Fisheries bioeconomics
Theory, modelling and management


J.C. Seijo
Departamento de Recursos del Mar
Mérida, Yucatán, México, and Centro Marista de Estudios Superiores
Mérida, Yucatán, México,

Departamento de Recursos del Mar
Mérida, Yucatán, México, and Instituto Nacional de Pesca
Montevideo, Uruguay

Departamento de Recursos del Mar
Mérida, Yucatán, México

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ISBN 92-5-104045-1

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Food and Agriculture Organization of the United Nations Rome, 1998

Preparation of this Document

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.


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.
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.

Hyperlinks to non-FAO Internet sites do not imply any official endorsement of or responsibility for the opinions, ideas, data or products presented at these locations, or guarantee the validity of the information provided. The sole purpose of links to non-FAO sites is to indicate further information available on related topics.


List of Figures
List of Tables
1.Inherent Characteristics of Fish Stocks
 1.1.Optimal allocation of renewable resources: basic assumptions
 1.2.The failure in the optimal allocation of fishery resources
  Property regimes, property rights and externalities
  High exclusion costs
  Social trap in fisheries, and the free rider behaviour
  High transaction costs
 1.3.Fisheries management plans
 1.4.A closing comment
2.Bioeconomic Models
 2.1.The Gordon-Schaefer model
  Marginal and average yields
  Effort levels at MSY, MEY and BE
  Model assumptions
 2.2.Fleet dynamics: a distributed-delay Smith's model
 2.3.Yield-mortality models: a bioeconomic approach
  Logistic model
  Exponential model
  A precautionary bioeconomic approach
  Yield-mortality models: a closing comment
 2.4.Age-structured bioeconomic models
 2.5.Intertemporal fisheries analysis
  Intertemporal preferences
  Neutral, positive and negative preferences
  Present value and discount rate
  The bioeconomic dynamic model and the price of time
  The effect of δ in fisheries: an alternative view
3.Ecological and Technological Interdependencies
 3.1.Technological interdependencies: heterogeneous fishing effort
  Static analysis
  Dynamic analysis
 3.2.Technologically interdependent fisheries: two fleets
  Case 1: Fleet 1 incidentally captures the target species of fleet 2
  Case 2: Fleets 1 and 2 affect each other
 3.3.Technological interdependencies: sequential fisheries
 3.4.Bioeconomics of ecologically interdependent stocks
  Case 1: competition
  Case 2: predation
 3.5.Techno-ecological interdependencies
  Case 1: competition
  Case 2: predation
 3.6.Multispecies fisheries and experimental management
4.The Systems Science Approach in Fisheries Bioeconomics
 4.1.The systems simulation approach
  Identification of bioeconomic information needs
  Fishery characterization
  Mathematical modelling of the fishery
  Data collection from primary and secondary sources
  Computer model
  Stability and sensitivity analyses
  Model validation
  Bioeconomic impact of alternative management strategies
 4.2.A numerical example
 5.1.State intervention criteria
  Conservation approach
  Economic approach
  Equity approach in resource use
  Intergenerational equity approach
  Other management approaches
 5.2.Management strategies
  Property regimes and allocation of property rights
  Regulation of catch composition
  Regulation of the amount of catch
  Extension programs and environmental education
 5.3.Multiple criteria optimization approach for fisheries management
  The multi-criteria objective function
  The “Complex” optimization method for non-linear functions with multiple criteria
6.Spatial Bioeconomic Models
 6.1.Spatial allocation of fishing intensity
 6.2.Short-run spatial dynamics: ALLOC model
  Spatial allocation of fishing intensity
  Distance to fishing grounds from different ports of origin
  Quasi rent of variable costs by fleet type from different ports of origin
  Spatial variations in net revenues
  Spatial CPUE
  Fleet dynamics
  Model assumptions
 6.3.Short and long-run geographic bioeconomic dynamics: CHART model
  Spatial specification of maximum biomass and recruitment
  Spatial distribution of recruitment patches
  Spatial distribution of resource biomass
  Spatial CPUE
  Short-run fleet dynamics: spatial allocation of fishing intensity
  Long-run fleet dynamics
  Model assumptions
 6.4.A spatial bioeconomic model for sedentary fisheries: the yellow clam Mesodesma mactroides of Uruguay, a study case
  The resource
  The fishery
7.Risk and uncertainty: a precautionary approach
 7.1.Precautionary approach to fisheries management
 7.2.Sources of uncertainty in fisheries
 7.3.Management decisions without mathematical probabilities
 7.4.Management decisions with mathematical probabilities
  The Bayesian approach
 7.5.Estimation of uncertainty in model parameters
  “Jackknife-bootstrap” estimations for confidence intervals
  Risk analysis and “bootstrap”
Author index
Subject index

List of Figures

2.1Population logistic growth model for K=3.5 million tonnes and r=0.36
2.2Gordon-Schaefer static model. Sustainable (a) biomass, (b) yield, and (c) total sustainable revenues (TSR) and costs (TC)
2.3Open access regime. (a) Sustainable average and marginal yields; (b) average and marginal costs, and revenues, as a function of effort under open access conditions
2.4Static (equilibrium) and dynamic trajectories of biomass (a), yield (b) and cost-revenues (c) resulting from the application of different fishing effort levels
2.5Dynamic trajectories of (a) biomass, (b) yield, (c) economic rent, and (d) fishing effort
2.6Bioeconomic Y–Z model: yield and biological production curves fitted to hypothetical data. The position of MSY, YMEY, MBP and YMBP is shown. A M value of 0.13/yr that maximized the goodness-of-fit criterion in equation (2.35) was used as input for running the model (adapted from Defeo & Seijo, in press)
2.7Age–structured bioeconomic model: dynamic effect of different tc in (a) biomass; (b) yield; (c) economic rent; and (d) fishing effort
2.8Intertemporal neutral preference (adapted from Randall, 1981)
2.9Intertemporal positive preference (adapted from Randall, 1981)
2.10Intertemporal negative preference (adapted from Randall, 1981)
3.1Dynamic behavior of stock biomass (a,b), yields (c,d) and economic rent (e,f) by fleet type
3.2Dynamic behavior of biomass (a), effort (b), yield (c) and economic rent (d) obtained by the artisanal and industrial fleets
3.3Bioeconomics of technologically interdependent fleets; (a) species biomass; (b) fishing effort; (c) yield; and (d) economic rent
3.4Sequential fishery. Dynamic fluctuations of: (a) biomass; (b) yield; (c) effort; and (d) economic rent generated by the industrial and artisanal vessels
3.5Dynamic trajectories of biomass (a,b), catch (c,d), and economic rent (e,f) generated by a fishery composed by two competing species
3.6Predator-prey relationship in ecologically interdependent fisheries. Dynamic trajectories of (a) prey and predator biomass, (b) effort, (c) yield, and (d) economic rent generated by two fleets.
3.7Techno-ecological interaction: stocks with a predator-prey relationship captured by 2 technologically interdependent fleets
4.1A system simulation approach to fisheries management (after Seijo, 1989)
4.2Fishery characterization
4.3Short and long-term dynamics of: (a) recruitment; (b) fishing effort; (c,d) yields; and (e,f) benefits/costs for the artisanal and mechanized fleet of a hypothetical shrimp fishery.
5.1Conceptual block diagram for multi-criteria optimization of fisheries
6.1Mesodesma mactroides. Observed vs. estimated densities of (a) recruits and (b) adults
6.2Seasonal variations in simulated fishing intensity by fishing ground from 1983 to 1992 for the yellow clam fishery of Uruguay
6.3Mesodesma mactroides. Comparison of observed vs. simulated: (a) seasonal fishing effort; and (b) catches by fishing ground (summer 1985)

List of Tables

2.1Parameters for the dynamic bioeconomic model (Gordon-Schaefer)
2.2Hypothetical data used for fitting the bioeconomic yield-mortality model (adapted from Caddy, 1986)
2.3Mean and 95% confidence intervals (percentile approach) of the RPs derived from the bioeconomic Y–Z model, estimated by bootstrap. B∞, MSY, YMBP, YMEY and MBP are given in tonnes, while mortality parameters are given on an annual basis (after Defeo & Seijo, in press)
2.4Parameters used for the dynamic age-structured model
3.1Input parameters defined for a simulation model (Seijo et al., 1996) directed to evaluate the dynamic behavior of a stock harvested by two technologically interdependent fleets
3.2Technologically interdependent fisheries: input parameters used in dynamic programming directed to simulate the behavior of fishery performance variables through time
3.3Input parameters of a multispecific dynamic bioeconomic model that represents a sequential fishery
3.4Techno-ecological interdependence. Parameters defined at the begining of the simulation run directed to evaluate the dynamic behavior of a prey and a predator captured by 2 technologically interdependent fleets
4.1Bioeconomic parameters of a hypothetical shrimp fishery
5.1Welfare criteria applied to marine fisheries
6.1Properties of the SAE model
7.1The Maximin criterion
7.2The Minimax regret criterion, and the regret decision table (US$'000)
7.3The Maximax criterion
7.4NPV(US$'000) of three alternative management strategies (D1,D2,D3) under two states of nature (SN1, SN2) with the corresponding probabilities of occurrence P1 and P2. EV: expected value; VAR: variance; SD: standard deviation
7.5The Bayesian criterion (US$'000)


SymbolMeaningUnit of measurement
aIntercept of the length-weight relationship---
AFinite rate of total mortality---
adCompensation factor---
ALIMFish for subsistence in the coastal zonetonnes
areaArea swept per daykm2/day
AREAArea occupied by the stockkm2
AVEAverage value of fishing effort$/ue
AYAverage yieldtonnes/ue
bExponent of the length-weight relationship---
Base run value for the β management criterion---
BPopulation biomasstonnes
BBEBiomass at bioeconomic equilibriumtonnes
B0Initial biomasstonnes
BEBioeconomic equilibrium:π(t)=0$
BeqEquilibrium biomasstonnes
BmaxMaximum biomasstonnes
BOPTOptimum biomasstonnes
BVirgin biomasstonnes
cUnitary cost of fishing effort$/ue
CincAverage incidental catch per fishing triptonnes
cpProcessing costs$/yr
CPUECatch per unit of efforttonnes/ue
CPUEmaxMaximum observed catch per unit of efforttonnes/ue
dDiscrete discount rate---
D1, D2,...DξAlternative management strategies in decision analysis---
DkhDistance from port h to fishing ground kkm
DAYSAverage number of fishing days per month#
DELHSAverage time delay of egg maturationmonths
DELmAverage time delay of vessels entry to the fisherymonths
DTTime incrementt
Eμ*Optimum vector value of the multiple criteria function---
Eβμβcriterion value of the management goal μ---
EμVector of values for the multi–criteria function corresponding to---
 the management option μ, assessed in time horizon (O,T) 
EMPEmployment generated by the fishery#
EVExpected value of the NPV$
EXPmExport earnings, harvesting sector$
EXPpExport earnings, processing sector$
fFishing effortue
fklFishing intensity exerted in site with geographic coordinates kldays
faCumulative spatial allocation of fishing intensity---
fBEFishing effort at bioeconomic equilibriumue
fMBPFishing effort at maximum biological productionue
fMEYFishing effort at maximum economic yieldue
fMSYFishing effort at maximum sustainable yieldue
fOPTOptimal effortue
FInstantaneous rate of fishing mortality1/t
FMBPInstantaneous fishing mortality at maximum biological1/t
FMEYInstantaneous fishing mortality at maximum economic yield1/t
FMSYInstantaneous fishing mortality at maximum sustainable yield1/t
FCDaily fixed cost per vessel$
FECMean fecundity per female#eggs
FISHmMean number of fishermen per vessel type m#ind
FRFinite rate of fishing mortality---
gDelay order---
gβφTarget for the βcriterion of the goal set φ in multi-criteria---
HProportion of females---
HmaxMaximum annual number of eggs produced by the spawning#eggs
HSNumber of eggs produced by the spawning stock#eggs
IIndifference curve---
ITGIndividual transferable ground---
ITQIndividual transferable quotatonnes
kLocality coordinate: latitude; fishing ground---
kpCurvature parameter of the von Bertalanffy growth equation1/t
KCarrying capacity of the environmenttonnes
lLocality coordinate: longitude---
LIndividual lengthmm
L50%Length at 50% gear retentionmm
L75%Length at 75% gear retentionmm
LAsymptotic length of the von Bertalanffy growth equationmm
LLiLower limit of constants or variable functions in the “Complex”---
LOSSValue of the loss matrix in the decision theory---
mType of vessel or fleet---
MInstantaneous rate of natural mortality1/t
MAGEMaximum aget
MBPMaximum biological productiontonnes
MEYMaximum economic yieldtonnes
MRFinite rate of natural mortality---
MSYMaximum sustainable yieldtonnes
MTPRMarginal time preference rate%
MVEMarginal value of fishing effort$/ue
MYMarginal yieldtonnes/ue
NPopulation abundance# ind
NPVNet present value$
NTNumber of recruits in each patch (CHART model)# ind
OVCOther variable costs (bait, maintenance and repair, gear$/yr
OSYOptimum sustainable yieldtonnes
pAverage price of a species$/tonnes
pcapProbability of capture---
PkProbability of finding the target species in fishing ground k---
PλProbability of occurrence of an event λ---
PincAverage price paid per ton of incidental catch$/tonne
PtarAverage price paid for target species$/tonne
PVπPresent value of net revenues$
qCatchability coefficient---
quaCatchability coefficient per unit area---
quasi πQuasi rent of variable costs$
QFisher income$/t
rIntrinsic rate of population growth---
RjEstimated recruitment at age j# ind
RklNumber of recruits located in the patch center of the cell klind/t
RiskklPerceived risk of fishing in ground kl1 to 3
RmaxMaximum observed recruitment# ind
RETRetention of fishing gear%
RNRandom variable of recruitment equationind/t
RVRandom variable of catch equationtonnes/t
siAge at sexual maturityt
SFinite survival rate---
S1,S2Specific gear retention constants---
SAEA(0, 1) distribution of fishing effort---
SELSelectivity of fishing gear%
SGNumber of rows in a geographic grid---
SNStates of nature---
tTimed, mo, yr
tcAge at first capturet
toHypothetical age at zero length (von Bertalanffy growtht
TCTotal costs$
TGNumber of columns in a geographic grid#
TRTotal revenues$
TSRTotal sustainable revenues$
TSGCell length for a specific spatial resolution (degrees, minutes,km
TTGCell width for a specific spatial resolution (degrees, minutes,km
ueUnit of effortvarious
UCatch per unit of effort (general notation)tonnes/ue
ULiUpper limit of constants or variable functions in the Complex---
vDiscount factor---
VNumber of vessels#
VARVariance of the expected NPV$
VCVariable costs of fishing effort$
wpwholesale price$
WIndividual weightg
WAsymptotic weightg
xDistance from the site kl to the center of the patchkm
xpex-vessel price$
YMBPYield at maximum biological productiontonnes
YMEYYield at maximum economic yieldtonnes
ZInstantaneous rate of total mortality1/t
ZMBPInstantaneous rate of total mortality at MBP1/t
ZMEYInstantaneous rate of total mortality at MEY1/t
ZMSYInstantaneous rate of total mortality at MSY1/t
αXYCompetition coefficient that measures the per capita effect of Y---
 on X 
αYXCompetition coefficient that measures the per capita effect of X---
 on Y 
βCriterion value with regard to a management option μ---
β1Predation coefficient---
β2Predation coefficient---
δContinuous discount rate---
εProportion of the catch that goes to the export market---
φFriction of distance---
γg(t)Output of the delay process (e.g. number of vessels entering#/t
 the fishery along the season) 
γ1(t)...γg-1(t)Intermediate rates of the delay process#/t
φFleet dynamic parameter---
λStates of nature in decision theory#
μManagement option---
πNet revenues$
πmMarginal rent$/ue
θAverage cost of oil and gas per km traveled$/km
σStandard deviation (0 < σ < 1) of patch density---
υ-μDecision parameter vector corresponding to a management---
 option μ 
υ-μ*Parameter vector for optimal control of the fishery---
ωProportion assigned to the crew as labor payment[0,1]
ξManagement options in decision theory#
ΩβμφNormalized deviation of the criterion β with respect to---
 management option μ and goal set φ 
ψTotal consumption---