catch). However, the inequality may have 

implications for the cost of a precautionary buffer (e.g., the cost of a buffer below MSY may be 

negative). Although OSY cannot in practice capture the full range of factors that determine a 

fishery’s overall net benefit to the Nation, it can capture many factors that MSY and MSY-based 

measures are not designed to address.

 OSY has rarely been estimated for U.S. fisheries and even more rarely, if ever, estimated based 

on broadly defined overall net benefit to the Nation. Obstacles to OSY estimates include 

inadequate data and particular technical challenges. The information required for estimating 

magnitudes and distributions of all the benefits and costs of harvesting and consuming fish has 

rarely been available. The lack of information is due to various factors, including limited 

economic data collection programs for many fisheries. Other factors include the challenges of 

developing economic and ecosystem models that can provide useful estimates of the

opportunity cost of using living marine resources and marine habitat to harvest fish. Accounting 

for that opportunity cost is an important but difficult step in moving toward ecosystem-based 

fisheries management (EBFM). 

Although the concept of OSY and the typically more narrowly defined concept of MEY have had limited 

use in U.S. fishery management, the concept of MEY is used extensively in Australian Commonwealth 

fisheries (Grafton et al., 2010). Vieira and Pascoe (2013), in a very useful paper, review relevant 

literature to provide a detailed description of the challenges to operationalizing MEY and, where 

possible, identify potential approaches to resolving them. They outline key economic definitions and 

concepts; discuss general experiences operationalizing MEY in Australian Commonwealth fisheries; and 

address issues relevant to particular types of fisheries (e.g., international and mixed-stock fisheries and 

fisheries with market power or highly variable stocks). In addition, Christensen, 2010; Sumaila and 

Hannesson, 2010; Norman-López and Pascoe, 2011; Grafton et al., 2012; and Squires and Vestergaard, 
14

2016 have expanded the concept of MEY to include a broader range of benefits and costs than were 

typically addressed.

Even though OSY is not among the reference points described in the NS1 Guidelines, it should be of 

great interest to policymakers. If, as in the NS1 Guidelines, OY is defined as a stable long-term average 

amount of desired sustainable yield, OSY can be a useful approximation of OY. Therefore, OSY provides a 

direct approach for assessing management performance in relation to the NS1 challenge of preventing 

overfishing while achieving OY. 

We expect steady progress in overcoming the modeling challenges associated with estimating OSY; 

however, data requirements for developing useful models of OSY are formidable. Given the current 

paucity of economic data—and particularly cost data—in many federally managed fisheries, new data 

collection programs are at least as important as modeling innovations to defining and managing for OSY. 

The basic economic data and analyses that will result in more informed decisions concerning the 

implementation of NS1 and most other fishery management actions are similar. In general, they are the 

data and analyses that can be used to assess the expected effects of such actions on the overall net 

benefit a fishery or set of fisheries in a large marine ecosystem provides to the Nation. Ideally, such 

assessments would begin with a prediction of how fishermen and others involved in the fishery will 

respond to the management action; include predictions of resulting biological, ecological, and economic 

effects, including cumulative effects; and present the result of those effects on overall net benefit to the 

Nation. 

Anderson and Seijo (2010) note that managing fisheries requires detailed knowledge of factors that 

influence fishing behavior, which can vary depending on fishermen’s cultural background and context, 

fishing technology used, and perceptions and strategic behavior affecting compliance with the 

regulatory scheme. Similarly, the National Research Council’s report (2013) on the effectiveness of stock 

rebuilding plans recognizes the importance of considering fishermen’s behavior. For example, it states 

that:

Fulton et al. (2011) suggest that human behavior is perhaps the greatest source of uncertainty in 

fisheries management, but the least adequately accounted for (see also Wilen, 2006). For 

example, fishermen’s decisions on where, when, for what species, and how to allocate fishing 

effort may affect the dynamics of rebuilding; reallocation of fishing effort can either slow or 

speed recovery. 

As one example of efforts to predict fishermen’s behavior, fisheries economists have since the 1980s 

modeled the factors that influence fishermen’s spatial and participation choices to understand the 

trade-offs of fishing in different locations. This knowledge can improve predictions of how fishermen will 

respond to the creation of marine reserves, changes in market conditions, or management actions such 

as the implementation of catch share programs or time and area closures. Similarly, predicting 

targeting-behavior changes is important in mixed-stock fisheries. Therefore, economic data and analysis 

are used both to predict the implications of the behavioral effects and how they will affect measures of 

expected overall net benefit to the Nation.
15

3. Applying Economic Principles to NS1 in a More Realistic Setting that Addresses the Complications of 

Dynamics, Uncertainty, and Stock Interactions

Economic principles apply to important aspects of fisheries management that are not captured in the 

simple setting described in Section 2. Three key aspects—fishery dynamics, uncertainty, and stock 

interactions—are discussed in Sections 3.1, 3.2, and 3.3, respectively, as well as in Appendixes 3 through 

5. Appendix 6 then addresses the importance of considering technological change and other factors 

that affect catchability. These other factors include density dependence, changes in environmental, 

biological, and management processes that affect how, when, where, and by whom fish are caught.

3.1 Dynamics: Discounting and Optimum Yield Trajectory

The NS1 Guidelines identify BMSY as the target stock level, provide a framework for determining the 

target time (Ttarget) to rebuild a stock, where Ttarget is the specified time period for rebuilding a stock that 

is considered to be as short a time as possible, taking into account the status and biology of any 

overfished stock, the needs of fishing communities, recommendations by international organizations in 

which the U.S. participates, and the interaction of the stock within the marine ecosystem. Ttarget shall 

not exceed Tmax, which is determined solely by biological factors. In Section 2, we used economics to 

develop the concept of OSY and identified BOSY as an alternative, generally more conservative and 

beneficial target. In this section, we address some limitations of MSY and OSY. In addition, we use 

economics to develop the concept of optimum yield trajectory (OYT), which is the sequence of harvests 

over time expected to maximize the discounted present value of the net benefit from a fishery while 

preventing overfishing.

In principle, such a framework can be used to address the following two questions.

1. How quickly should we rebuild an overfished stock from its current biomass level to a specific 

target level such as BMSY or BOSY? More specifically, what are the optimum yield, effort, and 

biomass trajectories (i.e., time paths) for attaining the target stock level, where the optimum 

trajectories are those expected to maximize the discounted present value of the net benefit 

from a fishery?

2. What are the optimum yield, effort, and biomass trajectories if the stock is not overfished or if a 

stable long-term biological or economic optimum does not exist because MSY or OSY is 

expected to change over time? 

The concept of OYT is required to address those two questions because OSY and MSY are long-term 

sustainable yield concepts that do not reflect current stock conditions and the benefits and costs of 

alternative time paths to a specific biomass target level. We use the term OYT instead of dynamic MEY 

to eliminate confusion about how inclusive the term MEY is and to make a clear distinction between the 

long-term sustainable economic yield concept of OSY and the dynamic desired yield trajectory concept 

of OYT. Just as OSY is in practice a proxy for OY when OY is defined as a long-term economic optimum, 

OYT is in practice a proxy for OY when OY is defined as a desired annual yield trajectory (i.e., a series of 

desired annual yields that can vary annually)

14

.

 

14 The NS1 Guidelines state that “While OY is a long-term average amount of desired yield, there is, for each year, 

an amount of fish that is consistent with achieving the long-term OY. A Council can choose to express OY on an 
16

For clarity in this section, we develop the concept of OYT in a deterministic setting without stock 

interactions. In Sections 3.2 and 3.3 and Appendixes 4 and 5, we discuss the complications of 

uncertainty and stock interactions. Addressing those complications, which are typical of most fisheries, 

is key to developing more useful fishery management models.

In practice, it is difficult to account for all benefits and costs in determining OYT. Typically not included

are: the opportunity cost of using living marine resources and marine habitat to harvest fish; benefits 

and costs beyond the harvesting sector; and equity and employment effects. For both OSY and OYT, 

modeling difficulties and lack of data are obstacles to generating a complete quantitative analysis. 

However, using qualitative analyses where quantification is not possible, as expressly provided for in EO 

12866, can enhance understanding of the range of likely outcomes and facilitate informed decisionmaking in the absence of perfect information.

Fisheries are inherently dynamic, and it is standard practice in economics to evaluate benefits and costs 

over time using a technique known as “time discounting.” Discounting is a complicated subject, but an 

important consideration in defining OYT. In general, OYT is defined in reference to a particular discount 

rate. The discount rate is intended to represent the rate of social time preference under the assumption 

that people generally prefer a reward today over the prospect of a similar reward in the future.

An important example is the simplest kind of time discounting—geometric—with a constant discount 

rate r. With a constant discount rate r, the discounted present value of a $100 bill received in t years 

from the present is $100/(1+r)

t

, and the discounted present value of receiving a $100 bill every year 

forever, beginning with one today, is $100*(1+1/r). As the time step becomes smaller, geometric 

discounting leads to exponential discounting in continuous time. 

The choice of what discount rate to apply to public policy analyses can be controversial because the 

discounted present value of a given stream of net benefits decreases as the discount rate increases. This 

is particularly true when future net benefits occur so far in the future that there are inter-generational 

effects. In fact, the inventor of optimal economic growth models, Frank Ramsey (1928), famously 

described the entire practice of discounting as “ethically indefensible” and one that “arises merely from 

the weakness of the imagination.” 

Nonetheless, discounting is standard practice in federal government economic analyses that satisfy EO 

12866 and other statutes. For analyses satisfying EO 12866, Office of Management and Budget Circular 

A-94 requires evaluation of proposed policies at a 7 percent real (inflation-adjusted) discount rate. 

Circular A-94 strongly encourages comparing policies using real discount rates of 3 percent and 7 

percent, though analysts may use a rate other than 3 percent if it can be justified or if it is used in 

addition to 3 percent. Therefore, NMFS and Council analysts have some flexibility with respect to which 

discount rates will be used.

Because OYT is defined in terms of the discounted present value of the net benefit from a fishery, time 

discounting plays a more important role in determining OYT if the discount rate is comparatively high, if 

a stock will take many years to rebuild, and if the costs occur well before the benefits (or vice versa).

 

annual basis, in which case the FMP or FMP amendment should indicate that the OY is an “annual OY.” An annual 

OY cannot exceed the ACL.” Therefore, OYT would identify the annual OYs over time and for each year the ACL 

should equal the annual OY, which is in part intended to prevent overfishing and rebuild overfished fisheries.
17

The traditional approach for estimating OYT in the bioeconomic literature is the deterministic optimal 

control model, as used, for example, by Clark (1990). With this approach, deterministic bioeconomic 

models are used to solve dynamic optimization problems, with an objective function representing the 

discounted present value of the stream of profits (and consumer surplus if adequate data are available). 

This value is maximized subject to a biological growth equation that includes the effects of the growth of 

individual fish, recruitment, natural mortality, and fishing mortality. 

Dynamic optimization problems are generally difficult to solve and it is useful to derive analytic solutions 

to gain insight, so simplified functional forms have often been used. This tradition goes back at least to 

the quadratic yield-effort curves in Gordon (1954) and Schaefer (1954). In fact, the standard 

bioeconomic model is often referred to as the Gordon-Schaefer model. Solutions of models with logistic 

growth and extensions (e.g., Pella and Tomlinson, 1969) are well analyzed (e.g., see Clark, 1990), and 

applications are widespread. 

For many years, most bioeconomic models used to estimate an incomplete version of OYT, which did 

not account for all the broadly defined benefits and costs of a yield trajectory, were based on a logistic 

growth function and surplus production. But as discussed in Appendix 3, age-structured bioeconomic 

models are increasingly the norm. For example, Kjaersgaard and Frost (2008) disaggregate effort; specify 

age-structured stock dynamics rather than surplus production; explicitly incorporate recruitment and 

selectivity; evaluate spawning stock biomass; allow discarding; specify multiple inputs, species, and 

fleets; spatially disaggregate harvesting; allow dynamic numerical allocation; and can perform both 

optimizations and feedback simulations. Bjørndal and Brasãao (2006) and Kompas et al. (2010), as well 

as other studies discussed in Appendix 3, incorporate age structure, explicit recruitment, and other 

features.

OYT with Fixed Stock-Level Targets

A dynamic optimization approach is appropriate for comparing the expected benefits, costs, and 

distributional effects of alternative rebuilding schedules and associated time paths of catch, biomass, 

and effort for attaining fixed-target stock levels (e.g., BMSY or BOSY) for overfished stocks. For example, 

Costello et al. (2012) use a dynamic bioeconomic optimization model that explicitly accounts for 

economics, management, and the ecology of size-structured exploited fish populations to estimate the 

optimal rebuilding strategy and economic returns from rebuilding for each of 18 hypothetical fisheries 

spanning a wide range of basic biological, harvest, and economic traits. They define the optimal 

rebuilding strategy as that which will provide the greatest net present value of the profits from the 

fishery over time. Although a broader measure of overall net benefit is required by the MSA, the NS1 

Guidelines, and EO 12866, the findings of Costello et al. suggest the kinds of results that might emerge 

from applying such an approach to NS115. 

 

15 Findings from Costello et al. (2012) include the following:

1. Under an optimal rebuilding strategy, stock recovery requires between 4 and 26 years (with a mean of 11 

years), depending on the fishery.

2. Our results suggest that the value [of recovery from a collapsed state] can be quite large (perhaps 2–5 

fold increases or greater in the value of a collapsed fishery), but the value may be strongly dependent on 

ecological, economic, and regulatory characteristics of the fishery.

3. A similar degree of heterogeneity exists in the economically optimal rebuilding time for a fishery (typically 
18

Larkin et al. (2011) discuss the use of bioeconomic modeling for developing rebuilding strategies. They 

identify problems with the commonly held belief that fishery closures are the “maximizing” approach to 

successful rebuilding. In addition, they note that when economic, social, and cultural considerations are 

included in developing optimal rebuilding plans, the most rapid rebuilding plan is often not the optimal 

plan. Larkin et al. also state that “bioeconomic models, if properly used, can help managers develop 

objective analysis in order to select rebuilding strategies that have the best chance to maximize social 

welfare” and that “bioeconomic models can also be used to help managers balance the risk to 

protecting fishery stocks against the economic and social risks to fishermen, processors, and the 

communities that depend on their activities.”16

The maximum allowable rebuilding time (Tmax) prescribed in the NS1 Guidelines does not address 

economic considerations and could often preclude the use of rebuilding periods that would increase the 

discounted present value of the net benefit from a fishery. However, OYT, constrained by the rebuilding 

periods specified in the NS1 Guidelines and BMSY or BOSY target stock level, can be used to identify the 

best catch, effort, and biomass time paths given those constraints.

OYT without Fixed Stock-Level Targets

Ignoring the dynamic nature of fisheries and managing fishery resources for a nonexistent, long-term 

biological or economic optimum will result in inappropriate targets for yield, effort, and stock conditions 

and, therefore, decrease the discounted present value of the net benefit from a fishery. For example, 

simply excluding technological change from population and bioeconomic models can create various 

problems. 

First, when stock assessments are based principally on catch-per-unit-of-effort (CPUE) data and do not 

 

8–20 years), which, according to our results, typically involves small (though non-zero) increasing harvest 

during the rebuilding trajectory. 

4. While a biologically based rebuilding policy that does not consider economics will always be the fastest 

way to achieve rebuilding goals, our results show that the economically optimal policy often takes a little 

longer but leads to substantially higher value.

5. Efforts to rebuild and recover the world’s fisheries, whether collapsed or heading towards collapse, will 

benefit greatly from an improved understanding of the long-term economic benefits of recovering 

collapsed stocks, the trajectory and duration of different rebuilding approaches, variation in the value and 

timing of recovery for fisheries with different economic, biological, and regulatory characteristics, 

including identifying which fisheries are likely to benefit most from recovery, and the benefits of avoiding 

collapse in the first place.

6. Getting better estimates of cost parameters and discount rates will be particularly useful given that these 

parameters are often poorly known and yet affect results as shown [in this paper].

7. In cases where a decision has already been made to rebuild, then it may be desirable to calculate 

economically optimal policies with an endogenous rebuilding constraint. 

16 These papers (Costello et al., 2012; Larkin et al., 2011) were included in an Organisation for Economic Cooperation and Development (OECD) series on the economics of rebuilding fisheries. The OECD (2012) report, 

Rebuilding Fisheries: The Way Forward, includes references to other papers in that series.
19

fully account for the effects of technological change, technological change is a source of upward bias in 

those assessments. Second, if effort controls are the principal management tools used to control catch, 

and technological change is not fully accounted for, the resulting effort controls will be inadequate and 

catch will be too high. Finally, technological change tends to increase OSY and OYT by decreasing the 

costs of harvesting, processing, and marketing fish, and perhaps by increasing product quality and 

therefore the prices of fish and seafood products. Because technological change lowers the costs of

harvest, leaving fish in the water to lower harvest costs is no longer as important. Therefore, accounting 

for technological change and other factors that will change over time is key to effective fishery 

management. Squires and Vestergaard (2013) provide an excellent discussion of the importance of 

accounting for technological change and its effects on optimal harvest strategy. Appendix 6 addresses 

the importance of considering technological change and other factors that affect catchability.

The OYT of any stock that requires conservation and management is constrained by its OFL, ABC, and 

ACL. However, when the stock is not overfished, its OYT is not constrained by a fixed-target stock level. 

In such cases, and if a stable OSY does not exist, OYT can be assessed using OYT control rules; relatively 

short-term forecasts of the net benefits of alternative catch, effort, and biomass time paths; and 

adaptive management that responds to changes in stock conditions and other determinants of OYT 

(including our understanding of those determinants).

These dynamic optimization concepts and related decision support methods for OYT and OY control 

rules need to be further developed and operationalized to support fisheries management where longterm sustainable yield approaches have proved to be less useful.

3.2 Uncertainty and Fishery Management under NS1

Uncertainty is an important aspect of both preventing overfishing and attaining optimum yield, the core 

requirements of NS1. Harvest levels that prevent overfishing are estimated under uncertainty about 

stock size, stock dynamics, fisherman behavior, ecosystem effects, and other factors. Optimum yield 

must also be interpreted in light of these uncertainties and others such as uncertainty about costs and 

benefits, market dynamics, and regulations17.

Over the past decade, incorporating uncertainty into efforts to prevent overfishing has been a focus 

within the US fisheries management community. The NS1 Guidelines require that scientific uncertainty 

be considered in setting ABC and recommend that management uncertainty be accounted for in the 

ACL, if an ACT or functional equivalent is not used and in the ACT if one is used. Specifically, the NS1 

Guidelines stipulate that ACL cannot exceed ABC, where ABC is based on an ABC control rule that 

accounts for scientific uncertainty in the OFL, any other scientific uncertainty, and the Council’s risk 

policy. The 2016 revisions to the NS1 Guidelines removed the explicit language stating that Councils 

could “choose to use a single control rule that combines both scientific and management uncertainty and 

supports the ABC recommendation and establishment of ACL and if used ACT.”

The buffers between OFL and ABC, between ABC and ACL, and between ACL and ACT provide insurance 

against undesirable outcomes. Therefore, optimal buffer size will depend both on the cost of that buffer 

relative to the cost of other methods of providing the same level of protection and on the benefits of 

various levels of protection against the undesirable outcome. Actions that could reduce both uncertainty 

 

17 Useful surveys of uncertainty in fisheries management can be found in Charles (1998) and Berkson et al. (2002). 
20

and appropriate buffer sizes include:

 More timely and accurate catch monitoring

 More timely and accurate stock and rebuilding monitoring

 Quicker adjustments to ACLs and AMs

 Better understanding of how fishermen will respond to AMs and other management actions

 In some circumstances, the use of large marine protected areas

Estimating OY under uncertainty requires information on economic and social factors. In a static 

framework, such as the model of OSY depicted in Figure 2, one method for addressing uncertainty 

would be to estimate the sustainable revenue and cost curves in terms of expected revenue and cost, 

and add confidence limits to both curves. However, setting harvest levels in fisheries is by nature a 

dynamic problem, because current harvest affects future stock dynamics and attainable harvest. Given 

uncertainty in a dynamic setting, a common approach is to develop a feedback control policy using the 

tools of optimal control or Markov decision processes (MDPs). Such models are commonly used in 

ecology, engineering, genetics, and economics. They have been used for the management of animal 

populations since at least Reed (1974) and D. Anderson (1975), and for fisheries since at least Ludwig 

(1979) and Reed (1979). Under this type of approach, OYT would be defined in terms of mapping from a 

current observed stock level into a harvest recommendation; that is, it would be a feedback control rule 

(see Beddington and May (1977) for an early example of this point). We describe some of the methods 

available to develop such an approach in Appendix 4.

It's important to note that preventing overfishing is necessary but not sufficient for attaining OY. That is, 

preventing overfishing is a requirement, but satisfying that requirement does not imply that the 

requirement to attain OY has been met. In principle, overfishing and optimum yield would best be 

addressed simultaneously within a unified framework. One approach to a joint treatment of overfishing 

and OY would be to treat OY as an objective to be optimized subject to constraints that prevent 

overfishing. An alternative would be to treat OY and overfishing as dual objectives in a joint

optimization framework, allowing the assessment of trade-offs between them. Developing the 

analytical and institutional capability to treat OY and overfishing jointly would support better fishery 

management in the future.

3.3 Additional Trade-Offs in a Fishery with Stock Interactions

When there are significant ecological interactions (e.g., predation and competition) or economic 

interactions (e.g., market interactions or stocks are caught together) among two or more stocks in a 

fishery, MSY, OSY, or OYT for the entire fishery is not the sum of the independently determined MSYs, 

OSYs, or OYTs of its individual stocks. Stock interactions result in a new set of trade-offs that cannot be 

adequately addressed in terms of differences in levels of sustainable yield and biomass for each stock. 

This section extends the concepts of MSY, OSY and OYT to a mixed-stock fishery with stock interactions 

and demonstrates that economics provides a framework for addressing those trade-offs. 

3.3.1 MSY in a Fishery with Stock Interactions

Researchers have demonstrated that ignoring ecological interactions (predation and competition) 

among the stocks in a fishery results in incorrectly specified reference points. For example, Link et al.
21

(2011) note that “exploring the use of model outputs at the aggregate or systemic levels is something 

that is sorely needed and requires much greater attention in the near future.” They recognize the need 

to address biological trade-offs resulting from ecological interactions. In addition, they reference a study 

from the Northeast Fisheries Science Center (2008) that suggests that expected aggregate yield and BMSY

are lower, and that overall fishing mortality rates should be lower, for stocks as a whole than singlespecies results suggest. 

Similarly, Mueter and Megrey (2006) estimate maximum multispecies surplus production (equivalent to 

maximum sustainable yield) for groundfish complexes in the Eastern Bering Sea/Aleutian Islands region 

and the Gulf of Alaska. They find that their estimates are smaller than the sum of single-species MSY 

proxies from recent stock assessments for each groundfish complex. In another example, Kasperski 

(2015) finds that because arrowtooth flounder negatively affect the growth of other stocks, MSYs for 

Pacific cod and Alaska pollock—economically and ecologically important target stocks in the Bering 

Sea/Aleutian Islands groundfish fishery—would be greater if the arrowtooth flounder biomass was well 

below its BMSY and possibly below its MSY-based MSST. 

These results suggest that when there are significant interactions among two or more stocks, aggregate 

MSY reference points (MSYF) for all the stocks in a fishery should be determined simultaneously, using 

known interactions among those stocks. That is, MSYF should be used to determine MSY reference 

points for the fishery as a whole, including associated reference points for individual stocks. Given the 

critical role of MSY in the MSA and NS1 Guidelines, it is important to address the concept of MSY for a 

fishery as a whole—and the trade-offs between trying to do what is best for each stock and what is best 

for the fishery as a whole—in terms of maximizing sustainable yield. Because this discussion is in terms 

of MSY, these trade-offs reflect differences in long-term sustainable yield among the stocks in a fishery 

rather than trade-offs between current and future yields.

Appendix 5 provides a numerical example of the aggregate MSY for a two-stock fishery in which the only 

stock interactions is that both stocks are caught together. The key points of this simple example in which 

the independently determined MSY level of effort is greater for stock 1 than for stock 2 (i.e., EMSY1 > 

EMSY2) are as follows:

1. The sum of the MSYs for the two stocks does not represent an attainable MSY for the fishery as 

a whole. 

2. The level of effort that generates MSY for the fishery as a whole (EMSYF) is less than the MSY level

of effort for stock 1 (EMSY1) but greater than the MSY level of effort for stock 2 (EMSY2).

3. If the MSY reference point for the fishery as a whole (MSYF) is used, the biomass targets for 

stocks 1 and 2 are the sustainable biomass levels associated with the level of effort that 

generates MSY for the fishery as a whole (EMSYF); therefore, the target level for stock 1 is greater 

than its BMSY , the target level for stock 2 is less than its BMSY, and attaining MSY and BMSY for 

either stock would prevent the attainment of MSY and BMSY for the other stock and for the 

fishery as a whole.

4. A choice needs to be made among the reference points that will support MSY for one stock, 

MSY for the other stock, or MSY for the fishery as a whole.
22

However, there is a potentially critical problem with the concept of an aggregate MSY. It is the implicit 

assumptions that an additional metric ton of sustainable yield of any stock is equally important and that 

its importance does not depend on the level of sustainable yield for any stock. There are at least three 

possible fixes if these assumptions are not valid. First, we can recognize this as an additional advantage 

of using aggregate OSY instead of aggregate MSY as a reference point because those assumptions are 

not implicit in the concept of an aggregate OSY. Second, we could apply different weights to reflect the 

differences in the importance of an increase in sustainable yield among stocks and among levels of 

sustainable yield for individual stocks. However, the determination of the appropriate weights will be a 

challenge. Third we can present the multi-dimensional surface (i.e., sustainable yield possibilities 

frontier) that depicts the various levels of sustainable yield that are simultaneously attainable for the 

stocks in a fishery and then determine how to select the optimum point on that surface. MSY frontiers 

are an area of ongoing research (e.g., Flaaten 1988).

3.3.2 OSY in a Fishery with Stock Interactions

For simplicity, we discuss the extension of the concept of OSY to a mixed-stock commercial fishery using 

the same two-stock fishery example we used in Section 3.3.1 and the simple model of OSY we discussed 

in Section 2.2.2. The main points from the numerical examples discussed in Appendix 5 are as follows: 

1. If the ex-vessel prices of the two stocks differ, the levels of effort that maximize sustainable 

yield (EMSYF) and sustainable revenue (EMSRevF) for the fishery as a whole are not the same. 

Therefore, simply changing the objective from maximizing sustainable yield to maximizing 

sustainable revenue changes the maximizing level of effort for the commercial fishery as a 

whole, and associated biomass target levels for both stocks. 

2. The cost of fishing effort is considered in determining OSY levels of effort, catch, and biomass 

for the fishery as a whole. Note that OSY cannot be determined separately for each stock

because the same effort, and therefore the same cost, is associated with catching both stocks 

together.

3. EOSYF is less than the EMSYF; therefore, the fishery as a whole OSY-based biomass target for each 

stock will be greater than the associated MSY-based biomass target.

4. The EOSYF-based biomass target for at least one of the stocks will be greater than its 

independently determined MSY-based biomass target. But, depending on the differences in 

prices for the two stocks and the cost per unit of effort, the EOSYF-based biomass target for the 

other stock can be greater than, less than or equal to its independently determined MSY-based 

biomass target.

Interactions among stocks can be much more complex than the examples just discussed, in which the 

only interaction is that two stocks are caught together in a single fishery. For example, L.G. Anderson 

(1975) considers the ecological interactions of two stocks in the case of two single-stock fisheries where 

the biomass of each stock depends on the biomass of the other stock. He also analyzes technical 

interactions between two stocks in the case of two single-stock fisheries that each take some of each 

other’s target species as incidental catch because neither fishery uses perfectly selective fishing gear. He 

notes that in both cases it is possible to discuss an MSY for both fisheries combined, and that this will 

occur when the sum of the yields from the two fisheries is a maximum. He presents the conditions for a 

combined static MEY for the two fisheries and shows that those conditions will not hold if each fishery is 
23

managed to obtain its individual MEY. 

More recently, Anderson and Seijo (2010) consider four possible combinations of ecological and 

technical interactions and determine that static MSYs and MEYs for fisheries and/or fleets combined 

cannot be determined by independently estimating MSYs and MEYs by species:

 Combination 1: Each of two heterogeneous fleets harvests a different species; the two species 

compete with each other for an ecosystem-limiting factor such as space or food.

 Combination 2: Each of two heterogeneous fleets harvests a different species; one species is the 

prey of the other.

 Combination 3: Two fleets with different fishing power and unit costs of effort compete for a 

stock in the same fishery.

 Combination 4: A multispecies fishery where a fleet incidentally harvests the target species of 

another fleet in addition to its own target species.

These results suggest that when there are significant interactions among two or more stocks in a fishery, 

OSYF-based reference points for all stocks should be determined simultaneously using known 

interactions among those stocks. That is, just as MSYF should be used to determine MSY reference 

points for the fishery as a whole, OSYF should be used to determine OSY reference points for the fishery 

as a whole, including associated reference points for individual stocks in the fishery. Using OSYF-based 

reference points accounts for the trade-offs between trying to do what is best for each stock and what is 

best for the fishery as a whole in terms of maximizing overall net benefit. Because this discussion is in 

terms of OSY, which is a stable, long-term sustainable economic yield concept, these trade-offs reflect 

ongoing differences in the overall net benefit from a fishery rather than trade-offs between current and 

future overall net benefits. 

Unlike the concept of aggregate MSY, the concept of aggregate OSY is not based on the implicit 

assumptions that an additional metric ton of sustainable yield of any stock is equally important and that 

its importance does not depend on the level of sustainable yield for any stock. 

3.3.3 OYT in a Fishery with Stock Interactions

The OYT for a stock of fish is the catch trajectory (or time path) that is expected to maximize the 

discounted present value of the net benefit from a fishery, given current conditions for the stock and 

expected changes in ecological, environmental, and economic conditions; fishery technological 

characteristics (e.g., gear selectivity); and distribution of catch among user groups (e.g., fleets). If the 

OYT for a stock is determined in part by an MSY- or OSY-based target biomass level (e.g., BMSY or BOSY) 

and an MSY- or OSY-based fishing mortality limit (e.g., FMSY or FOSY), and if there are significant 

interactions among two or more stocks in the fishery, the target and limit for the fishery as a whole and 

associated stock-specific targets and limits attempt to capture those stock interactions. In such cases, 

targets and limits based on MSY and OSY for a fishery as a whole will be more useful in determining 

OYTs than the independently determined MSY and OSY for each stock in a fishery.

In addition to affecting the stock-level targets that constrain the OYTs of individual stocks, stock 

interactions mean that OYTs for individual stocks should not be determined independently. The catch 

trajectory of each stock can affect the discounted present value of the net benefit of catch trajectories 

of other stocks in a fishery. Therefore, stock interactions should be accounted for to the extent 
24

practicable to simultaneously estimate OYTs for all stocks in a fishery. The resulting OYTs for individual 

stocks can be substantially different than those that are determined independently, and can identify 

additional trade-offs among stocks in a mixed-stock fishery. 

3.3.4 Concluding Remarks Concerning an Aggregate MSY, OSY and OYT for a Fishery as a Whole 

The 2013 National Research Council report on the effectiveness of stock rebuilding plans includes the 

following relevant conclusions concerning the trade-offs between MSY-based reference points for a 

fishery as a whole and those that are independently determined for individual stocks. 

 Fisheries management involves trade-offs among harvested species that interact, even if these 

trade-offs are not explicitly considered in management decisions. 

 Our understanding of how ecosystems function is improving, in some cases enough to 

contribute to the models used in fisheries management. For example, stock assessments can be 

linked with multispecies models.

 If the concern is about long-term risk of recruitment failure, or, worse, extinction, then the 

MSST is the incorrect threshold. The specification of the MSST is not based on recruitment 

failure or extinction.

 Rebuilding of mixed-stock fisheries will remain challenging because of the need to weigh tradeoffs among species.

 Attempting to deal with the mixed-stock problem will require analyses and modeling of

fisheries and economics data to identify appropriate solutions, as well as flexibility to apply

mixed-stock exceptions (where applicable).

 One challenge is the development of mixed-stock fisheries models that allow for evaluation of

trade-offs.

 A second challenge is to design operational regulations with incentivesfor fishing practicesthat

adequately protect weak stocks while providing fishing opportunities for healthy stocks.

 For mixed stocks, the stock-specific approach that ignores species interactions can result in 

fisheries forgoing yield of a healthy stock to allow rebuilding of a weak stock.

 In general, the current requirements have led to socioeconomic considerations playing a 

secondary role in the design of rebuilding plans.

Froese et al. (2015) note that one of the few currently uncontested tenets of EBFM is that maximum 

sustainable yields cannot be achieved simultaneously for all exploited stocks in an ecosystem. 

Therefore, alternative sustainable yield and biomass targets (or reference points) are required.

Kasperski (2015) provides additional evidence to support the use of reference points (e.g., MSYs, OSYs, 

and OYTs) for a fishery as a whole and the associated reference points for individual stocks. He finds 

that, because arrowtooth flounder negatively affect the growth of Pacific cod and pollock in the Bering 
25

Sea/Aleutian Islands groundfish fishery, substantially increasing the harvest of arrowtooth to decrease 

its biomass is optimal in the multispecies model because it leads to increased growth and therefore 

greater potential harvests of cod and pollock. He estimates that such a harvest strategy for arrowtooth 

would increase the net present value of the three-species fishery by more than $5 billion for 2010 

through 2040, which is about a 33 percent increase in net present value. In such a case, using an 

arrowtooth flounder biomass target of BMSY and a fishing mortality limit of FMSY would appear to be 

detrimental to the fishery as a whole.

Most recently, Jacobsen et al. (2017) note that “single-species assessment approaches may 

overestimate the availability of win–wins by failing to account for trade-offs across interacting species”

and Burgess et al. (2017) “use a general analytical theory to identify (i) characteristics of fish stocks that 

tend to facilitate or inhibit the precision and accuracy of reference points from single-species 

assessments, (ii) characteristics of ecosystem components that introduce the greatest bias/imprecision 

into single-species reference points and (iii) warning signs within single-species frameworks that 

important ecosystem components may not be adequately accounted for.”

NMFS recognizes the importance of the concept of an aggregate MSY or OY. For example, the 

Ecosystem-Based Fisheries Management Policy of the National Marine Fisheries Service (National 

Marine Fisheries Service 2016) encourages developing and monitoring ecosystem-level reference points. 

Similarly, the Supplementary Information presented with the NS1 Guidelines indicates that NMFS 

proposed using aggregate MSY estimates as one method to facilitate the incorporation of EBFM into U.S. 

federal fisheries management. In addition, the NS1 Guidelines indicate that:

 Stocks may be grouped into complexes where, for example, stocks in a multispecies fishery

cannot be targeted independent of one another.

 MSY may be specified for the fishery as a whole.

 There are several types of models that can be used for estimating MSY for an aggregate group 

of stocks, including the fishery as a whole.

 An OY established at a fishery level may not exceed the sum of the MSY values for each of the

stocks or stocks complexes within the fishery. 

 Aggregate level MSY estimates could be used as a basis for specifying OY for the fishery. 

 When aggregate level MSY is estimated, single stock MSY estimates can also be used to inform 

single stock management. For example, OY could be specified for a fishery, while other 

reference points are specified for individual stocks in order to prevent overfishing on each stock 

within the fishery.

 Exceptions to the requirement to prevent overfishing could apply under certain limited 

circumstances, if harvesting one stock at its optimum level may result in overfishing of another

stock when the two stocks tend to be caught together. This is referred to as the mixed stock 

exception. 
26

Further, in response to comment 17 in the 2016 final rule to revise the NS1 guidelines, NMFS noted that: 

“Fundamentally, aggregate MSY is an additional limit on the management system that encourages more 

conservative EBFM-based measures. Even when aggregate level MSY is estimated, stock-specific MSY 

must still be used to inform single stock management. Other annual reference points (within the ACL 

framework) must also be specified in order to prevent overfishing from occurring in single stocks” (see 

81 FR 71858; 10/18/16). 

NMFS received a number of questions by the Councils related to the aggregate MSY provision in the NS1 

guidelines and posted responses to those questions on its website.18 In those responses, NMFS noted 

that: “Given the MSA’s requirement to end and prevent overfishing, individual stock SDC should be 

specified (as opposed to SDC for a complex as a whole), based on the best scientific information 

available. Further, if Councils are able to manage stocks with individual ACLs, they should do so to 

prevent overfishing. Even in these cases, Councils may still estimate aggregate MSY for a complex or 

functional group and apply such information to the management of the individual stocks within the 

complex or group.”

The NS1 Guidelines do not specify which SDC should be used for individual stocks when an aggregate 

MSY is used. One possibility is to use SDC that are based on independently determined MSYs that do 

not account for stock interactions and that cannot be achieved simultaneously for all harvested stocks in 

an ecosystem. Another approach is to use SDC that are based on MSYs determined simultaneously for 

the individual stocks and the fishery as a whole, that account for stock interactions to the extent 

practicable given our current understanding of those interactions and that can be achieved 

simultaneously for all harvested stocks in an ecosystem. The use of an aggregate MSY with 

independently determined MSYs for the individual stocks is internally inconsistent because, as noted in 

Section 3.3.1 and earlier in this section, the sum of the independently determined MSYs cannot be 

attained and are not associated with the aggregate MSY. The inconsistency results from considering 

stock interactions in determining the aggregate MSY but ignoring them with independently determined 

MSYs for the individual stocks. We are not suggesting that NMFS should consider switching to a fishery 

management method where: 1) we manage based solely on an aggregate MSY or 2) ignore the NS1 

requirements to prevent overfishing and rebuild overfished fisheries. Rather, we are questioning the 

use of MSYs to set SDC if those MSYs do not account for stock interactions. If MSYs and SDC are used for 

individual stocks, shouldn't we use MSYs and SDC that account for those interactions? The use of MSYs 

and SDC for individusal stocks that are based on an aggregate MSY, could eliminate the need for the 

mixed stock exception (i.e., exceptions to requirements to prevent overfishing). When there are 

significant stock interactions, additional consideration is needed concerning the trade-offs between 

doing what is best for each stock individually and what is best for the fishery as a whole whether in terms 

of maximum sustainable yield, optimum sustainable yield or optimum yield trajectory. The sustainable 

yield possibilities frontier (i.e., MSY frontier) mentioned in Section 2 is an appropriate tool to analyze 

tradeoffs associated with significant ecological interactions such as predator-prey relationships and 

inter-specific competition. For the latter, preliminary results from our current research demonstrate the 

existence of points on the MSY frontier that are related to aggregate MSY where no stocks is overfished. 

As noted in Section 3.3.1, the implicit assumptions of the simple concept of an aggregate MSY are that an 

additional metric ton of sustainable yield of any stock is equally important and that its importance does 

not depend on the level of sustainable yield for any stock. The validity of these assumptions needs to be 

18 See NOAA Fisheries Responses to CCC NS1 Questions at: https://www.fisheries.noaa.gov/national/laws-andpolicies/2016-revisions-national-standard-1-guidelines
27

assessed and, if they are found to be invalid, alternative aggregate concepts should be used.

In evaluating the trade-offs that occur because of interactions among stocks, it is important to recognize 

the following: 

 The MSA requirements to prevent overfishing and to rebuild overfished fisheries are intended to 

ensure that the Nation will realize the full potential of its fishery resources in perpetuity. 

 Those fishery resources contribute to the food supply, economy, and health of the Nation and 

provide recreational, social, and cultural opportunities. 

 Commercial and recreational fishing constitute a major source of employment and contribute 

significantly to the Nation’s economy.

 Many coastal areas depend on fishing and related activities, and their economies have been 

badly damaged by overfishing. 

 Fishery resources are finite but renewable. If placed under sound management before 

overfishing has caused irreversible effects, fisheries can be conserved and maintained to provide 

optimum yields on a continuing basis. 

Therefore, the objectives of preventing overfishing and rebuilding overfished fisheries are intended to 

help meet the goal of realizing the full, sustainable potential of the Nation’s fishery resources, in part by 

preventing irreversible effects. However, if significant stock interactions occur, that goal could be 

hindered by using reference points based on independently determined MSYs for individual stocks to 

assess whether a fishery is overfished and should be rebuilt, or whether overfishing is occurring. On the 

other hand, using reference points based on MSY or OSY for the entire fishery and the associated 

reference points for its individual stocks accounts for those interactions as much as possible, given the 

available information, and could contribute to achieving that goal.

Because of technical interactions among stocks, fishermen will seldom be able to reach ACLs for all the 

stocks in a fishery without exceeding some ACLs. However, they will be better able to reach that goal if 

those ACLs are based on reference points associated with the MSY or OSY of the fishery as a whole, or if 

they have better incentives to change their fishing practices in ways that decrease incidental catch or 

bycatch of the stocks with the ACLs that constrain total catch for the fishery. If bycatch is monitored 

adequately and if all catch is counted against fishermen’s quotas, individual fishing quotas (IFQs) and 

other catch share programs can provide incentives for developing and using fishing practices that reduce 

bycatch rates and associated fishing mortality for constraining stocks. For example, the evaluation of the 

West Coast Groundfish IFQ (National Marine Fisheries Service 2013) includes the following statement 

concerning this potential benefit:

1. Results from 2012 indicate a substantial reduction in the amount of bycatch, which occurs when 

fishermen are fishing for one species, but unintentionally catch other creatures that live near that 

species. Because fishermen have more flexibility under a catch shares program, they can be more 

selective in the areas they target. Two years into the catch shares program, catch of unwanted 

species, or bycatch, remains lower than the two prior years structured under trip limit management. 

This is good news for certain species that need rebuilding and for fishermen who can focus on their 

target species.

2. At the same time, results show that the groundfish fleet was able to catch a greater percentage, 

29%, of their target species (other than whiting), which is up from 24% in 2011. This result highlights 

the increased diversity of the landings and the fishermen’s ability to target new areas and markets.
28

In addition to affecting technical interactions among stocks, management regimes can affect the cost of 

effort, ex-vessel prices, the distribution of catch among user groups (e.g., fleets), and other 

determinants of MSY, OSY, OYT, and the overall net benefit provided by a fishery.
29

4. Conclusions 

Since the 2007 MSA reauthorization, NMFS and its partners in the federal fishery management 

community have developed and implemented a framework for preventing overfishing and rebuilding 

overfished fisheries, yet the economic content of this framework has received relatively little attention. 

In this paper, we argue that economic ideas and analyses are relevant to both preventing overfishing 

and achieving OY, the dual objectives of NS1, where achieving OY includes rebuilding overfished 

fisheries.

Because preventing overfishing and rebuilding overfished stocks imply opportunity costs and behavioral 

responses from affected people, they have an important economic component. Similarly, achieving 

optimum yield necessarily includes an economic dimension because optimum yield reflects the value of 

fish and fishing to people. 

In addition to being relevant to each of NS1’s objectives, economics provides a framework for 

considering how the two objectives relate to one another: preventing overfishing often requires harvest 

reductions, and optimum yield is best understood as an answer to the question of how to manage these 

and other trade-offs.

Though we argue that the economic content of NS1 deserves more attention, we recognize that 

progress in this area will require a major effort, similar to that mounted for developing the ACL

framework. New models and new data sources will be needed. Dynamics and discounting, uncertainty, 

and stock interactions are significant challenges to economic analysis. In the appendices that follow, we 

explore these challenges in more detail.

4.1 Key Points

The most important points we make in this paper are included in the Executive Summary and repeated 

here. 

1. Economic concepts and analyses can contribute to understanding of the trade-offs inherent in 

fisheries management decisions that aim to prevent overfishing while achieving OY. For example, 

understanding how fishermen and others involved in the fisheries are likely to respond to 

alternative management actions is critical to determining or modifying those trade-offs.

2. Because uncertainty is inherent in fisheries, preventing overfishing is meaningful only in probabilistic 

terms. A greater probability of preventing overfishing generally comes at greater cost, in terms of 

forgone yield. In other words, reducing yield is a form of payment to insure against overfishing.

3. Optimum yield is defined by the MSA in terms of benefits to the Nation. Including economic 

benefits generally leads to harvest policies that imply higher levels of biomass and overall net 

benefit and lower levels of effort and catch. For example, OSY is normally a more conservative 

reference point than MSY and it results in greater overall net benefit to the Nation.

4. Measures to achieve the joint goals of preventing overfishing and attaining OY are more likely to 

succeed if they account for system dynamics, uncertainty, stock interactions, and the effects of 

alternative management regimes.
30

4.2 Important Topics for Future Work

Developing the analytical and institutional capability to treat OY and overfishing jointly would support 

better fishery management in the future.

1. We expect steady progress in overcoming the modeling challenges associated with estimating OSY 

and OYT. However, the data requirements for developing models that are increasingly useful for 

policy discussions are formidable. Given the current paucity of economic data—and particularly cost 

data—in many of our federally managed fisheries, the development of new data collection programs 

is at least as important as modeling innovations to defining and managing for OY. 

2. The maximum allowable rebuilding time (Tmax) prescribed in the NS1 Guidelines has no economic 

content and could often preclude the use of the rebuilding periods that would increase the

discounted present value of the net benefit from a fishery. However, the OYT, constrained by both 

the rebuilding periods specified in the NS1 Guidelines and the BMSY or BOSY target stock level, can be 

used to identify the best catch, effort, and biomass time paths given those constraints.

3. Accounting for technological change and other sources of variability in the catchability coefficients 

used in population and bioeconomic models is important to developing more useful fishery 

management models.

4. The NS1 guidelines describe a framework for specifying ABC, ACLs, and accountability measures. 

The guidelines require ABC control rules that are used to specify ABC and that account for 

uncertainty in the OFL and for the Council’s risk policy. The guidelines also note that: 1) ACTs can 

be used to account for management uncertainty and 2) if an ACT, or functional equivalent, is not 

used, management uncertainty should be accounted for in the ACL. The following points concern 

the determination of these buffers, which are key elements of the effort to address uncertainty and 

prevent overfishing:

a. Further research is required to determine when it would be appropriate to assess all sources 

of uncertainty and variability together to establish the buffer between OFL and ACT, if one is 

used, or between OFL and ACL if an ACT is not used. Such research would help determine if 

the explicit option for “A Council to choose to use a single control rule that combines both 

scientific and management uncertainty and supports the ABC recommendation and 

establishment of ACL and if used ACT”, which the 2016 NS1 Guidelines eliminated, should 

be included again. All sources of uncertainty and variability can be treated simultaneously 

for estimating OSY and OYT. 

b. The buffer provides insurance against an undesirable outcome. Therefore, optimal buffer 

size will depend both on the cost of that buffer relative to the cost of other methods of 

providing the same level of protection and on the benefits of various levels of protection 

against the undesirable outcome. To determine optimal buffer size, it is important to decide 

whether the undesirable outcome we should insure against is: 1) Occasionally exceeding an 

ACL or even the OFL; or 2) Stock collapse and not rebuilding overfished fisheries. 

c. The following methods could reduce both uncertainty and appropriate buffer sizes: more 

timely and accurate catch monitoring; more timely and accurate stock and rebuilding 

monitoring; quicker adjustments to ACLs and AMs; a better understanding of how fishermen 
31

and others will respond to AMs and other management actions; and the use of large marine 

protected areas. The best mix of the alternative methods for dealing with uncertainty will 

depend on the effectiveness and cost of each method and each feasible mix of methods.

5. The management regime will affect the trade-offs and challenges that confront fishery managers, as 

well as their success in preventing overfishing while achieving OY. The management regime (e.g., 

managing with race for fish versus a catch share system) affects harvest costs, ex-vessel prices, fish 

utilization rates, product quality, gear selectivity, bycatch, safety, compliance, management costs, 

and other outcomes that determine OY. Therefore, changes to the management regime beyond 

simply implementing the NS1 Guidelines can be critical for meeting the NS1 challenge. These 

changes could include taking management actions to address the perverse incentives that increase 

the difficulty of meeting that challenge. 

6. Recognizing the importance of MSY, OSY, and OYT reference points for a fishery as a whole—as well 

as the associated reference points for individual stocks—is an important step toward both EBFM and 

the use of reference points that are critical for meeting NS1. However, developing such reference 

points requires more information and better models than are currently available for most, if not all, 

fisheries. For example, it will require better estimates of the opportunity cost of using living marine 

resources and habitat to harvest fish.

Overcoming these challenges will be the work of years. However, advances in our ability to meet the 

dual objectives of NS1 and to move toward EBFM can be made with improved data and models and 

increased recognition of the need to go beyond the use of stable, single-species, long-term sustainable

biological yield concepts and models.
32
33

APPENDIX 1. A More Comprehensive Model of OSY

The simple model of OSY presented in Section 2 has several limitations, including the following:

1. It is based on the assumption that the ex-vessel price of fish and the marginal cost of effort are 

constant.

2. It considers only a subset of the costs and benefits that determine overall net benefit to the 

Nation for each sustainable level of yield and associated sustainable levels of biomass and 

effort. Specifically, it does not consider external costs of harvesting fish; benefits or costs in 

post-harvest sectors (e.g., fish dealers, processors, wholesalers, and retailers); net benefits to 

consumers; fishery management costs (e.g., monitoring, reporting, enforcement, and 

management decision-making costs); or distributive impacts and equity. 

3. It is designed for a stock of fish that is taken only in one commercial fishery and not in any 

recreational or subsistence fisheries. 

4. It does not show how a change in the fishery management regime will affect OSY through its 

effects on the ex-vessel price and the marginal cost of effort.

5. It is designed for a single stock that has no significant ecological or economic interactions with 

other living marine resources.

6. It considers neither uncertainty nor the dynamic nature of fisheries.

7. It ignores technological change and other factors that affect catchability. 

This appendix explores extensions to the Section 2 model to address the first three limitations. We 

discuss the fourth limitation in Appendix 2; the fifth limitation in Section 3.3 and Appendix 5; the sixth 

limitation in Sections 3.1 and 3.2 and Appendixes 3 and 4; and the final limitation in Appendix 6. The last 

two limitations apply to the concept of OSY itself, not just the simple version of OSY discussed in

Section 2. 

A1.1 Addressing Assumptions of Constant Ex-Vessel Fish Price and Marginal Cost of Effort

Economic research is necessary to determine the extent to which the price of fish is expected to 

increase as the sustainable level of catch decreases from MSY. It may be appropriate to assume a 

constant price for a fishery that accounts for a small part of the total supply of a species, or if there are 

other species (or other sources of food) that are very good substitutes for that species for the postharvest sectors and consumers. However, if neither of those conditions is met, prices will be higher for 

lower levels of sustainable catch. In addition, reductions in revenue that would otherwise result from 

lower levels of catch can be partially, fully, or more than fully offset by the price increase. Vieira and 

Pascoe (2013) note the following: 

Given that most empirical studies (in Australia and elsewhere) have found that fish prices are 

generally inflexible, a default position may be to estimate MEY as the yield that maximises 

industry profits at the prevailing price—as is current practice. However, where there is evidence 

of price flexibility, research needs to be undertaken to derive more appropriate catch–price 
34

relationships to further refine the model and ensure that the target reference point reflects the 

yield that maximises total benefits to the broader society (industry and consumers).

The age structure of a stock associated with a set of sustainable levels of catch, effort, and biomass can 

affect the size composition of the catch, which will in turn affect the average ex-vessel price if the price 

is size dependent. The management system can have much stronger impacts on price than those 

associated solely with quantity landed or size of fish. The timing of landings, their disposition, and 

quality may be much more important and have less to do with the ACL or even gear and area restrictions 

than with the incentives created by the management system. For example, moving from a race for fish 

to an individual fishing quota (IFQ) in the Alaska halibut fishery led to substantial price increases because 

it increased quality, eliminated supply gluts, and allowed more fish to be sold fresh.

The assumption of constant marginal cost is less problematic because we are discussing a stable longterm sustainable economic yield model for which all inputs are variable; however, economic research is 

required to assess this assumption for specific fisheries. Nonetheless, it should be noted that the 

regulatory approach also impacts costs. Controlling catch with a competitively fished ACL that creates a 

race for fish may lead to higher marginal costs than a regulatory approach like IFQs or cooperatives that 

provide incentives for efficient harvest (see Appendix 2).

A1.2 Including a More Complete Set of Benefits and Costs for Commercial Fisheries

The benefits to the Nation from the commercial, recreational, and subsistence harvest of fish include 

income, employment,19 consumption, recreational, and existence benefits. This section focusses on the 

benefits and costs provided by a commercial fishery. Sections A1.3 and A1.4 address the benefits and 

cost provided by recreational and subsistence fisheries, respectively. 

For a commercial fishery, the associated costs include the costs of the fuel, labor, boats, equipment, 

facilities, and other market inputs used to harvest fish and to provide them to consumers. The cost of 

using any of these market inputs is the value of the highest-valued alternative use of that input; this is 

referred to as the opportunity cost of that input. In the absence of significant market failure, the market 

price of an input provides a useful estimate of its opportunity cost, and it is not necessary to adjust the 

market price to estimate the opportunity cost of a market input.

External Costs

Living marine resources and their habitats are also used to harvest fish. Because the Nation derives 

benefits from competing consumptive and nonconsumptive uses of those marine resources, or simply 

from their existence, there are opportunity costs associated with using marine resources to harvest fish. 

Typically, society bears these opportunity costs while producers and consumers of seafood do not, and 

the costs are not captured by market prices. These external costs are thus imposed on others rather 

than on each fishing operation or consumer based on use. 

The external cost that has received the most extensive treatment in the fisheries economics literature is 

the stock externality: an interaction among fishermen over time in which a (private) unit of catch at one 

point in time tends to lower reproductive output and reduce the stock in current and future periods, 

 

19 Broadly defined income and employment benefits include those for the harvesting and post-harvesting sectors, 

as well as resulting indirect and secondary income and employment impacts.
35

thus reducing catch per unit of effort and raising costs for each fishing operation for a given level of 

catch. In the absence of an effective fishery management regime, this stock externality will result in 

overfishing, overfished fisheries, and a substantial reduction in the overall net benefit that fisheries 

provide to the Nation. The simple model of OSY depicted in Figure 2 accounts for the stock externality 

related to the effect of catch on sustainable yield. Five examples of external costs that are not 

accounted for in that model are presented below. Some of these costs are associated with forgone 

benefits from public goods.20

1. Bycatch mortality of fish, sea turtles, marine mammals, and seabirds eliminates other uses of 

and benefits from these living marine resources. The opportunity cost of using these living 

marine resources to harvest fish should be included as one of the external costs of harvesting 

fish.

2. Fishing can adversely affect the productivity of fish habitat and the habitat of other living marine 

resources. The forgone benefit to the Nation resulting from decreased habitat productivity is an 

opportunity cost that should be included as one of the external costs of harvesting fish. 

3. Each sustainable level of biomass for a stock will affect the productivity of other stocks in the 

fishery and large marine ecosystem. If a lower sustainable level of biomass for a stock decreases 

the productivity of other stocks, the forgone benefit to the Nation resulting from the decrease in 

fishery productivity is an opportunity cost of fishing. Conversely, if a lower sustainable level of 

biomass for a stock increases the productivity of other stocks, there are benefits associated with 

that increased productivity. Such costs and benefits should be included in any analysis of net 

benefit to the Nation.

4. Each sustainable level of catch and the associated sustainable levels of biomass and effort for a 

stock of fish will have ecosystem effects that could change levels of biodiversity and ecosystem 

services and the benefits derived from them. Any measurable decrease or increase in those 

benefits should be included in the estimate of the cost or benefit of a lower sustainable level of 

biomass and a higher sustainable level of effort. Biodiversity and ecosystem services are public 

goods (Bulte et al., 1998; Van Kooten and Bulte, 2000).

5. Any costs associated with harvesting-sector accidents that are not reflected in the harvesting 

costs depicted in Fig. 2 should be considered.

Many of these types of external costs can be difficult to estimate because they are difficult to observe or 

because they occur outside of markets. However, they tend to be higher at higher sustainable levels of 

effort and catch and lower levels of biomass. Thus, they typically result in higher marginal harvesting 

costs and lower OSY and, therefore, higher BOSY, lower EOSY, and decreased commercial harvesting-sector 

profit. Therefore, including these external costs, which is both required and appropriate, typically results 

in an even more conservative reference point. 

External costs can also cause misalignment between the interests of individual fishermen and 

consumers and the objective of sustainable fisheries. They can result in various (often co-occurring) 

 

20 A public good is a good for which: 1) The use of the good by one individual does not diminish its use by or value 

to others; and 2) Use or enjoyment by others cannot be excluded. That is, it is a good that is both nonrivalrous and 

nonexcludable.
36

undesirable outcomes, including overfishing and excessive levels of bycatch, habitat degradation, and 

fishing capacity.

Benefits and Costs beyond the Harvesting Sector

As noted earlier, the simple model of OSY depicted in Figure 2 does not address benefits and costs in the 

post-harvesting sectors, net benefits to consumers, or distributive impacts and equity. Economic 

benefits beyond the harvesting sector can be measured in terms of profits in those sectors and 

consumer surplus.21 Typically, the ex-vessel-level analogue to consumer surplus provides a useful 

approximation of net benefit to the post-harvesting commercial sectors and to final consumers (see Just 

et al., 2004). Therefore, an estimate of ex-vessel demand for fish can be used to approximate that set of 

net benefits. Such an approximation can be used to replace the sustainable revenue curve in Figure 2 

with a curve that also captures net benefits for each sustainable level of effort and its associated 

sustainable levels of catch and biomass. However, if this method is not useful for a particular stock of 

fish, or if it is important to know the distribution of net benefits beyond the commercial harvesting 

sector, separate estimates of the net benefits for each post-harvesting sector and for final consumers 

would be useful. Such estimates would require substantially more information.

If the price is lower for a higher sustainable level of catch (i.e., if the ex-vessel demand curve slopes 

down to the right), the sum of post-harvesting-sector profits and consumer surplus will increase as the 

sustainable level of catch increases, and the difference between MSY and OSY will decrease. 

Alternatively, if the price of fish is not affected by a change in the sustainable level of catch, neither is 

that sum nor OSY. 

Therefore, including post-harvesting-sector profits and consumer surplus in the determination of OSY 

will either increase OSY toward MSY or not change it. Grafton et al. (2012) show that including postharvesting-sector profits and consumer surplus increases dynamic MEY toward MSY, but that there 

remains a broad range of parameter values for which dynamic MEY < MSY and dynamic BMEY > BMSY. 

Similarly, Vieira and Pascoe (2013) demonstrate that when the price of fish is determined by level of 

catch, and ex-vessel demand for fish is used to estimate net benefits beyond the commercial harvesting 

sector, considering these benefits increases MEY but does not increase it to MSY.

In addition to direct effects, the harvesting and post-harvesting sectors can experience secondary effects 

on income and employment. These effects are measures of economic activity and not of economic 

benefits in the sense of the earlier discussion (e.g., in Section 2.2). As a result, they can affect overall net 

benefits through their distributional or equity effects. These secondary impacts can be estimated using 

regional input-output models; computable general equilibrium (CGE) models (Seung and Waters, 2006; 

Norman-López and Pascoe, 2011); or economic (“shadow”) prices (Squires and Vestergaard, 2016). The 

traditional input-output model approach assumes that excess capacity persists in the harvesting and 

post-harvesting sectors and that additional workers employed come from the ranks of the unemployed. 

Conversely, CGE models assume full employment, so in these models an increase in catch transfers 

labor, capital, and other inputs from other sectors.

These secondary economic impacts typically increase as sustainable catch increases, meaning that 

including these impacts in the determination of OSY tends to increase it toward MSY. In fact, 

 

21 Consumer surplus is the difference between the benefits consumers receive from a good (e.g., seafood) and 

what they must give up to attain it. 
37

Christensen’s (2010) conclusion that MEY = MSY is based on the assumption that “the more jobs and the 

more value generated, the higher the benefit to society.” However, as noted by Sumaila and Hannesson 

(2010), this conclusion ignores the costs associated with increasing sustainable catch to MSY. Although 

these economic impacts are not useful measures of the benefits and costs throughout the postharvesting sectors, they do provide information concerning the distributive effects of alternative 

sustainable catch levels. As stated in EO 12866, distributive impacts and equity should be considered in 

determining broadly defined net benefits. In fact, the intra- and inter-generational distributions of 

benefits and costs associated with fishery management actions are often critical to determining the 

preferred alternative. 

If society determines that benefits and costs to different groups or individuals should receive different 

weights, the overall net benefit to the Nation from each sustainable catch level (and its associated 

sustainable levels of biomass and effort) depends on the magnitude and distribution of its associated 

costs and benefits. OSY can account for these distributional effects by applying appropriate welfare 

weights to benefits and costs to generate social prices (Little and Mirrlees, 1974; Squire and van der Tak, 

1979). The net effect on OSY of considering external harvesting costs, benefits and costs beyond the 

harvesting sector, and distribution of benefits and costs will vary by fishery.

Fishery Management Costs 

Fishery management costs (e.g., monitoring, reporting, enforcement, and management decision-making 

costs) should also be considered in determining the overall net benefit of a fishery to the Nation. For 

example, if fishery management costs increase as fishing effort increases, those costs affect the marginal 

cost of effort and should be accounted for in determining OSY. Similarly, if fishery management costs 

differ significantly among alternative fishery management approaches, those differences can be 

important factors in selecting which approach to use. The costs of monitoring and reporting can be 

substantial if the management approach and fishery require observer coverage. 

There are several reasons a single measure of a fishery’s overall net benefit to the Nation cannot 

typically be provided: 

 Both quantitative and qualitative estimates are used when the former are not available for all 

benefits and costs. 

 Net benefits include potential economic, environmental, public health and safety, and other 

advantages that cannot always be readily valued in monetary terms. 

 It can be difficult to determine the weights that should be given to the benefits and costs that 

accrue to different groups or individuals. 

 Levels of uncertainty often differ for projections of different types of costs and benefits, and 

there is often no good way for analysts to account for those differences in monetary terms. 

Therefore, the analysis of the costs, benefits, and distributional effects of alternative sustainable catch 

levels (and associated sustainable levels of biomass and effort) might include projections of various 

types of impacts at each level, rather than a single measure of overall net benefit to the Nation. 

Therefore, an analyst provides information to fishery management decision-makers, but those decisionmakers, not the analyst, are responsible for determining which alternative will provide the greatest 

overall benefit to the Nation.
38

A1.3 Extending the Model to Account for Net Benefits from Recreational Fisheries 

Net benefit in the recreational sector can be thought of as the sum of profits from for-hire businesses, 

which offer fishing trips to anglers, and net benefit to anglers from for-hire fishing and all other modes 

of fishing, as measured by consumer surplus or compensating variation22 associated with their fishing 

experiences.

Revealed preference and stated preference models have been used to estimate net benefit to anglers,

whether their catch is retained or released. For example, Lew and Larson (2012) used data from a stated

preference survey to estimate the economic value anglers place on, or their willingness to pay for, 

saltwater boat fishing trips in Alaska. Data from these surveys was also used to assess anglers’ responses

to changes in such fishing trip characteristics as number of fish caught, bag limit, and fish size. An 

important implication of this study, and many other studies concerning the benefits anglers receive from 

recreational fishing, is that the benefits depend on trip characteristics that reflect much more than level 

of catch. This means that changes in the size composition of the stock, as well as changes in other 

determinants of trip characteristics, can affect the benefits received by recreational fishermen under 

each set of sustainable level of catch and biomass. As with commercial fisheries, external costs and 

benefits need to be accounted for.

A1.4 Extending the Model to Account for Net Benefits from Subsistence Fisheries 

As with recreational fisheries, revealed preference and stated preference models can be used to 

estimate net benefit to subsistence fishermen, their families, and their communities. Such benefits can 

include the perceived value of a range of traditional uses of harvested fish by subsistence fishermen;

increased food quality; sharing of subsistence resources within social networks; combining time and 

money of multiple households to increase harvesting efficiency; lack of reliance on market economies;

maintenance of cultural traditions; and the other values of the subsistence fishing experience (Berman,

1998; Schumann and Macinko, 2007; Gerlach and Loring, 2013). Cost survey data can then be used to 

estimate harvesting and household-processing costs. These costs include the cost of fuel, equipment,

and other fishing inputs needed to harvest fish; times and modes of travel for fishing; and the costs of 

processing and preparing the catch for consumption in the home (Gerlach and Loring, 2013; HimesCornell et al., 2013). Other costs that should be accounted for include any external costs and benefits,

and the opportunity costs of labor and other inputs that are not necessarily given full economic values 

by the market.

As with recreational fisheries, the characteristics and uses of subsistence fishing trips affect the benefits 

of subsistence fishing. Therefore, the benefits received from subsistence fishing for each set of 

sustainable level of catch and biomass are determined by a large set of variables.

When a stock is harvested in more than one type of fishery (e.g., commercial, recreational, and 

subsistence), the overall net benefit to the Nation for a given sustainable level of catch (and associated 

levels of biomass and effort) will depend on the distributions of catch and effort among those fisheries.

The same is true when multiple fleets or multiple types of commercial, recreational, or subsistence 

fisheries generate different net benefits per unit of catch.

 

22 Compensating variation measures how much compensation an angler would require to prevent a decrease in his 

or her utility if the fishing experiences were not available.
39

APPENDIX 2. The Management Approach and Its Effects on OSY

The regulatory approach used to manage catch, and the incentives it creates, can strongly affect both 

the benefits and costs of harvesting fish. Changes in marginal cost and marginal revenue affect not only 

the net benefits from the fishery but the OSY and the associated levels of biomass (BOSY) and effort 

(EOSY). The regulatory approach and the specific design of the system can also impact other outcomes 

such as safety, bycatch, habitat destruction, fishery management costs, and distribution of catch among 

sectors. These outcomes also affect the overall net benefits derived from the fishery. Differences in net 

benefits, OSY, BOSY, and EOSY are generally most profound when moving from a race for fish allocation 

system to a catch share system that creates incentives for individuals to maximize the value they can 

generate from their exclusive catch privilege by reducing their harvesting costs and/or increasing their 

ex-vessel revenue. 

In this appendix we focus primarily on how the management system affects net benefits, OSY, BOSY, and 

EOSY, where, as with the simple model of OSY presented in Section 2.2, net benefits are narrowly defined 

as the difference between revenue and costs in a commercial fishery. We begin by discussing examples 

of fisheries in which catch share systems were implemented to illustrate how those management 

changes can impact harvest costs, fish prices, and utilization rates. We then use a simple GordonSchaeffer model to illustrate how those changes affect OSY, BOSY, and EOSY. We conclude with a 

discussion of broader impacts of these types of management changes on net benefits and distribution of 

those benefits and implications for OSY. The potential for the management system to affect MSY, BMSY, 

and EMSY though its effects on the determinants23 of those three variables is noted here but not 

discussed elsewhere in this appendix.

A2.1 Ending the Race for Fish

When fisheries are managed solely by closing a fishery each year after the total allowable catch (TAC)

(i.e., ACL or ACT) is caught, but fishing capacity is not constrained, and catch is allocated based on who 

can land it first, a race for fish ensues. This approach often leads to excessive fleet capacity and fishing 

effort that increases harvest costs, creates supply gluts, and reduces product quality, the price and the 

net value of catch (National Research Council (NRC) 1999; Homans and Wilen, 2005). A catch share 

system allocates exclusive privileges to harvest a portion of the TAC to individuals (e.g., an IFQ) or 

groups (e.g., fishing cooperatives). Those holding catch shares have the incentive to maximize the net 

value they can generate with them. Often these systems enable the season length to be extended and 

eliminate supply gluts, enabling more careful handling of fish and potentially additional fresh or even 

live sales of catch - all of which can substantially increase the value of the catch (Homans and Wilen,

2005). Individual vessels may be able to reduce costs by operating more efficiently. In addition, costs 

may be reduced further if transferability of catch privileges allows consolidation of catch by fewer, more 

efficient vessels. Later in this section we discuss several real-world examples that highlight these 

changes.

Perhaps the best examples of an extreme race for fish and the effects of ending it with a catch share 

system are the Pacific halibut fisheries in British Columbia (BC) and Alaska. In both cases, the fisheries 

 

23 The definition of MSY presented in the NS1 Guidelines and reproduced in Section 2.2 of this paper identifies the 

following determinants of MSY: prevailing ecological, environmental conditions and fishery technological 

characteristics (e.g., gear selectivity), and the distribution of catch among fleets. As noted elsewhere in this paper, 

regulatory and market condition can affect gear selectivity and the distribution of catch among fleets.
40

had been managed with limited seasons that had constrained catch and conserved biomass. However, 

these measures had led to continually decreasing season length culminating in short derby fisheries, 

reduced product quality, and supply gluts as well as safety concerns, gear conflicts, lost gear, ghost 

fishing, and other negative effects of the race for fish (National Research Council 1999). An individual 

vessel quota (IVQ) system was implemented in the BC halibut fishery in 1991, and an individual fishing 

quota (IFQ) system was implemented in Alaska in 1995. In the first 3 years of the IVQ system, the BC 

halibut fishery enjoyed more than a 50 percent increase in price relative to the Alaska fishery, which was 

still operating under a race for fish (Casey et al., 1995). Herrmann (1996) estimates IVQs increased the 

value of landings of BC halibut by over C$23 million in the first 4 years of the IVQs. In 1995, an IFQ 

system was implemented in the Alaskan halibut fishery and lengthened its season from a few days to 

245. Alaska enjoyed a smaller price increase (only about 10 percent) and induced a price drop in the BC 

Halibut fishery, which now had to compete in the fresh market against Alaskan halibut (Herrmann and 

Criddle, 2006). Although a decrease in the number of boats participating in the Alaska halibut fishery 

may have reduced costs, consolidation in the fishery was purposely constrained to maintain or increase 

the small owner–operator nature of the fishery and protect remote fishing communities.

In other Alaskan fisheries in which catch shares were implemented, reduction in capacity and related 

cost savings were major objectives and outcomes. Both the Bering Sea Aleutian Island (BSAI) pollock and 

crab fisheries were initially managed with hard TACs and seasonal closures that led to a race for fish and 

excess harvesting and processing capacity. The introduction of catch shares (cooperatives in the pollock 

fishery and IFQs in the crab fishery) lead to substantial reductions in the number of vessels participating 

and higher capacity utilization, with accompanying reductions in fixed costs and increases in technical 

efficiency (Felthoven, 2002; Schnier and Felthoven, 2013). Abbott et al. (2010) also found that 

productivity and remuneration of crew increased post-IFQ for the BSAI crab fishery.

Changes that occur after introduction of catch shares are complex and not always uniform across 

sectors. Dupont et al. (2005) found that implementation of IFQs in the Scotia-Fundy mobile gear 

groundfish fishery increased prices, which benefited all vessels. However, only larger vessels saw 

productivity gains and reduced harvest costs. IFQs reversed a declining trend in productivity for the large 

vessels, but productivity continued to decline for the smaller vessels. A meta-analysis of U.S. catch share 

systems by Birkenback et al. (2015) found strong evidence that catch shares tend to increase season 

length but cause mixed results regarding changes in prices. Many factors can impact prices, making it 

difficult to identify the impact the catch share system had. Catches, revenues, and costs are also strongly 

influenced by exogenous factors that influence fishery productivity and cost and thus profit. Also, many 

catch share systems did not have a substantial race for fish prior to implementation so expectations of 

price gains would be lower. Nevertheless, there is substantial empirical and theoretical evidence to 

suggest that implementing catch shares in a fishery where catch had been allocated through a race for 

fish can substantially increase profits either through increasing revenue, decreasing harvest costs, or 

both.

A2.2 Prices, Costs, and OSY

The Gordon-Schaeffer model, introduced earlier in this paper, can be used to demonstrate how changes 

in harvest costs or prices induced by management changes can alter OSY, BOSY, and EOSY. Figure 3 shows 

two sustainable revenue curves with the solid line representing sustainable revenue (price * annual 

yield) in the initial unregulated open access (UOA) fishery and in the final catch share (CS) fishery. The 

dashed sustainable revenue curve shows the result of prices decreasing as a result of compressed 

seasons, supply gluts, and reduced quality induced by containing total catch to the MSY level with a race 
41

for fish that produces a derby (DB) fishery. The underlying relationship between effort and catch is not 

changed, but the revenue curve is lowered at every point due to the lower ex-vessel price of fish. The 

figure also shows the total cost lines with the solid line representing costs per unit of fishing effort in the 

unregulated open access and catch share fisheries. The dashed total cost line has an increased (doubled) 

slope representing the increased cost associated with the excess fishing capacity and race for fish 

induced by the derby fishery. The assumption is that fishing capacity continues to increase in the derby 

fishery until it drives costs up to the point where profits are fully dissipated. The model assumes, 

conservatively, that marginal costs and prices return to unregulated open access levels under a catch 

share system, though we might expect prices to rise and costs to fall further relative to open access 

levels. 

The effort level and revenue move from point A under unregulated open access (the point at which 

effort has risen to where revenues equal costs in the unregulated fishery), to point B under the derby 

fishery with a TAC set to achieve MSY. This assumes costs have risen until they equal revenues in the 

derby fishery and a new bioeconomic regulatory equilibrium has been established. Effort and revenue 

then move to point C when the catch share system is implemented. This assumes that harvest is set at 

the level that maximizes equilibrium profit and that the marginal cost and prices returned to the levels 

that prevailed in the unregulated open access fishery. Note EOS under the derby fishery (though never 

observed because the TAC was set to achieve MSY24) had shifted far left from 40 to 25 given the lower 

revenue and steeper cost curves associated with the derby fishery. EOSY is higher and BOSY is lower with 

the catch share system than with prices and costs associated with the derby fishery. In general, 

increases in ex-vessel prices or decreases in marginal cost tend to move OSY closer to MSY.

 

24 If the catch had been set lower (at the OSY level given the harvest costs and prices that prevailed under a TAC 

set at MSY), we would expect the harvest costs to rise and prices to fall until again there were no profits. 

Otherwise, incentives to increase capacity to get a bigger share of the catch would persist, again shifting EOSY left. 
42

Figure 3: Sustainable revenue, total cost, and optimum sustainable yield with increasing prices and 

decreasing costs (cost and revenue are in millions of dollars). 

A2.3 Conclusions

Controlling catch with only seasonal closures may be successful at constraining catch and rebuilding 

biomass and increasing sustainable harvest. However, that method of controlling catch can lead to a 

race for fish that drives up costs and decreases revenue. The fishery examples discussed here illustrate 

that catch share systems can increase prices and revenues and decrease costs, thereby greatly 

increasing fishery profits. The exposition with the Gordon-Shaeffer model demonstrates that those 

changes in costs and prices can also alter the OSY effort, harvest, and biomass levels, where in this case 

OSY is determined based on a narrow measure of net benefit (i.e., maximize sustainable profit). Catch 

share systems may also have broader effects that impact net benefits from fisheries, including reducing 

gear conflicts and bycatch, but also distributional effects that may not always be considered positive. 
43

APPENDIX 3. Dynamics and Discounting

Many bioeconomic models are based on a logistic growth equation, which lacks age structure and other 

realistic features included in the modern stock assessment models that are often used to estimate MSY.

Age-structured population dynamics are, however, increasingly incorporated as constraints in 

bioeconomic models (Gulland, 1983; Deacon, 1989; Bjørndal and Brasão, 2006; Tahvonen, 2009a, 

2009b; Kjaersgaard and Frost, 2008; Kompas et al., 2010; Tahvonen et al., 2012; Quaas et al., 2013). Agestructured estimates of OSY allow more useful comparisons of OSY to MSY for stocks managed using 

age-structured stock assessments. Ideally, we would want to compute OSY using the exact population 

model that is used to compute MSY; in practice, this ideal may be difficult to achieve.

Using alternative population models to compute OSY is an area of active research. In this section, we 

consider a simple class of models called Deriso-Schnute Biomass Models (Quinn and Deriso, 1999). 

These models contain an explicit representation of age-structured population dynamics with agedependent growth, and thus provide a rigorous foundation for a general theory for analyzing agestructured catch and effort data (e.g., Schnute and Fournier, 1980; Fournier and Archibald, 1982;

Schnute, 1985). 

An objective function must be specified in the definition of OYT, which is usually assumed to be additive 

over time (i.e., time separable). The class of objective functions we consider here is restricted to a set of 

time-separable quadratic objective functions from which OYT is defined subject to a linear constraint 

that represents population dynamics under the assumption that recruitment is an exogenous process.

Linearity in population dynamics based on age structure and reproduction is based on Leslie (1945). 

Because OYT depends on both an economic objective and a biological growth equation, the meaning of 

“optimum” can be ambiguous or, worse, ill posed. Under the conditions outlined here, dynamic 

optimization of expected economic profits, subject to a (restricted) linear growth equation, is a wellposed problem because: 1) A unique solution to the problem exists; and 2) The solution can be 

represented as a system of linear difference equations. The bioeconomic model and theory described 

here are abstract; they contain restrictive assumptions with respect to both biology and economics.

These assumptions are necessary to reach a compromise between an analytically tractable dynamic 

model under uncertainty and one in which age structure is an explicit feature, with growth based on 

biological principles. 

Models in fisheries economics deal with uncertainty in many ways, including simply ignoring its 

presence, as in the simple OSY model depicted in Figure 2. Rational expectations models represent 

another approach. In these models, uncertainty is represented with random variables. Decisions in the 

model are based on mathematical expectations of these random variables, conditional on information 

available to the decision-maker at the time a decision is made. In other words, decisions in the model 

are based on mathematically optimal (i.e., rational) forecasts. However, solving this type of 

maximization problem can be difficult or impossible, especially if the objective function or constraints 

contain random variables or stochastic processes. Therefore, a first priority is to verify that the 

maximization problem under uncertainty that defines OYT is well posed in that a unique solution exists 

and is computable. 

We assume that there is a known objective function, such as expected profits over time in present-value 

terms. For example, an objective function with discount factor

0 1   

, variable cost parameter

 , 
44

positive adjustment cost parameter , and positive parameters and that represent stock and 

congestion externalities in terms of catch and biomass , could be specified as

(1)

The quadratic dynamic adjustment cost term in the previous equation is essentially a penalty on 

variability in catches. Suppose that recruitment is an exogenous stochastic process that may be 

affected by other processes, such as climate. The simplest assumption is that biomass , catch , and 

recruitment r are related by a linear growth equation, which includes a coefficient on the 

right-hand side such that

(2)

The set of linear growth functions that are admissible in the linear-quadratic class of rational 

expectations models includes autoregressive and moving average stochastic processes. Equation (2) can 

serve as a linear constraint in a stochastic dynamic optimization problem with a quadratic objective 

function, as in equation (1). A theory of quadratic eigenproblems has been developed in the applied 

mathematics literature (e.g., Higham and Kim, 2001) to handle multivariate versions of equation (2) as 

constraints in dynamic optimization. However, whether the set of linear growth equations included in 

the linear-quadratic class of rational expectations models can handle an age-structured population is an 

open research question. 

The application of Bayesian methods to rational expectations models is not straightforward because it 

involves imposing an analyst’s subjective beliefs on the model. Unrestricted vector autoregressions, a 

natural empirical alternative to a theoretical rational expectations model, are readily adapted to 

Bayesian analysis. However, the relationship of Bayesian analysis to rational expectations is complicated 

and beyond the scope of this document. Instead, the models under consideration here are treated in a 

classical likelihood framework. 

In the case of a single endogenous state variable (the stock) and no constraints, a linear-quadratic 

stochastic dynamic optimization problem is solved by factoring a characteristic polynomial. In the case 

of a single control variable, the quadratic formula is used to derive these factors, which are a conjugate 

pair. In general, adding a constraint like (2) to a linear-quadratic stochastic dynamic optimization 

problem adds a degree to its characteristic polynomial so that it becomes cubic instead of quadratic. A 

technique for solving cubic equations, usually referred to as Cardan’s formula, is directly relevant to 

single-stock cases. However, in cases of multiple stocks, a cubic characteristic polynomial (which is a 

matrix polynomial) presents a major hurdle because a general theory of cubic eigenproblems does not 

currently exist. 

Clark (1990) describes some elements of bioeconomic theory with age-structured populations using a 

cohort model. An empirical application of this theory is available in Clark (1976). Deriso (1980) follows

this approach and analyzes OYT harvesting strategies in a classical delay-difference population model.

Quinn and Deriso (1999) review these models and describe them as representing a middle ground 

between simple (but unrealistic) production models and more complicated (i.e., vector-based) agestructured population models. The first group of delay-difference models reviewed in Quinn and Deriso 

  

t

c t b

2

1

0

1 Max E ( ) ( ) .

2

t

t t t t t

t

     b c c c c







                

t

r

t b t

c

0 1   

1

.

t t t t b b c r     
45

(1999) is based on Leslie matrices, with population dynamics represented in age-specific linear 

projection matrices. This first approach does not explicitly consider effects of individual growth; 

however, it does satisfy equation (2). 

The review in Quinn and Deriso (1999) also refers to a second set of delay-difference models called 

Deriso-Schnute Biomass Models, based on work in Deriso (1980) and Schnute (1985). These models 

explicitly consider the effects of individual growth through a second-order difference equation that 

relates age-dependent growth increments over time (i.e., Ford’s equation). This particular mathematical 

structure is important because second-order difference equations often represent market dynamics and 

optimal dynamics in economic models. Representing both types of dynamics is important in analyzing 

fisheries because externalities typically cause actual outcomes to deviate from socially optimal 

outcomes.

The starting point for the bioeconomic theory posited here is Ricker’s (1975) exposition of von 

Bertalanffy’s equation and its relation to Ford’s growth equation. Schnute (1985) expressed the latter in 

terms of , the weight of fish at age a in period t, with the assumption that Ford’s growth coefficient 

is a fraction, . Under this assumption, the annual weight increment decreases by a constant 

factor in each period according to a simple second-order difference equation, 

(3) 

for all and given for . A solution of this difference equation can be found in Appendix A 

of Schnute and Fournier (1980). Second-order difference equations can be used to describe dynamics in 

many economic models. For example, Ford’s growth equation has a natural economic interpretation:

The annual rate of return (in terms of growth) of leaving an individual fish in the water is a geometrically 

decreasing function of its age. 

Though a formal proof is beyond the scope of this paper, a linear growth equation that is equivalent to 

equation (2) exists that is both a delay-difference model that can be derived from Ford’s growth 

equation (3) and compatible with optimal control theory for linear-quadratic systems. A derivation of 

this linear growth equation from a set of first principles for delay-difference models, as expressed in the 

works cited previously, involves some restrictive compromises. Familiar restrictions on delay-difference 

models—for example, those found in Schnute (1985)—apply here. These restrictions include known 

(i.e., extrapolated) prerecruitment weight, knife-edged recruitment, infinitely lived individuals, constant 

natural mortality, and knife-edged selectivity. In addition, recruitment is simplified here and assumed to 

be an exogenous stochastic process. This assumption omits effects of any type of known (i.e., expected) 

compensatory response. The most important compromise in the approach outlined here involves a 

survival fraction , which Schnute (1985) interprets as the share of fish not caught in the fishery 

that survives to the next period (i.e., escapement). Unfortunately, that algebraic form does not simplify 

in the solution of the associated dynamic optimization problem. 

The approach described here treats fishing and natural mortality as simultaneous processes. Therefore, 

instead of treating survival to the next period as conditional on survival in the fishery, the treatment 

here assumes that fishing and natural mortality are additive (hence separable) for each point in time, as 

in Baranov’s catch equation. In other words, the age-dependent survival fraction applies to the entire 

population of each cohort in a period, which determines the total number in that cohort for the next 

wat,

0 1   

1 1 1 1 ( ), w w w w a t a t a t a t        

   

t 1 wa0a  0

0 1   
46

period. 

Treating fishing and natural mortality as concurrent additive processes produces symmetry in the 

growth model, which can be expressed simply in terms of state variables. Traditionally, the set of state 

variables in delay-difference models has been the number of individuals in a cohort at the start of a 

season, before fishing occurs. Here, state variables instead represent the numbers of fish in each cohort 

net of fishing mortality. An advantage of the latter representation of the system is that analyzing its 

limiting behavior and calculating probabilities of various events are straightforward undertakings. 

Under the interpretation above, an approximation can be made that yields , and that 

because and are positive, and by assumption (to ensure that the growth model is stable), 

there is an upper bound on biological growth and survival parameters such that . A slight 

modification implies . In words, Ford's growth coefficient must be smaller than a ratio of 

rates, with natural mortality in the numerator and survival from natural mortality in the denominator.

According to the condition on that precedes equation (2), this bound is a necessary and sufficient 

condition for stationary dynamics in a linear bioeconomic model. 

This abstract bioeconomic model is obviously not plausible in every setting. Some parts of the model 

may be relaxed. For example, Ford’s growth equation could be modified to include a dynamic forcing 

function such as climate change, or the assumption of knife-edged selectivity could be replaced by a 

more flexible functional form. Any major modification to the model would probably preclude closedform solutions. The problem may still be well posed but the analytical approach would be replaced by a 

numerical procedure for computing the solution. In such cases, recursive methods based on dynamic 

programming (e.g., Bellman’s equation) are popular, and are formally equivalent to an approach based 

on Euler equations. 

With respect to estimating OSY, the economic component of the model described here does well in 

representing the negative externalities that are thought by economists to be prevalent in fisheries. 

Multivariate versions of the model described here could be used to define OSY for mixed-stock fisheries. 

On the other hand, perhaps the most important shortcoming of the model here in terms of economic 

analysis is its simple approach to variable commercial operating costs: Only a single linear term, which is 

proportional to catch (or effort), is present to represent these market-based costs. Although such a 

simple approach may be adequate in an abstract model, it misses interesting and important questions, 

such as how a change in fuel prices, bag limits, or ESA interactions would affect OSY. Consequently, in 

addition to relaxing key restrictions on biology and selectivity, another high priority for future work is to 

extend the cost structure of the bioeconomic model outlined here to explicitly account for variable 

inputs across the suite of users and uses. Mathematically, the most convenient way of extending this 

cost structure might be to estimate a static system for derived input demand and to incorporate this 

structure directly into the model. 

Such a static demand system, and outputs from the model outlined here, could be used as inputs to a 

CGE model of a regional economy to examine OSY on a broader scale. In that approach, a CGE model 

could represent the value to the overall economy of a particular region from economic activity directly, 

and indirectly, related to fishing (Waters et al., 2014). Then the CGE model—instead of the more 

traditional and restrictive objective based on net benefits (i.e., profits) to the fishing industry—would be

the basis for computing OSY. 

     (1 )    1

(1 ) 1/    

     (1 ) / 
47

APPENDIX 4. Modeling Uncertainty

The previous appendix introduced stochastic stock dynamics, which are an important source of 

uncertainty in the setting of harvest control rules. Other uncertainties important to fisheries 

management include process error (such as stochastic stock dynamics, environmental conditions, catch 

prices or non-market values); observation error (such as inexact knowledge of stock biomass); and 

model error (such as uncertainty about the proper specification of stock-recruitment relationships). 

In a modeling context, incorporating uncertainty into management decisions requires that the 

uncertainty have a formal representation and that the decision-maker’s attitude toward risk be defined. 

Uncertainty and risk are important subjects in many fields, and the concepts and terminology 

surrounding them are not consistent across or even within fields. Most models build on an assumption

that uncertainties can be meaningfully represented as probabilities, though other approaches exist (see, 

for example, Regan et al. [2005] and Prato [2009]). In economics, an influential tradition has been to 

distinguish between risk as a situation in which probabilities of outcomes are known and uncertainty as 

a situation in which the probabilities are not known.25 However, recognition that the classical approach 

to decision-making under uncertainty (which was developed with respect to gambling problems) is not 

well suited to many decision problems led to the development of the theory of subjective probability 

(Savage, 1954) and the preference state approach (Arrow, 1964). 

Here, we apply the term “uncertainty” to any situation in which a random variable appears, whether a 

probability distribution is assigned to its possible realizations or not. We treat risk as a reflection of the 

importance of uncertainty to decision-makers. Risk attitudes or risk preferences capture managers’ 

attitudes toward possible realizations of values that are a function of underlying random variables. Thus, 

risk may be represented as statistics regarding outcomes such as expected loss or maximum possible 

loss, or as the probabilities of particular undesired outcomes (e.g., the probability of overfishing). 

Risk is significant to the development of harvest control rules because it affects a choice among actions 

in relation to managers’ objectives. For example, one very conservative approach to management under 

uncertainty is the maximin strategy, whereby a policy is designed to achieve the best outcome in the 

worst possible realization of model states or parameters. The probabilities of outcomes need not be 

considered in the maximin strategy. If probabilities of outcomes are available, functions of uncertain 

outcomes and their probabilities can be calculated. A decision-maker is risk neutral if he or she wants to 

maximize the expected value of a variable (or function thereof) without respect to other moments of 

the distribution. In most bioeconomic analyses, the assumption is that fisheries managers are risk 

neutral, though other risk preferences, such as risk aversion, may be represented. This is significant 

because the MSA seems to suggest a risk-averse posture toward overfishing, and the NS1 Guidelines 

even more so. 

One general approach to the representation of risk preference is a utility function, which represents the 

value of possible outcomes to decision-makers. For example, a commonly used risk-averse utility 

function is the mean of a random variable less a penalty for that variable’s variance. Utility curves, which 

are broadly applied in economics and engineering, have been applied in fisheries, including, for example, 

by Mendelssohn (1982) and Mäntyniemi et al. (2009). Another common approach to risk management is 

 

25 This distinction is generally attributed to Frank Knight (1921), although some authors argue that the distinction is 

based on a misunderstanding of Knight’s work (see, for example, Langlois and Cosgel [1993]).
48

based on constraining the probability of a given undesired outcome to no greater than some acceptable 

level, as in Shertzer et al. (2008). When an objective function is also specified, at least implicitly, this 

approach amounts to solving a chance-constrained program; for example, 

maximize f(X)

subject to p(X ≤ K )≤ L

where X is a random variable, K is a limit on X, and L is a limit on the probability that X exceeds K. For 

example, fisheries managers may seek to maximize expected profitability in a fishery subject to the 

constraint that the probability of overfishing does not exceed 10 percent. (Note that utility and chanceconstrained approaches are not mutually exclusive: The function f(X) could be a utility function and the 

problem could be solved subject to chance constraints.)

Because a traditional focus of dynamic optimization in fisheries has been on stochastic state dynamics, it 

will be convenient for us to frame the discussion here in terms of Markov decision processes. The 

general idea of a Markov decision process is to identify a control rule, known as the optimal policy. This 

policy specifies, for any given realization of a random state variable, the action that maximizes system 

performance in expectation. Formally, a Markov decision process is a collection of sets {A, S, P, W}, 

where A is the set of actions available to a decision-maker, S is a set of random state variables, P is a set 

of Markov transition probabilities that govern the evolution of the variables in S, and W is the rewards 

realized by the decision-maker for taking a particular action in a particular state. Given a suitably defined 

objective—usually the expected sum of periodic values or utilities—the solution of an MDP is a function 

π(S), which gives the optimal action for a realized state. Dynamic programming methods are used for 

this type of analysis to compute decision rules and value functions (Rust, 2008). 

Observation error, or uncertainty about true state value, has received less attention than process 

uncertainty in the optimal control literature. Sethi et al. (2005) address observation uncertainty within 

the MDP framework, an approach that yields a mapping from current observed state to optimal harvest. 

Moxnes (2003) treats observation error by applying the Kalman filter in the framework of stochastic 

optimization in policy space, an alternative to stochastic dynamic programming. An alternative approach 

to incorporating observation uncertainty is the partially observable Markov decision process (POMDP), a 

Bayesian framework in which a policy maps beliefs into actions. The POMDP is essentially a Bayesian 

approach to optimal control of a hidden Markov model. A preliminary application of the POMDP to 

fisheries management is Tomberlin (2008). 

Model uncertainty—that is, uncertainty about model parameters or, more generally, model structure—

has received little attention in the bioeconomics literature. Walters (1986) describes a model-averaging 

approach to model uncertainty in fisheries. In the larger dynamic optimization literature, robust 

optimization, in which expected performance is maximized under the worst-case model realization, has 

received considerable attention (Nilim and El Ghaoui, 2005; Woodward and Shaw, 2008). Woodward 

and Tomberlin (2014) apply robust dynamic optimization as a framework for precautionary 

management of a fishery when population growth parameters are uncertain. 

Delage and Mannor (2010) present a percentile optimization to Markov decision processes under both 

reward and state dynamics uncertainties. Basically, this approach provides an intermediate ground 

between the solution of the dynamic optimization problem-based nominal (point-estimate) parameter 

set and the robust alternative, which yields very conservative policies. Percentile optimization provides a 
49

choice parameter reflecting the degree of risk decision-makers are willing to assume, and the sensitivity 

of solutions to this parameter can be explored. 

Reinforcement learning is another technique that may be applied to problems with observation and 

model uncertainty. This technique has been broadly applied in engineering and computer science, but 

we are aware of only one application to natural resource management (Fonnesbeck, 2005). 

Though the work of Delage and Mannor (2010) is specifically directed at the problem of model 

uncertainty, it is similar in spirit to the Prager and Shertzer (2010) probability-based approach to ACLs. 

Both might be considered instances of chance-constrained programming, an approach to constrained 

optimization under uncertainty in which a solution is valid as long as the probability of constraint 

violation is within an acceptable range. 

Another approach to constrained optimization under uncertainty is stochastic programming with 

recourse, in which the potential to undo damages from a current action (e.g., overfishing due to an 

overly optimistic biomass estimate) by counteracting future actions (e.g., reducing next year’s harvest) is 

considered at the time of the original decision. Whether such recourse is available in a fisheries 

management context will depend on the biological and institutional setting, and is complicated by the 

reality that in many cases the option of recourse will itself be uncertain. As mentioned earlier, utility 

theory provides another approach to decision-making under uncertainty. There does not seem to be 

clear correspondence between chance-constrained programming and utility theory except in very 

simple cases.

In summary, stochastic dynamic optimization models provide a way to estimate OYT under various types 

of uncertainty and for deriving risk metrics associated with particular harvest levels. Because these 

models can be difficult to implement, it is worth considering whether they are worth the effort. 

Specifically, we would like to know: 1) whether the management implications of stochastic models differ 

enough from deterministic models to warrant the extra modeling effort; and 2) whether nonoptimizing 

approaches may serve just as well in particular cases. 

With regard to the first question, Andersen and Sutinen (1984) note that differences between policies 

derived from deterministic and stochastic models are often not great, whereas Sethi et al. (2005) find 

that under some conditions the differences are substantial. We do not expect a general answer to this 

question to emerge soon. With regard to the second question, stochastic simulation models of a small 

set of candidate policies (Kjaersgaard and Frost, 2008; Semmens, 2008) may often conform more closely 

to the Council process than general optimization models, and may be more easily implemented than a 

full optimization model. 

To reiterate an earlier point, estimation of OYT is based on maximizing overall net benefits to the Nation 

subject to biological and, in principle, other (e.g., ecological, environmental, and social) constraints. For 

purposes of estimating OYT, scientific and management uncertainties as well as risk metrics can be 

captured independently of the process of defining ABC or ACL (though either of these may appear as 

explicit constraints on OYT). Thus, it is possible to estimate OYT without developing sequential buffers 

for scientific and management uncertainty, and an argument can be made that treating these 

uncertainties simultaneously is preferable. For example, based on stochastic simulation of Gulf of 

Mexico red snapper and grouper fisheries, Semmens (2008) concluded, “Importantly, the results suggest 

that all sources of uncertainty and variability should be assessed together to determine the appropriate 

buffer.” Further research is required to determine under what circumstances it would be appropriate to 
50

assess all sources of uncertainty and variability together to establish the buffer between OFL and ACT, if 

one is used, or between OFL and ACL if an ACT is not used. Our point is that regardless of how scientific 

and management uncertainty are treated in the development of ABCs and ACLs, they can be treated 

simultaneously for the purposes of estimating OYT. 
51

APPENDIX 5. Numerical Examples of Aggregate MSY and OSY in a Two-Stock Fishery with a Technical 

Interaction

Ecological interactions occur due to predation and competition; and those interactions tend to affect the 

overall net benefit derived from the use and existence of living marine resources and their habitat. For 

example, increasing the biomass of a prey species for an endangered marine mammal could provide 

non-market benefits that exceed the loss in market benefits in the fishery for that prey species. 

Technical and market interactions are the two types of economic interactions. Technical interactions 

occur when two or more stocks are caught together. Market interactions occur either when the exvessel prices of two or more stocks are interdependent or when the input prices (e.g., the price of labor 

or the lease price of a fishing vessel) for harvesting one stock are dependent on the harvest levels of 

other stocks. This appendix presents numerical examples of aggregate MSY and OSY in a two-stock 

fishery with a technical interaction.

A5.1 MSY Example

As depicted in Figure 4, the sustainable yield for each stock and the associated sustainable stock 

biomass are functions of the fishing effort that is jointly applied to both stocks.26 Therefore, the 

sustainable yield curve for the fishery is the vertical summation of the sustainable yield curves for the 

two stocks.

In this example, the following occur as effort increases (see Table 1 and Figure 4):

1. As effort increases from 0 to 60: 

 The sustainable level of biomass for each stock decreases.

 The sustainable yields of both stocks and the fishery increase.

 The sustainable yield of stock 2 reaches its maximum (MSY2) of 3,600 metric tons (t) and its

MSY level of effort (EMSY2) of 60.

2. As effort increases from 60 to 92: 

 The sustainable level of biomass for each stock continues to decrease.

 The sustainable yield of stock 2 decreases because the difference between the actual level 

of effort and EMSY2 increases; and because the difference between the stock 2 biomass level 

that supports MSY2 (BMSY2) and the actual stock 2 biomass also increases.

 The sustainable yields of stock 1 and the fishery as a whole continue to increase.

 The sustainable yield for the fishery as a whole reaches its maximum (MSYF) of about 42,300 

t and its MSY level of effort (EMSYF) of 92. At that level of effort, the increase in the 

sustainable yield for stock 1 is exactly offset by the decrease for stock 2, and the biomasses 

of stocks 1 and 2 are at levels that support MSYF (BMSYF1 and BMSYF2). Therefore, BMSYF2 is less 

than BMSY2.

3. As effort increases from 92 to 100:

 

26 This model assumes that the relative catchability of the two species is fixed and partly depends on a specific 

regulatory approach. Therefore, a change to the regulatory approach can substantially alter relative catchability. 

For example, a catch share system may provide incentives for fishermen to alter gear, timing, or location of fishing 

in ways that reduce catch rates of the weaker stock, enabling a higher level of sustainably catch from the stronger 

stock without overfishing the weaker stock.
52

 The sustainable level of biomass for each stock continues to decrease.

 The sustainable yields of stock 2 and the fishery as a whole decrease because effort exceeds 

EMSY2 and EMSYF by larger amounts, the biomass of stock 1 decreases farther below BMSYF1, and 

the biomass of stock 2 decreases farther below both BMSY2 and BMSYF2.

 The sustainable yield for stock 1 continues to increase (but by less than the decrease in 

sustainable yield for stock 2). It reaches its maximum (MSY1) of 40,000 t and its MSY level of 

effort (EMSY1) of 100. Therefore, BMSYF1 is greater than BMSY1.

4. As effort increases beyond 100: 

 The sustainable level of biomass for each stock continues to decrease.

 The sustainable yields of both stocks and the fishery as a whole decrease because EMSY1, 

EMSY2, and EMSYF are being exceeded by larger amounts and because the biomasses of stocks 

1 and 2 are decreasing farther below BMSY1, BMSYF1, BMSY2, and BMSYF2.

The main implications of this example are as follows:

1. The level of effort that generates MSY for stock 1 (EMSY1) exceeds the level of effort that generates 

MSY for stock 2 (EMSY2); therefore, the sum of the MSYs for the two stocks is not attainable.

2. The level of effort that generates MSY for the fishery as a whole (EMSYF) is less than EMSY1 and greater 

than EMSY2.

3. If the MSY reference point for the fishery as a whole (i.e., the aggregate MSY reference point) is 

used, the biomass targets for stocks 1 and 2 are the sustainable biomass levels associated with 

EMSYF; therefore, the target level for stock 1 (BMSYF1) is greater than BMSY1, the target level for stock 2 

(BMSYF2) is less than BMSY2, and attaining MSY and BMSY for either stock would prevent the attainment 

of MSY and BMSY for the other stock and for the fishery as a whole.

4. A choice needs to be made among the reference points that will support MSY for stock 1, MSY for 

stock 2, or MSY for the fishery as a whole.

However, as noted in Section 3.3.1, there is a critical problem with the concept of an aggregate MSY if 

the following implicit assumptions are not valid: 1) an additional metric ton of sustainable yield of any 

stock is equally important and 2) that its importance does not depend on the level of sustainable yield 

for any stock. Section 3.3.1 also includes three possible fixes if these assumptions are not valid.
53

Table 1. Sustainable yield when MSY1, MSY2, and MSYF levels of effort are jointly applied to both 

stocks in a two-stock fishery with a technical interaction that results in the stocks being caught 

together (catch in metric tons).

MSY1 MSY2 MSYF

Fishing effort 100 60 92

Catch for stock 1 40,000 33,600 39,744

Catch for stock 2 2,000 3,600 2,576

Total catch 42,000 37,200 42,320

Notes:

MSY1 is the independently determined MSY for stock 1.

MSY2 is the independently determined MSY for stock 2.

MSYF is the MSY for the fishery as a whole when the interaction between the stocks is considered.

Figure 4. MSY for a two-stock fishery as a whole when both stocks are caught together.
54

A5.2 OSY Examples

For the OSY examples, we use the same sustainable yield curves as in the MSY example and the simple 

model of OSY we discussed in Section 2.2.2. In Figure 5, we replaced the sustainable yield curves in 

metric tons for the two stocks from Figure 4 with sustainable revenue curves in dollars of ex-vessel 

revenue. We also added a total cost curve for harvesting both stocks together. 

Sustainable revenue and associated sustainable levels of biomass for each stock, as well as the narrowly 

defined measure of overall net benefit, are functions of the fishing effort that is jointly applied to both 

stocks. Therefore, the sustainable revenue curve for the fishery as a whole is the vertical summation of 

the sustainable revenue curves for the two stocks. The OSY level of effort for the fishery as a whole is 

that with the greatest difference between the total revenue and total cost curves. As in Figure 2, this is 

the level of effort at which marginal cost and marginal revenue are equal. 

CASE 1

For this example, we use ex-vessel prices of $100 and $5,000 per metric ton, or about $0.05 and $2.27 

per pound for stocks 1 and 2, respectively, to transform the sustainable yield curves in Figure 4 into the 

sustainable revenue curves in Figure 5. In addition, we use a cost of $100,000 per unit of fishing effort to 

generate the total cost curve. Table 2 presents the sustainable yield, revenue, and cost, and a narrowly 

defined measure of overall net benefit for Case 1 and each of five levels of effort. The five levels of 

effort are those associated with:

1. MSY1,

2. MSY2, 

3. MSYF, 

4. maximum sustainable revenue for the fishery as a whole (MSRevF), and 

5. OSY for the fishery as a whole (OSYF).

Because the same underlying sustainable yield functions are depicted in Figures 4 and 5, the EMSY1 and 

EMSY2 are 100 and 60, respectively, in both figures. In addition, because the only difference between the 

sustainable yield curves in Figure 4 and the sustainable revenue curves in Figure 5 is in their vertical 

scaling based on the ex-vessel price of each stock, the levels of fishing effort that maximize sustainable 

revenue for stocks 1 and 2 (EMSRev1 and EMSRev2) are equal to EMSY1 and EMSY2, respectively. Therefore, BMSY1 

and BMSRev1 are equal; and BMSY2 and BMSRev2 are equal. 

However, because the ex-vessel prices of the stocks differ, the levels of effort that maximize sustainable 

yield (EMSYF) and sustainable revenue (EMSRevF) for the fishery as a whole are not the same. In this 

example, a large difference in prices in favor of stock 2 resulted in a large difference between the EMSYF 

of 92 and the EMSRevF of 63, which is much closer to the EMSY2 of 60. Because EMSYF is greater than EMSRevF, 

BMSYF1 is less than BMSRevF1, and BMSYF2 is less than BMSRevF2. This example demonstrates that simply 

changing the objective from maximizing sustainable yield to maximizing sustainable revenue can 

substantially change the maximizing level of effort for the commercial fishery as a whole, and associated 

biomass target levels for both stocks. 

The cost of fishing effort is considered in determining OSY levels of effort, catch, and biomass. In this 

example, the fishing effort that produces the OSY for the fishery as a whole (EOSYF) is 54, because at this 

level of effort the slopes of the revenue and cost curves are equal (i.e., marginal revenue is equal to 
55

marginal cost). This is less than the EMSY2 of 60, the EMSRevF of 63, the EMSYF of 92, and the EMSY1 of 100. 

Therefore, BOSYF1 is greater than BMSY1, and BOSYF2 is greater than BMSY2. These results mean that, in this 

example, OSYF is a more conservative reference point than MSY and MSRev for the commercial fishery 

as a whole or than MSY1 and MSY2, and that MSRevF is a more conservative reference point than MSYF.

In this example of two stocks that are caught together, OSY cannot be determined separately for stocks 

1 and 2 because the same effort, and therefore the same cost, is associated with catching both stocks 

together.

Table 2. Sustainable yield, revenue, and cost, as well as a narrowly defined measure of overall net 

benefit, for Case 1 when MSY1, MSY2, MSYF, MSRevF, and OSYF levels of effort are applied jointly to 

both stocks In a two-stock fishery (catch in metric tons and both revenue and cost in millions of 

dollars). 

Case 1 MSY1 MSY2 MSYF MSRevF OSYF

Fishing effort 100 60 92 63 54

Catch for stock 1 40,000 33,600 39,744 34,524 31,536

Catch for stock 2 2,000 3,600 2,576 3,591 3,564

Total catch 42,000 37,200 42,320 38,115 35,100

Revenue for stock 1 $4.0 $3.4 $4.0 $3.5 $3.2

Revenue for stock 2 $10.0 $18.0 $12.9 $18.0 $17.8

Total revenue $14.0 $21.4 $16.9 $21.4 $21.0

Total cost $10.0 $6.0 $9.2 $6.3 $5.4

Revenue - cost $4.0 $15.4 $7.7 $15.1 $15.6

Notes:

MSY1 is the independently determined MSY for stock 1.

MSY2 is the independently determined MSY for stock 2.

MSYF is the MSY for the fishery as a whole when the interaction between the two

stocks is considered.

MSRevF is the maximum sustainable revenue for the fishery as a whole when the 

interaction between the two stocks is considered.

OSYF is the optimum sustainable yield for the fishery as a whole when the interaction 

between the two stocks is considered.

The sustainable revenue curves are based on ex-vessel prices of $100 and $5,000 per 

metric ton for stocks 1 and 2, respectively. A cost of $100,000 per unit of fishing effort 

was used to generate total cost.
56

To prevent the labeling in Figures 5 – 7 from becoming too complicated, only the levels of effort for

MSY1, MSY2, MSYF, and OSYF and the associated levels of total sustainable revenue are labeled. 

However, because levels of both effort and biomass are arrayed on the horizontal axis, the positions of 

EMSY1, EMSY2, EMSYF, and EOSYF on that axis identify the corresponding positions of BMSY1, BMSY2, BMSYF, and 

BOSYF, respectively.

Figure 5. MSY and OSY for a two-stock fishery as a whole when the two stocks are caught together; 

the price of stock 2 is substantially greater than that of stock 1 (i.e., $5,000 versus $100 per metric 

ton); the cost of a unit of effort is $100,000; and overall net benefit is narrowly defined (Case 1).

CASE 2

If the ex-vessel prices of stocks 1 and 2 are changed substantially in favor of stock 1 from $100 to $300 

per metric ton and from $5,000 to $100 per metric ton, respectively, the EOSYF increases from 54 to 58 

and the EMSRevF increases from 63 to 97. However, because the sustainable yield curves do not change, 

the EMSYF of 92, the EMSY1 of 100, and the EMSY2 of 60 do not change (Table 3 and Figure 6). Therefore, in 

this case, EOSYF < EMSY2 < EMSYF < EMSRevF < EMSY1. This means that, as in Case 1, BOSYF1 > BMSY1 and 

BOSYF2 > BMSY2. Therefore, in both Case 1 and Case 2, OSYF is a more conservative reference point than the 

MSY and MSRev for the fishery as a whole, MSY1, and MSY2. However, Case 2 differs from Case 1 in that 

MSRevF is a less conservative reference point than MSYF.

0.0

5.0

10.0

15.0

20.0

25.0

0 10 20 30 40 50 60 70 80 90 100 110 120

Revenue and Cost ($ millions)

Fishing Effort →

← Biomass

Stock 1 Revenue Stock 2 Revenue

Total Revenue (TR) Total Cost

TR at EMSY1

TR at EOSYF

TR at EMSY2

TR at EMSYF

EOSYF EMSY2 EMSYF EMSY1
57

Table 3. Sustainable yield, revenue, and cost, as well as a narrowly defined measure of overall net 

benefit, for Case 2 when MSY1, MSY2, MSYF, MSRevF, and OSYF levels of effort are applied jointly to 

both stocks in a two-stock fishery (catch in metric tons and both revenue and cost in millions of 

dollars).

Case 2 MSY1 MSY2 MSYF MSRevF OSYF

Fishing effort 100 60 92 97 58

Catch for stock 1 40,000 33,600 39,744 39,964 32,944

Catch for stock 2 2,000 3,600 2,576 2,231 3,596

Total catch 42,000 37,200 42,320 42,195 36,540

Revenue for stock 1 $12.0 $10.1 $11.9 $12.0 $9.9

Revenue for stock 2 $0.2 $0.4 $0.3 $0.2 $0.4

Total revenue $12.2 $10.4 $12.2 $12.2 $10.2

Total cost $10.0 $6.0 $9.2 $9.7 $5.8

Revenue - cost $2.2 $4.4 $3.0 $2.5 $4.4

Notes:

MSY1 is the independently determined MSY for stock 1.

MSY2 is the independently determined MSY for stock 2.

MSYF is the MSY for the fishery as a whole when the interaction between the two

stocks is considered.

MSRevF is the maximum sustainable revenue for the fishery as a whole when the 

interaction between the two stocks is considered.

OSYF is the optimum sustainable yield for the fishery as a whole when the interaction 

between the two stocks is considered.

The sustainable revenue curves are based on ex-vessel prices of $300 and $100 per 

metric ton for stocks 1 and 2, respectively. A cost of $100,000 per unit of fishing effort 

was used to generate total cost.
58

Figure 6. MSY and OSY for a two-stock fishery as a whole when the two stocks are caught together, 

the price of stock 1 is greater than that of stock 2 (i.e., $300 versus $100 per metric ton), and the cost 

of a unit of effort is $100,000 (Case 2).

CASE 3

In Case 3 (Table 4 and Figure 7), the ex-vessel prices are the same as in Case 2, but the cost per unit of 

effort is decreased from $100,000 to $75,000. In this case, EOSYF increases to 68, but because the 

sustainable yield and revenue curves are the same as for Case 2, the EMSRevF, EMSY1, EMSY2, and EMSYF

remain at the same levels. Therefore, for Case 3, EMSY2 < EOSYF < EMSYF < EMSRevF < EMSY1. Consequently, 

BOSYF1 > BMSY1 but BOSYF2 < BMSY2. Thus, in Case 3, OSYF is a more conservative reference point than 

MSRevF, MSYF, and MSY1, but it is a less conservative reference point than MSY2. This means that there 

are trade-offs among MSYs for the two stocks, the MSY for the fishery as a whole, and the OSY for the 

fishery as a whole. Therefore, a choice needs to be made among the reference points that will support 

MSY for stock 1, MSY for stock 2, and MSY or OSY for the fishery as a whole.

As noted in Section 3.3, the NS1 Guidelines recognize the importance of the concept of aggregate MSY 

for a group of or all the stocks in a fishery. However, the NS1 Guidelines do not address the use of 

reference points related to aggregate MSY or OSY as alternatives to independently determined and 

stock-specific reference points when the former are associated with greater effort and, consequently, 

lower biomass for one or more stocks.
59

Table 4. Sustainable yield, revenue, and cost, as well as a narrowly defined measure of overall net 

benefit, for Case 3 when MSY1, MSY2, MSYF, MSRevF, and OSYF levels of effort are applied jointly to 

both stocks in a two-stock fishery (catch in metric tons and both revenue and cost in millions of 

dollars).

Case 3 MSY1 MSY2 MSYF MSRevF OSYF

Fishing effort 100 60 92 97 68

Catch for stock 1 40,000 33,600 39,744 39,964 35,904

Catch for stock 2 2,000 3,600 2,576 2,231 3,536

Total catch 42,000 37,200 42,320 42,195 39,440

Revenue for stock 1 $12.0 $10.1 $11.9 $12.0 $10.8

Revenue for stock 2 $0.2 $0.4 $0.3 $0.2 $0.4

Total revenue $12.2 $10.4 $12.2 $12.2 $11.1

Total cost $7.5 $4.5 $6.9 $7.3 $5.1

Revenue - cost $4.7 $5.9 $5.3 $4.9 $6.0

Notes:

MSY1 is the independently determined MSY for stock 1.

MSY2 is the independently determined MSY for stock 2.

MSYF is the MSY for the fishery as a whole when the interaction between the two

stocks is considered.

MSRevF is the maximum sustainable revenue for the fishery as a whole when the 

interaction between the two stocks is considered.

OSYF is the optimum sustainable yield for the fishery as a whole when the interaction 

between the two stocks is considered.

The sustainable revenue curves are based on ex-vessel prices of $300 and $100 per 

metric ton for stocks 1 and 2, respectively. A cost of $75,000 per unit of fishing effort 

was used to generate total cost.
60

Figure 7. MSY and OSY for a two stock fishery as a whole when the two stocks are caught together, 

the price of stock 1 is greater than that of stock 2 (i.e., $300 vs. $100 per metric ton), and the cost of a 

unit of effort is reduced to $75,000 (Case 3).
61

APPENDIX 6. Catchability: A Critical Parameter in Stock Assessment and Bioeconomic Models

Catchability is a critical parameter in most stock assessment and bioeconomic models. It is the 

parameter (either a constant or variable) that relates an index of relative abundance to population size 

(absolute abundance). Equivalently, it is the proportionality parameter between fishing effort and 

fishing mortality—or the portion of the stock captured by one unit of effort where CPUE, based on 

fishery-dependent or fishery-independent data,

27 is the index of relative abundance (Wilberg et al.,

2010).

In addition to these definitions of catchability, Wilberg et al. (2010) provide a useful review of the theory 

and evidence for time-varying catchability, its effects on stock assessment estimates, and methods of 

including time-varying catchability in stock assessments. Their review indicates that there is strong 

evidence that time-varying catchability is common for most fisheries in which fishery-dependent data 

are used to estimate CPUE, as well as for many fisheries in which fishery-independent survey data are 

used to estimate CPUE. Wilberg et al. state that trends in catchability over time can cause biased 

estimates of stock size and fishing mortality rates in stock assessment models that do not compensate 

for such trends. They therefore recommend that time-varying catchability be assumed and that multiple 

methods of including it be applied.

With few, if any, exceptions, CPUE is estimated with fishery-dependent data or fishery-independent data 

for only part of the range of a stock, and fishing and surveying locations are not randomly selected.

Fishermen use a variety of criteria (e.g., convenience, familiarity, expected costs and revenue, and 

safety) to decide which areas to fish and which to avoid. Similarly, various factors determine which areas 

are surveyed. For example, surveys are less likely to occur in areas that cannot be surveyed successfully 

with available survey gear and in areas that are too expensive to survey. If fish do not behave the same 

in both fished and unfished areas, or in both surveyed and unsurveyed areas, CPUE estimates will be 

biased, and changes in actual population size will not be proportional to changes in CPUE (i.e., 

catchability is not constant). Even if data were available for the whole population, other factors can 

explain why catchability would not be constant or, equivalently, why there is a nonlinear relationship 

between the index (CPUE) and the actual population.

Hannesson (1983),

28 Squires and Vestergaard (2015), Hilborn and Walters (1992), Walters (2003), and 

Wilberg et al. (2010) address the implications of density-dependent catchability. For example, if there 

are area-specific differences in fish density, density-dependent catchability contributes to the problems

associated with not having CPUE data for the entire range of a stock and is one reason there is a 

nonlinear relationship between the index (CPUE) and the actual population. The explanations of densitydependent catchability include the following: 1) Gear saturation can occur in some areas; 2) Fish 

behavior can include density-dependent gear avoidance; and 3) As a stock’s size changes, its spatial and 

intra-annual distributions can change.

Density dependence is just one reason catchability can vary over time. Changes in environmental, 

biological, and management processes may also drive changes in catchability, in part by affecting how, 

 

27 Fishery-dependent data are collected from fishing vessels during normal fishing operations as opposed to 

fishery-independent data that are, for example, collected during a scientific survey cruise.

28 Hannesson (1983) is the earliest, theoretically rigorous economics paper on time-varying and density-dependent 

catchability we are aware of. However, it was not the first paper on this topic. For references to other papers on 

this topic, see Wilberg et al. (2010). 
62

when, where, and by whom fish are caught (Hannesson, 1983; Wilberg et al., 2010; Vestergaard and 

Squires, 2013 and 2015).

If catchability increases as abundance declines—because of density dependence or other reasons—

CPUE can remain high despite decreases in abundance. This condition can cause hyperstable CPUE. If a

stock assessment model does not account for this increase in catchability, the hyperstable CPUE masks a 

decline in stock abundance and thus contributes to overfishing and increased chances of the stock 

becoming overfished. However, when a stock is actually recovering, hyperstable CPUE understates the 

rate and level of recovery and can unnecessarily prolong the use of relatively low quotas. Conversely, if 

CPUE decreases more rapidly than stock size, catchability exhibits hyperdepletion (Wilberg et al., 2010).

Sources of time-varying catchability that tend to increase catchability over time become increasingly 

problematic if they are not accounted for in stock assessment and bioeconomic models. In the 

remainder of this appendix, we discuss one source of time-increasing catchability: increases in 

productivity resulting from technical change and increased technical efficiency. However, many of our 

conclusions apply to other sources of increases in catchability over time.

Various problems can arise by excluding technological change and increased technical efficiency from 

stock assessment and bioeconomic models. First, when stock assessments are based principally on 

fishery-dependent CPUE data, and the effects of technological change and increased technical efficiency 

are not fully accounted for, those changes are a source of increasing upward bias in estimates of 

population size. Second, if effort controls are the principal management tools used to control catch, and 

if technological change and increased technical efficiency are not fully accounted for, the resulting effort 

controls will be inadequate and catch will be too high.

Finally, technological change and increased technical efficiency tend to affect OSY and OYT by 

decreasing the cost of harvesting, processing, and marketing fish. These factors may also increase

product quality and therefore the prices of fish and seafood products.

29 When technological change and 

increased technical efficiency lower the costs of harvest, leaving fish in the water to lower harvest costs 

(the traditional marginal stock effect) becomes less important. Moreover, not accounting for 

technological change and increased technical efficiency creates an opportunity cost of forgone resource 

rent and consumer benefit that increases over time. Therefore, accounting for technological change, 

increased technical efficiency, and other factors that will change over time is necessary for effective 

fishery management.

For example, technological change and increased technical efficiency affect the rent-maximizing levels of 

resource stocks, and can cause dynamic BMEY to be less than BMSY. This result is counter to the 

conclusions that: 1) Dynamic BMEY or BOYT is greater than BMSY when technological change and increased

technical efficiency are not accounted for; and 2) Static equilibrium BOSY is greater than BMSY (Squires and 

Vestergaard, 2013 and 2015). Technological change and increased technical efficiency lower the costs of 

finding and harvesting fish over time, and therefore decrease the benefit of leaving unharvested fish in 

the water to lower costs. The distance between dynamic BMEY and BMSY is determined by the rate of 

intrinsic growth, the discount rate, and the rates of technological change and increases in technical 

efficiency. The marginal stock effect has no impact on the final result, and affects only the approach 

path to dynamic BMEY, which is determined by biological and economic parameters.

 

29 Other effects of technological change and increased technical efficiency (beyond decreasing harvesting costs) 

affect OSY and OYT but do not affect catchability. 
63

LITERATURE CITED

Abbott, J. K., B. Garber-Yonts, and J. E. Wilen. 2010. Employment and remuneration effects of IFQs in the 

Bering Sea/Aleutian Islands crab fisheries. Mar. Resour. Econ. 25(4):333–354.

http://dx.doi.org/10.5950/0738-1360-25.4.333

Andersen, P., and J. G. Sutinen. 1984. Stochastic bioeconomics: a review of basic methods and results.

Mar. Resour. Econ. 1:117–136. [Available at http://www.jstor.org/stable/42628850.]

Anderson, D. 1975. Optimal exploitation strategies for an animal population in a Markovian 

environment: a theory and an example. Ecology 56:1281–1297. http://dx.doi.org/10.2307/1934697

Anderson, L. G. 1975. Analysis of open-access commercial exploitation and maximum economic yield in 

biologically and technologically interdependent fisheries. J. Fish. Res. Board Can. 32:1825–1842.

http://dx.doi.org/10.1139/f75-217

Anderson, L. G., and J. C. Seijo. 2010. Bioeconomics of fisheries management, 320 p. Wiley-Blackwell, 

Hoboken, NJ.

Arrow, K. J. 1964. The role of securities in the optimal allocation of risk-bearing. Rev. Econ. Stud. 31:91–

96. [Available at http://www.jstor.org/stable/2296188.]

Beddington, J. R., and R. M. May. 1977. Harvesting natural populations in a randomly fluctuating 

environment. Science. 197:463–465. http://dx.doi.org/10.1126/science.197.4302.463

Berkson, J. M., L. L. Kline, and D. J. Orth, eds. 2002. Incorporating uncertainty into fishery models. Am. 

Fish. Soc. Symp. 27, 208 p.

Berman, M. D. 1998. Sustainability and subsistence in arctic communities. Inst. Soc. Econ. Res., Univ.

Alaska Anchorage, 26 p. [Available at http://www.iser.uaa.alaska.edu/request.php?id=933.]

Bjørndal, T., and A. Brasão. 2006. The east Atlantic bluefin tuna fisheries: stock collapse or recovery? 

Mar. Resour. Econ. 21:193–210. [Available at http://www.jstor.org/stable/42629504.]

Bulte, E., H. Folmer, W. Heijman. 1998. Dynamic and static approaches to mixed good management: the 

case of minke whales in the Northeast Atlantic. Eur. Rev. Agric. Econ. 25:73–91.

http://dx.doi.org/10.1093/erae/25.1.73

Burgess, M.G., Giacomini, H.C., Szuwalski, C.S., Costello, C., Gaines, S.D. 2017. Describing ecosystem 

contexts with single-species models: A theoretical synthesis for fisheries. Fish and Fisheries 18: 264-284.

Casey, K. E., C. M. Dewees, B. R. Turris, and J. E. Wilen. 1995. The effects of individual vessel quotas in 

the British Columbia halibut fishery. Mar. Resour. Econ. 10:211-230. [Available at 

http://www.jstor.org/stable/42629588.]
64

Charles, A. T. 1998. Living with uncertainty in fisheries: analytical methods, management priorities and 

the Canadian groundfishery experience. Fish. Res. 37:37–50. http://dx.doi.org/10.1016/S0165-

7836(98)00125-8

Christensen, V. 2010. MEY = MSY. Fish Fisheries. 11:105–110. http://dx.doi.org/10.1111/j.1467-

2979.2009.00341.x

Clark, C. W. 1976. A delayed-recruitment model of population dynamics, with an application to baleen 

whale populations. J. Math. Biol. 3:381–391. http://dx.doi.org/10.1007/BF00275067

Clark, C. 1990. Mathematical bioeconomics: the optimal management of renewable resources, 2

nd ed., 

400 p. Wiley Interscience, New York. 

Costello, C., B. P. Kinlan, S. E. Lester, and S. D. Gaines. 2012. The economic value of rebuilding fisheries. 

OECD Food, Agriculture and Fisheries Papers 55, 69 p. OECD Publishing, Paris. 

http://dx.doi.org/10.1787/5k9bfqnmptd2-en

Deacon, R. T. 1989. An empirical model of fishery dynamics. J. Environ. Econ. Manage. 16:167–183.

http://dx.doi.org/10.1016/0095-0696(89)90007-7

Delage, E., and S. Mannor. 2010. Percentile optimization for Markov decision processes with parameter 

uncertainty. Oper. Res. 58(1):203–213. http://dx.doi.org/10.1287/opre.1080.0685

Deriso, R. B. 1980. Harvesting strategies and parameter estimation for an age-structured model. Can. J.

Fish. Aquat. Sci. 37:268–282. http://dx.doi.org/10.1139/f80-034

Dupont, D. P., K. J. Fox, D. V. Gordon, and R. Q. Grafton. 2005. Profit and price effects of multi‐species 

individual transferable quotas. J. Agric. Econ. 56(1):31–57. http://dx.doi.org/10.1111/j.1477-

9552.2005.tb00121.x

Federal Register. Executive Order 12866 of September 30, 1993. Regulatory Planning and Review

58(190). [Available at http://cdn.loc.gov/service/ll/fedreg/fr058/fr058190/fr058190.pdf.]

Federal Register. 50 CFR Part 600 Magnuson-Stevens Act Provisions; Annual Catch Limits; National 

Standard Guidelines; Final Rule, 74(11). January 16, 2009. [Available at 

https://www.gpo.gov/fdsys/pkg/FR-2009-01-16/pdf/E9-636.pdf.]

Felthoven, R. G. 2002. Effects of the American Fisheries Act on capacity, utilization and technical 

efficiency. Mar. Resour. Econ. 17:181–205. [Available at http://www.jstor.org/stable/42629363.]

Flaaten, O. 1988. The economics of multispecies harvesting: theory and application to the Barents Sea 

fisheries. Berlin: Springer-Verlag.

Fonnesbeck, C. J. 2005. Solving dynamic wildlife resource optimization problems using reinforcement 

learning. Nat. Resour. Model. 18:1–40. http://dx.doi.org/10.1111/j.1939-7445.2005.tb00147.x

Fournier, D., and C. P. Archibald. 1982. A general theory for analyzing catch at age data. Can. J. Fish.

Aquat. Sci. 39:1195–1207. http://dx.doi.org/10.1139/f82-157
65

Froese, R., C. Walters, D. Pauly, H. Winker, O. L. F. Weyl, N. Demirel, A. C. Tsikliras, and S. J. Holt. 2015. A 

critique of the balanced harvesting approach to fishing. ICES J. Mar. Sci. 73:1640–1650.

http://dx.doi.org/10.1093/icesjms/fsv122

Fulton, E. A., A. D. M. Smith, D. C. Smith, I. E. van Putten. 2011. Human behavior: the key source of 

uncertainty in fisheries management. Fish Fisheries. 12(2011):2–17. http://dx.doi.org/10.1111/j.1467-

2979.2010.00371.x

Gerlach, S. C., and P. A. Loring. 2013. Rebuilding northern foodsheds, sustainable food systems, 

community well-being, and food security. Int. J. Circumpol. Health 72:21560. 

http://dx.doi.org/10.3402/ijch.v72i0.21560

Gordon, H. S. 1954. The economic theory of a common-property resource: the fishery. J. Polit. Econ.

62:124–142. [Available at http://www.jstor.org/stable/1825571.]

Grafton, R. Q., T. Kompas, L. Chu, and N. Che. 2010. Maximum economic yield. Aust. J. Agric Resour.

Econ. 54:273–280. http://dx.doi.org/10.1111/j.1467-8489.2010.00492.x

Grafton, R. Q., T. Kompas, T. N. Che, L. Chu, and R. Hilborn. 2012. BMEY as a fisheries management target. 

Fish Fisheries. 13:303–312. http://dx.doi.org/10.1111/j.1467-2979.2011.00444.x

Gulland, J. A. 1983. Fish stock assessment: a manual of basic methods, 236 p. John Wiley and Sons, New 

York.

Hannesson, R. 1983. Bioeconomic production function in fisheries: theoretical and empirical analysis. 

Can. J. Fish. Aquat. Sci. 40:968–982. http://dx.doi.org/10.1139/f83-123

Herrmann, M. 1996. Estimating the induced price increase for Canadian Pacific halibut with the 

introduction of the individual vessel quota program. Can. J. Agric. Econ. 44: 151–164.

http://dx.doi.org/10.1111/j.1744-7976.1996.tb00190.x

Herrmann, M., and K. Criddle. 2006. An econometric market model for the Pacific halibut fishery. Mar.

Resour. Econ. 21:129–158. [Available at http://www.jstor.org/stable/42629501.]

Higham, N. J., and H.-M. Kim. 2001. Solving a quadratic matrix equation by Newton's method with exact 

line searches. SIAM J. Matrix Anal. and Applic. 23:303–316.

http://dx.doi.org/10.1137/S0895479899350976

Hilborn, R., and C. J. Walters, eds., 570 p. 1992. Quantitative fisheries stock assessment: choice, 

dynamics & uncertainty. Chapman and Hall, New York.

Himes-Cornell, A., S. Allen, G. Auad, M. Boatman, P. M. Clay, M. Dalton, S. Herrick, D. Kotowicz, P. Little, 

C. Lopez, P. Loring, P. Niemeier, K. Norman, L. Pfeiffer, M. Plummer, M. Rust, M. Singer, and C. Speirs. 

2013. Impacts of climate change on human uses of the ocean and ocean services. In Oceans and marine 

resources in a changing climate: technical input to the 2013 national climate assessment, p. 64–118.

http://dx.doi.org/10.5822/978-1-61091-480-2_4
66

Homans, F. R., and J. E. Wilen. 2005. Markets and rent dissipation in regulated open access fisheries.

J. Environ. Econ. Manage. 49:381–404. http://dx.doi.org/10.1016/j.jeem.2003.12.008

Jacobsen, N.S., Burgess, M.G., Andersen, K.H. 2017. Efficiency of fisheries is increasing at the ecosystem 

level. Fish and Fisheries 18: 199-211.

Just, R. E., D. L. Hueth, and A. Schmitz. 2004. The welfare economics of public policy: a practical 

approach to project and policy evaluation, 712 p. Edward Elgar Publishing, Cheltenham, England.

Kasperski, S. 2015. Optimal multi-species harvesting in ecologically and economically interdependent 

fisheries. Environ. Resour. Econ. 61: 517–557. http://dx.doi.org/10.1007/s10640-014-9805-9

Kjaersgaard, J, and H. Frost. 2008. Effort allocation and marine protected areas: Is the North Sea plaice 

box a management compromise? ICES J. Mar. Sci. 65:1203–1215.

http://dx.doi.org/10.1093/icesjms/fsn088

Knight, F. H. 1921. Risk, uncertainty, and profit. Houghton-Mifflin, Boston.

Kompas, T., R. Q. Grafton, and T. N. Che. 2010. Bioeconomic losses from overharvesting tuna. Conserv.

Letters 3:177–183. http://dx.doi.org/10.1111/j.1755-263X.2010.00103.x

Langlois, R. N., and M. M. Cosgel. 1993. Frank Knight on risk, uncertainty, and the firm: a new 

interpretation. Econ. Inq. 31:456–465. http://dx.doi.org/10.1111/j.1465-7295.1993.tb01305.x

Larkin, S. L., S. Alvarez, G. Sylvia, and M. Harte. 2011. Practical considerations in using bioeconomic 

modelling for rebuilding fisheries, 39 p. OECD Food, Agriculture and Fisheries Papers, no. 38. OECD 

Publishing, Paris. http://dx.doi.org/10.1787/5kgk9qclw7mv-en

Leslie, P. H. 1945. On the use of matrices in certain population mathematics. Biometrika 3:183–212.

http://dx.doi.org/10.1093/biomet/33.3.183

Lew, D. K., and D. M. Larson. 2012. Economic values for saltwater sport fishing in Alaska: a stated 

preference analysis. North Am. J. Fish. Manage. 32(4):745–759.

http://dx.doi.org/10.1080/02755947.2012.681012

Link, J. S., R. J. Gamble, and M. J. Fogarty. 2011. An overview of the NEFSC’s ecosystem modeling 

enterprise for the Northeast U.S. Shelf large marine ecosystem: towards ecosystem-based fisheries 

management. U.S. Dept. Commer., NOAA. Northeast Fish. Sci. Cent. Ref. Doc. 11-23; 89 p. [Available at 

https://repository.library.noaa.gov/view/noaa/3970/Print]

Little, I. M. D., and J. Mirrlees. 1974. Project appraisal and planning for developing countries, 388 p. 

Heinemann, London.

Ludwig, D. 1979. Optimal harvesting of a random fluctuating resource. I: application of perturbation 

methods. SIAM J. Appl. Math. 37:166–184. http://dx.doi.org/10.1137/0137011
67

Mäntyniemi, S., S. Kuikka, M. Rahikainen, L. T. Kell, and V. Kaitala. 2009. The value of information in 

fisheries management: North Sea herring as an example. ICES J. Mar. Sci. 66(10):2278–2283.

http://dx.doi.org/10.1093/icesjms/fsp206

Mendelssohn, R. 1982. Discount factors and risk aversion in managing random fish populations. Can. J.

Fish. Aquat. Sci. 39:1252–1257. http://dx.doi.org/10.1139/f82-166

Moxnes, E. 2003. Uncertain measurements of renewable resources: approximations, harvesting policies 

and value of accuracy. J. Environ. Econ. Manage. 45:85–108. http://dx.doi.org/10.1016/S0095-

0696(02)00011-6

Mueter, F. J., and B. A. Megrey. 2006. Using multi-species surplus production models to estimate 

ecosystem-level maximum sustainable yields. Fish. Res. 81:189–201.

http://dx.doi.org/10.1016/j.fishres.2006.07.010

National Marine Fisheries Service. 2013. The West Coast groundfish IFQ fishery: results from 2012, the 

second year of catch shares. NOAA Fisheries, Silver Spring, MD. [Available at 

http://www.westcoast.fisheries.noaa.gov/publications/fishery_management/trawl_program/yr2-

rpt.pdf.]

National Marine Fisheries Service. 2016. Ecosystem-based fisheries management policy of the National 

Marine Fisheries Service, policy directive 01-120. NOAA Fisheries, Silver Spring, MD. [Available at 

https://www.fisheries.noaa.gov/resource/document/ecosystem-based-fisheries-management-policy]

National Research Council. 1999. Sharing the fish: toward a national policy on individual fishing quotas, 

436 p. National Academies Press, Washington, DC. http://dx.doi.org/10.17226/6335

National Research Council. 2013. Evaluating the effectiveness of fish stock rebuilding plans in the United 

States, 154 p. National Academies Press, Washington, DC. http://dx.doi.org/10.17226/18488

Nilim, A., and L. El Ghaoui. 2005. Robust control of Markov decision processes with uncertain transition 

matrices. Oper. Res. 53(5):780–798. http://dx.doi.org/10.1287/opre.1050.0216

Northeast Fisheries Science Center. 2008. Assessment of 19 Northeast groundfish stocks through 2007: 

report of the 3rd Groundfish Assessment Review Meeting (GARM III); Woods Hole, 4–8 August, 884 p.

U.S. Dept. Commer., NOAA Fisheries, Ref Doc. 08-15. [Available at 

https://repository.library.noaa.gov/view/noaa/5227.]

Norman-López, A., and S. Pascoe. 2011. Net economic effects of achieving maximum economic yield in 

fisheries. Mar. Policy. 35:489–495. http://dx.doi.org/10.1016/j.marpol.2010.12.001

Organization for Economic Co-operation and Development. 2012. Rebuilding fisheries: the way forward, 

100 p. OECD Publishing, Paris. http://dx.doi.org/10.1787/9789264176935-en

Pella, J. J., and P. K. Tomlinson. 1969. A generalized stock production model. Inter-Am. Trop. Tuna 

Comm. Bull. 13:416–497. [Available at http://aquaticcommons.org/id/eprint/3536.]
68

Prager, M. H., and K. W. Shertzer. 2010. Deriving acceptable biological catch from the overfishing limit: 

implications for assessment models. North Am. J. Fish. Manage. 30:289–294.

http://dx.doi.org/10.1577/M09-105.1

Prato, T. 2009. Adaptive management of natural systems using fuzzy logic. Environ. Model Softw.

24:940–944. http://dx.doi.org/10.1016/j.envsoft.2009.01.007

Quaas, M. F., T. Requate, K. Ruckes, A. Skonhoft, N. Vestergaard, and R. Voss. 2013. Incentives for 

optimal management of age-structured fish populations. Resource Energy Econ. 35:113–134.

http://dx.doi.org/10.1016/j.reseneeco.2012.12.004

Quinn, T. J., and R. B. Deriso. 1999. Quantitative fish dynamics, 560 p. Oxford University Press, New York.

Ramsey, F. P. 1928. A mathematical theory of saving. Econ. J. 38:543–559.

http://dx.doi.org/10.2307/2224098

Reed, W. J. 1974. A stochastic model for the economic management of a renewable animal resource. 

Math. Biosci. 22:313–337. http://dx.doi.org/10.1016/0025-5564(74)90097-2

Reed, W. J. 1979. Optimal escapement levels in stochastic and deterministic harvesting models. J.

Environ. Econ. Manage. 6:350–363. http://dx.doi.org/10.1016/0095-0696(79)90014-7

Regan, H. M., Y. Ben-Haim, B. Langford, W. G. Wilson, P. Lundberg, S. J. Andelman, and M. A. Burgman. 

2005. Robust decision-making under severe uncertainty for conservation management. Ecol. Appl.

15:1471–1477. http://dx.doi.org/10.1890/03-5419

Ricker, W. E. 1975. Computation and interpretation of biological statistics of fish populations. Bull. Fish.

Res. Board Canada, No. 191, 1st ed., 382 p. Depart. Environ., Fish. Mar. Serv., Ottawa. [Available at 

http://www.dfo-mpo.gc.ca/Library/1485.pdf.]

Rust, J. 2008. Dynamic programming. In The new Palgrave dictionary of economics, 2

nd ed. (S. N. Durlauf 

and L. E. Blume, eds.). Palgrave Macmillan, London.

Savage, L. J. 1954. The foundations of statistics, 310 p. Wiley, New York.

Schaefer, M. B. 1954. Some aspects of the dynamics of populations important to the management of the 

commercial marine fisheries. Inter-Am. Trop. Tuna Comm. Bull. 1:25–56. [Available at 

http://aquaticcommons.org/3530/1/Vol._1_no._2.pdf]

Schnier, K. E., and R. G. Felthoven. 2013. Production efficiency and exit in rights-based fisheries. Land 

Econ. 89: 538-557. [Available at http://muse.jhu.edu/issue/27587.]

Schnute, J. 1985. A general theory for analysis of catch and effort data. Can. J. Fish. Aquat. Sci. 42:414–

429. http://dx.doi.org/10.1139/f85-057
69

Schnute, J., and D. Fournier. 1980. A new approach to length-frequency analysis: growth structure. Can.

J. Fish. Aquat. Sci. 37:1337–1351. http://dx.doi.org/10.1139/f80-172

Schumann, S., and S. Macinko. 2007. Subsistence in coastal fisheries policy: What's in a word? Mar.

Policy. 31(6):706–718. http://dx.doi.org/10.1016/j.marpol.2006.12.010

Semmens, K. A. 2008. Buffering uncertainty: setting annual catch limits under the Magnuson-Stevens 

Fishery Conservation and Management Reauthorization Act of 2006. M.S. thesis. Univ. Delaware, 

Newark, DE.

Sethi, G., C. Costello, A. Fisher, M. Haneman, and L. Karp. 2005. Fishery management under multiple 

uncertainty. J. Environ. Econ. Manage. 50:300–318. http://dx.doi.org/10.1016/j.jeem.2004.11.005

Seung, C., and E. Waters. 2006. A review of regional economic models for fisheries management in the 

U.S. Mar. Resour. Econ. 21:101–124. [Available at http://www.jstor.org/stable/42629497.]

Shertzer, K. W., M. H. Prager, and E. H. Williams. 2008. A probability-based approach to setting annual 

catch levels. Fish. Bull. 106:225–232. 

Squire, L., and H. G. van der Tak. 1979. Economic analysis of projects. The Johns Hopkins University 

Press, Baltimore, MD. [Available at 

http://documents.worldbank.org/curated/en/954731468156870423/pdf/794880PUB0Econ00Box37737

2B00PUBLIC0.pdf.] 

Squires, D., and N. Vestergaard. 2013. Technical change and the commons. Rev. Econ. Stat. 95:1769–

1787. http://dx.doi.org/10.1162/REST_a_00346

Squires, D., and N. Vestergaard. 2015. Productivity growth, catchability, stock assessments, and 

optimum renewable resource use. Mar. Policy. 62: 309–317.

http://dx.doi.org/10.1016/j.marpol.2015.07.006

Squires, D., and N. Vestergaard. 2016. Putting economics into maximum economic yield. Mar. Resour.

Econ. 31:101–116. [Available at http://www.journals.uchicago.edu/doi/full/10.1086/683670.]

Sumaila, U. R., and R. Hannesson. 2010. Maximum economic yield in crisis? Fish and Fisheries. 11:461–

465. http://dx.doi.org/10.1111/j.1467-2979.2010.00381.x

Tahvonen, O. 2009a. Economics of harvesting age-structured fish populations. J. Environ. Econ. Manage.

58:281–299. http://dx.doi.org/10.1016/j.jeem.2009.02.001

Tahvonen, O. 2009b. Optimal harvesting of age-structured fish populations. Mar. Resour. Econ. 24:147–

169. [Available at http://www.jstor.org/stable/42731377.]

Tahvonen, O., M. F. Quaas, J. O. Schmidt, and R. Voss. 2012. Optimal harvesting of an age-structured 

schooling fishery. Environ. Resour. Econ. 51(4):21–39. http://dx.doi.org/10.1007/s10640-012-9579-x

Tomberlin, D. 2008. An approach to managing fisheries when weak and strong stocks mix. In
70

Proceedings of the fourteenth biennial conference of the International Institute of Fisheries Economics 

& Trade; Nha Trang, Vietnam, 22–25 July. CD ROM, ISBN 0-9763432-5-8.

Van Kooten, G. C., and E. H. Bulte. 2000. The economics of nature: managing the biological assets, 528 p. 

Wiley-Blackwell, Hoboken, NJ. [Available at http://www.wiley.com/WileyCDA/WileyTitle/productCd0631218947.html.]

Vieira, S., and S. Pascoe. 2013. Technical reviews for the Commonwealth Fisheries Harvest Strategy 

Policy: economic issues. Australian Govern. Dept. Agric., Fish. and Forestry, Canberra. [Available at 

http://data.daff.gov.au/data/warehouse/9aam/9aame/2013/TechReviewCommFishHarvestStrategyPoli

cy/CommFishHarvestStratPolicyEcoIssue201305_v1.0.1.pdf.]

Walters, C. 1986. Adaptive management of renewable resources, 374 p. MacMillan Publishing Company, 

New York. http://dx.doi.org/10.1002/bimj.4710310614

Walters, C. 2003. Folly and fantasy in the analysis of spatial catch rate data. Can. J. Fish. Aquat. Sci.

60:1433–1436. http://dx.doi.org/10.1139/f03-152

Waters, E. C., C. K. Seung, M. L. Hartley, and M. G. Dalton. 2014. Measuring the multiregional economic 

contribution of an Alaska fishing fleet with linkages to international markets. Mar. Policy 50:238–248.

http://dx.doi.org/10.1016/j.marpol.2014.07.003

Wilberg, M. J., J. T. Thorson, B. C. Linton, and J. Berkson. 2010. Incorporating time-varying catchability 

into population dynamic stock assessment models. Rev. Fish. Sci. 18:7–24.

http://dx.doi.org/10.1080/10641260903294647

Wilen, J. E. 2006. Why fisheries management fails: treating symptoms rather than the cause. Bull. Mar.

Sci. 78:529–546. [Available at 

http://www.ingentaconnect.com/contentone/umrsmas/bullmar/2006/00000078/00000003/art00008.]

Woodward, R. T., and W. D. Shaw. 2008. Allocating resources in an uncertain world: water management 

and endangered species. Am. J. Agric. Econ. 90(3):593–605. http://dx.doi.org/10.1111/j.1467-

8276.2008.01141.x

Woodward, R. T. and D. Tomberlin. 2014. Practical Precautionary Resource Management Using Robust 

Optimization. Environmental Management, 1-12. https://doi.org/10.1007/s00267-014-0348-1