FAO FISHERIES TECHNICAL PAPER 368 Fisheries bioeconomics Theory, modelling and management |

by

**J.C. Seijo**

Departamento de Recursos del Mar

CINVESTAV-IPN Unidad Mérida

Mérida, Yucatán, México, and Centro Marista de Estudios Superiores

Mérida, Yucatán, México,

**O.Defeo**

Departamento de Recursos del Mar

CINVESTAV-IPN Unidad Mérida

Mérida, Yucatán, México, and Instituto Nacional de Pesca

Montevideo, Uruguay

**S.Salas**

Departamento de Recursos del Mar

CINVESTAV-IPN Unidad Mérida

Mérida, Yucatán, México

The designations employed and the presentation of material in this publication do not imply the expression of any opinion whatsoever on the part of the Food and Agriculture Organization of the United Nations concerning the legal status of any country, territory, city or area or of its authorities, or concerning the delimitation of its frontiers or boundaries.

M-40

ISBN 92-5-104045-1

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**Food and Agriculture Organization of the United Nations Rome, 1998© FAO**

The evaluation and mathematical representation of dynamic trends in populations of fishery resources was originally considered solely in terms of the interaction between the intensity of fishing and the biological constraints that determine the productivity of marine ecosystems. While detailed study of fish population dynamics and fish stock assessment is still valid, the subject of fish population dynamics is progressively being treated in combination with those economic forces driving the dynamics of a fishery, such as rent, human employment and food production. This combined activity is referred to as ‘Bioeconomics’ and FAO has already issued a number of publications of more specialized software in this area, but has not so far produced a text containing theory and examples of application. The present text fills this void, and focuses particularly on problems faced by developing countries in this field.

We wish to express our gratitude to the working group of Fisheries Bioeconomics at CINVESTAV,
especially to Miguel Cabrera, Anita de Alava and Jose Luis Cabrera for their help in the edition of
the manuscript. We acknowledge Rognvaldur Hannesson for his detailed revision of the
manuscript and John Caddy for his useful comments and editorial review. Eduardo Pérez helped
us in the elaboration of the subject index. Enzo Acuna, Jorge Gonzalez, Minerva Arce and
Eduardo Balart provided valuable comments that improved the text. Hector Mares elaborated the
cover of this book. We wish to express our deepest gratitude for those students who attended the
postgraduate course of *Fisheries Bioeconomics* at CINVESTAV-Unidad Mérida (México) and in
several Institutions of Latin America, during the last ten years.

Juan Carlos Seijo wish to express his gratitude to Ceci, Juan Carlos Jr. and Adrianita for being a permanent source of motivation and love. Omar Defeo dedicates this book to Anita, Diego, his parents and brothers. Silvia Salas dedicates it to her daughter Nayelli and her parents.

**Distribution**:

All FAO Members and Associate Members

FAO Fisheries Department

FAO Fishery Officers in FAO Regional Offices

Non-governmental Institutions

Seijo, J.C.; Defeo, O.; Salas, S.Fisheries bioeconomics. Theory, modelling and management.FAO Fisheries Technical Paper. No.368. Rome, FAO. 1998. 108p. |

ABSTRACT |

This book is presented in seven Chapters. Chapter 1 describes the basic assumptions underlying the optimal allocation of natural resources and the inherent characteristics of fisheries that determine, under unrestricted access, the failure to allocate resources, economic inefficiency and overfishing. To mitigate these undesired effects, the bioeconomic literature invokes the allocation of property rights, which in turn must be implemented within a management context. Thus, in this Chapter we suggest some guidelines to conduct management plans. Static and dynamic bioeconomic models are presented in Chapter 2 as a theoretical framework for the design of intelligent management schemes aiming at sustainable use of fish stocks. Classic models are shown, such as the Gordon-Schaefer based on the logistic. We also develop new bioeconomic approaches, such as a distributed-delay model to add realism to Smith's fleet dynamics approach. Chapter 2 also includes an introductory version of a bioeconomic yield-mortality model, and dynamic age-structured models. A comparison of the dynamic and static trajectories is stressed. The price of time and its implications for optimal resource allocation over time is also discussed. For the sake of adding realism to the above models, the systems approach is used in Chapter 3 to model different technological and ecological complexities that occur in marine fisheries. Ecological interdependencies (competition, predation), as well as technological interdependencies resulting from fleets with different fishing power and/or gear types, operating on components of a stock, or on different target species of a “mixed stock”, are specified and modelled. In Chapter 4 we provide practical guidelines for the application of the systems science approach as a systematic and robust methodology for modelling fisheries. We present theory and examples on how to model the short and long run dynamics of the stock and the fishery, including the application of distributed delay models to represent from hatching/spawning processes to intra and interannual dynamics of fishing fleets. Chapter 5 gives an overview of a number of alternative methods for managing fisheries, and develop a bioeconomic approach to fisheries management with multiple criteria, introducing a nonlinear optimization algorithm. In Chapter 6 we relax the dynamic pool assumption of models developed in Chapters 2, 3 and 4 and introduce spatial bioeconomic considerations in modelling fisheries, notably the distance from ports to fishing grounds in order to further understand short-run decision-making of fishers in their allocation of fishing intensity. Stochastic models are detailed, also adding a degree of complexity to the interdependencies discussed in Chapter 3. The incorporation of risk and uncertainty in bioeconomic modelling and a formal decision analysis has been scarcely documented in the fisheries literature. In Chapter 7 we present some alternative ways of contending with risk and uncertainty in a precautionary fishery management context. Some aspects of decision analysis are detailed. Mathematical decisions with and without mathematical probabilities are emphasized, and some resampling techniques such as the bootstrap are used to estimate variances of parameters in yield-mortality models described in Chapter 2. Bootstrapping is also used in a simple and direct approach to risk analysis and precautionary fishery management. |

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Symbol | Meaning | Unit of measurement |
---|---|---|

a | Intercept of the length-weight relationship | --- |

A | Finite rate of total mortality | --- |

a_{d} | Compensation factor | --- |

ALIM | Fish for subsistence in the coastal zone | tonnes |

area | Area swept per day | km^{2}/day |

AREA | Area occupied by the stock | km^{2} |

AVE | Average value of fishing effort | $/ue |

AY | Average yield | tonnes/ue |

b | Exponent of the length-weight relationship | --- |

bβ | Base run value for the β management criterion | --- |

B | Population biomass | tonnes |

B_{BE} | Biomass at bioeconomic equilibrium | tonnes |

B_{0} | Initial biomass | tonnes |

BE | Bioeconomic equilibrium:π(t)=0 | $ |

Beq | Equilibrium biomass | tonnes |

B_{max} | Maximum biomass | tonnes |

B_{OPT} | Optimum biomass | tonnes |

B_{∞} | Virgin biomass | tonnes |

c | Unitary cost of fishing effort | $/ue |

Cinc | Average incidental catch per fishing trip | tonnes |

c_{p} | Processing costs | $/yr |

CPUE | Catch per unit of effort | tonnes/ue |

CPUE_{max} | Maximum observed catch per unit of effort | tonnes/ue |

d | Discrete discount rate | --- |

D_{1}, D_{2},...D_{ξ} | Alternative management strategies in decision analysis | --- |

D_{kh} | Distance from port h to fishing ground k | km |

DAYS | Average number of fishing days per month | # |

DEL_{HS} | Average time delay of egg maturation | months |

DEL_{m} | Average time delay of vessels entry to the fishery | months |

DT | Time increment | t |

E_{μ}* | Optimum vector value of the multiple criteria function | --- |

E_{βμ} | βcriterion value of the management goal μ | --- |

E_{μ} | Vector of values for the multi–criteria function corresponding to | --- |

the management option μ, assessed in time horizon (O,T) | ||

EMP | Employment generated by the fishery | # |

EV | Expected value of the NPV | $ |

EXP_{m} | Export earnings, harvesting sector | $ |

EXP_{p} | Export earnings, processing sector | $ |

f | Fishing effort | ue |

f_{kl} | Fishing intensity exerted in site with geographic coordinates kl | days |

fa | Cumulative spatial allocation of fishing intensity | --- |

f_{BE} | Fishing effort at bioeconomic equilibrium | ue |

f_{MBP} | Fishing effort at maximum biological production | ue |

f_{MEY} | Fishing effort at maximum economic yield | ue |

f_{MSY} | Fishing effort at maximum sustainable yield | ue |

f_{OPT} | Optimal effort | ue |

F | Instantaneous rate of fishing mortality | 1/t |

F_{MBP} | Instantaneous fishing mortality at maximum biological | 1/t |

production | ||

F_{MEY} | Instantaneous fishing mortality at maximum economic yield | 1/t |

F_{MSY} | Instantaneous fishing mortality at maximum sustainable yield | 1/t |

FC | Daily fixed cost per vessel | $ |

FEC | Mean fecundity per female | #eggs |

FISH_{m} | Mean number of fishermen per vessel type m | #ind |

FR | Finite rate of fishing mortality | --- |

g | Delay order | --- |

g_{βφ} | Target for the βcriterion of the goal set φ in multi-criteria | --- |

optimization | ||

h | Port | --- |

H | Proportion of females | --- |

Hmax | Maximum annual number of eggs produced by the spawning | #eggs |

stock | ||

HS | Number of eggs produced by the spawning stock | #eggs |

i | Species | --- |

I | Indifference curve | --- |

ITG | Individual transferable ground | --- |

ITQ | Individual transferable quota | tonnes |

j | Age | --- |

k | Locality coordinate: latitude; fishing ground | --- |

kp | Curvature parameter of the von Bertalanffy growth equation | 1/t |

K | Carrying capacity of the environment | tonnes |

l | Locality coordinate: longitude | --- |

L | Individual length | mm |

L_{50%} | Length at 50% gear retention | mm |

L_{75%} | Length at 75% gear retention | mm |

L_{∞} | Asymptotic length of the von Bertalanffy growth equation | mm |

LLi | Lower limit of constants or variable functions in the “Complex” | --- |

method | ||

LOSS | Value of the loss matrix in the decision theory | --- |

m | Type of vessel or fleet | --- |

M | Instantaneous rate of natural mortality | 1/t |

MAGE | Maximum age | t |

MBP | Maximum biological production | tonnes |

MEY | Maximum economic yield | tonnes |

MR | Finite rate of natural mortality | --- |

MSY | Maximum sustainable yield | tonnes |

MTPR | Marginal time preference rate | % |

MVE | Marginal value of fishing effort | $/ue |

MY | Marginal yield | tonnes/ue |

N | Population abundance | # ind |

NPV | Net present value | $ |

NT | Number of recruits in each patch (CHART model) | # ind |

OVC | Other variable costs (bait, maintenance and repair, gear | $/yr |

replacement) | ||

OSY | Optimum sustainable yield | tonnes |

p | Average price of a species | $/tonnes |

pcap | Probability of capture | --- |

P_{k} | Probability of finding the target species in fishing ground k | --- |

P_{λ} | Probability of occurrence of an event λ | --- |

Pinc | Average price paid per ton of incidental catch | $/tonne |

Ptar | Average price paid for target species | $/tonne |

PVπ | Present value of net revenues | $ |

q | Catchability coefficient | --- |

qua | Catchability coefficient per unit area | --- |

quasi _{π} | Quasi rent of variable costs | $ |

Q | Fisher income | $/t |

r | Intrinsic rate of population growth | --- |

R_{j} | Estimated recruitment at age j | # ind |

R_{kl} | Number of recruits located in the patch center of the cell kl | ind/t |

Risk_{kl} | Perceived risk of fishing in ground kl | 1 to 3 |

Rmax | Maximum observed recruitment | # ind |

RET | Retention of fishing gear | % |

RN | Random variable of recruitment equation | ind/t |

RV | Random variable of catch equation | tonnes/t |

s_{i} | Age at sexual maturity | t |

S | Finite survival rate | --- |

S1,S2 | Specific gear retention constants | --- |

SAE | A(0, 1) distribution of fishing effort | --- |

SEL | Selectivity of fishing gear | % |

SG | Number of rows in a geographic grid | --- |

SN | States of nature | --- |

t | Time | d, mo, yr |

t_{c} | Age at first capture | t |

t_{o} | Hypothetical age at zero length (von Bertalanffy growth | t |

equation) | ||

TC | Total costs | $ |

TG | Number of columns in a geographic grid | # |

TR | Total revenues | $ |

TSR | Total sustainable revenues | $ |

TSG | Cell length for a specific spatial resolution (degrees, minutes, | km |

seconds) | ||

TTG | Cell width for a specific spatial resolution (degrees, minutes, | km |

seconds) | ||

ue | Unit of effort | various |

U | Catch per unit of effort (general notation) | tonnes/ue |

ULi | Upper limit of constants or variable functions in the Complex | --- |

method | ||

v | Discount factor | --- |

V | Number of vessels | # |

VAR | Variance of the expected NPV | $ |

VC | Variable costs of fishing effort | $ |

w_{p} | wholesale price | $ |

W | Individual weight | g |

W_{∞} | Asymptotic weight | g |

x | Distance from the site kl to the center of the patch | km |

xp | ex-vessel price | $ |

Y | Yield | tonnes |

Y_{MBP} | Yield at maximum biological production | tonnes |

Y_{MEY} | Yield at maximum economic yield | tonnes |

Z | Instantaneous rate of total mortality | 1/t |

Z_{MBP} | Instantaneous rate of total mortality at MBP | 1/t |

Z_{MEY} | Instantaneous rate of total mortality at MEY | 1/t |

Z_{MSY} | Instantaneous rate of total mortality at MSY | 1/t |

α_{XY} | Competition coefficient that measures the per capita effect of Y | --- |

on X | ||

α_{YX} | Competition coefficient that measures the per capita effect of X | --- |

on Y | ||

β | Criterion value with regard to a management option μ | --- |

β_{1} | Predation coefficient | --- |

β_{2} | Predation coefficient | --- |

δ | Continuous discount rate | --- |

ε | Proportion of the catch that goes to the export market | --- |

φ | Friction of distance | --- |

γ_{g}(t) | Output of the delay process (e.g. number of vessels entering | #/t |

the fishery along the season) | ||

γ_{1}(t)...γ_{g-1}(t) | Intermediate rates of the delay process | #/t |

φ | Fleet dynamic parameter | --- |

λ | States of nature in decision theory | # |

μ | Management option | --- |

π | Net revenues | $ |

πm | Marginal rent | $/ue |

θ | Average cost of oil and gas per km traveled | $/km |

σ | Standard deviation (0 < σ < 1) of patch density | --- |

υ^{-}_{μ} | Decision parameter vector corresponding to a management | --- |

option μ | ||

υ^{-}_{μ}^{*} | Parameter vector for optimal control of the fishery | --- |

ω | Proportion assigned to the crew as labor payment | [0,1] |

ξ | Management options in decision theory | # |

Ωβμφ | Normalized deviation of the criterion β with respect to | --- |

management option μ and goal set φ | ||

ψ | Total consumption | --- |