This is to certify that the

dissertation entitled

 

COMPREHENSIVE SIMULATION MODEL OF A TROPICAL
DEMERSAL FISHERY: RED GROUPER (Egineghelus morio)
OF THE YUCATAN CONTINENTAL SHELF

presented by

has been accepted towards fulfillment
of the requirements for

Juan Carlos Seijo G. i
Doctoral degreein Resource Development ?

Mm
A

Majorprofeaor
Manfred Thullen

1;, .l M choher 29I 1986

 

 

 

 

 

 

 

 

I MSU
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Ti'ENSIVE SIMULATION MODEL OF A TROPICAL

y.
:IL FISHERY: RED GROUPER (finineghelug genie)
OF THE YUCATAN CONTINENTAL SHELF

BY

JUAN CARLOS SEIJO G.

A DISSERTATION

Submitted to
f Michigan State University
in partial fulfillment of the requirements

for the degree of
DOCTOR OF PHILOSOPHY

Department of Resource Development

 

 

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ABSTRACT

Wuaeounsususxvs SIMULATION MODEL or A TROPICAL
mu FIS‘HERY: RED GROUPER (magnum min)

.bonductlrl OF YUCATAN CONTINENTAL SHELF

snaiyv.= ' BY

and Juan Carlos Seijo G.

Management of renewable resources such as ocean
fisheries, is a complex process requiring understanding of
resource biology and ecology as well as the economic and
institutional factors affecting behavior of fishermen as
resource users.

Different approaches have been used to aid decision-
making through modelling efforts such as: the surplus yield
approach, the bioeconomic approach and the dynamic pool
approach. It is also recognized that the approaches
mentioned above involve only a partial conceptualization of
the fishery resource system. Therefore, the major objective
of this dissertation was the development of a comprehensive
simulation model integrating biological, economic, and
institutional factors. The systems simulation methodology
was applied to model a tropical demersal fishery: red
grouper (figlngpnglgg nmgjg) of the Yucatan continental
shelf. The following steps were taken: (1) identification of

 

. the fishery system. (2) design of causal and block dia;rwrw“ T-’""*

 

  

 

   

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Juan Carlos SeiJo G.

‘Iaalysis to estimate confidence intervals for model inputs
and important performance variables, and (9) conducting
simulation experiments to observe the impacts of alternative
management strategies. In order to deal with the uncertainty
inherent in ocean fisheries, random variables were generated
with an exponentially autocorrelated probability density
function. This modelling effort involved the design of a
feedback loop to estimate population structure and
recruitment over time. Concerning fishing effort, the
distributed DELAY model was applied to model vessel entry
and exit to the fishery. The comprehensive nature of the
validated model allows for observing the dynamic behavior of
performance variables such as fish biomass, fishery yield,
net revenues of different types of vessels, direct

employment, availability of seafood in coastal communities

and export earnings.

 

   
   
  

ACKNOWLEDcEvga':

' A Dimitri "
‘fl1880rtatluu

suggesticr

Dr, '.' ~ DEDICATION
Sta rTo Cecilia, Juan Carlitos and Adrianita who always have

i. been a source of love and encouragement.

   
  
 

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prevention a: i

   
   

To the Inafz‘u': ' -_L .~ L . . .. , Lute

 
  

    
  

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-‘figdur1ng the different stages of my doctorfi

   

 

   
 

ACKNOWLEDGEMENTS

 
  
 

‘3 wflghrto express my deepest gratitude to Dr. Manfred
'flissertat.::

”Shullen for his motivating guidance, support for a broad
:;::;;ic development, and friendship.

CC: 1 sincere appreciation to Dr.Danie1 E.Chappe11e, my‘
dissertation director, for his detailed reviews and useful
suggestions during the development of this dissertation.

To the guidance and dissertation committee : Professors
Dr. Daniel E. Chappelle, Dr. Manfred Thullen, Dr. Milton
Steinmueller, Dr. Thomas Manetsch and Dr. Lawrence Libby for
their academically stimulating comments and suggestions
during the development of my doctoral program.

I also wish to manifest my gratitude to the Graduate
Affairs Committee for the opportunity to learn , as a
Teaching Assistant, from distinguished faculty of the
Department.

To The Thoman Foundation which funds The Thoman Fellow
Program For The Prevention of Hunger and Malnutrition and
Dr. H.C. Bittenbender its leader for the opportunity of
experiencing a multi-disciplinary exercise for the
prevention of famine in the developing world.

To the Instituto Tecnologico de Merida and Instituto
Nacional de la Pesca for their financial and logistical

support during the different stages of my doctoral program.

To the staff biologists and administrators of to," ‘ '

 

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:‘75‘ EiSSértation figures. To Jose Almeida who helped to
"iiitggkfishing effort information.

To*tverardo Pech, Eustaquio Canche and Don Roberto Pech
for providing valuable insights concerning fishing effort of
traditional coastal communities.

A number of good friends and colleagues were sources of
encouragement and stimulating discussions. My sincere
appreciation to Omar Bagour, Carl Gibson, Joel Lichty, Pedro
Montanez, Pedro Herrera, Herberto Gutierrez, Elias Daguer, i
Armando Molina, Miguel Sarlat, Ruben Encalada, Jorge Zavala,

Julio Segovia and Mario Gonzalez.

Finally, I wish to express my gratitude to my

father(+), mother, and brothers Jorge, Emilio (+), Jose,

Eduardo, Miguel and Alfonso for being motivating forces in

different stages of my educational life.

       
 

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TABLE OF CONTENTS

 

CHAPTER I. INTRODUCTION............ ...... 1
. Law of the Sea Treaty: Rights and Obligations.... 2
' Common Property Resources ....................... 5 .
Exclusion Costs and Free Rider Behavior..... 6 “ f
Transactions Costs.......................... 8
Mexico: Ocean Fisheries Policies................. 11 1
Impact Analysis of Fisheries Management Q;
Strategies....................................... 15 »
Study Objectives................................. 17
Research Approach................................ 18

CHAPTER II. REVIEW OF THE LITERATURE....... ...... 20 1‘.
Population Dynamics and Biology of The Red 9
Grouper (E pigeph elu s ngjo). ................ 20 ’

Habitat.............. ............. 23 '.
Spatial and Temporal Distribution........... 23

Depth Distribution.......................... 24 .
Seasonal Abundance......... ................. 24 ‘,-;
Temperature of Occurrence of Red Grouper.... 2a 1 V
Reproduction, Recruitment and Growth........ 25

Predation and Fishing Mortality............. 27

Stock Assessment............................ 27
Fisheries ModellingQOIIOCOICODIIUOIIOOCIIOCIIIIII 28

 

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Surplus Yield Model......................... 28 ifh ,

Advantages and Limitations............. 29 #.3+

Assumptions......... 3O 5,; h

Extensions of The Surplus Yield Model.. 30 '4““

I 'Bioeconomic Models of Fisheries............. 31 gflp r
Open Access Equilibrium................ 32 hi 3

' Open Access Equilibrium of Multispecies W. ;
Fisheries.............................. 3H if ‘h

Regulated Equilibrium.................. 42 m. w

Fisheries Dynamic Pool Approach............. ”3 NJ‘N

AssumptionSUIIOCIOOIIOIO IIIOCIOIIOIIIII ”7
Extensions of the Beverton- Holt Model.. #9
Fisheries Management Alternatives........... 50

Regulating Catch Composition........... so _75 ‘1
Regulating catCh size-assassssssneossss 5° .» a”: ' l 1
Maintaining Efficiency in the Fishing :1. ‘ ,.‘_ -,

Processes-oases... oases-assessesecseaos 5,1. y;:"““W.I
Redistribution of Wealth,,,_,__.....b.q a.».r... .

    

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“DIX hnezionOIOOOIIIIIOODOOOOOOIIOOOOOI‘IOIIIIDIQO
. Systems Simulation Approach......................
' vhf}. .System Identification-oassesses-loosesassess
Model Decomposition.........................
System Causal Diagram.......................

Primary Data Sources........................
Secondary Data Sources......................
Mathematical and Computer Model... ..............
Mathematical Model..........................
Population Dynamics of the Red Grouper.

Fishing Effort and Catch...............

Costs and Revenues Analysis............

Model Assumptions......................

Computer Model..............................
Model Stability........................

General Model Characteristics..........

Time Frame........................

Level of Aggregation..............

Functional Form of the Equations..
Uncertainty.......................

Monte Carlo Analysis........... .........
Model Validation and Sensitivity Analysis........
Model Validation. ...........................
Sensitivity Analysis........................
Simulation of Management Strategies..............

CHAPTER IV. RESEARCH RESULTS.........................
Survey Results...................................
Information Obtained from Primary and
Secondary Sources...........................
Stability Analysis...............................
Model Validation.................................
Sensitivity Analysis.............................
Monte Carlo Analysis.............................
Simulation Results...............................
Red Grouper Biomass.........................
Fishery Yield...............................
Costs and Returns...........................
Fish for Coastal Zone Consumption...........
Fishery Direct Employment...................
Resource Management Strategies...................
Allocation of Exclusive Property Rights.....
Limited Entry to the Fishery................
Minimum Size Regulation.....................
Price contrOISIIIOOOOIIIIOIOOOOIIIIOIIOICIII

CHAPTER V. SUMMARY, CONCLUSIONS AND RECOMMENDATIONS..
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Data Collection and Analysis.....................

  
  
 
 
 
 
 
  

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W firsnmmifibw DIAGRAM OF COMPUTER MODEL............
’ :PPENDME- MONTE CARLO MODE 0? PROGRAM SIMERO........

AEPENDJEX F. SIMULATION RESULTS........................

LIST OF: REFERENCESOOIOOU.0.000000.......IOOOIIIOIIIIII

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LIST OF FIGURES

‘1 table Open Access Equilibrium.......................
'2 Population Equilibrium Curves of
". 1 Hu1t189601es Fisheries...........u............
‘ 3 Sustainable Yield Curves of Two Species.......
5 Maximum Economic Yield of
i Multispecies Fisheries................ .. .....
5 Diagram of the Main Processes modelled by the
Dynamic Pool Approach to Fisheries Management.
6 Study Region: Peninsula de Yucatan............
7 Red Grouper Fishery: System Identification....
8 Major Components of the Red Grouper Fishery...
9 Causal Diagram of the Red Grouper Fishery.....
10 Block Diagram of Red Grouper Fishery..........
11 Model Validation: Simulated and Actual Catch..
12 Model Validation: Catch per Unit of
Effort of Traditional Vessels.................
13 Model Validation: Catch per Unit of
Effort of Modern Vessels......................
1A Simulation of Modern Fleet Size...............
15 Model Validation: Simulated Population
Structure........... .... ................
16 Model Validation: Simulated Biomass by Age
Group.........................................
17 Red Grouper Biomass over Time.................
18 Yield of Traditional Fleet: Red Grouper
Fishery.................. . ................
19 Yield of Modern Fleet: Red Grouper Fishery....
20 Random Variable of Catch Equation of
Traditional Fishermen.........................
21 Random Variable of Catch Equation:
Modern vessels........... .....................
22 Annual Net Revenues of Modern Vessels
Targetingat Red Grouper. u.u.u.n.u.u.u.
23 Red Grouper For Coastal Zone Consumption......
2n Direct Employment Generated by
Harvesting of Red Grouper.....................
25 Resource Management Strategies:
Biomass Effect................................
26 Resource Management Strategies:
Fishery Yield Effect..........................
27 Price Control Policy. Effect on Net Revenues..
28 Resource Management Strategies:

Effect on Direct Employment...................

     
  

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Page
1 "{‘FBIOdk Diagram: Variables and Parameters.... 7n
1§Ore ‘ _Cost Analysis of Traditional Vessels....... 88

"' 7 r Cost Analysis of Modern Vessels............ 89 7
c; , ‘ Red grouper Fishery: Fishing F1eet......... 10"
Effective Fishing Time per Year............ 105
<6 , Catch per Unit of Effort................... 106

‘7 Error Analysis Expressed in 1 for DT: .5.... 107
,6 , Error Analysis Expressed in 1 for DT:.05... 108
“9 Sensitivity Analysis: Effect of 10%
Decrement in Initial Biomass, TFB(0)

Expressed in 1. ........................... 118
10 Sensitivity Analysis: Effect of 10%
Increment in Initial Biomass, TFB(O) .
Expressed in $................. ............ 119 ‘
11 Monte Carlo Analysis of Fishery Yield .
by Type of Vessel, CATCHT(t), CATCHM(t). .... 121 l
12 Monte Carlo analysis of Net Revenues 1!
by type of vessel, PFTT(20),PFTM(20)....... 122 j
13 Monte Carlo Analysis of Red Grouper '
Biomass, TFB(10), TFB(20).................. 123 .
1n Costs and Revenues of Traditional 1
Fishermen.................................. 132 j
15 Costs and Revenues of Modern Fishermen..... 133 g
16 Impact of Resource Management Strategies... 1H1 J
8.1 Values of Constants and Parameters......... 168
8.2 Initial Values of State Variables.......... 171

      
 

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CHAPTER I
INTRODUCTION

Management of renewable resources such as ocean
con“
fisheries is a complex process that requires understanding
(it-'3. - .1),
of resource biology and ecology as well as the economic and

 

institutional factors that affect the behavior of fishermen _‘fII
as resource users._ T 1*
Developing coastal states like Mexico have .i

substantially increased their fishing effort in order to

 

provide their growing population with domestic protein rich
1 food. In addition, ocean fisheries are-also perceived as
important sources of foreign exchange by most developing
nations, which can help to alleviate foreign debt problems.
In order to sustain the yield of fisheries resources
over time and protect the fragile ecosystems in which they
live, an integration of biologic, ecologic, economic and
institutional factors is required to aid the decision-making
process. Therefore, the purpose of this study is the
development of a comprehensive model as a tool for fisheries
resource management using the systems simulation approach.
To deal with the factors mentioned above, the following
topic areas will be discussed in this chapter: (1) the Law
of the Sea Treaty and resulting property rights and

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. obligations of coastal states, (2) the inhorea

-ih., coast. 1:,

mgr/leteristics of ocean fisheries and the as a

 

 

 

    
  
   
     
   

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of its major fisheries and, (A) a brief discussion of the
role that the systems simulation approach can play, when
conducting impact analysis of fisheries management
decisions.

Finally, study objectives and a summary of the research

approach are also presented in this chapter.
Law of the Sea Treaty: Rights and Obligations

In April 1982, 130 nations signed the Law of the Sea
Treaty which included recognition of 200 miles jurisdiction
to coastal nations. This newly acquired Exclusive Economic
Zone involves a set of property rights as well as
obligations that each coastal nation needs to satisfy.

One rationale behind this treaty dealing with biotic
resources was the international concern of over-exploitation
of fisheries resources in the last three decades. Because
of the common property character that existed before 1982,
fisheries resources beyond the 12-mile Territorial Sea and
Contiguous Zone were owned in common by all coastal States
capable of harvesting them. This yielded satisfactory
results under conditions of light use of fish stocks, which
prevailed in most areas prior to World War II. With a few

localized exceptions, biological depletion did not occur as
a consequence of unrestricted harvesting in the marine
fisheries.

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Wistdouac«(1982: 139) has pointed out:

&
,‘oestsrnco the supply of fish was usually unlimited relative
to demand, individual harvesters did not need to fear

*Qxlrttzthat competitors would catch any fish that they left

unharvested. Therefore, individual fishermen could
”decide upon an optional rate of harvest over time
without experiencing undue pressures to overinvest in
the short run in order to maximize their share of a
finite supply of fish.

After the Geneva Conventions of 1958 and 1960 that
emerged from the United Nations Conferences on the Law of
the Sea (UNCLOS I and II), many issues remained
controversial. Among them were the concern of fisheries
development and conservation. As soon as it became clear
that the third UNCLOS conference, which started on December
3, 1973, would establish a 200 miles Exclusive Economic
Zone, unilateral extensions began to develop at an increased
rate (Ross, 1982). Mexico in 1976 was among the countries
that claimed 200 miles of Exclusive Economic Zone (EEZ)
before UNCLOS III was convened. It should also be mentioned
that a large number of bilateral agreements had been reached
between 1976 and 1980 between coastal states who wished to
continue to carry out operations in those areas (Johnston,
1981). This was the case in the agreement between Mexico

and Cuba concerning the harvesting of red grouper

(iningnnglns mgz19)1 in Yucatan's Continental Shelf. Most of

these agreements were designed to define the terms andnlgi;ifi

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I51) That maintenance of living resources in their EEZ was
not endangered by overexploitation, (2) That populations of
harvested species were maintained or restored to levels that
would produce sustainable yield levels and, (3) That
populations harvested and interdependent fisheries were
maintained above levels at which their reproduction become
seriously threatened (Johnston, 1981L

Article-61 further established that another major
objective of the treaty was to provide for the harvesting of
the entire allowable catch of living resources within the
EEZ; 'The portion in excess of the domestic harvesting
capacity shall be made available by agreement to foreign
fishing subject to coastal regulations" (Burke, 1983:31L

The above statement implied a permanent obligation of
coastal nations to conduct research efforts to determine the
amount of fish biomass in their EEZ. Then, they must
establish the portion of the exploitable population that
could be harvested domestically and the portion that could

be made available as surpluses to foreign fishing fleets,

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dynamic computer models to simulate the complexities of
ocean fisheries (Grant et al., 1981; Allen and Mc Glade,
1986; Gislalon et al., 1982L

Common Property Resources

The problem of the 'bommons" has been widely discussed
in the literature concerning open access to renewable
resources (Harding, 1973; Gordon, 195a; Eckert, 1979L
According to Howe (1979:291) there are two conditions for
the existence of a common property resource: "(1)
unrestricted access to the resource system by all those who
care to use it, and (2) some kind of adverse interaction
among the users of the [ecosystem]"(i.e” the creation of
externalities among users). Fishing externalities are
understood as external effects caused by individual
fishermen but not included in their accounting system.
Agnello and Donnelley (1976) have recognized three types of
negative externalities in most fisheries:

(1) Stock externalities. This type of externality occurs
when entry affects the magnitude of fish population
and hence the harvesting costs of other fishermen.

(ii) Crowding externalities. Arise when vessel congestion
on the fishing grounds increases marginal catch
costs.

(111) Fishing gear externalities. Exist when the type of
gear used changes the population dynamics of the

target species and associated bycatch.

IN

   
  

   
  

 

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“wanesseso£.ocesn fisheries, there are a number of
5
.”lifiirent.resource characteristics requiring further
f".3§‘93 in order to understand interdependencies among

407: users.

.0'8E‘ ’ .5,“

WMWMMMMM
I15“Because migratory characteristics of most ocean
fisheries involve high costs of excluding others from
exploiting the resource, a fisherman may not benefit by
postponing a catch with the expectation of catching a larger
and probably more valuable fish later, since that fish is
likely to be caught in the meantime by another fisherman.
Given that sustainable yield is only reached when, for any
specific fishery size, the harvest per period is just equal
to the natural growth (Munro, 1981) of each cohort of the
population structure, species can be decimated if fish are
caught more rapidly than they can reproduce. However, a
single fisherman cannot affect the size of the stock by
reducing his rate of catch unless all or most other
participants in the fishery agree to abstain proportionately
(Eckert, 1979).

Without an agreement to limit catches, the main result
of a single fisherman's reduced rate of catch is to lower

the costs of other fisherman without necessarily increasing

DI

u—flflrease the grate of catch and thus contribfik,il$”?

 

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:1: benefits. Consequently, each fisherman is likely tn;wy .

    
  
   
  
  
   
    

 

  
 

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ifishermen desire.
of tn

aggregate fishing behavior that no one involved with the

That is, micro-motives seem to result in

fishery would want. The fishery sustainable yield, which is
the long-run preferred result by all fishermen, is usually
dominated by marginal benefits of an individual fisherman's
increased harvesting rate (dominant production function) or
by uncertainty of future resource availability.

The sustainable yield choice will have higher payoffs
only when the number of individual fishermen selecting it
reachesa certain threshold. This threshold is the point at
which the level of biomass over time is sustained by the
appropriate fishing effort of most fishermen involved in the
fishery.

As is also recognized in the literature, the size of
the group of fishermen is a relevant factor affecting the
avoidance of this social trap (Schmid, 1978). If the group
is large, a fisherman may be an unintentiggal {£33 Line:
given that he doesn't see how to avoid the macro-result
(fishery destruction) when he cannot be sure that other
fishermen will act in concert. If the group is small,

exclusion costs are not lower, but the non-contributing

‘ filhermen are easier to identify, therefore reducing tn._72?~1‘

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- lfdes group size, another factor that may play an

'rtnnmirole in trying to avoid Hardin's (1973) "tragedy

 

they do not calculate benefits of increasing harvesting rate
apart from themselves. They rather behave consistently with
the community shared objective of sustaining the yield of
the fishery in question. This involves conditioning or
adjusting the intertemporal preferences in resource use of
each individual fisherman to those shared by most members in
the community. This may take place when the level of
overexploitation affects all fishermen involved and
voluntary collective action is sought by most members of the

community to prevent resource depletion.

Jiisnllzanmiiansgasis

Marine fisheries also involve high transaction costs
which generate another source of attenuation of property
rights that prevent the market from allocating fisheries
resources over time in such a manner that net present value
of the fishery is maximized. It should be mentioned,
however, that when talking about net present value of the
fishery, intertemporal choices of individual fishermen

should be taken into account through different rates of

discount reflecting different prices of time. The &tipmeaifi'

‘ .v refines of "traditional fishermen” (fishermen» .f

l
.a‘; .

smell :~.;2‘..:;.-. ‘ ~-
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,gdiertgiststus of the former.
. (the.

  

Thansactions costs involve a group of costs discussed
ih°the literature as information costs, enforcement or
péfldeing costs and contractual costs (Schmid, 1978; Randall,
1981).

Ocean fisheries involve high information goats that
result from interdisciplinary research efforts of
biologists, oceanographers, fisheries economists, system
scientists, among others, needed to keep track of (1) fish
population dynamics, (2) spatial and temporal distribution

of fish species, and (3) changes in physical and chemical
factors that affect the distribution of fish in the marine
ecosystem.

Managing this type of renewable resource also involves
gnfggggmgpt g; policing costs that result from enforcing
fisheries regulations and protecting fishing property
rights. Usually these costs tend to be so high that rights
granted to future generations (through regulations that are
aimed at sustaining and even increasing the yield of the
resource over time) and to fishermen of today (through
allocation of exclusive property rights) may become empty
Hahn. ’

h"'Jlll'ociern fishermen" (those who use larger

_ ft “and capital intensive fishing gear) because of the

  
   

   
    

 

 

 

  

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‘ sensing capabilities to monitor uses of ocean

Finally, in cases of countries such as Mexico, where

 

' " ’.f~§there_have been legislative efforts to foster collective E
forms of organizations in the fisheries sector, contractual .—
gpgtg may become a significant variable. Costs involved in
organizing a fishermen cooperative for voluntary collective ,

1 action are usually substantial. An important analytical r”
issue concerns identifying who pays for the contractual

costs, the fishermen or the State (which fosters this form

of organizationL
The fisheries economics literature usually advocates

the allocation of private property rights to individuals to

  
  
  
  
   
  
  
  
  
  
  
 

overcome the depletion problem. Many regulatory schemes have

been advocated to deal with this problem. Some can be

.. n—aul—‘s m.

classified as regulating catch composition and others as
regulating catch size (Pearse, 1980; Scott, 1979). ‘

Some of these institutional structures have been

 

applied by the Mexican government which has conducted a
number of legislative efforts to sustain the yield of its
major fisheries and at the same time increase welfare of
coastal rural communities by allocating them exclusive
Property rights to those fishery resources.

To better understand how Mexico is dealing with the

    
     
 

lsnagement of its fisheries (since Mexico is the case stuS‘fi ‘
/\ .lC av. !‘€-
this research) one needs to review its his ‘
tion ng i;- 'n r- - l“ ,
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'Mexico: Ocean Fisheries Policies

 

_The first Fisheries Law of Mexico was issued by
;::sident Calles in 1925 to regulate both marine and fresh
water fishing. This law reflected concerns about the need
for establishing closed seasons for different fish species,
and the establishment of harvesting zones, coastal zones
refuges and fish sanctuaries. In 1932, the Government of
President Ortiz Rubio promulgated a new Fisheries Law, by
which "The protection of the state was granted to fishermen
organized in groups, with the goals of improving economic
and social conditions" (Banco Nacional de Comercio Exterior,
1981:”17). The following year, by-laws governing application
of this law were issued. "Reserved fisheries zones" and
"common exploitation zones" were established. The former
,were to be conceded preferentially to collectively organized
fishermen. The latter were to be reserved exclusively to
fishermen organized in cooperatives so as to ensure their
own subsistence (op cit., p.417). In 19u7, President Miguel
Aleman granted exclusixg Light; to fishermen's cooperatives
to exploit nine species of economic importance, among which
were shrimp, oyster, queen conch and lobster (Departamento
de Peace, 1977). 9 "19
After these laws were established, ”There. was £3 &

80126 5“,: H4 . ,a; 7-'-"5LYU "

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gpallocation of exclusive property rights, was

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a‘1ypturned into practical achievements" (Banco Nacional

         

.dt '
fi Esmercio Exterior, 1981:”18). It seems that the 19“?

1t at thv J? '_
provision of exclusive exploitation rights given to “1%
cooperatives for certain species, was not a sufficient :1-
condition for them to exercise their rights and strengthen
their organizations. High costs of excluding other
fishermen who do not have the right to harvest these 1,1
specific set of species may have caused an empty right to be l
7 , conveyed to traditional fishermen organized in cooperatives.

Additionally, high transaction costs involved in organizing 171

cooperatives, may have prevented many traditional fishermen

 

from getting organized. 1"
In the period 1971-1979, a series of laws were issued 7

by the federal government which included creation of a State

 

“k. "1; 1.

owned bank (BANPESCA) and a State owned corporation

, -n'-1~1-:-

(PROPEMEX). In addition, in 1982 the Mexican banking system

 

,
1
.‘

became expropriated by the federal government. As a result,

   
  
  
  
  
   
    
     
  

the public sector is the only financing source for fisheries

’-
1
1
2

investment projects.

2.7““ u :.

It should also be recognized that at the beginning of
Mexico's legislative effort in the fisheries sector, the
federal government was hoping to achieve a change in

performance via factor ownership transfers (e. 3" fish 1;,
04¢. ’

   

species Lgsgzygg for traditional fishermen), but failed
539111; .
hmoosnize the total institutional framework
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13

legislative efforts, incomes of

.s-; e
' f» tional fishermen may be reduced in the long-run, given

    

‘~th:t they have not been able, as yet to avoid the "tragedy .:
he - 1:
of the commons." Two of the reserved species for r

"Hil1

CH_.
traditional fishermen cooperatives,queen conch(§jjgmhg§ 3

81831) and spiny lobster (Eanuljrus gzsus) have been }
reported as overexploited in the coastal area of Quintana !
Boo, Yucatan (Fuentes et al., 1986; Cruz et al. 1985M
Harvesting of both species is being regulated by the
Ministry of Fisheries. In addition, one major fishery of
Yucatan Continental Shelf, the red grouper (Epinephglus
mgnlg), seemed to have reached its maximum sustainable yield
in 1972 and since then the catch per unit of effort has been
slowly decreasing (Chavez, 1983). 9
A factor that may be affecting behaviors of traditional t 91
fishermen is the high injgrmgtign 32;; involved in keeping

track of fish population dynamics and migratory patterns as

 

 

well as information related to factors that affect fish

ecosystem performance. Research and extension programs on

  
  
  
   
     
      

fisheries ecosystems of different areas, may help reduce
these high information costs. It should be recognized
however, that all these efforts to reduce transactions costs
faced by traditional fishermen require that they be borne by

government, hence a subsidy from the government to the

 

 

frishermen. People not interested in fish or equity prL ‘
finger an»: ' ‘

Y;,¢_z~~~ unwilling riders when paying thair,

”51%,;ygffl f1: cries sector h3§ -;_ ,

   

 
   

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I , programs, with the long-run objectives of prevention
”I! __ ..

alihgffl ccurrent extreme malnutrition status of 19 million

1h

:: at, in October 1983, issued the "National Food
L1983-1988” This program began by first recognizing
1'9
Roxicans as indicated by their deficits in consumption of
:alories and proteins. Second, the program addressed the
gerious concern of the increasing dependence on basic food
products from external suppliers. During 1980-1982, the
import/total production ratio for basic food stuffs was, 19%
for corn, 30.6% for beans and ”0.62 for sorghum. Food
imports have increased substantially in the last 20 years.
In the 1965-1969 period Mexico imported 283 thousand tons of
basic grains, oleaginous grains and sorghum, while in the
1980—1983 period the country imported 20 million tons of the
same food products (Comision Nacional de Alimentacion,
1983). It should also be recognized that Mexico's high
rates of population growth have contributed substantially to
this food deficit.

One of the main characteristics of this food program,
as contrasted to ones developed before 1982, is recognition
of the increasing and relevant role that the fisheries
sector may play in the alleviation of Mexico's malnutrition
and foreign debt problems. In addition to agriculture,
adequate management of ocean fisheries resources may provide

an alternative nutritional supplement to Mexican food

o‘- .1

[or and malnutrition.
Ch LJC do. . 1 J .1 ‘.,.r:

9%... we fisheries 1soctor has;

“"5 xx. m -. .~ , -33 ”75"

  

 

 

 

 

   
   
  
  
 

 

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-nlso, domestic fish consumption has increased

    

.. substantially. Direct fish consumption increased 632 in the
”a”, ‘ ‘ ‘- é;riod 1976-1980 (Secretaria de Programacion y Presupuesto, filtf
1982). It should be mentioned, however, that in relative bki
terms fish consumption represents a very small component of
the average Mexican diet. This diet is based mainly on
corn, beans and beef produced inland where the majority of

the population has been settled for centuries. 1

This substantial and promising growth of the fisheries f

  
  
  
  
   
   
  
      
   
      

sector requires a study of the biological, ecological and
economic interdependencies involved in ocean fisheries
resources in order to predict impacts of alternative

resource management strategies.

 

1
Impact Analysis of Fisheries Management Decisions .y

Fisheries resource managers lack information concerning
fish population dynamics and information about the linkages
involved between the alternative institutional structures
(management variables) and the performance of the fishery
system.

Different approaches have been used to aid the

.decision-making process through modeling efforts such as.

;;§tho surplus yield aDDPOSCh (Schaefer, 195A), the bios
.. .. 'i'

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'13: the use of system simulation to estimate the
tra-

  

This type

  

‘H i rhinos of alternative management strategies.
‘ ' fo $969111“ effort requires a W when!) that
involves biological, economic, and institutional dimensions
in order to provide integrated guidelines for renewable J ‘
resource management (Ervik et al., 1981; Walters, 1980).
Concerning the need for comprehensive fisheries .
modelling Richard C. Hennemuth, Director of the Northeast 5
Fisheries Center at Woods Hole, has pointed out: (Cited by
Gulland, 1981)
Successful management, the fulfillment of expectations, : V“
will depend to a large extent on adequate advice based 3
on good models. The simpler models include only one ‘1
effect. There are no interactions and multiple effects
are ignored. Regulations of fishing mortality on a

single-species stock assumes no interactions with any .
other component of the system.

 

i

1

Gulland (1981) further argues that few general ’ 1

descriptions of the complete fisheries management system i
have been given in the literature and suggests that models ~fi

of complete systems do not exist. Rather there are a number

of models describing individual parts of the system; these , y

can be grouped into: 3? H

(1) Biological models describing fish stocks and their . 3

ecosystems.
(ii) Bioeconomic models describing the interdependencies "t; ’

between fish stocks and fisheries revenues and Zfljf l 3‘

costs under a set of static equilibrium conditiena

:fiii".3? ------ iheoretieal considerations have been r
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:%§1§ type of models would result in what Anderson
an(Op. cit) calls "bioregunomic" models of fisheries.
(iii) Hodels describing actual operations of individual

lelements of the fishing industry ashore and at sea.
:{IIt should be mentioned, however, that a balanced
combination of "reductionist" and "holistic" approaches2 may
allow the possibility of integrating biologic, economic and
institutional factors needed to approach reality in the
modeling effort.

Study Objectives

The major objective of this study is development of a
comprehensive model that integrates biological, economic and
institutional factors using a system simulation approach.
Research results are intended to provide guidelines to
decision-makers responsible for managing ocean fisheries
over time. Also, the resulting simulation model may be of
interest to the academic community interested in renewable
resource modeling.

In order to achieve the main objective, this research
effort involves: (1) development of a simulation model of
the red grouper fishery which specifies the biological,

economic and institutional factors which may determine the

 

 

    
     

 

 

 

 

 

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18

   

  
    

: idyfij 6060f the fishery over time, and (2) simulation of
‘jflrfiélanéctcritcria such as:
3 ' ‘ (i) Het' revenues received by different groups of
fishermen over time.
(11) Income and employment levels of coastal communities
over time;
(iii) Sea food availability in coastal rural communities.

(iv) Level of fish biomass over time;

(v) Fish export revenues.

Given the above stated objectives, the following section ‘

discusses the research approach used in this study.
Research Approach

In order to achieve the above stated study objectives
the research approach used in this study involved the
following activities.

(1) Review the literature on fish population dynamics, j
especially for the red grouper in the Gulf of
Mexico;

(ii) Review literature on surplus yield and bio-economic \

   
  
  
    
  
 

models as well as dynamic pool models of fisheries.
Also, review available regulatory schemes for ocean
fisheries management.

(iii) Build a system causal diagram representing

biological, economic, and resource managenont H_M‘:,;r

subsystems specifying interface variables that vgjgfpg
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The above activities are discussed in greater detail in il'.
. Chapter 1:1,.which_deals with research methods.

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~wrcify system implicit form equations;

    
   

  

‘Interview decision-makers from the Ministry of

rx

        

Fisheries to identify their objectives and explore

"is
their alternative policy options. ‘-
‘Collect data from primary and secondary sources to (ya?
estimate parameters and specify the fishery system '§,§§
of explicit equations. r'i
Build block diagrams to represent the red grouper L‘fi!
fishery and specify the corresponding set explicit h F
equations. r g
Develop a mathematical model for the fishery. K?“
Develop a computer program that represents the E jg
specified mathematical model. (*4

   
    
    
   
  
   
  
    
   
   
    
 
 

Conduct stability analysis. W
Conduct sensitivity analysis. 5

Apply Monte Carlo analysis to obtain a set of

 

statistics which provides an estimate of
uncertainty in system performance.

Analyze model results.

Validate the model.

Run the model using different resource management
strategies and analyze resulting performance.

Derive conclusions and recommendations.

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CHAPTER II
REVIEW OF THE LITERATURE

In order to build a comprehensive model of the red
grouper fishery of the Peninsula of Yucatan, it was
necessary to review the literature dealing with the biology
and population dynamics of the resource, the economic and
institutional factors that affect fishermen behavior, and
major approaches used to model ocean fisheries. To
accomplish this, the following set of topic areas are
discussed in this chapter: (1) Population dynamics and
biology of the red grouper, (2) The surplus yield approach,
(3) Bioeconomic models of fisheries, (u) Fisheries
management and regulation, and (5) Fisheries dynamic pool
models.
Population Dynaggcs and Biology of the Red Grouper
mam
There are numerous and diverse processes at work in the
marine ecosystem, effecting its biotic components in a
variety of ways. The major processes effecting the biomass
of a given fish species like red grouper (Epinephglgs monig)
are the following (Laevastu and Larkin, 1981; Pitcher and
Hart, 1982):

,' an)

    
 

availability of proper f;

  
 

by temperature,

“1', gluing” with _cge of the spec; '45-..2...,.«z.-1. ‘

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'this ”factors such as spawning success, size of spawning , l
:‘.' ~-’ 3"

”Chi stock and mortality of eggs and larvae from various ‘-
causes including predation. It is also a function of
non-biotic factors such as currents and physical and
chemical conditions of estuaries and coastal
lagoons.

(111)19sislmal and instill: fish negation by other
species and by cannibalism.

(iv) Mgctglity from old age, spawning stress and disease.

(v) fijgzatigns including in-migration and out-migration

with respect to a given geographical area.

 

(vi) Pzggatiog by other fish species in the red grouper
ecosystem. ' I

(vii) Zzggatigg ty m g. Fishing mortality. 5

In addition, for the purpose of understanding the
biotic marine environment, it should be recognized that the E';t
variables mentioned above should also be taken into account
globally for all species in the regional ecosystem. As

Laevastu and Larkin (1981:6) have pointed out:

 
 
  
   
 
 

Although populations of some may decrease while
others increase with time, the standing stock of the
total biomass of finfish in a given region fluctuates
relatively little. The tgtal tigmagg is determined
by the total availability of phytoplankton,
zooplankton, and benthos as the bulk food and 1
determine the so-called 'motal carrying capacity“ of ,,n
any given region. _‘5

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(should be mentioned however, that for the purpose of
.‘_ liudy, the model that follows basically takes into
:iccouht'the red grouper fishery. To attempt to include in
3%; model all the biotic and abiotic components of a given
regional ecosystem goes beyond the objectives and
feasibility of building a comprehensive model that also
takes into account economic and institutional factors.
Nevertheless, it could have been desirable, if data were
available, to model the by—catch component (incidental
catch) of the red grouper fishery. This by-catch includes
species such as yellowtail snapper (931232; oncysucgs) and
white grunt (flggmulgn pltguggi).

Concerning the specific characteristics of the red
grouper of the Gulf of Mexico, Rivas (1970) and Solis (1969)
have published that this fish species is probably the most
abundant and commercially important grouper in the Gulf of
Mexico. The red grouper, which is called 'hero" in Mexico,
"cherna americana"in Cuba, “red grouper"and "sea bass" in
the 0.8” lives primarily in the rocky and coral reef
bottoms of the continental shelf. Its center of abundance
is Florida and Yucatan's continental shelves (Moe, 1969).
According to Rivas (1970), its average weight is 6.6 pounds

with the largest specimens weighing up to 38.5 pounds.

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The red grouper is an important member of the benthic,
gublittoral community of the eastern Gulf of Mexico. It is
iound only on rocky and reef bottoms within depths of 10 to
noo feet. It frequently occupies crevices, ledges and
caverns that are formed by the rugged limestone reefs.
These reefs normally'extend 2 to 8 feet above the sand and
shell bottom (Moyle and Cech, 1982; Moe, op. citJ. The
location dependence of red grouper to hard bottoms or

substrates has been also pointed out by Smith (1961L

finatial and Ismngnal Diairlhsilghi

For resource analysis purposes, the distribution in
space and time of red groupers is an important input for
delimiting the study region as well as for the modeling
process. It has been reported that seasonal distribution of
groupers in the Yucatan continental shelf exhibit a lgggl
mignatgny pattgrn from east to west during summer and fall
and from west to east during winter and spring. This
seasonal distribution might be caused by inflows of cold
waters comming from the Yucatan Channel. Analysis of age
composition of the catch show two distributional gradients:
one, from west to east where larger groupers are found in

the eastern part of the shelf, another, showing juveniles in

shallow waters and adults in deeper waters. (Valdez

, 6380; garcia and Mirands,,jg75;afi&3§§ '1iggé i "“

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"721qfltntzihytjgn‘ Studies conducted by Rivas (1970) of the

”Mloratory Fishing and Gear Research, found that red

grouper occurs in the northern Gulf‘in a depth range ofllto
Ga‘fathoms with a mean depth of about 22 fathoms. In this
area about 70% of the records extend from 13 to 31 fathoms.
In the southern Gulf (as discussed in Study Region section),
the range extends from 2 to 58 fathoms, with a mean depth of
29 fathoms. In this area 70% of records extend from 25 to
33 fathoms. This fish distribution was also pointed out by
a study made in the Campeche Bank of the Peninsula of

Yucatan (Doi, Mendizabal and Contreras, 1981L

§3§§gfl§l Atuggangg. As with most fisheries, seasonal
fluctuations of water temperature cause seasonal occurrence
of red groupers in the Gulf of Mexico. The above mentioned
studies found that temperature fluctuations in the Gulf do
not reflect four marked seasons, but basically two major
ones: the cold season (November through April) and the warm
season (May through OctoberL

With respect to the southern Gulf, Jarvis (1935) stated
that in the Campeche Bank, the biggest of the grouper catch,
including red grouper, is made between October and April.
Carranza (1959) has pointed out that off the coast of
Quintana Roo (in the Peninsula of Yucatan), the greats;
Qatohes are made during December and January.

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”In“ 5

.aiieason, temperatures range from 63' F to 811' F with mean 67'F.
prcavr e A

In the southern Gulf, during cold season bottom temperatures

at mean depth of 29 fathoms range from 7? F to 78’F with a

mean of 76°F. During warm season, temperatures range from

68'? to 82'F with a mean of 77°F (Rivas, 1968L

mystical Recruitment and my

According to a study of the biology of red grouper, Moe
(1969) found that this fish species is a protozynous
hermaphrodite. Information concerning sex, aging and growth
of red grouper presented in Moe's paper provided relevant
data for the population dynamics subsystem developed in this
study.

It was also found that ecru ment occurs in the
northern Gulf when young red groupers leave the near shore
reef environment at about 30 cm of length at 3 years of age
corresponding to attainment of sexual maturity. Length
frequency distributions taken in the Campeche Banks fishing
peaks at about 30 cm and sharply declines at H2 cm. This
indicates that the Mexican Fishery is composed primarily of
1 to 3 year old fish on the near shore banks and excludes
the older, large fish in the offshore deeper waters
(Bardach, 1958; Solis, 1969). Therefore, recruitment of red
grguper to the fishery in Yucatan's continental shelf ocean;

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7m36,11g detfiryhgre: R = Average Recruitment
!""Concerning growth, parameters have been estimated for

l
. M )‘~v..
11.,

Fed grouper using Von Bertalanffy's growth equation by a
number of authors. The estimated equations are presented as

follows (Moreno, 1980:12).

Doi et al.(1981):

—O.159(t+1.21) 3
L:80.2 1-e (cm) W:0.0000138L (kg)

Hoe(1969):

-0.179(t+0.u99) 2.9294
L=67.2 1-e (cm) w=0.0000366L (kg)

Huhlia (1976):

-O.112(t-0.09) 2.5895
L=928.ou 1-e (mm) w=o.ooo1u791L (g)
(14:2‘ ‘ ttin‘

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. iflfik Io predation mortality information was found for this

species.

With respect to fishing mortality, factors that
determine the levels of fishing effort and corresponding
fish catch are discussed in sections dealing with open
access and regulated fisheries. In both of the above
mentioned reports, fishing mortality was estimated in the
interval of [.15 to .24]. The available information
concerning natural and fishing mortality suggests the need
for estimating both types mortalities for each age cohort in
the population structure, in order to conduct meaningful

%ohort survival analysism

MW

There are a number of total biomass estimations
available for the Campeche Bank (Klima, 1976; D01,
Mendizabal and Contreras, 1981). The latter provided a
figure of 138,000 metric tons. This estimate was also
reported in the second Joint meeting of the West Central
Atlantic Fisheries Commission (Comision de Pesca para el

Atlantico Atlantico Centro—Occidental, 1981:"1) It should be

mentioned that for the purpose of this study, simulatiogfiggJVG

.9..rfint will he conducted using the figure mentioned abog;uf”

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This method involves a black box approach to modelling
which is concerned only with inputs and outputs to the t
I biomass of fish population. Biomass regeneration, :1

considered as a single process, is the basis of the first

and simplest type of model, called surplus yield, surplus

Illa

production, or the Schaefer model (195R). '
Versions of the surplus yield model differ in their

choice of exact form of the rate of change of biomass in the

population (Pitcher and Hart, 1982). The most common forms

are those developed by Schaefer, Fox and, Fella and 1

 

Tomlinson. Schaefer's (1959) classical model used logistic
growth, an S-shaped curve, similar to Graham's (1935) model. k1

Schaefer growth of biomass is presented in equation (1):

 
  
     
    

....... = k are) (1- (mu/3..) - c (rm) (1)

Where:
3(t) = Fish biomass in time t.

%5 Maximum biomass which could be supported by the
11 ,"
m2;-

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k a hiomass growth rate

      

  
   
 

 

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. ”hiuetton is the following:

   

1' infi‘ "’ x' ' !
dB(t) fl
aka...- a k B(t) (-ln (B(t)/B°°)) - C(E,q) (2) .1
dt 1
Falls and Tomlinson (1969) developed a model version 3

l whose growth in biomass was continuously variable in shape,

which involves fitting an additional parameter, m.
...... = k B(t) (1 — B(t)m-1/&n) - C(E,q) (3)

According to Pitcher and Hart (1982:225): “It is
crucial to realize that predictions of maximum and optimum
yield from these types of models depend entirely on the
exact form of the growth function, so it is very important
to choose the one which best resembles the growth of the

stock in question."

and effort data, the type of information accumulated over
many years in most fisheries. As Pitcher and Hart
(1982:232) have pointed out:

MSY (Maximum Sustainable Yield) is seductively easy to
calculate, in fact no biologists need be employed‘in
the fishery and managers do not even have to get the
hands and feet wet in examining actual fish. issue
Just as the assumption of a single biomass re; 11
,‘IUnction provides the surplus yield app ,4,

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Aflxaniaaes and Limitaiicnsi The major practical advantage )‘
of surplus yield approaches is that they require only catch t

  

   

f fiugiieal biological processes which actually generate
“JLI:s; through time. It is well known that changes in
Dialass are made up of contributions from the separate but
2;;sracting processes of recruitment, growth and mortality,
which were pointed out at the beginning of this Chapter. In
addition, population processes may be altered by different
age structures in the fish population and age structure is

also ignored by the surplus yield approach (Jensen, 1973L

Assumptions. Some of the most relevant assumptions involved
in the "Surplus Yield Model"are the following (Tyler and
Gallucci, 1980; Zubey and Jones, 1978):

1. The model deals only with equilibrium yield, meaning
that stock structure and age distribution of the catch
have stabilized at the current level of fishing effort.
Therefore, high rates of change in fishing effort levels
will invalidate application of the model.

2. Biotic and non-biotic factors affecting resource
ecosystem are assumed constant.

3. The rate of recruitment and the natural mortality rate
are assumed constant regardless of stock size.

n. The rate of population growth is assumed independent of

the age composition of the population.

 

to the catchable stock is not involved in the model.

    

5. The time lag between spawning and recruitment of progeny ‘-

    
  
  

 

 
      
  
   

   
 

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_‘dIal with multi-species fisheries, where multiple species
5::rbeing caught in the same fishery at the same time.
idalter (1973) pointed out that the rate of change in
biomass now was likely to be influenced by past biomass
just as much, or even more, than by current biomass level.
-Walter (1978) made a further important advance by
considering the actual fishing effort which should be used
when variable recruitment is incorporated in the Schaefer
Model.

-Beddington and May (1977) and Schnute (1977) included
environmental randomness in the surplus yield model.
-Hilborn (1979) and Uhler (1980) have compared Schnute's
method with the standard estimation techniques using
simulation approaches. They found that Schnute's method is
the least likely to be biased.

As can be observed from the above section, neither the
original model nor current extensions of the surplus yield
method, have developed the fishing effort function, C (E,q),
more than specifying it as the result of constant fishing

effort, E, and the catchability coefficient, q, using a

particular gear.

Wmum

A Bioeconomic models of fisheries presuppose an:
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“ relat iv‘
'.3E' equilibrium. Biological equilibrium of the fish stock

‘ Fm
“‘Afittaoined when additions through individual growth and

'"pp‘. -
Efiocruitment are balanced by reductions through natural and

fishing mortality. Economic equilibrium of the fishery is
achieved when revenues equal cost such that there is no
incentive for fishing boats' entry or exit. The two
equilibrium conditions are interrelated because fishing
mortality affects stock growth and because stock size
affects catch per unit of effort, and consequently revenue
per unit of effort (Anderson, 198“; Clark, 1985»

It should also be mentioned that another common
denominator in the fisheries economics literature is
recognition of the failure of market institutions to utilize
common property resources in a way which maximizes
individual benefits without exhausting the fishery itself
(Gordon, 1954; Crutchfield, 1969; Clark, 1976; Anderson,
1977; Bell, 1978»

In the discussion that follows, both open access
equilibrium and regulated equilibrium are analyzed to
illustrate the need for government intervention in the
management of ocean fisheries.
ngn Aggggs Eggiljbgigm, In models of market-oriented free

enterprise economies, the fishing industry is characterized

‘by the following assumptions: :gg

(i) Fish are homogeneous

5 7 {here are numerous vessels and be
'nal cost of prceuczn the

 

V)
l-'-‘

I
.1: ~ 1: ‘l,7j.!‘flf" r'*«cioi& .nutndlliu

a, « _ . - f :4 ‘thbs nsnw beat.

_1 » 115
l
I. VJ‘ALj‘
r
,1
-1nsoal
-‘:f£ups
.‘.0m
'1‘.
%
J. J
7
I
‘ s
‘ 7 uklfei
- -';anan
seal bedoa;1c~3saa — ,. ’ ,

 

     

15.830318113 81 \"1. auzln. wit-””1 ...,-
. ( _ _ .a” 4;. . I

.._ ,sn.mono:s 3a71Q193no

   

:ssoisqnuees saiwoilolnldfi ‘

.:_J'

  

 

 

    

 

 

    

 

M02 .

 

 

 

P1
P2
I
I
AC1 L : ‘~D
0 C1 C2 Catch/t
Figure 1. Open Access Equilibrium. (Adapted from Bali, 1980)
The intersection of DD, the demand curve, and MC the
marginal cost curve (Point e) is of particular interest At

that point, price is P1 and the corresponding total revenue

(TB) is P1c1. At that level of harvest,

average cost is AC1
and T61 = (AC1)C1. Therefore,

TR>TC and consequently at
point e fishermen would be earning an economic profit well

above normal. However, at point e, society through

individual action has allocated units of effort so th at
marginal cost producing the last fish is equal to what

consumers are willing to pay.
$91.2.

2.4. .2.

3 ', any production to the right of e is sot-apt:

     
 

 

 

34

called MEY or Maximum Ecggomic Yiglg.
It should be mentioned, however, that MEY’is*un§tabl§

with a common property resource since TR>TC and fishermen
are earning an economic profit. Since entry to the fishery
is relatively easy, the above normal returns, economic rent,
will encourage more fishermen to enter the fishery. Catch
will increase thereby lowering prices and raising MC and AC.
Entry will continue until AC = D at point f. When this
point is reached, market equilibrium is attained since TR =
TC. No entry or exit should take place and economic profits
will be zero.

Therefore, as most fisheries economists have pointed
out, the free enterprise system will lead in the case of
common property resources to overproduction and consequently
to an excess number of fishermen and vessels in the fishery.
As a result, with this excessive fishing effort the fishery
may reach levels of exhaustion and in some cases to
depletigg of the fish species.

It should be mentioned that Open access equilibrium can
also»be‘ana1yzed when considering multispecies fisheries,

like in the case of the red grouper (Epinephelus morio)

 

fishery of the Peninsula of Yucatan that also involve

substantial amounts of catch of white grunt (Haemglo

:3

 

alumierl) as well as yellow tail snapper (93mm;
ELLX§2L1§), among other species.
Ellen Assess Eggiligngmo; Multi species Fishegigs, May et

8141979), Anderson (1977), Pauly (1979). ROthSChild (1967)

 

 

35

recognized that in some fisheries the gear comes into
contact with stocks of different species and, as a result, a
mixed catch is obtained. This is usually the case in
tropical demersal fisheries like red grouper using handlines
and longlines in which a variety of other fishes (like those
mentioned above) are also caught from the coral reefs and
rocky bottoms of tropical ocean ecosystems.

This is the case of a traditional fishery of the Port
of Chicxulub in the Peninsula of Yucatan, which consists of
a group of boats“ with non-discriminatory gear, harvesting
fish from a number of independent species such as red
grouper, yellow tail snapper, and white grunt, among others.

The quantity caught of either type of fish depends upon
the effort used the size of the respective populations, and
the degree to which the fish species associate with one
another.

Each species may have a normal populatign equilibrium
93113 as represented in Figure 2.

“Usually of 1-3 tons of capacity and 18 to 24 feet of
length.

 

 

36

Population 4r
She

   

Populanon
EquiHbruun Curve
of Red Grouper

    

 

 

 

E3

Fishing Effort/Unit of Tune

Figure 2. Population Equilibrium Curves of Multispecies
Fisheries.

Applying Anderson's (1977) analysis of multispecies

fishery to this case, we can observe from Figure 2 the

following:

(1) Without predation by man, red grouper will have a

natural population equilibrium size cM‘ P1.

Similarly, the natural population equilibrium curve

of yellow snapper will be P2.

(11) with fishing effort E, a new equilibrium will be

reached, at lower population size, like P3 and Pu

 

 

 

37

respectively.

(iii) When fishing effort reaches E2, the stock size of
yellow snapper will be zero but that of red grouper
will be P5,

(iv) When fishing effort reaches E3, the population of
red grouper will also be destroyed.

It should be pointed out that Anderson's analysis
assumes equal catchability of the two species. The downward
sloping shape of the population equilibrium curve reflects
the resulting smaller levels of fish population as fishing
effort increases.

In the same manner we can also derive the sustained
yield gpxygs for each species, using the surplps yiglg
apprgggh discussed in the preceding section. The total
sustainable yield from the fishery is the sum of those from
both species. In Figure 3 we can observe that with fishing
effort E1, the equilibrium yield of red grouper will be Y1-
With this same level of effort, traditional fishermen will
also be harvesting Y2 units of yellow snapper.
Consequently, the total sustainable yield at this level of
Y1 and Y2. The total revenue earned will depend on the
relative prices of the two Species.

The fishery will reach maximum sustainable yield, MSY,
at the level of effort where the sum of the individual

sustainable yield is a maximum.

 

 

 

 

38

 

 

 

 

‘l
Ynfld
Sustainable Yield Curve
Y1.---‘---- f
Y - ----- - «- -I ------ O
: : Red Grouper
l I
| I
I a
I I
l I
' I
I
I l' -
jIE1 |E2 .-
| I
l I
l I
I , E/T
ll : .
I 1
Yield : I
I I
I I
I I
I I
l lSustainable Yield Curve
. |
I of
I
I Yellow Snapper
I
I
I
|
I
Figure 3. Sustainable Yield Curves of the Two Species

Source:

After Anderson (1977)

 

 

 

39

It should be mentioned, however, that to operate at MSY
in a multispecies fishery makes even less sense than in
fisheries of a single specie, because that criteria does not
take into account the relative market values of the two
species.

This consideration leads to the representation of the
Maximum Economic Yield criteria, MEY, which would take into
account the relative prices of both red grouper and yellow
snapper.

As a result, we obtain a sustainable total revenue
curve for the fishery by the vertical summation of the
revenue curve of two species. This is represented in Figure
1L The shape of this curve depends upon: (H) the shape of
the individual yield curves and (2) the relative prices of
the two types of fish.

From Figure A we see that the shaded area corresponds
to the revenue earned from yellow snapper5. Beyond fishing
effort 52, yellow snapper is exhausted and consequently
revenue is obtained only from red grouper.

The gpgn access piggcgngmic equilibrium of the fishery
is achieved at that level of effort where total sustainable

revenue,TR,equalstotalcost,TC1.

 

5Below the shaded area the revenue is derived from the
grouper catch.

 

 

 

U0

   
  
   
   
 

 
  
  
   

 

 

Population
by
‘1
Weight
POpulaflon
Equilibrium
'3
Population (Red Grouper)
Equilibrium
(YeHow Snapper)
E2 ES
Fishing El‘fort/t
$ ‘1

TC

...-..---.-----...-....-1

 

   

  

E2 E3 E4 E

Flshing Efl‘ort/t

Figure 9. Maximum Economic Yield of Multispecies Fisheries
Source: Adapted from Anderson (1977)

 

 

“1

In a multispecies fishery, this equilibrium correSponds
to fishing effort Eu (See Figure ll), which is greater than
level 52. This results in the elimination of the yellow
snapper fishery. Consequently, Open access equilibrium may
lead to the depletion pf the gmallgg stpgk in a multispecies
fishery. In addition, red grouper (the bigger of the two
populations) will also be harvested beyond the point of
maximum economic yield5 53. Fishing effort will be expanded
to the point where TC equals TR‘which correspond toleffort
Eu.

It should be mentioned however, that in the case in
which the relative price cost structure is such that the
cost intersects the revenue curve to the left of E2, the
open access fishery will utilize both species.

On the other hand, if a cost curve still intersects the
revenue cost to the right of E2, the use of government
regulatiggs that shift the total cost curve to the left up
to TC (see Figure I) may cause that: (1) the fishery
utilizes the two species, and (2) the depletion of the
smaller stock will be prevented.

In addition to the analysis presented above, Wilson
(1982) has discussed an institutional approach to the
complexities of multispecies fisheries, pointing out the
relevance of transactions costs and the form of

organization.

 

6At this point, the slopes of the TC and TR curves are
equal, and consequently marginal revenue equals marginal
cost.

 

“2

It should also be mentioned that a number of authors
have applied the Lotka-Volterra model to multispecies
fisheries to determine the possibility of existence of
predator-prey relationships as well as competition. All of
these analyses indicate the need for management strategies
that take into account the high diversity nature of tropical
demersal ecosystems.

The need for government intervention to avoid the
'tragedy of the commons" which is more dramatic in the case
of multispecies fisheries, leads the discussion to the next
section which deals with recent theoretical developments of

what is called "regulated equilibrium."

Regglatgg Equilibcium
Recognition of the need for regulating commercial
fisheries to overcome market failure involved in open access
equilibrium has resulted in a number of research efforts in
the fisheries economics literature (Hannesson, 1978;
Crutchfield, 1979; Clark, 1980; Anderson, 1983).
In his "Preliminary Theory of Fisheries Regulation
Development," Lee G. Anderson (1983:2) pointed out that:
A theory of regulation development should focus on
various aspects of the regulatory process so as to
describe what can be called a cegglatory equilibrium
position. Given the structure of prices and costs, the
population dynamics of the fish stock, and ease of exit
and entry, this equilibrium will be a function of the
regulation techniques used and the way they are
enforced.
Even though Anderson recognizes that the important

aspects of the regulatory equilibrium will be the level of

output, the efficiency of production and the administrative

 

“3

output, the efficiency of production and the administrative
and enforcement costs, he fails to recognize what Professor
Schmid (1978) has defined as "substantive performance" of
alternative policy actions. Substantive performance is
evaluated in terms of the distribution of wealth effects of
available public choices.

But before getting into the discussion of criteria for
evaluating an ocean fisheries regulatory system, it seems
appropriate to list some other goals that a society may wish
to attain in fisheries management:

(1) Maintenance of balance of payments equilibrium
(ii) Reduction in structural unemployment
(iii) Provision of recreational activities
(iv) Regional and community nutritional improvements,
The above mentioned desired outcomes of fisheries
management may be used as system performance variables in

addition to achieving bioeconomic equilibrium through time.

WWMW

In addition to the surplus yield and bioeconomic models
discussed above for both independent and multi-species
fisheries, more complex models have been developed to
represent the dynamic nature involved in the management of
renewable resources.

The dynamic pool approach has been characterized
basically by (1) the separation of processes which alter
fish population biomass ix) be described explicitly as

components in the model, and (2) the population age

 

 

 

uu

structure.

The simplest formulation of the theory of fishing
(Russell, 1931 - from Cushing, 1968), clearly identified the
four main processes taking place in the fishery. Two of
these, recruitment of new individuals (R) and tissue growth
(G), added to stock biomass, whereas the other two
processes, natural mortality (M), and mortality from fishing
(F), reduced stock biomass.

Pitcher and Hart (1982:251) developed a diagrammatic
model of a fishery with the loss and gain rates correctly
identified (Figure 5). The solid lines of Figure 5
represent £193 of biomass and broken lines represent
influence; which alter the rates of change. It should be
mentioned that net migration has been included in the
diagram to make it more realistic.

Each of the five processes in fishing could be broken
down or decomposed into submodels, and a major issue in the
modeling process is to decide how far this decomposition
should go. It can be observed that the "recruitment sub-
model" could be elaborated to include egg and fry survival
and growth and survival of the prerecruit stages. Concerning
recruitment of tropical demersal resources, Pauly (1986)
suggests that one consider spatial differences in
recruitment and seasonal fluctuations of recruitment.
Natural mortality, representing losses to predators,
senescence and disease, could further depend upon predators'

feeding habits, pollution and spawning stress.

 

 

Environmental
Variables
e.g. Temperature

#5

 

Recruits _
R IIIII£IOIIMIIOIIIIIIOIIOIJ

 

 

 

Growth Rate.

G

Recruitment

Rate, R

 

 

 

Neon-...;

 

Carrying
Capacity
of the
Ecosystem

 

 

 

Y

 

 

 

II...0......III-II‘IIOIOCICUIIICIII‘

Competition
fo r
food

5”“‘IIHICCOIOOOOIIOCCDIIW

 

Stock Biomass

Exploitable.

 

 

A

Environmental
Variables

V

Reproduction
Egg Survival
Fry Survival
and Growth
Pre-Recruit

Survival and
Growth

I...IIIIIIICCOCIIOOIIIIOIIIIIICCI-CUIIICCOIOICIIDI'

POO".-IOIUIIIIIIIOIOIIOO:

 

E

nvironmental
Factors
Disease

Senescence

 

 

 

’OII-UUIICCIIIOOCCIUCOCO-III...-

Fishing
Mortality Rate,

F

 

 

Management

Non - BiOtiC I.....“IIRIIDIOOIIIII-I.........n...
Factors

 

Yield

to
Man. Y

 

Natural

Mortality Rate. N

 

1

,t

 

 

Ecosystem

 

 

 

 

Net Migration

 

 

§¢

 

CW... D
C

 

Biotic
Factors

D

Figure 5. Diagram of the Main Processes Modelled by the
Dynamic Pool Approach to Fisheries Management.
After Pitcher and Hart (1982).

Source:

 

 

 

46

The fishing mortality rate could also constitute a sub-
model by making it a function of time varying fishing
effort of different groups of fishermen which use different
technology and consequently involve various levels of catch
per unit of effort, CPUE. In addition, the number of vessels
in the fishery may vary over time, because of the entry and
exit mechanisms that take place when TR x TC.

Net migration could also be further decomposed when
making it a function of biotic as well as non-biotic
factors which determine the spatial and temporal behavior of
species.

The dynamic pool models are based on the initial works
of Beverton and Holt (1957) and are basically presented as a
set of four integral equations, which lead up to a function
estimating the yield from the fishery.

-The first equation states that the total numbers of
fish in the stock in time t, N(t), are given by the integral

of numbers at all ages 1:

t
N(t) = -/. Ni(r) d1 (u)
tr

Where:

tr - age of recruitment to the fishable stock.

t the maximum age of fish in the stock.

N1(t) = numbers of fish of i different ages.

47

- A similar integral gives the numbers caught, C(t),

as:
t
C(t) =f F1”) Ni(1') dT (5)
tr
Where: tr is the actual age at first capture by
the gear used in the fishery.
Fi(t) is the instantaneous rate of
fishing mortality on age 1.
- The biomass, B(t),.of the fish stock can be
calculated as:

t
/; Ni(T) widT (6)

l“

B(t)

Where: W1 is the mean weight of fish aged 1.

- The total yield, Y(t), from the fishery can be

expressed as:

t
Nth-j; rim vim wi d7 (7)
1"

Equation (4) is the general yield equation underlying
all dynamic pool models.

In order to solve equation (u) analytically, Beverton
and Holt hadtto make a number of simplifying assumptions and

choose suitable functions for F(t), N(t), and Wi.'

Aiiflmflfiignfi. Among the assumptions, the one that must be
relaxed is concerned with assuming constant fishing
mortality. It fails to account for forces that may

influence harvesting behavior of fishermen over time.

48

This assumption might have severe effects on policy
impact analysis of fisheries management programs, because:
(1) In the case of marine commercial fisheries one of the

most important controllable variables within the model

is the fishing mortality or harvesting rate. This
implies that when a comprehensive simulation model is
run to measure impacts of different policy instruments,

1; may pggyigg migleadigg gutguts as a result of not

taking into account:

(a) sayingnmegta; attitgdes of different groups of
fishermen regarding their intertemporal
preferences in the use of fish resources.

(b) The gififlecegt type; 9; technolggy used by the
different groups of fishermen.

(c) The Lgtgs 9; response of fishermen communities to
institutional changes and innovations.

(2) The sgcig-econgmic impact analysis of different policy
instruments cannot be carried on efficiently when
the social dimension of a model is highly aggregated if
not neglected. This type of analysis is especially
useful in countries where the government is playing an
increasing role in controlling the use and development
of renewable natural resources. For instance, it is
fundamental to be able to measure the distribution of
income and employment effects of alternative courses of

action.

 

 

”9

fixtggglggg 91 the flgyectgg-Holt flgdgl. There have been

extensions to the Beverton-Holt model, some of which are

summarized as follows.

-C1ayden (1972) simulated the fishing effort and catches of

15 coastal nations over 23 years.Ten dynamic pool models

were built and run, each of which had 15 sub-models

representing the fishing efforts of each of the fleets.

Fishing mortality was assumed proportional to effort and

constant over all ages in the fishery.

-Garrod and Jones (197“) developed a simulation model for

the Arcto-Norwegian cod fishery describing growth by a
conventional von Bertalanffy curve but included a Ricker
recruitment equation.

-Walters (1969) also used a Ricker curve in the simulation
of the Arctic cod stock. The Ricker curve used by Walters
was not as complex as the version used by Garrod and Jones.

Wilson (1979) used a randomized recruitment sub-model on a

freshwater seine and trawl fishery.

-Swartzman et a1. (1983) developed a fisheries management
algorithm which included an age structured stochastic

recruitment sub-model. This effort provides a significant

aid in the analysis of fisheries that exhibit substantial

environment-dependent recruitment variability.

Smith et al.(1982) built a simulation model that

incorporated the human dimension through a decision-making

feedback mechanism.‘This modeling effort included some of

the biological and social factors that affect fisheries

resources and their use over time.

 

50

Fisheries Management.Alternatives

Fisheries management involves a decision-making process
that faces a set of regulatory problems that could be
classified as follows:

.Eflflfléflinzififl£h.Qmmxfiuiign

In open access fisheries (unregulated fisheries) fish may be
harvested even when they are too small, or fishing in
certain locations at certain times may interfere with
spawning and recruitment, thereby reducing yield that could
be achieved with discriminating fishing, even with the same
amount of effort” As a result, fisheries agencies in most
coastal countries have imposed: (1) minimum mesh sizes and
other controls on gear selectivity,(2) introduced closed
seasons and (3) restricted fishing in certain areas like
estuaries, to protect and enhance the productivity of fish
stocks (Pearse, 1980).

Essul§£l££.§§££h §iz§

The determination of the desired lgygl f catch is an

 

important concern to fisheries management. It should be
mentioned however, that in addition to the Maximum
Sustainable Yield (MSY), and the Maximum Economic Yield
(MEY) criterias discussed above, authorities in Canada,
United States and other coastal countries have adopted the
"optimum yield" criteria. The latter criteria has been
developed to provide the maximum benefit to the nation in
accordance to biological, economic and socio-cultural

considerations.

 

51

In order to control catch size, coastal nations have
usually adopted a variety of regulations that affect fists;
snpnn; 2; fishing effiort. .But,tx>effectively manipulate
control variables to attain a desired level of catch, it
seems appropriate to first determine variables that
determine total fishing effort and then consider the main
types of regulations that affect those variables.

As recognized by Anderson (1977), fishing effort is a

function of:

(i) The nnmbsr of fishing boats

(ii) Their individual haryssping power (type of

fishing gears)

(iii) Their spspis; distribupipn, and
(iv) The total time spent fishing.

 

Given that the fishing effort is a function of the above
mentioned variables, the set of regulations that seem to
affect them may be classified as (1) Limited entry of
fishery (Rettig and Ginter, 1978), (2) Gear selectivity, (3)
Fish quotas, (A) Taxes and/or subsidies, and (5) Restricted

fishing areas.

Maintaining Erficisncy in the Fishing Prpcsss

A third source of regulation efforts is related to the
concern that most coastal states have of achieving and
maintaining economic efficiency in fishing. The problem of
gygrsxpsnsipn is often seen as one of too many vessels, but
as pointed out be Pearse (1980),'Ht.is only a superficial

52

manifestation of the more fundamental economic problems of
excessive employment of labor and capital, and therefore
excessively high opportunity cost fishing."

It should be mentioned, however, that whether labor inputs
are or are not excessive is also a function of the socio-
cultural context of the fishing community. This is the
case, for instance, of traditional fishing communities which
have a segment of the fishing industry exercising fishing
effort for mainly "subsistence" purposes.

Redistribnping Wssith

Some countries, such as Mexico, have designed institutional
structures to foster redistribution of wealth. This has
been done tur allocating exclusive property rights on
specific fisheries to groups of low income fishermen. In
the case of Mexico, this allocation of property rights has
fostered collective organizations by requiring fishermen to
form fishing cooperatives to be subject to exclusive fishing
rights and state subsidies.

Other types of problems in ocean fisheries that have
usually called for regulatory schemes include interventions
to: (Scott, 1979)

- Protect product quality
- Improve working conditions
- Prevent monopolistic practice

In snnmary, there are four major sets of government
interventions discussed in the literature of fisheries
regulations, each of them attempts to solve specific

problems of coastal fisheries. An appropriate combination

53

of interventions that regulate the composition and size of
the catch, and maintain efficiency in the fishing process
may be used to achieve spns goals of the regional community.
However, as mentioned in the section on regulated
equilibrium, there are other desired outcomes or goals that
decision-makers may wish to attain such as reduction in
structural unemployment, redistribution of wealth, etc.
Inclusion of the additional goals as system desired outputs
requires that alternative regulatory schemes be evaluated in
terms of their impact on those performance variables.

After discussing alternative modeling efforts and
management strategies, the following chapter will present a
comprehensive simulation model based on the systems

simulation approach.

CHAPTER III
RESEARCH METHODS

The research approach used in this study is presented
through the discussion of the following sections: (1) the
study objectives, (2) the study region, (3) the systems
simulation approach used for the development of the red
grouper fishery model, (A) data collection for parameter
estimation, (5) development of mathematical and computer
models, (6) sensitivity analysis and model validation, (7)
Monte Carlo analysis for the estimation of uncertainty in
system performance, and (8) simulation of resource

management alternatives.

Study Objectives

Given the context of the problem, the main objective
of this study is the integration of biologic, economic and
institutional factors using a system simulation approach to
provide emu operational. simulation model for demersal
fisheries resource management. An additional objective
involves conducting dynamic impact analysis to simulate the
effect of alternative management strategies on a set of
performance variables. These include red grouper biomass,
fishery yield, net revenues of traditional and modern
vessels, direct employment, food availability in coastal

rural communities, and export earnings.

 

 

55

The following section discusses the study region

selected for this research effort.

Study Region: Yucatan Continental Shelf

The geographical study region selected for this
research project is the continental shelf of the Peninsula
of Yucatan. Boundaries of this region involve both
political/administrative and ecological considerations (see
Figure 6). The area covering this region is consistent with
the regionalization developed by the Ministry of Fisheries
for planning purposes. There are ten ports included in this
region: Celestun, Sisal, Chuburna, Chelem, Progreso
(Yucalpeten), Chicxulub, Telchac, Dzilam Bravo, Rio Lagartos
and El Cuyo. The major target fish in these ten ports is
the red grouper (Epinepheips ngnjp). It accounts for 27.9%
of the total fish catch in the State of Yucatan (Secretaria
de Pesca, 198A). ‘The study region also takes into account
the migratory patterns of this species and the fishing
grounds most commonly selected by the different types of

fishermen of this coastal area.

mm MW bu 0

According to Rivas (1970), the depth range in which red
grouper is found in the Gulf of Mexico is between 3 to 58
fathoms. In the Southern Gulf, about 70% of red grouper
records extend from 25 to 33 fathoms. Juveniles of the red
grouper population occur in shallower than the mean depth,

while the adult population is usually found deeper than the

L24’

 

~23:

:22'

 

 

 

5“”.
‘Eal

 

56

 

95°Iong. w 8'9" 88" 37°

    
     
    
     
   

   

-21° PENINSULA -
OF
YUCATAN
i Cllcstu'n 6 Chlcxlolub
-200 2 Sisal 7 “it“!!! _

   

     
          
  

3 Chuburnd B Dzilam Bravo

4 Choi-‘m 9 Rio Loganoa

 

10 El Cuyo

 

5 Progrggo

 

 

Figure 6. Study Region: Yucatan Continental Shelf.

 

 

57

mean depth. Those weighing less than 3 pounds were recorded
in depth of less than 15 fathoms, and those weighing an
average of 11 pounds were taken at more than #0 fathoms.

One interesting feature of this study region is the
fact that different types of fishermen apply their fishing
effort at different depths because of the size
characteristics of their fishing vessels. Most traditional
fishermen use boats with capacity of 1 to 3 tons and
consequently tend to fish closer to the shore (usually at
depths of 3 to 15 fathoms, where most of the juvenile
population is found) as compared with fishermen organized in

cooperatives or private fishermen which own larger and more

capital intensive vessels.

Eisnipg Efifprt Charagpsristics in the Study ngion

This study region is characterized as hosting different
types of fishermen involving different: (1) sizes of vessels
and fishing gear, (2) levels of catch per unit of effort
and, (3) age composition of the catch.

The fishermen involved in the red grouper fishery can
be grouped by type of technology in two major categories:
those who use traditional fishing methods in small vessels
(22 to 30 feet long) and those who use capital intensive
technology in larger vessels (#0 to 75 feet long). Given
that these two groups apply different fishing effort, they

usually have different catch levels per unit of effort.
(humently there are 1500 fishing vessels that have the

characteristics of the smaller Type I vessel. However, it is

 

 

 

58

estimated that only approximately 970 are applying their
fishing effort to the red grouper fishery. The rest are
focusing on other coastal fisheries such as shark, lobster,
anchovie, sea trout, snook, king and spanish mackerel, etc.

Concerning the larger Type II vessels, approximately
230 are oriented to the red grouper fishery while the rest
are targeting red snapper and shrimp species (Secretaria de
Pesca, 1984). A more detailed description of fishing effort
by type of vessel is presented in the survey results section
of Chapter IV.

The approach selected to study the above described

fishery is presented in the following section.
Systems Simulation Approach

The system simulation approach is a problem-solving
process of 'bbtaining particular time solutions of.a
mathematical model corresponding to specific assumptions
regarding model inputs and values assigned to parameters"
(Manetsch, 1982:8-1). Shannon (1975) defines simulation as
the process of designing a model of a real system and
conducting experiments with this model for the purpose of
either understanding the behavior of the system or of
evaluating various strategies for operating the system.

The primary reason for using simulation is that many
models cannot be adequately analyzed by standard
mathematical techniques such as Laplace transformation

(Payne, 1982; Manetsch and Park, 1982). This is usually the

59

case when the interactions between variables are nonlinear
or when random effects are inherent in the system.

As recommended by Professor Manetsch (1975) there are a
number of basic steps involved in the process of system

modeling. They are discussed in the following subsections.

Systsm Identificatipn

This major step results from linking;the statement of
needs and a specific statement of the problem to be solved,
which was discussed in the above sections and is summarized
as follows.

In coastal communities in Mexico, located in the
Peninsula of Yucatan, there are mainly two groups of
fishermen. One group that could be described as "modern"
iflsnernsn (fishermen cooperatives and private sector
corporations) who use capital intensive technologies and
more complex fishing gear, and another group represented by
Jfirggjtipnsij fishgrmgn (fishermen of coastal rural
communities) who use small boats and rudimentary fishing
gear. The former base their fishing effort using state
owned fleets or private sector boats. These are business
oriented fishermen having as their major goal profit
maximization. The latter group is involved in fisheries
primarily for subsistence purposes.

Another important actor in this fisheries community is

the federal government represented by the Minispry pf
Elahsniss.

60

The major goals of the Mexican government concerning
the fisheries sector can be described as follows:

(Secretaria de Programacion y Presupuesto, 1983:304)

(i) To contribute to improvement of the nutritional levels
of the population;

(ii) To generate employment mainly in depressed or
stagnant coastal regions;

(iii) To increase the inflow of foreign exchange through
exports of fisheries products;

(iv) To promote regional and community develOpment to

improve the standards of living of fisheries workers;

(v) To sustain the yield (biologic and economic) of its

major fisheries over time.

Both groups of fishermen as well as decision-makers

from the Ministry of Fisheries lack information concerning

 

the population dynamics of the red grouper and impacts on
the yield of the fishery over time resulting from their
fishing efforts and regulations respectively.

Figure 7 identifies the fishing system, including
definition of exogenous and controllable inputs, design

parameters, and desired and undesired outputs.

61

Environment

Exogenous Inputs

'0

 

Overt Controllable
Inputs Sources
(i) Goverment

(i) Traditional
and _ modern

fishermen

Overt Required Input:

 

-Gasoline_
- Ice D
- Bait.etc.
Figure 7. Red

FISHERY SYSTEM

Red grouper population dynamics

function of different
(Fishing

‘Production
groups of fishermen

effort functions)

-Bioeconomic equilibrium conditions

 

 

0-

System Design Pa rameters

Grouper Fishery:

Desired Outputs

- increase
income levels

- Increase
nutritional
levels

— Reduce
unemployment

- Sustained
yield of

fishery

Undesired Outputs

-Fishery
exhaustion
-Ma ldistribution

of wealth
(fish resources)

System Identification

 

62

Q_sir§g thppts. The system desired outputs are the
following:
a. Increase local income and employment in the regional
community. This desired output is measured in terms of:
-Direct income effect in the Yucatan fishing community
by type of fishermen. Pesos/year
-Community Employment Level by type of fishermen. Man
hours/year
b. Increase community food availability.
-Community fish availability from traditional fishermen
catch. Tons of fish/year
c. Increase profit of both traditional and modern fishermen.
-Net revenues received by type of fishermen.
Pesos/year
d. Increase export earnings.
-Red grouper export earnings. Dollars/year
e. Sustain the yield of the red grouper fishery over time.

- Biomass level. Tons/year

Endssirsd Quipygs. The fishery system undesired outputs and
corresponding performance variables are the following:
a. Dissipation of economic rent.
-Economic rent by type of fishing vessel. Pesos/year
b. Exhaustion of the red grouper fishery.
- Red grouper biomass level. Tons/year
c. Exhaustion of other species resulting from mixed catch.

-Yellowtail snapper and white grunt biomass.

Tons/year.

 

63

Envirpnnental (Exogenous) Inputs

a. Weather conditions in the Gulf of Mexico.
- Wind in miles/hour
- Seasonal. bottom water temperatures. Celsius degrees.
b. Government budget constraint.
- Fisheries Development Bank budget to finance fishing
vessels (pesos/year)
c. Prices of red grouper for local market, processing and

export market in pesos/ton and dollars/ton respectively.

Overt (CpntrollapieQ Inputs. Includes variables that can be

ganggsg during system operation to alter the performance of
the system in providing desired outputs.
(1) Ministry of Fisheries

- Regulations affecting the size of fish caught.
Minimum size of fish in cm.

- Regulations affecting the amount of fishing effort.
Maximum number of fishing vessels/year with
specific types of fishing gear.

- Allocation of the Ministry of Fisheries budget for:

(1) financing vessels and fishing gears, (2) research

and extension programs, (3) public investment in

coastal infrastructure. Pesos/year.

-Direct investments in fishing fleets. Pesos/year.

(ii) Traditional and Modern Fishermen

- Amount of time dedicated to the fishery. Days/year

- Type of fishing gear used.

6U

- Exit and entry to the fishery.

- Number of fishermen per boat. Man-hours/year

- Capability of changing to another fishery if
necessary.

- Willingness to use new technology if available.

- Conservation attitude of different groups of
fishermen representing their intertemporal

preferences in the use of resources.

Overt (Necessary) Input . Inputs necessary in order for the

system to function. This type of input basically includes
gas and oil, fish bait, ice and food. They are an important

component of the fishery variable costs.

Essign Parameters. Important decision variables which are

attributes to the system structure and have an impact upon

the system desired output.

a. Selected classification of groups of fishermen according
to their fishing technology.

b. Production functions or fishing efforts of different
types of fishermen according to size of vessel used
(length in feet), effective fishing time (days/year),

types of fishing gear, and labor (man-hours/year).

65

c. Red grouper population dynamics
- Application of the "cohort survival method" (Ricker,
1975;Isard, 1975; Pitcher and Hart, 1982) taking into
account the dynamic behavior of fishing mortality.
-Red grouper size in length and weight as a function of
biological age using Von Bertalanffy growth equation
estimates for red grouper of Yucatan's continental
shelf (Doi et al., 1981L
After the system was identified, the model was decomposed

into subsystems in order to handle its complexity.

Mode; Depomposition

This model. was decomposed ixfix: three system sub-
structures that interact to provide the overall system its
unique behavior. Figure 8 shows the red grouper fishery
system decomposed into three interacting subsystems. Figure
8 emphasizes the interface variables, which are the outputs
of one subsystem that acts as inputs to the other
subsystem(s).

As shown in Figure18, interface variables between the
biological and economic subsystem are fishing effort (t) and
fish catch (t). Interface variables between the economic
and institutional subsystem are export earnings (t), net
profits per type of vessel (t), employment (t), management
policies and regulations. Finally, fish biomass (t) becomes
the interface variable between the biological and resource

management subsystems.

RED GROUPER

66

FISHE RY SYSTEM

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Water Mature . Stock of Fish
Availability of Biological B'Omass 4
Nutrients SubsyStem Fish Biomass(t)
Weather
Fish
Cetht) Fishing Effort (ti
Export g Distributional
Earnings (tl Resource Impacts
Management -Nutritional
Subsystem Impacts
Profits
by
ssel ment(
Typelt
Management
Weather Policies and
. Regulations (1)
E c o n o mic - -

i Flsh Prediction
mgtg°gd Subsystem IL Price of Fish
__ Net

L _ Revenues

 

 

Figure 8. Major Components of the

Red Grouper Fishery.

67

WWW

The above system decomposition is presented in more
detail in the system causal diagram shown in Figure 9. In
this causal diagram, solid lines represent flows of fish in
kilograms, solid lines with a $ sign on them represent £l2E§
p; pssps, and broken lines represent infipsnpss which alter
the rates of change. In the left side of the diagram, the
biological subsystem is expressed with the four main
processes that determine the amount of fish biomass over
time: recruitment and growth that add biomass to the
fishery and natural and fishing mortality that reduce the
level of biomass over time. These four processes are further
specified by including variables affecting each of them.

In the economic subsystem fishing effort is made a
function of the type and number of fishing vessel and
fishing gears used, the number of effective fishing days and
labor per type of vessel. Total costs involved in the
different fishing effort functions are obtained by
estimating the corresponding fixed and variable costs.
Total revenues result from the catch allocated to local
market and processing. It can also be observed from the
diagram that a component.of the catch goes for subsistence
consumption in the coastal communities.

Exit and entry of different types of vessels is also
represented in the model through linkages between net

revenues and number of vessels.

68
BIOLOGICAL SUBSYST EM

 

    
  

PHYSICAL

CHEMICAL
FACTORS

  
 
 

o ........-....-.J

 

 

PREDATION
MORTALITY

AVAILABLE
NUTRIENTS

 

NATURAL
MORTALITY

 

PREDATION SENESCENCE

TEMPERATURE MORTALITY MORTALITY

 

LEGEND
flaw of flch

flow of monoy
------------ flow of Inform-clan

 

nouns 9. RED enoupen FISHERY:

 

 

'.
.
...
‘.

'-
...
.
v

POLUT ION
MORTALITY

DISEASE
MORTALITY

   
  

SPAWNING
STRESS
MORTALITY

  
 
 

SYSTEM CAUSAL omenm,

 

 

 

 

 

......
I
FISH
CATCH
:5
I

  

ans-...

..
Ont-"......“
"- . .

 

 

/

“‘""““‘k.......
I

FISHING
EFFORT

rip—c... .

DEPRECIATION

 

 

   
 
 
    

 

 

 

 

 

...-IOU".

 

 

RESOURCE MANAGEMENT SUBSYSTEM

 

 

 

 

EXPORT
PRICE

PRICE
CONTROLS

 

 

 

 

 

 

 

 

 

 

 

 

 

 

      

TA X ES on
SUBSIDIES

 

 

 

 

 

 

 

 

 

69

In addition to biomass level, fish production, net
revenues by type of vessel (and corresponding technology) as
well as how those revenues are distributed among different
groups of fishermen are input variables to the resource
management subsystem. With these spinpis, the resource
management subsystem rssponse involves allocation of
property rights and regulations that affect both the
composition and size of the catch, i.e. influences
management decisions of private firms.

In order to conduct quantitative analysis of the
relationships presented in the causal diagram of Figure 9,
data were collected to fit equations and estimate model

parameters.
Data Collection and Analysis

Data were collected from both primary and secondary
sources to estimate parameter and fit equations of the

mathematical model that will be presented in the next

section.
Elfinary Data Soprcss

Primary data sources were used to obtain information
mainly about traditional fishermen, given that there was no
information available on their fishing effort and catch as
well as their cost and revenue functionsc As a result, a

survey was designed and implemented in the study region.

fiflrvgy Design. In order to obtain the required data, a

questionnaire (see Appendix A) was developed and applied in

70

four of the 10 ports that allocate fishing effort to the red
grouper fishery. The ports selected were Chuburna, Chelem,
Progreso and Chicxulub. These ports were chosen because they
host most traditional vessels involved in harvesting red
grouper. The sample size was estimated using information
from a presampling effort conducted in the port of
Chicxulub. From this data set, the standard deviation of
relevant parameters such as effective fishing time, number
of fishermen per vessel and fish catch were used to estimate
sample sizes and select the larger sample. The standard
deviation that provided the larger sample size was the one
associated with effective fishing time and this was the
sample size eventually selected.

Therefore, in order to be (1-a)% confident that the
error li-uidoes not exceed a value d, the required sample
size from an assumed normally distributed population is the

following (Battacharya and Johnson, 1977):

Zqé. 0
n = ...........
d
Where
n = Sample size
(1 = Significance level
Zq%= Value obtained from the normal probability table.
a = Standard deviation
d = Specified error bound
i .-. Sample mean

C

: Population mean

71

For a 95% confidence level (a :.05), an error d::.30
of an hour and a standard deviation 0 = .816, the required

sample size estimated was n = 28.

It was obtained applying the above equation:

(1.96).816 2

After the sample size was determined, a list of traditional
fishermen was obtained from the Ministry of Fisheries branch
in the State of Yucatan, and a number was assigned to each
fishermen listed . ‘Then, in order to give each member of
the population the same opportunity of being included in the
sample, 28 random numbers were generated from a calculator
and used to select the fishermen to be interviewed.

When the survey was being implemented some of the
randomly selected fishermen were not available to be
interviewed. In these cases, additional random numbers were
generated in) select substitute fishermen to be included in
the sample.

mm Data M5 c

For information concerning modern fishermen, datawere
obtained from a fisheries research institution located in
Progreso, Yucatan (Burgos and and Lope, 198“).

It should also be mentioned that to supplement these
data, interviews were conducted with 'modern" fishermen of
Yucalpeten (where landing of vessels takes place) mainly to
obtain costs and revenues information. In addition,

information was also obtained from government publications

72

dealing with fisheries statistics (Gobierno del Estado de
Yucatan, 1983; Secretaria de Pesca, 1984; Secretaria de

Programacion y Presupuesto, 1982).

Mathematical and Computer Model

A more detailed statement of the system is presented in
Figure 10, a block diagram for the red grouper fishery
system. The purpose of the diagram is to explicitly define:
(Manetsch, 1975)

a. Model components in terms of their input and output
variables.

b. Interactions among model components in terms of specific
variables.

0. Model exogenous variables and their points of impact
upon the system.

d. Policy variables (controllable inputs) and their points
of impact upon the system.

6. Performance variables to be used by decision makers to

evaluate system performance.

This block diagram also facilitates analysis of a
complex system of equations where multiple interactions are
involved. 'To follow this diagram, Table 1 presents a
definition of variables and parameters of the diagram and

their corresponding units of measurement.

 

 

  
  

SRiCDII-DRm

 

(FFi>_1(t)‘SRi_1(t)-FPi(t))dt

 

FPi CD

 
   

 

 

 

 

 

 

 

in
1
fig: 7 {—1.} AT“) _Rll MC 0
dCAT 0:1'fl1-BAFCI) 1 BAFCD
I 1'1 I TRTCD

PT; /J_‘|

 

[HF [m

FBiCt)

 

 

 

 

1~MR SS

NBORN(t) n

  

 

 

(
AFP(t) 12>?

    

     

31
= 0:1 HF +R1l-BAFG)

 

 

PFTTCD TPFTT Ct)

 

  

 

 

decision
block

 

 

 

 

 

 

 

 

 

 

  

 

 

2 EM PCt

decision T
block

 

 

 

 

 

 

 

 

 

 

 

 

 

 

IFBE MFVCt)
TRIPM+R4itl n
+
'=3 /LVM:7
l MFVCt)
DF R2 ‘ TI
. I L4
l3
CMiCD CAM(t):{ 0:2 DF 2+R2‘BAFCO' L
CAMCt) Rnl .
PM-
_EML, PE 1., '
,fl2
d.TCM_[ 72 ”I 1 ]{CAM(t)_R2, M020) 9
dCAM [GQ'BQ‘BAFCI)JllUQI_ BAFCt)

 

72
E‘ TCMctl (2)-FA
+

 

 

 

 

 

EERG (t)

FAC Ct)

 

 

  

 

 

7n

 

 

Table 1. Block Diagram: Variables and Parameters
Unit of
Symbol Description Measurement
ACCi Composition of foreign vessel catch %
by age i
ACTi Composition of traditional vessel %
catch by age 1
ACMi Composition of modern vessel %
catch by age 1
ACTFV(t) Number of traditional vessels entry #/t
or exit per unit of time t
ACMFV(t) Number of modern vessels entry
or exit per unit of time t #/t
a,, 6, Production function parameters kg
of traditional vessels
a,,IL Production function parameters kg
for modern vessels
AFB(t) Adult fish biomass in time t Tons
AFP(t) Adult fish population in time t # of fish
BAF(t) Relative biomass availability 1
factor in time t
CAM(t) Catch of modern vessels per trip Tons/trip
in time t
CAT(t) Catch of traditional vessels Tons/trip
per trip in time t
CATCHT(t) Total catch of traditional Tons/year
fishermen in time t
CATCHM(t) Total catch of modern fishermen Tons/year
in time t
CC Total catch of Cuban fishermen Tons/year
based on a yearly quota
CCi Fishing mortality by age 1 z/Yea’

from Cuban fishermen catch

75

Unit of
Measurement

CTi

DELI

DEL2

DF

DRi(t)

DT
EERG(t)
EGG
EGGS(t)
EMI

EM2

EMP(t)
ENEXT

ENEXM

FBi(t)

FPi(t)

Fishing mortality by age 1
from modern fishermen catch

Fishing mortality by age i
from traditional fishermen catch

Mean delay of traditional vessel
entry or exit to de fishery

Mean delay for modern vessel
entry or exit to the fishery

Average effective fishing
time per trip (modern vessel)

Total mortality rate of fish
of age 1 in time t

Time increment

Export earnings from red grouper
Average number of eggs per gonad
Spawned eggs in time t

Red grouper fillet for export
market

Frozen red grouper for export
market

Direct employment in time t

Entry or exit parameter for
traditional vessels

Entry or exit parameter for
modern vessels

Biomass of fish of age 1
in time t

Fish population of age i
in time t

Years

# of days

%/year

t
Dollars/year
# of eggs

# of eggs/t
%

persons/year

% of total
vessels

% of total
vessels

Tons

# of fish

76

Unit of
Measurement

FST(t)
FMT(t)
FPT(t)
FMM(t)
FPM(t)
FAC(t)

7.

HF

K
Li

MC1(t)

MC2(t)
MFB(t)
MFP(t)

Fishing mortality rate of fish
of age i in time t

Fish for subsistence consumption
in time t

Fish for local market from

traditional vessel catch in time t

Fish for processeng from

traditional vessel catch in time t

Fish for local market from
modern vessels catch in time t

Fish for processing from modern
Vessels catch in time t

By-catch of red grouper fishery
in time t

Constant in total cost equation
of traditional vessels

Constant in total cost equation
of modern vessels

Average number of fishermen per
traditional vessel

Average number of fishermen per
modern vessel

Number of effective fishing time
per trip (traditional fishermen)

Order of the distributed delay
Average length of fish at age 1

Marginal cost of traditional
vessels

Marginal cost of modern vessels
Juvenile fish biomass in time t

Juvenile fish population in
time t

Tons/t

Tons/t

Tons/t

Tons/t

Tons/t

Tons/t

Pesos/ton

Pesos/ton

#/vessel

#/vessel

# of hours

cm

Pesos/ton

Pesos/ton
Tons

# of fish

77

Unit of
Measurement

MFV(t)
MR

NBORN(t)

PEI

PE2

PFAC
PFTM(t)

PFTT(t)

PMI

PM2

PTI

PT2

R1(t)

R2(t)

R3(t)

Rfl(t)

SEAFC(t)

Modern fishing vessels in time t
Natural mortality rate

Fish population of age 0 in
time t

Export Market price of red
grouper fillet

Export market price of frozen
fish

Price of by-catch

Net profits of modern vessels
in time t

Net profits of traditional
vessels in time t

Local market price for adult
fish

Price of red grouper for
processing (adults)

Coastal market price

Price of red grouper for
processing (juveniles)

Random variable of catch
equation in time t
(traditional vessels)

Random variable of catch
equation in time t
(modern vessels)

Random variable of total trip
equation (traditional vessels)

Random variable of total trip
equation (modern vessels)

Seafood availability in coastal
communities in time t

# of vessels

%/year

# of fish
per year

Dollars/ton

Dollars/ton

Pesos/ton

Pesos/year
Pesos/year
Pesos/ton
Pesos/ton

Pesos/ton

Pesos/ton

Kg/day

Kg/day

# of trips/
year

# of trips/
year

Tons/year

Symbol Description Unit of
Measurement

SRi(t) Survival rate of red grouper Z/year
of age 1 in time t

SMI Proportion of fish catch for %
local market (modern)

8M2 PrOportion of fish catch for z
processing (modern)

STI Proportion of fish catch for %
subsistence consumption

8T2 Proportion of fish catch for %
local market (traditional)

8T3 Proportion of fish catch for 1
processing (traditional)

SS Spawning success factor Z

TCM(t) Total costs of modern vessels Pesos/year
in time t

TCT(t) Total costs of traditional Pesos/year
vessels in time t

TFB(t) Total fish biomass in time t tons

TFP(t) Total fish population in time t # of fish

TFV(t) Number of traditional fishing # of vessels
vessels in time t

TRIPM Number of trips of modern # of trips
vessels per year

TRIPT Number of trips of traditional # of trips
vessels per year

TRM(t) Total revenues of modern vessels Pesos/year
in time t

TRT(t) Total revenues of traditional Pesos/year

vessels in time t

TPFTM(t) Accumulated net profits of modern Pesos
vessels in time t

Symbol Description Unit of
Measurement

TPFTT(t) Accumulated net profits of Pesos
traditional vessels in time t

VAR1 Variance of catch equation Kg
(traditional vessels)

VAR2 Variance of catch equation Kg
(modern vessels)

Wi Average weight of fish at age 1 Kg

The specific relationships shown in the block diagram
of Figure 10 are presented in 23 set of equations that

conform to the model structure.

Mathsnatica 1 Mogei

The mathematical model for thelwuigrouper fishery is

discussed in this section by major system components.

Pppnlapion Dynamics pf the Red Grouper. The dynamics of

this biotic resource were modeled applying the main concepts

of the "cohort survival method" (Nisbet and Gurnet, 1982;
Clark, 1985; Gulland, 1977,1983; Ricker, 1975) to develop a

general equation for the population structurelusing Euler

numerical integration. The method is based on the dynamic

accounting of inflows and outflows of each age cohort of the

population structure. The number of organisms in cohort i

in time t+DT. Fpi(t+DT), is obtained by integrating the

survival rate of cohort i-1 in time t, SR1-1(t)FP1_1(t),
minus the death rate of cohort i in time t, DRi(t)FPi(t),

minus the rate at which organisms of age cohort i grow into

8O

cohort i+1 in time t, SR1(t)FPi(t).

This can be expressed as follows:

3;" = 531-1(t)FPi-1(t)-(DRi(t)+SRi(t))FPi(t) (8)

By definition DRi(t)+SRi(t) = 1, hence equation (8) can be

represented as:

---- = SR1-1(t)FP1-1(t)-Fpi(t) (9)
Integrating equation (9) over the interval (t,t+DT), we

obtain:

t+DT t+DT
I1; FPi(T)dT = L[SR1_1(T)FP1_1(T)-Fpi(T)]dT (10)

Using Euler numerical integration (Cheney and Kincaid, 1985)

the number of red groupers of age 1 in time t+DT is obtained

by equation (11):

FPi(t+DT) : FPi(t)+DT(SRi-1(t)FPi-1(t)-FP1(t)) (11)

Summing up overall.age groups welobtain the total red
grouper population in time t.

20
TFP (t) = 2 FPi (t)

(12)

To estimate the population of new born groupers, the

following equations were developed:

dNBORN

...... : FPj(t)*EGGj*SS (13)
dt

Where: 3 < j < 20

81

Integrating equation (13) we have:

t+DT t+DT
jC NBORN(T)dT - jg [ij(T)*EGGj*SS]dT (1n)

Using Euler integratioh we obtain:

NBORN(t+DT) : NBORN(t)+DT*(FPj(T)*EGGj*SS) (15)

Where:

FPj(t) = Spawning stock in time t.

The spawning success parameter was estimated by
determining the number of eggs required to survive given the
estimated number of recruits and the spawned stock. It
should be mentioned that recruitment to the fishery takes
place at age one, while biological recruitment to the stock
of adults begins at age 3.
Both males and females were considered as spawners
because red groupers are protozinous hermaphrodites. Also,
they are expected to Spawn once a year (Moe, 1969; Doi,
Mendizabal and Contreras, 1981L. Nevertheless, it would
have been desirable to express Spawning per adult as a
function of their age. But because of a lack of data, an
average number of eggs provided by the above mentioned
authors was used (1.5x106).
For the red grouper, W to the fishery takes

place at age 1, given that:
(1) fishing effort cfi‘ traditional fishermen occurs
between 3 and 15 fathoms where most of the juvenile

p0pulation is found.

82

(ii) a non-discriminatory fishing gear is used.

As a result, catch data are available from age 1 and
up.‘This unfortunate situation from a biological viewpoint,
facilitates the following population structure analysis.

To estimate population biomass, the number of organisms
in each age group was multiplied by their corresponding

weight and then summarized over all ages.
2

TFB (t) : FPi (t) W1 (16)
1:1

Eishing Efjprt sng Qatgh. Fish catch equations were
developed for both traditional and modern fishermen. It was
assumed that (fine Cuban fleet fishing in Yucatan's
Continental Shelf (within Mexico's EEZ) was catching the
average 5000 tons/year reported by Doi et al. (1981L
Using data collected from the survey, a catch function was
estimated for different types of vessel j, fitting;a Cobb-
Douglas production function (Anderson, 1981; Hanneson,
1983). The independent variables are: effective fishing
time, an exponentially autocorrelated random variable, and
biomass availability over time. Catch per trip equations
were developed for both traditional and modern vessels.

(a,HF6") + R1(t))*BAF(t) (17)

(a,DFB’) + R2(t))*BAF(t) (18)

CAT(t)

CAM(t)

Where R1(t) and R2(t) are exponentially autocorrelated
random variables, of catch per trip equations of traditional

and modern vessels, with variances VAR1 and VAR2, and

correlation coeficient XLMDA.

83

Multiplying equations (17) and (18) by TTRIPT(t) and
TTRIPM(t) respectively we obtain total annual catch of both
traditional and modern vessels.

CATCHT(t)

CAT(t)*TTRIPT(t) (19)
CATCHM(t)

CAM(t)*TTRIPM(t) (20)
Variables BAF(t), TTRIPT(t) and TTRIPM(t) are determined as
follows:

BAF(t) = TFB(t)/TFB(O) (Laevastu et al., 1981) (21)

TTRIPT(t) - TFV(t)*(TRIPT + R3(t)) (22)
TTRIPM(t) - MFV(t)*(TRIPM + Ru(t)) (23)

Where R3(t) and R4(t) are random variables representing
uncertainty concerning the number of fishing trips per year,
and TRIPT and TRIPM are the average number of trips per
type of vessel/year.

TTRIPT(t) = Total number of fishing trips per year of
traditional vessels having red grouper as
target species.

TTRIPM(t) : Total number of fishing trips per year of
modern vessels having red grouper as target
species.

The rate at which fishing vessels entry or exit the red

grouper fishery over time is determined by equations (24)

and (25).
dTFV
---- : ACTFV(t) (2“)
dt
dMFV
---_ = ACMFV(t) (25)

dt

8"

Integrating equations (24) and (25) we obtain the

accumulated number of both types of vessels in time t.

t+DT
jf ACTFV(T)dT (26)
t

t+DT
jr ACMFV(T)dT (27)
t .

Using Euler numerical approximation we obtain:

TFV(t+DT) TFV(t) +,DT*(ACTFV(t)) (28)

MFV(t+DT)

MFV(t) + DT*(ACMFV(t)) (29)

Where ACTFV(t) and ACMFV(t) represent the entry (or exit) of
both traditional and modern vessels to the red grouper
fishery over time.

There are time delays inherent in the processes of
entering or leaving the fishery from the moment a fishermen
faces economic rent or negative net revenues to the moment
in which entry or exit takes place. Some of the most
important time lags occur in:

(i) the decision-making process of entering or leaving the
fishery,
(ii) the time required to obtain public financing to
buy vessels and gears, and
(iii) The time it takes to receive a vessel after it has

been ordered.

The number of vessels entering or leaving the fishery were
obtained by the application of the distributed delay model
(Manetsch, 1976, 1977; Roberts et.al" 1983).

85

A Kth order distributed delay is defined by the

following first-order differential equations.

dr1 k

--_ : --- (X(t) - F

dt DEL 1(t)) (30)
df'2 k (

-—- : --- r -

dt DEL 1(t) r2(t)) (31)
df‘k k

......— : --- (1" _ (t) - ((3))

dt DEL k 1 rk (32)
Where:

x(t) = input to the delay process
r (t) y(t) is the output of the delay

r (t), r (t),..., rk(t) are the intermediate rates

DEL :Expected value of the transit time of an

individual entity through the given process

k = order of the delay

The parameter k specifies a member of the Erlang family
of density functions which describes the transit times of
individual entities as they pass through the delay process.

It should be mentioned that the model includes delays
With different values for the parameter DEL (DEL1:1.51and
DEL2=2., for traditional and modern vessels, respectively).

These average delay parameters were determined through

86

interviews with fishermen who have experienced entry and/or
exit to the fishery.

The outputs of the distributed delays are ACTFV(t) and
ACMFV(t).

Cpsps ang Rsyenues Anaiysi . Accumulated net profits are
estimated by equations (33) and (34) as follows:

-t+DT
TPFTT(t+DT) TPFTT(t) + jf TRT(T) - TCT(T)dT (33)
t

TPFTM(t+DT)

t+DT
TPFTM(t) + jf TRM(T) - TCM(T)dT (34)
t

Total revenues are estimated from equations (35) and (36).

TRT(t) PT1*FMT(t) + PT2*FPT(t) (35>

TRM(t)

PM1’FMM(t) + PMg’FMM(t) + PFAC*FAC(t) (35)

Even though fishermen are assumed to be price takers,
in the study region they are paid different prices, PT1,
PT2: PM1 and PM2 mainly for two reasons: first, there are
different prices according to the size of the fish and
second, there are different prices according to destination
of the fish. The latter results from different prices paid
for red grouper in the local market and by those who buy it
for further processing.

Concerning the price of the bycatch, PFAC, this
involves usually a lower price than that paid for red
grouper as target species.

Interviews with both traditional and modern fishermen

Provided estimates of costs of operating a vessel in the

87

red grouper fishery for a year. These costs are presented in
Tables 2 and 3.

From Table 2 it can be observed that annual total costs
per traditional vessel represent $ 3,167,560.0 Pesos. An
averagetraditional. vessel undertakes 210 effective fishing
days from which approximately 85 days or #0% of the fishing
effort is oriented towards the red grouper fishery. Hence,
annual total cost of having red grouper as the target
species is proportionately estimated as being $ 1,267,02HJ)
per year per boat. Concerning modern vessels, it is
estimated that 62% of the fishing effort per year is
allocated to red grouper, the remaining 38% has octopus
(thppps nsys and Qppppps yplgsris) as target species.
Consequently, from the estimated total cost per modern
vessel, $ 2H,191,0004) per year, $ 1H,998,420JD corresponds
to the red grouper catch (Table 3). Total costs were
estimated considering operating costs, fixed costs, and
Opportunity costs of labor and capital.

Depreciation was based upon 10% of the boat value, 20%

of the engine value, and 10% of value of fishing gear and

other equipment.

88

Table 2. Costs Analysis of Traditional Vessels (Pesos).

COSTS AMOUNT TOTAL
Mine Costs 272,560.0
. Bait 27,360.0
. Fuel 82,080.0
Maintenance uo,ooo.o
. Ice 0.0
. Gear Replacement 5n,72o.o
. Food and Beverages 68,u00.0
Elm Casts 575,ooo.o
. Depreciation 175,000.0
. Interest HO0,000.0
Oppprtnnity Cpst 2,320,000.0
2.: Capital and Labs:
. Labor 1,620,000.0
. Capital 700,000.0
M 9932; 3,167.56o.o

Note: Estimates are based on prices of June, 1985.

89

Table 3. Costs Analysis of Modern Vessels (Pesos).

COSTS AMOUNT TOTAL
Opsraping gpsps u,241,000.
. Bait 65,000.0
. Fuel 1,936,000.0
. Maintenance 300,000.0
. Ice 325,000.0
. Gear Replacement 250,000.0

. Food and Beverages 1,365,000.0

Eixgg Cpsts 6,100,000.0
. Depreciation 1,300,000.0
. Interest u,800,000.0

Qppgttunitx 22st 13,850,ooo.o
91.9221ial and Labs;

. Labor 5,u50,ooo.o
. Capital 8,uoo,ooo.o

Total Costs 2"i191i000-0

Note: Estimates are based on prices of June, 1985.

90

Making total costs a function of effective fishing

time, results in equations (37) and (38).

TCM(t) = 7,*DF (38)
Where:

HF(t)= Effective fishing time of traditional vessels
in time t
DF(t): Effective fishing time of modern vessels in
time t
To estimate marginal costs, MCI(t) and MC2(t), catch
equations (17) and (18) are used to substitute fishing
effort or effective fishing time by yield in total cost
equations. This was done in order to find the first
derivative of the total cost function with respect to a
change in yield.
This procedure is presented in the following set of

equations:
From catch equations (17) and (18) we have that:

1 CAT(t) 1/6
........ - R1(t) '

a, BAF(t)

HF (39)

1 CAM(t) 1/[3
........ - 82(t)
a, BAF(t)

DF (NO)

91

Substituting HF and DF in equations (37) and (38) we have

 

 

 

 

 

 

 

that: { T
1 CAT(t) 1/3
TCT(t) = 7; --- -------- - R1(t) ' ("1)
a. BAF(t)
_ J
I ' 1
1 CAM(t) V5
TCM(t) = ‘% --- -------- - R2(t) 2 (42)
a2 BAF(t)
Making x : cAt(t) ‘ (43)
n
1 CAT(t) 1/5
u : {-—-}{ -------- - R1(t) ‘ (All
0! BAF(t)
c = 7; (constant) (“5)
We have that:
d cun du
----- = cnun-1 --- (A6)
dx dx
Given that:
dTCT
------ = MC (t)
dCAT 1 (D7)

Then, marginal cost of traditional vessels can be

estimated from the following equation:
71

MC1(t) = { -------------- }
a, *5, *BAF(t)

L 1 CAT(t) (n-1)
{---}{ ........ - R1(t) } (AB)
a. ' BAF(t)

 

 

92

Where:
1
n : -—-
B.

Analogously, a marginal cost equation was derived for

modern vessels.

Finally, direct employment, seafood availability in rural
coastal communities and export earning are represented by
EMP(t), SEAFC(t) and EERG(t) respectively and estimated by
equations (#9), (50) and (51).

EMP(t) =7, TFV(t) +7, MFV(t) (149)

Where‘n and X are the average number of fishermen per
traditional and modern vessels, respectively.
t+DT

SEAFC(t+DT) = SEAFC(t) +j; FST(T)dT (50)
Where FST(t) is the component of traditional fishermen catch
that is kept in the coastal community for subsistence
purposes.

t+DT

EERG(t+DT):EERG(t) + LICATCHM(T)(E1PE1(T)+E2PE2(T))]d7' (51)
Where PE1 and PE2 are the export prices of fillet and
frozen red grouper, and g1, 52 are the proportion of modern
vessels catch that goes to the export market.
ME§£1.A§§!fl£&19fl§n Some of the most important assumptions
involved in this model are the following.
a. It was assumed that effective fishing time per trip by

type of vessel, biomass availability, and an

C.

93

exponentially autocorrelated random variable which
accounts for uncertainty, determine catch per unit of
effort over time.

Age composition of the catch was assumed constant.

It was assumed that the average time delays involved in
entry and exit of vessels to the fishery were‘hS years
and 2.0 years for traditional and modern vessels
respectively.

Because of the sedentary nature and territorial behavior
of red groupers (E; nprip), net migration was assumed
equal to zero.

Concerning demand of fish, price-taking behavior was
assumed for red groupers at dockside. This seems to be a
reasonable assumption, given that there are numerous
harvesters and buyers within the study region. Price-
taking behavior was also assumed in the fishery inputs

market.

The values used for model parameters and for

initializing state variables in the computer model are

presented in Appendix B.

Sealants; ...dslno

A computer model was developed to simulate the state of

the fishery over time. This important step in the modeling

process was done on an IBM-PC using the MICROSOFT FORTRAN 77

compiler.

94

The general structure of the computer model involved
two major phases: initialization and execution (Manetsch,
1982a).

Inipislization Pnsss

a. Values were assigned to model parameters.

b. State and rate variables were initialized.

c. Time was initialized: T=0.

d. Run characteristics were specified: length, number,
output, etc.

ME I: Bias:

e. Time updated: T=T+DT.

f. State variables were computed.

g. Rate variables were computed for time T.

h. State and rate variables were printed.

i. Returned to (e) if simulation run was not completed.

A listing of the computer program and its corresponding
flow diagram are presented in Appendices C and D. It should
be mentioned that to obtain meaningful results from the

above structure, the stability of the model needs to be

considered.
Mpgsl Stapiiity. In order to have a stable computer model an

appropriate value for DT (time increment) was determined.
This value was required for stable simulation of
differential equations included in the model, such as
distributed delays.

Given that Euler numerical integration was used to

95

solve the differential equations, the necessary condition
for stable simulation of this model is that DT be selected
such that: (Manetsch, 1982a)

2 MIN [Dj] > DT > O (52)
DEL
Where Dj = --- and MIN [Dj] is the smallest delay
K

constant in the model.

The smallest delay constant involved intfluered grouper
model is for DEL = 1.5 and K s 3. Therefore, the upper bound
for DT in this model is 1.

In addition, given that this simulation model involves
feedback in the population dynamics component, for stable

simulation (using Euler integration) we must ensure that:

1 1
--- > DT > 0 Where: c : --- (53)
c Di

Therefore, the value of DT in this model must be in the
interval given by:

1 > DT > 0 (54)

In order to reduce the numerical integration error to

an acceptable level, below 5 %, DT was reduced till the
maximum error condition was satisfied.

figngrsl Mpgs; Charsctsristics.The>characteristicscfi‘the

red grouper simulation model concerning time frame, level of

aggregation, functional. form cM' the equations and
uncertainty are presented as follows:

a. Time Frame. Given the characteristics of the red grouper

population dynamics and the planning horizon of decision-

96

makers in the Ministry of Fisheries, this dynamic model
has a time horizon of 20 years. The time interval
(simulated time) which is thought to satisfy needs for
information and analysis is yearly information.

tn Level of Aggregation. This modeling effort involves a
macroscopic view of the world given that an attempt was
made to model the real world grouper fishery in terms of
aggregates of fundamental entities. It involves a
W flea process.

c. Functional Form of the Equation. Given the inherent
characteristics of the system, the equations that
describe the fishery system are non-linear.

d. Uncertainty. Elements of uncertainty enter the analysis
of ocean fisheries in three ways (Lewis, 1982).

(i) Uncertainties may exist about the current size of the
resource, mainly because of difficulties in observing
the stock.

(ii) Unpredictable changes in the environment may perturb
the natural rate of growth or deterioration of the
resource, as well as the effective fishing effort.

(iii) The market value of the red grouper and the cost of
catching it may be random owing to fluctuations in
economic conditions.

To deal with uncertainties involved in the red grouper
fishery, random variables are included in the catch
functions of traditional and modern vessels. It is assumed
that random variables for the red grouper fishery at one

point in time are not independent of previous values.

97

Today's catch is dependent to a certain extent on
yesterday's catch. Selection of fishing site is usually
dependent to a certain extent on previously selected site.
Environmental factors that affect resource availability (and
consequently fish catch) such as temperature, currents,
winds, etc. tend also to be dependent to a degree on
previous values.

Therefore, to deal with the above situation

exponentially autocorrelated random variables, R1(t) and

R2(t), were generated using a subroutine called EXACOR
(Manetsch, 1982). It should be mentioned that the "inverse

transformation method" (Gottfried, 198A) can be used to
generate random variables with a desired probability density
function. Random variables R3(t) and Ru(t) were set to
zero during similation runs because of lack of data. In
order to use this subroutine values were provided for the
autocorrelation parameter, XLMDA, and for the catch variance
of both traditional and modern vessels, VAR1 and VAR2.

This subroutine EXACOR transforms a: uniformly
distributed random number, generated by Function UNIF
(Thesen, 1985) in an exponentially autocorrelated random
variable. A listing of this subroutine is included in

Appendix C.

Monte Carlo Analysis
It is important to consider randomness in the values of
system parameters which vary from run to run, because there

is often error in estimating the values of such parameters.

98

Monte Carlo analysis is "a set of statistics which
gives an estimate of the uncertainty in system performance
due to within-run random variables and errors in estimating
system parameters" (Manetsch and Park, 1982).

The Monte Carlo method is concerned with estimating the
unknown numerical. value cfi‘ certain parameter cM‘ some
distribution. The general principles of the Monte Carlo
Method (Cheney and Kincaid, 1985; Hammersley and Handscomb,
1965) can be summarized as follows:

If x1,x2,.....,xn are independent random numbers

(uniformly distributed between 0 and 1), then the quantities

f1 : f(Xi) (55)
are independent random variates with expectation6..
Therefore,

_ 1 n

r = ---. .2 r, (56)

n 1:1

is an unbiased estimator of0 , and its variance is

1 1 2 2
---f (f(x) -0) dx = a /n (57)
n 0
The standard error of f is thus:

0? = o/Vfi- (58)
Given that in practice the standard error is not known, it
can be estimated from the formula

1 n _
s2 : --— 2 (ti - {)2 <59)

99

From the above formula we have an estimate oftsfor 0 and
finally obtain s/V33T.

Given that the sample size is large, a normal approximation
for the distribution of the sample mean f is appropriate.
When the sample size is large, the pOpulation (7 is unknown,
and the significance level is 0': .05, a 100(1-a) confidence
interval for 9 is given by :(Bhattacharyya and Johnson,
1977)

Q = f i- Z S/m <60)

“/2

Where: 20% 1.96

According to Manetsch et al.(1975), the Monte Carlo
process, operationally, involves the following set of steps:
a. Values are assigned to random model parameters.

b. The simulation model is run over the desired time
horizon.

c. Variables are computed over the time horizon which
measures the system performance.

d. Values are stored at the end of each simulation run.

e. Steps (a) through (d) are repeated a number of times
(usually 100 or more) to generate data from which
significant statistics can be computed.

f. Statistics are computed for each performance variable.

Monte Carlo analysis was conducted in this study to
obtain estimates of the uncertainty in system
performance, using the random variables generated by the

subroutine EXACOR. A listing of the computer program in

100
Monte Carlo mode is included in Appendix E.

Model Validation and Sensitivity Analysis

M9921 yaiidatipn
A model is validated by providing a correct
representation of the real system. Validation requires that
the model exhibit behavior characteristics of the system
itself. There are four major approaches suggested in the
literature to validate a simulation model (Payne, 1982;
Graybeal and Pooch, 1980):

(1) Compare simulated results with results historically
produced by the real system Operating under the same
conditions.

(ii) Compare model behavior with that established by
accepted theories. Model validity is based upon the
assumptions and theories.used, which determined the
structural form of the equations and values assigned
to parameters.

(iii) Validate the model with expert opinion concerning
behavior of the real system.

(iv) Use the simulator to predict results. The predictions
are then compared with the results produced by the
real system during some future period time.

The first three approaches were used to validate the
red grouper simulation model. Results were compared with
historical data, mainly catch data. Model behavior was

checked with major theories dealing with ocean fisheries.

101

Finally, results, equations and parameters were
presented in a seminar to experts on the red grouper fishery
of Yucatan's continental shelf, among them, biologists
Martin Contreras, Manuel Solis and Victor Moreno.

The output of this validation process is presented in
the results chapter.

Se v t Analysis

In most simulation models, some data used to develop

the model is subject to error, and often the model is used
to explore situations where operating conditions differ from
those for which data were observed. Therefore, in order to
establish confidence in model validity, it is necessary to
determine that reasonable changes in the model parameters or
operating conditions do not lead to unreasonable changes in
model conditions. A major approach to testing this aspect
of model behavior is by the use of sensitivity analysis.
The basic technique is to vary an input to the model by
using incremental changes, and then observe output behavior.
Sensitivity analysis provides a basis for identifying
decision variables (design parameters and controllable
inputs) most important to the decision-making process.

Sensitivity analysis was conducted in the red grouper
simulation model through: (1) changes in parameters of both
the biologic and economic subsystem and (2) changes in
controllable inputs in the economic and institutional

subsystems.

102

Simulation of Management Strategies

Resource management strategies were simulated to
observe the behavior of performance variables over time.
Performance variables observed over time included: fish
biomass, yield and net revenues of traditional and modern
fishermen, direct employment, available seafood in coastal
communities and export earnings.

Management alternatives considered in different
simulation runs included:

- Fish quota to Cuban fishing fleet

- Vessel quotas (limited entry to domestic vessels)

- Minimum fish size restrictions

- Fostering eXports through increased fish production.
This management strategy involves maintaining the status
quo of a domestic open access regime.

The results of simulating these management strategies

are presented in the next chapter.

CHAPTER IV
RESEARCH RESULTS

The purpose of this chapter is to present the major
research findings obtained in this study. Results are
discussed in the following sections:(1) study region survey
results, (2) stability analysis, (3) model validation, (ll)
sensitivity analysis, (5) Monte Carlo analysis, (6)

simulation results, and (7) resource management strategies:7

Survey Results

Inflprmation obtained from Primary and Secondary Sources

 

After data were collected from both primary and
secondary sources, they were analyzed and prepared in a set

of tables which are presented in the following subsections.

Fisning.£issp. The fishing fleet involved in catching red
grouper as the target species was estimated to be about 1210
vessels. As shown in Table ll, 80.16% of these vessels are
small boats of 20 to 30 feet of length. The remaining
19.8147. are vessels of ((0 to 75 feet. These vessels belong
to "traditionalI'and "modern" fishermen, respectively, as

defined at the beginning of Chapter III.

7Readers interested in acquiring a copy of computer
runs for stability analysis, sensitivity analysis, model
validation and Monte carlo analysis, please contact the
author at Centro de Investigacion Pesquera Yucalpeten,
Apartado Postal 73. Progreso, Yucatan, C.P. 97320 Mexico.

103

104

Table u. Red Grouper Fishery: Fishing Fleet.

 

VESSEL SIZE QUANTITY PERCENTAGE
(#) (1)

20 to 30 feet8 970 80.16

no to 75 feetb 2u0 19.8u

TOTAL 1210 100.00

 

Source: aSurvey conducted as part of this study.
Centro de Investigaciones Pesqueras Yucalpeten.

Fishing Eififprt. There are substantial fishing effort
differences among these two types of fishing vessels. Table
5 shows that the effective fishing time of Type I vessel
involves an average of 5.116 hours per day and a total of 873
hours per year per vessel. This last figure is obtained by
multiplying the number of fishing trips/year by the number
of days/trip and finally by the number of effective fishing
hours per day. On the other hand, Type II vessels have an
average of 10 hours/day of effective fishing and a total of
1367 hours per year per vessel. It can also be observed
from Table 5 that the number of fishing days per trip is 1
for the traditional small vessels and an average of‘HL52
days for the modern vessels. It should be mentioned that
the figure for days/trip refers to effective fishing days.
The total trip duration of Type II vessel is between 15 and

18 days but because of transfer time and weather conditions

105

the effective fishing time is reduced to an average of 10.52

days/trip.

Table 5. Effective Fishing Time per Year.

 

 

FISHING TRIPS/ TOTAL

VESSEL TYPE YEAR DAYS/TRIP HOURS/DAY HOURS

Type I 160a . 1.0 5.96 837
(20'to 30')

Type II 13 10.52 10.0 1367
(“0' to 75')

 

a. This figure includes an average of 85 trips to:fish
for red grouper and 75 trips having octopus as the target
species.

Source: Survey conducted as part of this study.

The differences between thislnu>types of vessels are

more significant when analyzing catch per vessel figures.

Eigh Qétgh. Because of different technology, the fish catch
of the two types of vessels differ substantially. It can be
observed from Table 6 that the average catch of traditional
vessels was estimated to be 7.1 Kg/hour or 38.7 Kg/day;
while the modern vessel obtains an average catch of 27.7

Kg/hour or 277 Kg/day.

106

Table 6. Catch Per Unit of Effort (Kg/day)

 

 

VARIABLE VESSEL TYPE 18 VESSEL TYPE llb
(20 to 30 feet) (40 to 75 feet)
Average Catch/hour 7.1 Kg/hour 2757 Kg/hour
.Average Catch/man 2.36 Kg/hour 3.95 Kg/hour
Average Catch/Day 38:7 Kg/day 277:00 Kg/day

 

Source: aSurvey conducted as part of this study.
bCentro de Investigaciones Pesqueras Yucalpeten.

It should be mentioned that the average number of
fishermen involved in the fishing effort of traditional
vessel is 3, while modern vessels includee7 fishermen per
trip.

This above described information was an input to the
modeling process for both model parameters and estimation

of fishing effort functions.

Stability Analysis

As mentioned during the research methods chapter, in
order to have a stable computer model, an appropriate value
for the time increment, DT, was selected. Determination of
DT also involved using a very small time increment in order
to reduce numerical integration errors to acceptable limits.
The analysis was conducted for all state variables using
DTe.005 as the convergence time increment. To run the model
without numerical integration errors involves a high trade-

off in computing time. Therefore, for this modeling effort,

107

the process of reducing DT was stopped when the integration
error was smaller than 5%.

Results of this analysis are presented in Tables 7 and
8. Some of the state variables exhibited substantially
larger integration errors than others for each value of DT.
Errors in state variables for different time increments, DT,
were estimated with respect to their values obtained using

DTs.005 as the convergence time increment.

Table 7. Percentage Errors in State Variables for DT =.5

 

 

T BIOMASS(t) TPFTM(t) MFV(t)
1 0.07 _o.21 -1.07
2 0.32 -0.2u -1.55
3 0.58 0.06 -1.00
A 0.77 0.u8 -0.96
5 0.91 0.97 -0.92

15 2.95 5.19 1.32

16 3.26 6.10 -1.28

17 3.61 7.20 -1.23

18 3.98 8.53 -0.89

19 n.22 10.10 2.37

20 u.01 11.76 7.31

 

108

Table 8. Error Analysis Expressed in 1 for DT=.05

 

 

T BIOMASS(t) TPFTM(t) MFV(t)
1 0.01 0.02 0.00
2 0.03 -0.02 0.00
3 0.05 -0.01 -0.52
. H 0.07 0.02 -0.u9
5 0.08 0.06 0.00
15 0.27 0.51 0.00
15 0.30 0.59 0.00
17 0.33 0.70 0.00
18 0.36 0.83 0.00
19 0.35 0.96 0.59
20 0.30 1.08 0.91

 

109

It can be observed from table 7 that state variables
such as TPFTM(t) involve more numerical integration error
than BIOMASS(t) or MFV(t). With DT=.5, the error exceeded
5 1 (Table 7).

Nevertheless, when DT was reduced from .5 to .05.
numerical errors for all variables were substantially
reduced. To achieve error levels below 5 z for all state
variables, the time increment selected was DT:JM5(Table
8). With this value of DT, both stability and numerical

error conditions are satisfied (Appendix F).

Model Validation

In order to validate the model, three major approaches
were used: (1) comparison of actual and simulated catch,
(2) verification of consistency with accepted theory, and
(3) discussion of simulation results with resource experts
and decision-makers.
£0mnachau1sd:lstual.aad.§lumuuaalEatshl

Red grouper catch data, historically produced by the
real system, were compared with simulated catch for the same
time period, 1976-1985. This comparisson is presented in
Figure 11 where simulated and actual catch are graphed
together. In this figure, the simulated catch begins in 1976
given that the needed initial values for the number
individuals of age i in the study region, FPi(0), were
estimated from an available publication on red grouper

population (Doi et al., 1981) which included data on age

110

composition of the population up to that year.

The most noticeable differences between simulated and
actual catch take place in years 1977 and 1979 due to the
stochastic nature of the model. Simulated catch exhibits a
satisfactory close pattern to actual catch taking into

account that fishing effort equations include a random

variable.

ACTUAL AND SIMULATED YIELD

12 RED GROUPER FISHERY

 

11»

r -
.‘l . a
I. I‘
a
10
f‘ '3
'2‘
. 1 ' ‘l " 0 1‘

 

(Tons)

 

 

 

:2
52
0:
a2 a
0.-
o t
s '1 .. “
’1
74 U
I)
O r—[ , fl T T 7 fi‘ 171 1 T V T— l T l
1077 10.0 19.5 1900 1995
TIME (Years)
a ACTUAL CATCH O SIMULATED CATCH

Figure 11. Model Validation: Comparison of Simulated and
Actual Catch.

The red grouper catch was a basis for validation given

that it is one of the performance variables available from

published information.

111

It should also be mentioned that the simulated changes
in fishing effort, in terms of number of fishing vessels,
are consistent with figures published by the Ministry of
Fisheries.

The simulation run generated, through the exit and entry
process built in the model, 2&1 modern vessels and 962
traditional boats which exercise their fishing power on the
red grouper fishery in 198A. The published figure, adjusted
for those vessels fishing for other species as main targets
and, substracting those vessels which have not Operated in
the last three years, results in 230 modern vessels and 970
traditional ones (Secretaria de Pesca, 1986).

It should be mentioned that one change was made to the
model initial conditions in order to take in to account that
since T=7, which corresponds to 1982, most of the modern
fleet are allocating their fishing effort to the octupus
fishery (Octopus maya) from September to December. This was
done by including an IF statement that specified a reduction
in the number of fishing trips per year from 13 to 9.
9.90m with legacies Illegal

As discussed in the fisheries bioeconomic theory, a
point is reached after which additional units of fishing
effort result in decreasing catch per unit of effort, CPUE
(Anderson,1977; Bell, 1982; Crutchfield) . This diminishing
marginal productivity of the resource with increasing
fishing effort, is present in the simulation results for
CPUE1 after T=11 and, for CPUE2 after T:6 (Figures 12 and
13).

112

CATCH PER UNIT OF EFFORT

TRADITIONAL VESSELS
000‘. ‘

0.044

 

0.002

0.00 ‘ .
0.000 "
0.000 1
0.000 J
0.002 a .- “

0.028 1 :1
0.020 J
00024 1 “
0.022 —

0.02 J

0.01 0 - j

0.0" T T— —T I T j I T—fi—fi I I— T j ‘I I T f *1
1010 1000 1000 1000 1000

CATCH PER FISHING DAY ITONSI

 

 

TIME lYEAR SI

Figure 12. Model Validation: Catch per Unit of Effort of
Traditional Vessels, CPUE1.

CATCH PER UNIT OF EFFORT

MODERN VESSE LS
0.31 ’

0.3 .
0.20 n
0.20 ' ‘ ..

0.27 ' I i.
0.20 1 ..

0.20 - '
0.20 - ..
0.23 -
0.22 a “
0.21 1

0.2 -1
0.10 4 i.
0.10 4
0.17 J
0.10 J

O.15,rr—1—;11nl*ljlrlllllll
1010 19.0 1985 1990 1905

TIME IYEARS)

 

CATCH PE R FISHING DAY ITONSI

 

 

Figure 13. Model Validation: Catch per Unit of Effort of
Modern Vessels, CPUE2.

113

Concerning total costs and total revenues, the

decreasing fishery yield with increasing effort results in:
TC > TR for T > 16.

which can also be expressed as net profits below zero:
PFTM < O. for T > 16.

As a result, the number of modern vessels aiming at red
grouper stops growing and even start declining because of
the entry and exit processes taking place with the
appropriate time DELAY. The simulated evolution of number of
vessels for both, traditional and modern sectors, is
presented in.AppendixIL.In the casecfi‘modern vessels for
instance, exit takes place a year after (assumed time lag)
of having PFTM < 0. This fishermen economic behavior is

presented in figure 14.

FISHING FLEET

MODERN VESSELS
31 0

 

3001
2.0-l
2.0-1
270 1‘
2.0-1*
250 e
260-1

2301

Human or vs $5515

220 -
210 e
200 ~

I‘D-l

 

 

 

100 fifi .
1070 1000

 

1 1 1 r 7 f l T

r
1905
TIME IYEAISI

Figure 14. Simulation of Modern Fleet Size.

114

From the point of view of fish population and biomass
by age group, these variables were graphed after 10 years of
simulation to observe whether the shape Of the curves
corresponded to the theoretically accepted one (Figures 15
and 16). Both curves exhibit a shape that is usually
presented in the fish population dynamics literature
(Everhart and Youngs, 1981; Gulland, 1983; Pitcher and Hart,

1982).

SIMU LATE D POPUL AT ION STRUCTURE

RED GROUPER OF YUCATAN CONTINENTAL SHELF

 

NUMBER 0? “SH MIllIONS

 

 

 

 

AGE (YEAR S)

Figure 15. Model Validation: Simulated Population Structure

115

SIMULATE D BIOMA SS

RED GROUPER OF YUCATAN CONTINENTAI. SHELF

 

FISH BIOMASS TONS
Thwsonds

 

 

 

 

rfi‘

O 5 10 15 2O
AGE (YEARS)

Figure 16. Model Validation: Simulated Biomass by Age Group

 

2112131129 2.1: the wiggles Mods}. and ..._s_Re vii; with
33.322122; m and m c n _____§Maker

A seminar was presented to researchers and decision
makers of the Ministry of Fisheries on January 9th, 1986.
During this seminar, the model, its assumptions and the
corresponding results were discussed.Participants in the
seminar found the results quite reasonable and made

suggestions concerning the assumptioncfi‘constant natural

116

mortality rate. Given that there is no published information
on natural mortality rates by age group (at least to the
knowledge of the author), it was agreed during the seminar
that further research needed to be conducted in order to
relax this assumption.

It was also mentioned during the meeting that research
was being initiated concerning age specific fecundity. In
this modeling effort, the number of eggs produced by all
spawners was considered constant for all age groups in the
spawning population given that the secondary data sources
dealing with fecundity of red grouper only sampled 14 gonads
from which an avemage of 1.5 million eggs per gonad
was estimated (Moe, 1969). It will definitely be more
appropriate 1x) have average fecundity per age group of the
spawning population.

In general, model structure and its behavioral
equations were considered to reflect important fishery
processes which are often overlooked by the fisheries

science literature.

117

Sensitivity Analysis

Concerning sensitivity analysis, model inputs and
design parameters were changed marginally in order to
observe whether reasonable changes in them generated
reasonable changes in model behavior. Initial fish biomass,
spawning success and, natural mortality among others, were
increased and decreased by 10%. Changes in controllable
inputs, such as fishing effort of domestic as well as
foreign fleet, were also entered as inputs to sensitivity
analysis and results are being reported in the section
dealing with resource management strategies.

Simulation runs involving changes in initial biomass
resulted in reasonable changes in state variables as well
as important rate variables such as fish catch. Simulation
runs were conducted with values of initial red grouper
biomass, TFB(0), within the interval [1214000,151000] Tons.
This interval is the result of decreasing and increasing by
10 5 an average of 138000. Tons of red grouper biomass
reported by Doi (et al.).

Effects of these changes are illustrated with state and
rate variables such as accumulated net revenues, TPFTM(t),
total red grouper biomass, TFB(t) and, fishery yield,
CATCH(t) ( Tables 9 and 10 ). To observe the effects caused
by changes in inputs or design parameters, the model was run
in deterministic mode. System performance in stochastic mode
(including random variables with the appropriate probability

density function) is discussed in the next section.

118

Table 9. Sensitivity Analysis: Effect of 10 z Decrement in
Initial Biomass, TFB(O), Expressed in 1.

T TFBCt) CATCH(t) TPFTM(t)
0 -10.00 00.00 00.00
1 -10.57 -10.58 -17.17
2 -11.06 -11.06 ~25.0H
3 -11.68 -11.53 -29.35
H -12.01 -12.01 -32.28
5 -12.49 -12.50 -3H.85
15 -18.50 -23.60 -58.15
16 ~18.58 -28.1fl -61.55
17 -18.11 -38.08 -65.08
18 -16.96 -37.38 -68.63
19 -15.16 -40.08 -72.12

119

Table 10. Sensitivity Analysis: Effect of 10 2 Increment in
Initial Biomass, TFB(0), Expressed in i.

T TFB(t) CATCH(t) TPFTM(t)
0 10 00 00.00 00 00
1 10 HO 1o.uo 17 51
2 10 93 10.93 29.73
3 11 nu 11.flfl 28 29
4 11.99 11.99 31 89
5 12 an 12.0“ 34 H2
15 18.95 18.95 58.07
16 19.87 19.87 62.10
17 20.89 21.n5 66.90
18 22.00 22.26 72.75
19 23.09 25.88 79.95

20 23.80 32.uu 88.62

120

The rate of spawning success, SS, an important
parameter of the system feedback component, was also changed
within the interval [1.10 x 10-6,1.3u x 10-61. This interval
is obtained from decreasing and increasing by 10% the
estimated 1.22 x 10'6 spawning success parameter. Shifting
of this parameter resulted in changes in the correct
direction involving reasonable magnitudes.

It should be mentioned that model performance variables
exhibited greatest changes when average natural mortality,
MR = .33 , was increased and decreased by 10 %. Simulation
runs were conducted for values of this parameter within the
interval [.29,.36].

The effects of changes in other inputs (controllable)
and design parameters are discussed in the section dealing

with simulation of management strategies.

Monte Carlo Analysis

As discussed in the reaserch methods chapter the model
was set into Monte Carlo mode in order to estimate
confidence intervals, 0 t Zoy's f¢fi§ for model inputs as well

2

as important performance variables.

Monte Carlo experiments were conducted githig a
simulation run to estimate the expected value and confidence
intervals for a randomly generated series of 100 traditional

and modern vessels catch.

121

Table 11 presents estimators and confidence intervals
for mean catch of both traditional and modern vessels,

respectively.

Table 11. Monte Carlo Analysis of Fishery Yield by type of
vessel, CATCHT(t) and CATCHM(t)

Statistic CATCHT(t) CATCHM(t)
(Tons/year) (Tons/year)

Average 29u9 6u56

Standard Deviation 417 908

Standard Error N2 91

95% Confidence 2867 < 9,< 3031 6278<£L < 6639

Interval.

By the Central Limit Theorem, it isiexpected that the
distribution is approximately normal. therefore, it can be
said that a 95% confidence interval for 0' and 92 is given

by:

82 for traditional vessels, and

1+

9.

82.: 178 for modern vessels

122

In addition an experiment was conducted by implementing

50 simulation runs to estimate the statistics of important

performance variables such as PFTT(t), PFTM(t), and TFB(t).

The results of this experiment are presented in Table 12 and

Table 13.

With 95 Z confidence, the intervals for the means,9,,

6,,(L of the above mentioned variables are the following:

9, 1 82
9, i. 272
9, i 2767

Table 12. Monte Carlo Analysis of Net Revenues by Type of

Vessel,

PFTT(20) and PFTM(20).
(Millions of Pesos)

Average

Standard Deviation

Standard Error

95 $ Confidence
Interval.

42

213 < 9, < 377

139

361 < 9, < 905

123

Table 13. Monte Carlo Analysis of Red Grouper
Biomass, TFB(10) and TFB(20).

Statistic TFB(10) TFB(20)
(Tons) (Tons)
Average 198834. 112769.
Standard Deviation 6757. 9887.
Standard Error 965. 1u12.

95 S Confidence 11169113 < 9. < 150725 110000 < 9, < 115537
Interval

In order to have an estimate of red grouper biomass in
1986, a Monte Carlo experiment was conducted with run length
of 10 years. This experiment provided the following

confidence interval for mean red grouper biomass:
96 g 1891

This biomass estimate which resulted from 50
independent simulation runs, provides an indication of the
current status of the red grouper population of Yucatan

Continental Shelf.

12H

Simulation Results

After implementing the comprehensive simulation model
developed in Chapter III for the red grouper fishery, the
main results (Appendix F) concerning rate as well as state
variables are discussed as follows (Chappelle, 1985;

Sassaman et al., 1969):

Reg ficogper Biomass

Total red grouper biomass over time, TFB(t), is
presented in Figure 17. It can be observed that fish biomass
(summing up age specific biomass), begins to decline after
year 3 (1979). This downward sloping section of the curve
shows a small inflection in year 7'(1983).'This is caused by
a reduction in fishing effort of the modern fleet resulting
from the allocation of an average 5 trips per year to the
octopus fishery (Octogus gays and Octopus vulgaris).

This change in fishing effort takes place from
September to December. It should be mentioned that during
the octopus season the fishing gear discriminates other
demersal Species like grouper, snappers and, grunts.
Concerning traditional fishermen, they had been incorporated
to the octopus fishery for a number of years before T=0,
therefore there was no need to include changesin their
fishing effort.

Total biomass declines to a level of 95000 Tons in year
T=20. This is basically the result of the existing open

access regime for this species.‘This overexploitation effect

125

indicates the need for government intervention to prevent

resource exhaustion.

RED GROUPER (E. morio) BIOMASS

YUCATAN CONTINENTAL SHELF
14 5

140
135
130-
125T
120-1

115.;

HSH BIOMASS ITONSI
Thousands

110i
105-1

100-

 

 

 

 

1916

r11 TTFfITT‘fiT—TTfijfii—I
1080 1905 1900 1995

TIME (YEARS)

Figure 17. Red Grouper Biomass Over Time

Fishery 1mg

Red grouper simulated catch of both traditional and
modern vessels is presented in Figures 18 and 19. Annual
catch of traditional vessels is sustained, with fluctuations
due to uncertainty, up to year T=15 (1991). After that point
in time, CATCHT(t) decreases to its lowest level of 1646
Tons in year T=20 (1996). Annual yield of modern fishermen

shows a decreasing trend after T:5 (1981).

126

YIELD OF TRADITIONAL FLEET

RED GROUPER FISHERY

 

3.7
3..
3.5 q
3.0 -'
3.3-1
3.?
3.1 "
a —
...}
2.sJ
2.7 -
2.. r
2 5 .
2.4
2.3 -
2.2 4
2.1 ..
a a
fs-J
LI-
1.74
“. r v r
1.7.

YIELD ITONSI
(Thousands)

 

 

1905
TIME (YEARS)

IDIO

Figure 18. Yield of the Traditional Fleet: Red Grouper
Fishery

It should be mentioned that, given the continuing entry
of new vessels to the fishery up to T=17, it would be more
realistic to analize the status of the fishery by observing
annual catch per unit of effort, CPUE1(t) and CPUE2(t),
which shows the actual status of the fishery over time
This can be observed from Figures 12 and 13 discussed in the

Model Validation section.

127

YIELD or MODERN FLEET

RED GROUPER F ISHERY

 

ITONSI

Tho u sands)

YIELD

I
5

 

 

 

V V I V V I I
1.85 1090 1995

TIME I YEARS I

l I I r
I 97. 10.0

Figure 19. Yield of Modern Fleet: Red Grouper Fishery.

The random variables generated for the catch equations
to incorporate uncertainty in the analysis are graphed in
Figure 20 and 21. This random yield component of'CATCHT(t)

and CATCHM(t) is generated by subroutine EXACOR using

128

variances VAR1 and VAR2 and correlation coeficient XLMDA,
estimated from monthly catch and effort data for 1984
(Burgos and Lope, 1985).

RANDOM VARIABLE OF CATCH EQUATION

T R AD I TIONAL VESSELS

 

12
104

D4

;&/\ A A
\J

 

 

RANDOMYIELD PER VESSEL (KG/DAY)

 

 

I 1.... ' ' ‘ I 1".0 ' ' 1”.
TM (YEARS)

I W | v I
1070 19.0

Figure 20. Random Variable of Catch Equation of Traditional
Vessels.

129

RANDOM VARIABLE OF CATCH EQUATION

MODERN VESSELS

AM /\

-1001

 

-200
-SOOq

-4001

RANDOM YIELD PER VESSEL IKG/ TRIP)

..“d

~0004

 

 

 

-700 r t r r r
1.7. TOOO

Y T

I' r I T T r T I V
TODD 19.0 1.95

IIME (YEAR 5)

Figure 21. Random Variable of Catch Equation: Modern
Vessels.

East: and Asturias

Annual net revenues obtained by fishermen involved in
the red grouper fishery are illustrated in Figure 22 where
net profits of modern fishermen are presented in bar diagram
format. It can be observed that total costs are greater than
total revenues in T=11 (1987) and T > 16 (1992). The first

occurrence of losses are related to uncertainty given that

the random variable R2 = -,595 (tons/vessel/trip) in T=11.

130

On the other hand, economic rent (difference between
fish resource dockside price and harvesting average cost
multiplied by total yield) is dissipated after T > 16
because catch per unit of effort, CPUE2, decreases to a
level at which average costs are greater than average
revenues. As a result, "exit" of modern vessels takes place

with its corresponding time lag.

ANNUAL NET PROFITS

CONSTANT PRICES

 

 

 

 

 

 

 

2J4
g
" S §
E 154 k s
8‘? ‘1 R §
3% . 9 §
g& 0;1\ » F§ 7 . .‘EufifiEgEg _

F1Sure 22. Annual Net Revenues of Modern Vessels Targeting
at Red Grouper.

131

Average and marginal costs and average revenues per
type of fishing vessel are presented in Tables 13 and 14.
Bioeconomic equilibrium occurs whenever average revenue
equals average cost, and consequently there is no stimuli
for entry or exit to the fishery.

As shown in Tables 13 and 14, the number of fishing
vessels increases over time up to the point at which
economic rent is dissipated. Ecooomic root is understood as
a payment in excess of what is needed to bring a factor into
production. It should be pointed out that open access
equilibrium is approximately observed, when TFV(t) = 1110
and MFV(t) = 292. As a result, entry of modern vessels to
the red grouper fishery stops at T = 16 (1992),‘when AC2 =
A32, and exit begins when T > 18 (1994). Concerning
traditional vessels, entry stops after T = 17 (1993) and

exit takes place when T > 18JTables 13 and 14)
floxlmom,ooogomjo‘ylolg, MEY, takes place when marginal
costs equal willingness to pay for the resource (average
revenue). Given the assumption of price taking behavior, in
the case of the red grouper fishery average revenue equals
marginal revenue. Therefore, MEY occurs at T = 16 for
traditional fishermen, the point at which MC1 = AR1. It is

observed when TFV(t) = 1082.

132

Costs and Revenues of Traditional Fishermen.

Vessel
TFV(t)

856
869
884
901
919

1062
1082
1103
1117
1116
1104

Ave.

Cost

ACICt)

435
367
378
405
329

372
397
459
588
516
849

Ave.

Revenue
AR1(t)

577
577
577

.577

577

577

577

577
577
577
577

Marginal Cost
MC1(t)

555
579
598
616
636
649

Table 13.
T Year
1 1977
2 1978
3" 1979
4 1980
5 1981

15 1991

16 1992

17 1993

18 1994

19 1995

20 1996
Note:

pesos per ton.

Costs and revenues are expressed in thousands of

133

Table 14. Costs and Revenues of Modern Fishermen.

T Year Vessel Ave Cost Ave. Revenue Marginal Cost

MFV(t) AC2(t) AR2(t) MC2(t)
1 1977 183 711 906 1164
2 1978 187 739 906 1149
3 1979 193 628 906 1150
1 1980 200 647 906 1172
5 1981 208 684 906 1199
15 1991 285 722 906 1151
16 1992 292 909 906 1519
17 1993 299 1018 906 1563
18 1999 301 1161 906 1611
19 1995 295 969 906 1664
20 1996 283 951 906 1698

Note: Costs and revenues are expressed in thousands of
pesos per ton .

134

In the case of modern vessels, marginal costs have been
greater than marginal revenue, M02 > A112, since the
simulation run was initialized. This means that there have
been oyocinvootmeot in the case of modern vessels, at least
from the point of view of the red grouper fishery. When
the marginal cost of catching an additional unit of the
resource is higher than marginal benefits derived from it,
a loss in welfare to society occurs. This loss is equal to
the opportunity costs of capital, labor and management used

to harvest the additional unit.

Elsi: I91 292.2122; Lone _Qn_C sumption

A component of the red grouper catch iszallocated for
local consumption in the Yucatan coastal area. It is
basically composed of: (1) the pr0portion of red grouper and
by-catch that fishermen take to their home for subsistence
purposes and, (2) the proportion of fish catch that is sold
in coastal markets of The Yucatan Peninsula.

The simulation run provided an estimate of the amount
of seafood generated by this fishery in coastal areas over
time, SEAFC(t). Estimates are presented in Figure 23.

According to the simulation results presented in
Figure 23 and Appendix H, the red grouper fishery might be
contributing at present time approximately 1000 tons of
protein rich seafood per year. From Figure 23 it can be
observed that SEAFC(20) may decrease to 500 tons per year

under the current Open access regime.

135

FISH FOR COASTAL ZONE CONSUMPTION

YUCATAN COASTAL ZONE

 

 

 

 

I -T n
I)
‘ 1
l.
.1

ah 0.. 1 0
sh
Z
9 .
w‘ ‘ (.
g“: 0.01 0 c ‘
n. O
3% ° ~
19" ..
8 .
9‘ 0.0-1

ml .

o A l I fi' T T r 1 I t Y 1 r r v— ‘

107. 10.0 19.5 1990 1995
TIME YEARS

Figure 23. Red Grouper for Coastal Zone Consumption.

Elohogx Qinect Emoloymont

Given the average number of fishermen per type of
fishing vessel, direct employment generated by red grouper
harvesting is basically determined by the entry and exit of
vessels to the fishery. Figure 24 shows the evolution of
accumulated direct employment for this fishery. Because of
the assumption of constant crew size, the shape of the curve
is very similar to the one that estimates the number of

vessels over time

136

FISHERY DIRECT EMPLOYM ENT

FROM TRADITIONAL AND MODERN VESSELS

 

NUMBER OF FISHERMEN
Thousands

 

 

 

 

30. r— 1*— t— I—r T j— r v r r I f I fi— 1 f I 1—
T .7. T “o T... TODD 19.5
TIME YEARS

Figure 24. Direct Employment Generated by Harvesting of Red
Grouper
Figure 24 shows that, under the current unlimited entry
regime, the number of fishermen employed at the present time
(1985), is in the order of 4600. The estimated number of _
fishermen that could be harvesting this resource at T:20,
may represent 5300 individuals. It can also be observed in

Figure 24, that when vessel exit to the fishery takes place,

the number of fishermen is consequently decreased.

137
Resource Management Strategies

Simulation of management strategies.of this tropical
demersal fishery involved a set of regulations affecting
both age composition of the catch and size of the catch. It
also included allocation of pr0perty.rightsix>a group of
resource users. Specifically, four management strategies
were simulated to observe the effect on system performance
variables: (1) allocation of exclusive property rights to
domestic fishermen, (2) Limited entry to the fishery, (3)
minimum size restrictions and, (4) price controls. Each of

these strategies was implemented for T > 10 .

Alloootioo of Exclusive Pnooocty Rights

As discussed in the in Chapter I, The Law of the Sea
establishes that coastal States must determine the portion
of the exploitable biomass that could be harvested
domestically and make available surpluses (if any) to
foreign fishing fleets through yearly quotas.

Overexploitation is present in the red grouper
fishery, given that catch per unit of effort has been
decreasing since 1972 (Chavez, 1983; Doi et alt, 198VL This
trend was also observed and discussed in the simulation
results section. Therefore, before limiting domestic fishing
effort, an alternative strategy is to provide exlusive
property rights to domestic fishermen by excluding foreign
fishing in the red grouper fishery. This was done in the
computer model with the following FORTRAN statement:
IF(T.GE.10) CCUB=0.

138

LIAHEEMEEQDIIQLQEEEiflEEX
An alternative strategy to mitigate overfishing involves a
limited entry policy that could be implemented to regulate
domestic fishing effort. This involves not allowing entry of
new traditional and modern vessels to the fishery,1except
for boat replacement purposes. This strategy is implemented
by the following statements:

IF(TFV.GE.975.) TFV=975.

IF(MFV.GE.250.) MFV=250.

Minimum Sig; Roguiation

This management strategy involves requiring harvested
fish to be adults. Consequently red grouper cohorts of ages
1 and 2 will not experience fishing mortality. This is done

by specifying age composition of the catch, ACTi and ACMi:

with the above mentioned constraints for T > 10.

Eahuiggamsfla

A policy instrument usually employed by Mexican
planners dealing with food products is concerned with price
ceilings. This management strategy is implemented in the
computer program by reducing red grouper and by-catch
dockside real prices by 20 Z.

Other resource management strategies such as closed
seasons, fish quotas and taxes were not simulated given
that: (1) there is an "spontaneous closed season" resulting
from fishing effort being diverted to the octopus fishery

from August to December, (2) There are substantial

139

constraints in the fisheries information system that1vill
make non-operational a regulatory scheme involving fish
quotas, which requires real time data, and (3) imposing
taxes to increase total costs and consequently decrease
fishing effort may foster severe catch information
distortions that would generate underestimation of fishing
mortality.

These management strategies can be identified in the
following Figures as:

Policy 1: cancel foreign fish quota

Policy 2: limited entry to domestic vessels

Policy 3: enforce minimum size restrictions

Policy 4: price controls on red grouper and by-catch

The effects and trade-offs of the above mentioned set
of resource management strategies, are discussed in terms of
important system performance variables.These performance
variables are compared according to the values they attain
at the end of the simulation run. Combinations of
management strategies were also made to observe system
performance and results and summarized at the end of the

chapter.

MWW

The impact on the amount of red grouper biomass over time is
is presented in Figure 25 and Table 15. Policies 1 and 3
generate the highest increments, 62 1 and 59 8 respectively.
Policy 2 and Policy 4 also improve the level of biomass with

increments of 13 1 and 15 5. These increments, expressed as

140

percentages, are estimated with respect to the base run,

which reflects the open access regime currently Operable in

the fishery.

RED GROUPER IIOMASS (TONS)
Th0usands

RESOURCE MANAGEMENT STRATEGIES

“amass EEFECI
no .

1saq (
140 4
1:04

120

 

1104

100*

 

 

.0 fl 1' I T
1... 1900

TIME (YEARS)

 

T I

10.8

. BASE RUN . m FOREIGN Hm AMIN. SIlE A P. CONTROL OLIMITED ENTRY

Figure 25. Resource Management Strategies: Biomass Effect

141

Table 15. Impact cd‘.Alternative Resource Management

Strategies.

Performance Policy 1 Policy 2 Policy 3 Policy 4

Variable % 1 1 1

Biomass 62 13 59 1”

Fishery yield 94 -4 86 -16

Net Revenues 73 9 54 -34

(Traditional)

Net Revenues 55 5 42 -33

(Modern)

Employment 13 -13 12 -19

Seafood 14 -2 11 -1

Availability

Fish Exports 15 -3 11 -5
131.913.22.11 _i__Y eld

The effect on domestic fishery yield with policies 1
and 3 involve substantial improvements: 94 % and 87 %
'respectively (Table 15 and Figure 26). With these management
strategies the red grouper catch will approximate the
maximum sustainable yield reached in 1972. On the other
hand, imposing either limited entry restrictions or price
controls, generate reductions in annual fish catch with

respect to the base run (Table 15).

142

R ESOURCE MANAGEMENT STRATEGIES

FISHERY YIELD EFF ECT

14

13-1

12‘

11-1

 

10

 

RED GROUPER YIELD (TONS)
Thousands

 

 

 

1 no ' 1 no 1905
TIME (YEARS)
DIAS! RUN ONO FOREIGN FISHING A MIN. SIZE A P. CONTROL . OLIMITED ENTRY

Figure 26.Resource Management Strategies:Fishery Yield
Effect.

MW

To observe the effect on net revenues of both,
traditional and modern fishermen, note that Table 15 show
that accumulated net revenues increase with Policies 1,2?

and 3 and decrease with price control policies (Figure 27)

143

RESOURCE MANAGEMENT: PRICE CONTROL

DIRECT INCOME EFFECT

 

 

 

 

 

a
O
W
W
S
fl
0
m”
51

g
..a
g3
~’0
ӣ5
2
K
2 —o.a-
&
.- -0.4«
"2" —o..-

—O.D-
-1.2
TIME (YEARS)
U BASE RUN 0 PRICE CONTROL

Figure 27. Price Controls Policy: Effect on Net Revenues.

mm

The resulting impact on direct employment is presented
on Figure 28. With limited entry, direct employment becomes
a constant that involves lower employment levels when
compared to the base run. With policy 1 and 3, employment of

fishermen increases 13 Z and 12 1 respectively.

199

RESOURCE MANAGEMENT STRATEGIES

DIRECT EMPLOYMENT EFFECT
0.1

 

 

 

 

6 e'.
5 s. 4 q /
“1‘ ..I /
£11; 5.3
mg 5.2 . /
63 5.1 1 / '
0
:.:~5 ‘ 1 /
g 4-0 /
D to .1
z s 7 - . .
. ' + + 3 =‘ ‘?__7 - '3 ‘4’
4.0 .
4.5
4.4
4.3
"a I fit r I f r f I I ‘r 1
I... 1900 1906
TIME (YEARS)
lsAsE RUN ONO FOREIGN FISHING AMIN.SIZE AP. CONTROL OLIMITED 5191117

Figure 28. Resource Management Strategies: Effect on Direct
Employment.

Sgofooo Avaiiability ago Egoort Earnings
Finally, it can be observed from Table 15, that Policy

1 and 3 result in higher levels of seafood availability in
coastal communities. Also export earnings eXperience
increments in the order of 15 1 when compared to the Open
access simulation run.

0n the other hand, Policies 2 and 4, both generate

small decrements with respect to the base run.

When more than one resource management starategies were

included in the same simulation run, policies 1 and 3

145

combined yielded highest system desired output.

Discussion of the results described in this Chapter and
analysis of‘traoe-offocu‘alternative management regimes,
are presented in Chapter V, which deals with Conclusions

and Recommendations.

CHAPTER V
SUMMARY, CONCLUSIONS AND RECOMMENDATIONS

Ihi this final Chapter the following sections are
presented: (1) a summary of the research, (2) a discussion
of the major conclusions derived from this research effort,
(3) study implications, (4) study limitations, and (5)

recommendations for further research.

Summary

Management of renewable resources such as tropical
fisheries, is a complex process that requires an
underStanding of the resource biology and ecology, as well
as the economic and institutional factors that affect
behavior cM‘ fishermen as resource users. Inherent
characteristics of this common property resource are also
important. These include: high exclusion costs, free rider
problems, and high transactions costs, mainly enforcement
and information costs.

It should be pointed out that fisheries resource
managers require information concerning dynamics of fish
populations and factors that determine their spatial and
temporal distribution. Management of ocean fisheries also
demands information about linkages between resource
management strategies and fishery system performance.

Different approaches have been used to aid the
decision-making process through modelling efforts.‘These are

discussed in the fisheries science literature as the surplus

146

147

yield approach, the bio-economic approach and the dynamic
pool approach. It is also recognized in the literature, that
"u.few general descriptions of the complete management
system have been given. It is therefore not surprising that
models cu? the complete system do not exist" (Gulland,
1981:130). Rather, there are a number of fisheries models
describing individual parts of the system, these can be
grouped into (I) biological models describing fish
populations and the ecosystem in which they live, (2) bio-
economic models describing large scale interactions between
fish stocks and fishing effort by a set of equilibrium
conditions, and (3) models describing actual operations of
individual elements of the fishing industry.

Therefore, the major objective of this dissertation was
to develop a comprehensive model integrating biological,
economic and institutional factors using the systems
simulation approach.

The systems simulation approach iseaproblem-solving
process of designing a model of a real system such as an
ocean fishery, and conducting experiments with this model
for the purpose of either understanding the system or of
evaluating various strategies for the operation of the
system.‘This involves obtaining solutions over time of a
mathematical model based on specific assumptions regarding

model inputs and values assigned to parameters.

The systems simulation methodology was applied to model
a tropical demersal fishery: red grouper (Eoiooohoioo moLio)

of the Yucatan continental shelf. To develop a comprehensive

148

simulation model for this species, the following steps were

taken:

(1)

(ii)

(iii)

(iv)

§X§L§E ligatiiisatiaa. A first step in this
process involved linking the needs statement
discussed above with a conceptual identification
of the fishery system. This required a definition
of exogenous and controllable inputs, design
parameters, and desired and undesired outputs of
this trOpical demersal fishery.

.floosi Decomposition. The red grouper fishery
system was decomposed into three interacting sub-
systems: biological, economic and resource
management. This model decomposition emphasize
interface variables that link the sub-systems
together.

Design of System Causal Diagra . This diagram was
built to represent cause and effect relationships
between relevant variables of each subsystem.‘This
is a conceptual model of the fishery showing flows
of fish, dollars and information.

Doss,goiiectioo jog Parameter Estimation

Data were collected from primary as well as
secondary sources to generate production functions
for traditional.and modern vessels.lhladdition,
these data were used to determine important design

parameters.

149

(v) Mathematical M2931
Implicit form equations were developed for
performance and rate variables using the fishery
causal diagram as a main reference. Then, a block
diagram was constructed using a set of basic
mathematical operations including:
. Arithmetic Operations
. Generation of explicit functions
. Generation of non-explicit functions
. Distributed DELAY functions
. Differentiation
. Integration
The resulting mathematical model involved 44
linear and non-linear equations. It should be
mentioned that uncertainty was included in the
model through generation of random variables with
an appropriate probability density function.

(vi) Comousec M2921
A computer simulation model (SIMERO) was developed
in FORTRAN 77 and implemented in a IBM-PC
microcomputer using a Microsoft FORTRAN Compiler.
The resulting computer program has 349 lines
(without including Comments). A second version of
this progranI(SIMERO-1) was developed for Monte
Carlo analysis purposes. SIMERO-1 has 376 lines

without including comments.

150

(vii) Stability Anaiysis
In order to have a stable computer model an
appropriate value for DT (time increment) was
determined. This value was required for stable
simulation of differential equations (converted to
difference equations) included in the model such
as distributed delays. Given that this simulation
model involves feedback in the population dynamics
component upper bounds were determined for values
of DT. It should be pointed out that in order to
reduce the numerical integration error (Euler
numerical integration) to an acceptable level,
below 5 z, DT was reduced to DT=.05
(viii) ,Moooi Validasioo
A model is validated by providing a correct
representation of the real system. Validation of
the model built fOr the red grouper fishery
involved checking if it exhibited behavior
characteristic cfi‘ the fishery system itself.
Model validation was conducted using three major
approaches (or validation norms):
a. Comparison of actual and simulated catch.
b. Consistency with accepted theory.
c. Discussion of the simulation model and results
with resource experts and decision-makers.
(ix) SGQSILiYIEY agaiysis
In order In) establish confidence in model

validity it was necessary to determine if

(x)

151

reasonable changes (marginal) in model parameters
or operating conditions lead or do not lead to
reasonable changes in behavior. Initial fish
biomass, spawning success, and the natural
mortality rate, among others, were increased and
decreased by 10 %. In general, the model exhibited
reasonable behavior when marginal changes in
parameters and controllable inputs were
implemented. It should be pointed out that model
performance variables exhibited greatest changes
when average natural mortality (MR) was increased
and decreased by 10 %. Simulation runs were
conducted for values of this parameter within the
interval [.29,.36].

WWW a 8's

The simulation model was put into Monte Carlo mode
in order to estimate confidence intervals for
model inputs as well as important performance
variables. Monte Carlo experiments were conducted
within a simulation to estimate the expected catch
value and confidence interval for a randomly
generated series of 100 traditional and modern
vessels. In addition, an experiment was conducted
by implementing 50 simulation runs to estimate
statistics of important performance variables such
as net revenues by fishermen type and total red

grouper biomass.

(xi)

152

Analysis of Simulation Results

A next step in this process involved analyzing
major simulation results. Red grouper biomass over
time (TFB(t)) begins to decline after year 3. This
downward leping section of the curve showed a
small inflection in year 7. This is caused by a
reduction in fishing effort of the modern fleet
resulting from allocating an average 5 trips per
year to fishing for octopus. Total biomass
(summing up over age specific biomass), declines
to a level of 95000 tons in T = 20.

Fishery yield of traditional vessels exhibit
sustainable levels up to T :15. After that point
CATCHT(t) decreases to its lowest level of 1646
tons in T = 20. On the other hand, considering
catch per unit of effort over time for the two
types of vessels (CPUE1(t)anHICPUE2) show that
fishery yield is decreasing per unit of effort.
This performance is specially significant in
modern vessels. This research result indicates
that the red grouper fishery of the Yucatan
continental shelf exhibits overexploitatnnh
Dissipation of economic rent is another simulated
performance of the current Open access regime. Net
revenues, contribution of seafood availability in
coastal communities, direct employment, and export

revenues all tend to decrease in the long run.

153

(xii) Simulation oi Managemeot Strategies
In order to guide management of this renewable
resource, four management strategies were
implemented to simulate impacts on performance
variables:
. Policy 1: Allocation of exclusive property
rights to domestic fishermen
. Policy 2: Limited entry of domestic vessels
. Policy 3: Enforcement of minimum size
restrictions
. Policy 4: Price controls on red grouper and
by-catch.
All. four policies increased fish biomass as expected.
However, they differ on the degree of impact on this
important performance variable. Policies 1znui3 had
the greatest desired effect on the red grouper
population. Policies 2 and 4 resulted in undesired
performance of important variables such as fishery
yield, employment, and seafood availability.
Choice of either policy 1 or 3 , involve important
distributional impacts on different resource users.
Policy 1 provides the highest benefits to domestic
fishermen and to the regional economy. With policy 1
the trade-off involves not allowing a foreign fleet to
harvest fish Species within Mexico's EEZ. This may have
economic as well political implications.

Decision-makers need to make a value judgement

154

concerning whose interests count the most when

regulating resource use and exploitation. Adapting

Policy 3 imposes severe restrictions to traditional
fishermen because their fishing vessel characteristics
allow them to fish only in near shore ecosystems where
juveniles are located.‘Therefore, in order to keep them

fishing, the Mexican government would need to provide

financing for acquiring larger vessels. The opportunity

cost of financing traditional vessels is the highest

economic alternative forgone.

Conclusions

The conclusions derived from this research study are

the following:
1. It was feasible to build a comprehensive simulation

using the systems simulation approach. This dynamic

model integrated biological, economic, and

institutional factors that determine the

performance of a tropical demersal fishery over

time. The systems simulation approach proved to be

a systematic and robust methodology for modelling

the dynamics of renewable resources, given the

comprehensive nature of ocean fisheries development
and management. As a problem-solving methodology it

allowed for conducting experiments dealing with

impacts cM‘ alternative resource management

strategies.

4.

155

The model was shown to be useful as a tool for
simulating alternative management strategies and
for observing the impacts on the fishery
performance variables.

Inclusion CH? the dualistic characteristics of
tropical fisheries, which involve modern and
traditional fishermen, allowed the possibility of
estimating important important performance
variables.
It is concluded that the spatial disaggregation of
fishing effort in tropical fisheries is fundamental
in order to conduct meaningful cohort survival
analysis of fish populations. The rationale behind
this statement is based on the fact that traditional
vessels usually apply their fishing effort in near
shore environments where most of the juvenile
population is located. As a result, differences in
age composition of the catch by type of vessel
become substantial. Therefore, disaggregating
fishing effort and catch over space results in more
realistic fishing mortality rates by age cohort.
The stochastic nature of ocean fisheries was also
incorporated in this simulation model. Random
variables were generated to represent uncertainties
that exist about the current size, and spatial and
temporal distributions of the resource, mainly
because of difficulties in observing the stock.

These random variables were alsoan1expression of

156

unpredictable changes:h1the natural environment,
which may affect effective fishing effort.

6. Among domestic management strategies, if a minimum
size regulation is enforceable, it provides the
highest desired impacts on performance variables. It
should be mentioned, however, that the trade-off of
this policy involves substantial investment in safer
and more efficient vessels and gear in order for
traditional fishermen to apply their fishing
effort in deeper waters where most of the adult fish

population is located.

IMPLICATIONS
Some of the most important study implications include
the following: 1
1. The application of the distributed DELAY model
(Manetsch, 1976), to represent the exit and entry
processes of vessels to the fishery. Such processes
involve time lags in:
. the decision-making process of entering or
leaving the fishery.
. the time required to obtain public financing to
buy vessels and fishing gears.
the time it takes to receive a vessel after it

has been ordered.

2.

157

Incorporation of random variables generated with an
exponentially autocorrelated probability density
function, to indicate that random variables for the
red grouper fishery at one point in time are not
independent of previous values. Today's catch is
dependent to a certain extent on yesterday‘s catch.
Selection cM‘ site is also dependent to certain
degree on previously selected sites.

Environmental factors that affect resource
availability and fishing effort (and consequently
fish catch), such as water temperature, currents and
winds tend also to be dependent to a degree on
previous values.

Dynamic marginal cost equations based on
Cobb-Douglas production functions which have
effective fishing time, biomass availability and a
random variate as independent variables were
develOped. These marginal cost equations allow for
the possibility of determining dynamic maximum
economic yields.

A dynamic feedback mechanism was designed to
estimate pOpulation structure and recruitment to
the fishable stock as a function of a time varying
spawning stock population, an average fecundity rate
and a spawning success parameter. This population
dynamics submodel could be applied to tropical as

well as non-tropical fisheries with appropriate

158

inputs.

5. The fishing mortality rate was decomposed by type
of vessel which resulted into time variants:

. fishing mortality rate by age cohort i, FRi(t),
. total mortality rate by age cohort, DRi(t)1 and
. Cohort survival rates, SRi(tL

6. The model develOped in this study could be used as a
tool to aid the decision-making process used in
managing tropical fisheries.

7. The simulation characteristics of the model,
provides the possibility of conducting a number of
resource management experiments to identify the
ojjoois and trade-offs involved in relevant
performance variables.

8. In the case of the red grouper fishery of the
Yucatan Continental Shelf) two resource management
strategies exhibited overall higher desired
performance:(i) Allocation of exclusive property
rights to domestic fishermen and,(ii) enforcement
of minimum size restrictions on this species.

9. Given that the computer model was developed and
implemented on an IBM PC using a Microsoft FORTRAN
compiler, the resulting software could easily be
implemented in IBM-PC compatibles, the kind of
microcomputers usually available hitropical coastal

nations.

159

Study Limitations

Some of the most important limitations involved in this

research effort, are as follows:

1.

Because of lack of information, it was not feasible
to incorporate into the the model the high diversity
of species usually present in tropical ecosystems.
It would have been desirable to model the dynamics
and interdependencies of tropical multispecies
fisheries.

When running the computer model, the population
dynamics component used the available average
fecundity rate. It would have been more appropriate
to include the average fecundity by age of spawners,

as indicated in the mathematical model.

3. Natural mortality was assumed as an average rate,

instead of being a function of age. This model
assumption, might be relaxed in the near future,
given that a group of marine biologists are
conducting studies to estimate this rate by cohort.
Estimation of the fishing effort function of
traditional fishermen was based on cross-section
data collected as part of this study. It would have
been more desirable to estimate production functions
based on time series which incorporate seasonal
variations in catch-effort relations.

The model would have been a more accurate
representation of reality if information about the

following system elements had been available and

160

included:

. Interdependencies of fish species in the tropical
ecosystem.

. Community intertemporal preferences in the use of
fish resources.

. Socio-cultural factors that affect behavior of
fishermen as resource users.

.Preferences of resource managers dealing with
intertemporal and distributional allocation of

fisheries resources.

Recommendations for Further Research
A number of future research efforts seem to be relevant to
the fisheries resource development field with emphasis in
resource modelling. In ranked order the following studies
are needed:

(i) DevelOpment of comprehensive simulation models for
other renewable resources and more specificallyfor
other biotic resources of marine ecosystems.

(ii) Research efforts concerning the nonsn dimension are
needed In) model decision-making mechanisms dealing
with:

. intertemporal preferences in (Hue use of
resources,

. socio-cultural factors that affect fishermen as
resource users,

. utility functions of resource managers.

(iii) Multiple-objective Optimization functions,could be

 

(iv)

161

incorporated in a simulation model like the one
develOped in this dissertation, to optimize
objective functions of different decision-makers
(fishermen and resource managers), in order to model
the human dimension of ocean fisheries.

Modelling efforts concerning recruitment of
tropical demersal fisheries should include biotic
as well as non-biotic factors in order to come up
with adequate representation of this important and
complex process. Also, time varying distributed
delay functions could be applied to model time lags

involved in recruitmnet processes.

(v) Parameters which are highly difficult to observe,

(vi)

(vii)

such as spawning success, could be estimated by
applying optimal control theory and dynamic
optimization algorithms.

Application of Monte Carlo analysis to estimate
confidence intervals of resource prices in order to
account f1”: uncertainty inherent in market
fluctuations and government interventions.
Multivariate analysis of fisheries production
functions to include variables such as:

. fishing skills

. type of gear

. vessel characteristics

. number of fishing vessels

. effective fishing time

 

162

. Environmental variables
fishing site

(viii) Biological and technological interdependencies
should be included in the analysis of tropical
fisheries to deal with a high diversity of species

and non-discriminating fishing gears.
(ix) Studies concerning age dependence of fecundity and
natural mortality are needed to provide data for
research efforts dealing with pOpulation dynamics of

tropical fisheries.

APPENDIX A

 

1.

163

APPENDIX A
FISHERMEN SURVEY

Questionnaire

Location

 

Are you involved full time in the fishing activity?

Yes ( ) No ( )

EL If you are involved in harvesting fish species, please

indicate the form of organization to which you belong
(if any), to carry out your fishing activity:

a. Fisheries OOOperatives ( )

b. Private firm ( )

C. Productos Pesqueros Mexicanos S.A de C.V. ( )
d. Harvest fish with someone who owns a boat ( )
e. Harvest fish with your own boat ( )

(If answer is d., proceed to interview the next

fishermen)

Please indicate the capacity and lengtthPthe fishing
vessel that you own:

 

 

CAPACITY LENGTH
1 to 3 tons ( ) 10 to 15 feet long
5 to 10 tons ( ) 16 to 25 feet long
11 to 15 tons ( ) 26 to 30 feet long
16 to 20 tons ( ) 31 to 35 feet long
21 to 30 tons ( ) 36 to 40 feet long
More than 30 tons ( ) 41 to 75 feet long

164

Please indicate the type of fishing gears that you use
in your fishing boat.

Hand lines ( )
Longlines ( )

Nets ( ) Please indicate the mesh size

 

Gill-nets ( )

How many fishing trips do you undertake per year?

# of trips per year

 

What is the average duratiOn of each of your fishing
trips?

# of days per fishing trip

 

How many hours,cn1the average,ck>you actually fish in
each of your fishing trips?

Hours fishing activity per trip

 

Do you always fish in the same fishing ground?
Yes ( ) No ( )
What is the depth range in which you fish most of the
time?
3 to 5 fathoms ( )
6 to 10 fathoms ( )
11 to 15 fathoms ( )
16 to 20 fathoms ( )
21 to 25 fathoms ( )
26 to 30 fathoms ( )
31 to 40 fathoms ( )
41 to 50 fathoms ( )
More than 50 fathoms ( ) How many?

 

 

165

10. How many fishermen go in your vessel during each
fishing trip?

# of fishermen

 

11. On the average, how much do you spend on the following
items per trip?

Gasoline and oil

 

Lines and hooks

 

Bait

 

Ice

 

12. On the average, how much do you pay per day to each of
the fishermen that fish on your boat?

$ per day per fisherman

13. How much do you think your vessel is approximately worth
today including both the boat and the fishing equipment?

Value of boat $

 

 

Value of equipment $

Total value of vessel $

 

14. Indicate the type of fish that you catch when you go
fishing, and please indicate the approximate number of
kilograms that you catch of each of them in an average

 

 

 

 

 

trip.
L S
Red grouper ( ) # of K8
Ocean perch ( ) # of Kg
Yellow snapper ( ) # of K8
Red snapper ( ) # of K8
White Grunt ( ) # of K8
King Mackerel ( ) # of K8

 

 

Spanish Mackerel( ) # of Kg

 

166

 

 

 

Barracuda ( ) # of Kg
Octopus ( ) # of Kg
Squid ( ) # of Kg
Shark ( ) # of Kg

 

15% From the above species could you indicate which one of
them you are mostly trying to catch as your major fish
target and where do you sell it?

Name of fish

 

For local market ( )
For processing plants ( )
16. In trying to catch the above indicated fish which are

the most common fish species thatyun1are also likely
to catch? Please indicate them in order of most

occurrence:

Name of fish

 

Name of fish

 

Name of fish

 

17. Do you keep some of your catch for your family
consumption?

Yes ( ) No ( )

 

If yes, how many kg/trip

18. If your answer was affirmative, what fish species do
you keep for consumption?

Species

 

19. If you are fishing for red grouper please indicate the
month(s) of the year that you catch the most:

January JUlY __-

February ___ August ___

 

167

March ___ September ___
April ___ October ___
May ___ November ___
June December

20. Have you or your organization received financial support
from the Fisheries Bank?

Yes ( ) No ( )

21. How many Kg. of fish would you be willing to accept
today as an equivalent of 100 Kg, of fish a year from today?

Kg. of fish today

 

22. For how many years would you like to keep fishing in the
coastal areas of the Peninsula of Yucatan?

# of years

 

23. If you were informed that one of the fish species that
you are currently catching is being depleted, would you
be willing to reduce fishing effort to protect the
species for future generations?

Yes ( ) No ( )

 

 

Thank you very much!

 

APPENDIX B

 

168

APPENDIX B
CONSTANTS, PARAMETERS AND STATE VARIABLES

Table B.1 Model Constants and Parameters.

Constant and parameter Value Unit of Measurement
"K6171"?3"'""""""""'"61’ """""""" i """"""
ACM(2) .19

ACM(3) .32 %

ACM(4) .09 %

ACM(5) .08 %

ACM(6) .06 %

ACM(7) .08 %

ACM(8) .06 %

ACM(9) .04 %

ACM(IO) .09 %

ACM(11) .03 %

0, .009016 %

012 .74995 %

ACT(I) .05 %

901(2) -30 I

ACT(3) .25 %

ACT(4) .20 %

ACT(5) .10 %

ACT(6) .06 %

ACT(7) ~0“ %

5‘ .859 I

5: .565 %

C1 2,7301 Thousand Pesos/Hour

C2 178.2130 Thousand Pesos/Day

169

Constant and parameter Value Unit of Measurement
EEGB""'"""""“""§666?6 ““““““ ;;;;;;;;; """
DELM 2.0 Years

DELT 1.5 Years

DF 10.52 Days

EGG 1.5 (105) # of Eggs/Gonad
541 .016 z

EM2 .043 7

ENTRYM .04 %

ENTRYT .02 %

EXITM .05 %

EXITT .05 %

HF 5.46 Hours

K 3, -

MR .33

PEI 2000.0 Dollars/Ton
PE2 6500.0 Dollars/Ton
PFAC 625.0 Thousand Pesos/Ton
PM1 750.0 Thousand Pesos/Ton
PM? 750.0 Thousand Pesos/Ton
PT1 700.0 Thousand Pesos/Ton
PT2 625.0 Thousand Pesos/Ton
33 1.22 (10-6) 5

SM) .2 %

3‘

SM2 .8

STI
ST2
3T3
TRIPM
TRIPT

170

Value Unit of Measurement
1 %
2 %
.7 %
13.0 Fishing Trips/Year
85.0 Fishing Trips/Year

A-.. I"

171

Table 8.2 Initial Values of State Variables.

State Variable Initial Value Unit of Measurement
'35?13""""""""§12§3655t“""‘“"'; """"""""
FP(2) 63817000. #

FP(3) 32056000. #

FP(4) 13300000. #

FP(5) 7543000. #

FP(6) 4787000. #

FP(7) 3025000. #

FP(8) 1709000. #

FP(9) 1039000. #
FP(10) 566000. #
FP(11) 253000. #
FP(12) 169000. #
FP(13) 113000. #
FP(14) 74000. #
FP(15) 44000. #
FP(16) 38000. #
FP(17) 27000. #
FP(18) 18000. #
FP(19) 9000. #
FP(20) 9000. #
TFB(0) 138000. Tons
CATCH(0) 9996. Tons/year
CATCHM(0) 6703. Tons/year
CATCHT(0) 2793. Tons/year

172

State Variable Initial Value Unit of Measurement
MFV(O) 180 #

TFV(O) 850 #

TPFTM(O) 1688 Millions of Pesos
TPFTT(O) 536 Millions of pesos
EMP(O) 3810 Individuals
SEAFC(O) 279 Tons

EERG(O) 2088 Thousands of Dlls.

 

APPENDIX C

 

00000OOOOOOOOOOOOOOOOOOOO 000

10
20

APPENDIX C
COMPUTER PROGRAM SIMERO

COMPREHENSIVE SIMULATION MODEL OF THE RED GROUPER
FISHERY OF YUCATAN'S CONTINENTAL SHELF.

JUAN CARLOS SEIJO.

PROGRAM SIMERO

DEFINITION OF VARIABLES AND PARAMETERS.

POPULATION AND BIOMASS BY AGE GROUP J: FP(J) AND FB(J).
COMPOSITION OF THE CATCH BY FLEET: ACT(J) AND ACM(J)

TOTAL, NATURAL AND FISHING MORTALITY BY AGE: DR(J),MR,FR(J).
FISHING MORTALITY BY AGE BY TYPE OF VESSEL: CT(J),CM(J),CC(J).
LENGTH AND WEIGHT OF FISH AGED J: L(J) AND W(J).

MATURING AND ADULT POPULATION AND BIOMASS: MFP,MFB,AFP,AFB.
NEW BORN POPULATION: NBORN.

TOTAL,TRADITIONAL AND MODERN VESSEL YIELD: CATCH,CATCHT,CATCHM.
CATCH PER UNIT EFFORT BY TYPE OF VESSEL: CPUEI AND CPUE2.
TOTAL NUMBER OF TRADITIONAL AND MODERN VESSELS: TFV AND MFV.
ANNUAL FISHING TRIPS BY TYPE OF VESSEL: TRIPT,TRIPM.
BIOMASS AVAILABILITY FACTOR: BAF.

RANDOM VARIABLES OF YIELD EQUATIONS: R1,R2.

DIRECT EMPLOYMENT: EMP

SEAFOOD AVAILABILITY IN COASTAL AREAS: SEAFC.

EXPORT EARNINGS FROM RED GROUPER PRODUCTS: EERG.

NET REVENUES OF TRADITIONAL AND MODERN VESSELS: PFTT,PFTM.
ACCUMULATED NET REVENUES: TPFTT,TPFTM.

TOTAL COSTS PER TYPE OF VESSEL: TCT,TCM.

TOTAL REVENUES PER TYPE OF VESSEL: TRT,TRM.

MARGINAL AND AVERAGE COSTS PER TYPE OF VESSEL: MC1,MC2,AC1,AC2.
DISTRIBUTED DELAY PARAMETERS: DEL,K.

DISTRIBUTED DELAY INTERMEDIATE RATES: RT(3),RM(3).

VARIANCE OF CATCH EQUATIONS: VAR1,VAR2.

REAL TFV,MFV,THF,TDF,BAF,PFTT,PFTM,TPFTT,TPFTM,ACI,AC2

REAL TFVE,MFVE,TTRIPT,CATCHT,CATCHM,FBE,DR,FR,FP,FB,UI,U2.
REAL NBORN,R1,R2,CPUE1,CPUE2,SR,CT,CM,MR,CC,L,W,TTRIPM,CAT
REAL CAM,MFP,MFB,AFP,AFB,TRIPT,TRIPM,HF,DF,MC1,MC2,AR1,AR2
EXTERNAL UNIF

DIMENSION RT(3),RM(3),ACT(20),ACM(20),DR(20),SR(20),L(20)
DIMENSION FP(20),FB(20),W(20),FR(20),CT(20),CM(20),CC(20)
DIMENSION SR1(20),SR2(20),SCACHT(20),SCACHM(20),SACI(20)
DIMENSION SAC2(20),SPFTT(20),SPFTM(20),STRT(20),STCT(20)
DIMENSION STRM(20),STCM(20),SEMP(20),SSEAFC(20),SEERG(20)
DIMENSION STFV(20),SMFV(20),STPFTT(20),STPFTM(20)

DIMENSION SMCI(20),SMC2(20),SAR1(20),SAR2(20)

WRITE (*,10)
FORMAT(24X,'SIMULATION MODEL OF THE RED GROUPER FISHERY')

WRITE (”,20)
FORMAT (31X,'YUCATAN CONTINENTAL SHELF')

MODEL CONSTANTS AND PARAMETERS
DATA K/3/,DELT/1.5/,DELM/2.0/,ST1/.1/,ST2/.2/,ST3/.7/

173

 

174

DATA SM1/.2/,SM2/.8/,EM1/.015/,EM2/.0u3/,PT1/700./
DATA PT2/525./,PM1/750./,PM2/750./,PFAC/625./

DATA PE1/2000./,PE2/6500./,HF/5.U6/,DF/10.52/,TRIPT/85./
DATA TRIPM/13./,ENTRYT/.02/,ENTRYM/.OU/,EXITT/.05/
DATA EXITM/.05/,CCUB/5000./,MR/.33/,ALPHA1/.009016/
DATA ALPHA2/.7U995/,BETA1/.859/,BETA2/.565/,C1/2.7301/
DATA C2/178.213/,S$/1.225-6/,EGG/1.5055/

DATA ACT(1)/.05/,ACT(2)/.30/,ACT(3)/.25/,ACT(N)/.20/
DATA ACT(5)/.10/,ACT(6)/.06/,ACT(7)/.ON/,ACM(1)/.01/
DATA ACM(2)/.19/,ACM(3)/.32/,ACM(N)/.09/,ACM(5)/.08/
DATA ACM(6)/.06/,ACM(7)/.08/,ACM(8)/.06/,ACM(9)/.OU/
DATA ACM(10)/.OU/,ACM(11)/.03/

INITIAL VALUES PHASE

RT(1):6.

RT(Z):6.

RT(3)=6.

RM(1)=3.

RM(2)=3.

RM(3)=3.

CATCHT:2793.

CATCHM=6703.

CATCH=CATCHT+CATCHM .

FP(1):9H276000.

FP(Z):63817000.

FP(3):32056000.

FP(N):13300000.

FP(5):75"3000.

FP(5):N787000.

FP(7)=3025000.

FP(8):1709000.

FP(9):1039000.

FP(10):556000.

FP(11)=253000.

FP(12)=169000.

FP(13)=113000.

FP(1N)=7NOOO.

FP(15)=NNOOO.

FP(16)=38000.

FP(17)=27000.

FP(18):18000.

FP(19)=9000.

FP(20)=9000.

DO 1 J:1,20

L(J)=80.2*(1.-EXP(-0.159*(J+1.21)))
N(J)=.0000138’(L(J)*'3.)

FB(J)=FP(J)’W(J)/1000.

CONTINUE

MFP:FP(1)+FP(2)
AFP:FP(3)+FP(A)+FP(5)+FP(6)+FP(7)+FP(8)+FP(9)+FP(10)+FP(11)+

FP(12)+FP(13)+FP(1u)+FP(15)+FP(16)+FP(17)+FP(18)+FP(19)+FP(20)

TFP:MFP+AFP

MFB:FB(1)+FB(2)
AFB=FB(3)+FB(H)+FB(5)+FB(6)+FB(7)+FB(8)+FB(9)+FB(10)+FB(11)+

30

HO

4.

175

FB(12)+FB(13)+FB(1N)+FB(15)+FB(16)+FB(17)+FB(18)+FB(19)+FB(20)

TFBzMFB+AFB

DO 2 J=1,20

CT(J)=ACT(J)*CATCHT/FB(J)

CM(J):ACM(J)'CATCHM/FB(J)

CC(J):ACM(J)'CCUB/FB(J)

FR(J)=CT(J)+CM(J)+CC(J)

DR(J)=FR(J)+MR

SR(J):1.-DR(J)

CONTINUE

CPUE1:.O388

CPUE2=.2723

MFV:180.

TFV:8SO.

TTRIPTzTFV'TRIPT

TTRIPM=MFV*TRIPM

FBE=138.E3

EMP=TFV*3.+MFV'7.

SEAFC:CATCHT'(ST1+ST2)

EERG:CATCHM*(PE1*EM1+PEZ*EM2)

ACTFV:O.

ACMFV:0.

TFVE=O.

MFVE=O.

FST:ST1*CATCHT

FMT:ST2’CATCHT

FPT=ST3TCATCHT

FMM:SM1*CATCHM

FPM=SM2*CATCHM

FAC=CATCHM'.25

TRT=PT1'FMT+PT2*FPT

TRM:PM1*FMM+PM2*FPM+PFAC*FAC

THF:HF*TRIPT'TFV

TDF:DF'TRIPN'MFV

TCT:C1'THF

TCM:C2'TDF

AC1:TCT/CATCHT

AC2:TCM/CATCHM

PFTT:TRT-TCT

PFTM:TRM-TCM

TPFTT=PFTT

TPFTM=PFTM

EGGS:EGG’SS

NBORNzEGGS'AFP

WRITE (‘,30)

FORMAT ('0',12X,'T',11X,'CPUE1',1OX,'CPUEZ',1OX,
'CATCH',8X,'BIOMASS')

WRITE (',AO) T,CPUE1,CPUEZ,CATCH,TFB

FORMAT (F15.1,2F15.N,ZF15.1)

1:0.
XLMDA=.3
VAR1=65E-6

VAR2=12H2S6E-6

 

176

R1=O.

R2=O.

T=O.

SPECIFICATIONS OF SIMULATION RUN.
DT:.05

RLGTH:20.

NIPP=1./DT+.OOO1

NIT:RLGTH/DT+.OOO1

NIOL:NIT/NIPP

EXECUTION PHASE

DO 3 I1:1,NIOL

DO A I2:1,NIPP

T:T+DT

COMPUTE STATE VARIABLES.

DO 5 J=20,2,-1
FP(J)=FP(J)+DT*(SR(J-1)‘FP(J-1)-FP(J))
CONTINUE
FP(1)=FR(1)+DT'((1.-MR)'NBORN-EP(1))
MFP=FP(1)+FP(2)
AFP=ER(3)+FP(“)+FR(5)+FP(6)+FP(7)+FP(8)+FP(9)+FP(10)+FP(11)+
FP(12)+FP(13)+FP(1H)+FP(15)+FP(16)+FP(17)+FP(18)+FP(19)+FP(20)
TFP:MFP+AFP

NBORN:EGGS*AFP

DO 6 J:1,2O

FB(J)=FP(J)‘W(J)/1000.

CONTINUE

MFB:FB(1)+EB(2)
AFB:FB(3)+FB(A)+FB(5)+FB(6)+FB(7)+FB(8)+FB(9)+FB(10)+FB(11)+
EB(12)+FB(13)+FB(1Q)+FB(15)+FB(16)+FB(17)+FB(18)+FB(19)+FB(20)
TEB:MFB+AFB

TPFTT=TPFTT+DT'(TRT-TCT)
TPFTM:TPFTM+DT‘(TRM-TCM)
IF(TFV.LT.850) ENTRYT:.O5
IF(TFV.GE.850) ENTRYT:.02
IF(MFV.LT.180) ENTRYM:.O5
IF(MFV.GE.180) ENTRYM:.OH
IF(PFTT.LT.O.) TFVE=TFV'(-EXITT)
IF(PFTT.GT.0.) TEVE:TFV*ENTRYT
IF(PFTT.EQ.O.) TFVE:O.

IE(RFTM.LT.O.) MFVE:MFV*(-EXITM)
IF(PETM.GT.O.) MFVE:MFV*ENTRYM
IF(PETM.EQ.O.) MEVE=O.
TFV:TFV+DT*(ACTFV)

MFV:MFV+DT'(ACMFV)

EMP:TFV'3.+MFV*7.
SEAFC:SEAFC+DT'(FST+FMT)
EERG:EERG+DT*(CATCHM*(PE1'EMT+PE2’EM2))
CALL DELAY(TFVE,ACTFV,RT,DELT,DT,K)
CALL DELAY(MFVE,ACMFV,RM,DELM,DT,K)
GENERATE RANDOM VARIABLES.

CALL EXACOR(XLMDA,VAR1,DT,I,R1)

CALL EXACOR<XLMDA,VAR2,DT,I,R2)
COMPUTE RATE VARIABLES. '

177

BAFzTFB/FBE

IF(T.GE.7.) TRIPM:9.
TTRIPT:TRIPT*TEV
TTRIPM=TRIPM*MFV
CATCHT:(ALPHA1*(HF'TBETA1)+R1)‘BAF’TTRIPT
CATCHM:(ALPHA2*(DF"BETA2)+R2)*BAF'TTRIPM
CATCH=CATCHT+CATCHM
CPUE1:CATCHT/(TEV*TRIPT)
CPUE2:CATCHM/(MFV'TRIPM’DF)

DO 7 J:1,2O
CT(J):ACT(J)'CATCHT/FB(J)
CM(J):ACM(J)'CATCHM/EB(J)
CC(J)=ACM(J)*CCUB/FB(J)
ER(J):CT(J)+CM(J)+CC(J)
DR(J)=ER(J)+MR

SR(J)=1.-DR(J)

CONTINUE

FST:ST1*CATCHT

EMT:ST2*CATCHT

EPT=ST3*CATCHT

FMM:SM1*CATCMM

FPM:SM2*CATCHM

FAC:CATCHM'.25
TRT:PT1*FMT+PT2*FPT
TRM:PM1*FMM+PM2'FPM+PEAC*FAC
AR1:TRT/CATCHT

AR2:TRM/CATCHM
THF:HF*TRIPT*TEV
TDF:DF*TRIPM*MFV

TCT:C1*THF

TCM:C2*TDE

CAT:CATCHT/TTRIPT
CAM=CATCHM/TTRIPM
U1:((1./ALPHA1)'((CAT/BAF)-R1))'*((1/BETA1)-1)
U2:((1./ALPHA2)*((CAM/BAF)-R2))*'((1/BETA2)-1)
MC1:(C1/(ALPHA1'BETA1'BAF))‘UT
MC2=(C2/(ALPHA2'BETA2‘BAF))‘UZ
AC1=TCT/CATCHT

AC2:TCM/CATCHM

PETTzTRT-TCT

PFTM:TRM-TCM

CONTINUE

SR1(I1)=R1

SR2<I1):R2

SCACHT(I1)=CATCHT
SCACHM(I1)=CATCHM
SAC1(I1)=AC1

SAC2(I1)=AC2

SMC1(I1)=MC1

SMC2(I1)=MC2

SAR1(I1)=AR1

SAR2(I1)=AR2

SPFTT(I1)=PETT

50

60

7O

80

90

100

110

120

130

1H0

150

160

170

11

12

13

178

SPFTM(I1):PFTM

STRT<I1>=TRT

STCT(I1):TCT

STRM(I1):TRM

STCM(I1)=TCM

SEMP(I1)=EMP

SSEAFC(I1)=SEAFC

SEERG(I1)=EERG

STFV(I1):TFV

SMFV(I1)=MFV

STPFTT(I1):TPFTT

STPFTM(I1):TPFTM

WRITE <*,50) T,CPUE1,CPUE2,CATCH,TFB

FORMAT (F15.1,2F15.u,2F15.1)

CONTINUE

WRITE (',60)

FORMAT ('1',12X,'T',9X,'RANVAR1',8X,'RANVAR2',
9X,'CATCHT',9X,'CATCHM')

DO 8 I1:1,NIOL

NRITE (',70) I1,SR1(I1),SR2(I1),SCACHT(I1),SCACHM(I1)

FORMAT (I15,2F15.6,2F15.1)

CONTINUE

WRITE (',80)

FORMAT ('1',12X,'T',11X,'ACTV',11X,'ACMV',11X,'PFTT',
11X,'PFTM')

DO 9 I1=1,NIOL

wRITE (*,90) I1,SAC1(I1),SAC2(I1),SPFTT(I1),SPFTM(I1)

FORMAT (I15,uF15.1)

CONTINUE

wRITE (*,1oo)

FORMAT ('1',12X,'T',12X,'TRT',12X,'TCT',12X,'TRM',12X,'TCM')

DO 11 I1=1,NIOL

NRITE (*,11O) I1,STRT(I1),STCT(I1),STRM(I1),STCM(I1)

FORMAT (I15,AF15.1)

CONTINUE )

NRITE 120

FORMAT (:1',12X,'T',12X,'EMP',1OX,'SEAFC',11X,'EERG')

DO 12 I1=1,NIOL

wRITE (*,130) I1,SEMP(I1),SSEAFC(I1),SEERG(I1)

FORMAT (I15,uF15.1>

CONTINUE )

wRITE * 1uO

FORMAT((:1',12X,'T',12X,'TFV',12X,'MFV',1OX,'TPFTT',
1OX,'TPFTM')

DO 11:1 NIOL

wRITE (*,156) I1,STFV<I1),SMFV(I1),STPFTT(I1),STPFTM(I1)

FORMAT (I15,uF15.1)

CONTINUE

EORAET((‘1§?12X,1T1,12X,'Mc11,12x,vMC2',12X,'MR1',12x,1MR2')

DO A 11:1 NIOL

wRITE (*,176) I1,SMC1(I1),SMC2(I1),SAR1(I1),SAR2(I1)

FORMAT (I15,HF15.1)

 

1A
180

190
15

1010

179

CONTINUE

WRITE (*,180)

FORMAT ('1',12X,'AGE',6X,'POPULATION',10X,'BIOMASS')
DO 15 J:1,20

WRITE (‘,190) J,FP(J),EB(J)
FORMAT (I15,2F17.1)
CONTINUE

END

SUBROUTINE EXACOR(XLMDA,VAR,DT,I,U)
IE(I.NE.O) GO TO 1

U=O.

B=XLMDA'*DT

A=(1.+B)/(1.-B)
R:UNIE(ISEED,JSEED)
XK=(A'12.’VAR)".5
XN=XK’(R-.5)
U=B*U-(1.-B)'XN

I:I+1

RETURN

END

SUBROUTINE DELAY<RINR,ROUTR,CROUTR,DEL,DT,K)
DIMENSION CROUTR(1)
DEL1=DEL/(FLOAT(K)'DT)
RIN:RINR

DO 3 I:1,K

ABC:CROUTR(I)
CROUTR(I)=ABC+(RIN-ABC)/DEL1
RIN:ABC

ROUTR:CROUTR(K)

RETURN

END

SUBROUTINE RANDOM(I,B)
INTEGER'Z ISEED,I

CHARACTER BYTE(2),B
EQUIVALENCE (ISEED,BYTE(1))
ISEED:I

ISEED=ISEED'2837+1
B:BYTE(2)

IE(ISEED.LT.O) ISEED:ISEED+32767+1
I:ISEED

RETURN

END

FUNCTION UNIECISEED,JSEED)
INTEGER'Z ISEED,JSEED,IEXPO
CHARACTER‘1 8(4),RBYTE
EQUIVALENCE (X,B(1))

CALL RANDOM(ISEED,B(2))
CALL RANDOM(ISEED,B(3))
CALL RANDOM<ISEED,B(1))
IEXPO:53

IF (B(3).LT.128) GOTO 1030
IEXPO=66

CALL RANDOM(JSEED,RBYTE)

 

1020
1030

180

IEXPO:IEXPO-u

IF (RBYTE.EQ.0) GOTO 1010
IF (RBYTE.GT.127) GOTO 1030
IF (RBYTE.GT.63) GOTO 1020
IEXPO:IEXPO-1

IF (RBYTE.GT.31) GOTO 1030
IF (RBYTE.GT.15) GOTO 1020
IEXPO=IEXPO-1

IF (RBYTE.GT.7) GOTO 1030
IF (RBYTE.GT.3) GOTO 1020
IEXPO=IEXPO-1

IF (RBYTE.GT.1) GOTO 1030
B(3):CHAR(ICHAR(B(3))-128)
B(A)=CHAR(IEXPO)

UNIF:X

RETURN

END

 

APENNDIX D

181

APPENDIX D

FLOW DIAGRAM OF COMPUTER MODEL

(:Stfrt)

Input
Constants and
Parameters

Initialize
B _ Rate and State
Variables

1

Specification
of Simulation Run

1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

[DO J=1,N10E];_

 

 

1
If -
,IDO J-1,NIPP]

 

 

 

 

 

 

 

Execution Phase]

. I Compute
State Variables

Generate
Random Variables

1 no
0 ‘ Compute 1
Rate Variables

yes

no =NIP [Eontinuej

yes 1
[Continue CRUDE)
1

Print
State and Rate ~—-—
Variables

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

182

 

Initialize
Population Structure

 

 

 

1

DO J:1,MAGE

1

Calculate
Fish Length
by Age J

1

Calculate
Fish Weight
by Age J

A 1

CalcUlate
Fish Biomass
by Age J

1

Calculate
Fishing Mortality
by Vessel at Age J

1

 

A

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Calculate
Cohort Survival rates

 

 

 

 

 

 

 

 

 

= MAG "°
yes
Continue
Initialize

 

other Variables

 

 

183

 

Execution
Phase

1

T=T+DT

1

Compute
State Variables

1

DO J=20,2,-1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Calculate
Population Structure
FPi(t+DT)

 

 

 

yes

 

Calculate
Spawning Stock

1

Estimate
Recruitment
FP1<t+DT)

1

Calculate
Fish Biomass
by cohort

1

Estimate
Seafood
Coastal Area

I 1

Calculate
Direct Employment

1

Calculate
Export Earnings

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Calculate
# of Vessels

 

 

 

 

alculate
Net Revenues

 

 

 

18A

 

Generation
of
Random Variables

1

Compute
Rate Variables

1

Calculate
Vesselk Fish Catch

 

 

 

 

 

 

 

 

 

 

 

 

 

Calculate
Fishery Yield

' 1

e:[DO J=1,MAGE]

 

 

 

 

 

1

Calculate
Fishing Mortality
by Cohort

1

 

 

 

 

 

 

Calculate
Cohort Survival Rates

 

 

 

"9 :MAG

yes

Calculate
Total Costs
TCk(t)

‘ v
' EstImate
Marginal Costs

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

EStimate
Total Revenues
TRk(t)
R > I no. A R < T
yes ¢ yes
Vessel Entry Vessel Exit

 

 

 

 

 

 

APPENDIX E

0 00000

APPENDIX E
MONTE CARLO MODE OF PROGRAM SIMERO

MONTE CARLO ANALYSIS OF A TROPICAL DEMERSAL FISHERY

RED GROUPER (E. morio) OF YUCATAN CONTINENTAL SHELF.
MONTE CARLO EXPERIMENTS TO ESTIMATE CONFIDENCE INTERVALS
FOR IMPORTANT PARAMETERS AND PERFORMANCE VARIABLES.

JUAN CARLOS SEIJO.

PROGRAM SIMERO

MONTE CARLO MODE.

REAL TFV,MFV,THF,TDF,BAF,PFTT,PFTM,TPFTT,TPFTM,AC1,AC2
REAL TFVE,MFVE,TTRIPT,CATCHT,CATCHM,FBE,DR,FR,FP,FB,U1,U2
REAL NBORN,R1,R2,CPUE1,CPUE2,SR,CT,CM,MR,CC,L,H,TTRIPM
REAL MFP,MFB,AFP,AFB,TRIPT,TRIPM,HF,DF,MC1,MC2,AR1,AR2
REAL BIOM,TBIOM,TCATT,TCATM,SUMCT,SUMCM,XMEANT,XMEANM,SSUMT
REAL SSUMM,S1,S2,SS1,SSZ,STDT,STDM,RV1,RV2,RN,SB,SSB,STDB
REAL PROFTT,PROFTM,XMEANB,XMPFTT,XMPFTM,SUMB,TTPFTT,TTPFTM
REAL SN,SS,SSU,SSS,SUMPT,SUMPM,STDPT,STDPM

EXTERNAL UNIF

DIMENSION RT(3),RM(3),ACT(20),ACM(20),DR(20),SR(20),L(20)
DIMENSION FP(20),FB(20),W(20),FR(20),CT(20),CM(20),CC(20)
DIMENSION RV1(100),RV2(100),TCATT(100),TCATM(100),BIOM(50)
DIMENSION PROFTT(50),PROFTM(50)

WRITE (',10)

FORMATCZOX,'SIMULATION MODEL OF THE RED GROUPER FISHERY')
WRITE (',20)

FORMAT (30X,'MONTE CARLO ANALYSIS')

MODEL CONSTANTS AND PARAMETERS

DATA K/3/,DELT/1.5/,DELM/2.0/,ST1/.1/,ST2/.2/,ST3/.7/
DATA SM1/.2/,SM2/.8/,EM1/.016/,EM2/.0U3/,PT1/700000./
DATA PT2/525000./,PM1/750000./,PM2/750000./,PFAC/625000./
DATA PE1/2000./,PE2/6500./,HF/5.U6/,DF/10.52/,TRIPT/85./
DATA TRIPM/13./,ENTRYT/.02/,ENTRYM/.ON/,EXITT/.05/

DATA EXITM/.05/,CCUB/5000./,MR/.33/,ALPHA1/9.016/

DATA ALPHA2/7U9.95/,BETA1/.859/,BETA2/.565/,C1/2730.1/
DATA C2/178213./,SS/1.22E-6/,EGG/1.50E6/

ACT(1)=.05

ACT(2)=.3O

ACT(3)=.25

ACT(“)=.20

ACT(5)=.10

ACT(6)=.06

ACT(7)=.OU

ACM(1):.01

ACM(2)=.19

ACM(3)=.32

ACM(N)=.09

ACM(5)=.08

ACM(6)=.06

ACM(7)=.08

185

186

ACM(8):.O6

ACM(9)=.ON

ACM(10)=.ON
ACM(11)=.O3

MONTE CARLO EXPERIMENT 1: ANALYSIS OF 50 SIMULATION RUNS.
NR:50.

TBIOM=O.

SUMB:O.

TTPFTT:O.

TTPFTMzo.

SUMPT:O.

SUMPM=0.

DO 9 M:1,NR

INITIAL VALUES PHASE
RT(1)=6.

RT(2)=6.

RT(3):6.

RM(1):3.

RM(2):3.

RM(3)=3.

CATCHT=2793.
CATCHM:6703.
CATCH=CATCHT+CATCHM
FP(1):9N275000.
FP(2):63817000.
FP(3):32056000.
FP(N):133000OO.
FP(5):75N3000.
FP(6):N787000.
FP(7)=3025000.
FP(8):1709000.
FP(9)=1039000.
FP(10):566000.
FP(11)=253000.
FP(12):169000.
FP(13):113000.
FP(1N)=7NOOO.
FP(15)=NHOOO.
FP(16)=38000.
FP(17):27000.
FP(18):18000.
FP(19):9000.
FP(20)=9000.

DO 1 J:1,20
L(J)=80.2'(1.-EXP(-O.159*(J+1.21)))
W(J)=.OOOO138*(L(J)*'3.)
FB(J)=FP(J)'W(J)/1000.
CONTINUE
MFP=FP(1)+FP(2)
AFP=FP(3)+FP(A)+FP(5)+FP(6)+FP(7)+FP(8)+FP(9)+FP(10)+FP(11)+
FP(12)+FP(13)+FP(14)+FP(15)+FP(16)+FP(17)+FP(18)+FP(19)+FP(20)
TFP:MFP+AFP
MFB=FB(1)+FB(2)

187

AFB:FB(3)+FB(A)+FB(5)+FB(6)+FB(7)+FB(8)+FB(9)+FB(10)+FB(11)+
FB(12)+FB(13)+FB(1N)+FB(15)+FB(16)+FB(17)+FB(18)+FB(19)+FB(20)
TFB:MFB+AFB

DO 2 J:1,2O
CT(J)=ACT(J)*CATCHT/FB(J)
CM(J)=ACM(J)*CATCHM/FB(J)
CC(J):ACM(J)*CCUB/FB(J)
FR(J)=CT(J)+CM(J)+CC(J)
DR(J)=FR(J)+MR
SR(J)=1.-DR(J)

CONTINUE

CPUE1:.O388

CPUE2:.2723

MFV=180.

TFV:850.

TTRIPT:TFV*TRIPT
TTRIPM:MFV'TRIPM
FBE=138.E3
EMP:TFV*3.+MFV*7.
SEAFC=ST1RCATCHT
EERG:CATCHM'(PE1*EM1+PE2'EM2)
ACTFV=O.

ACMFV:O.

TFVE:O.

MFVE=O.

FST:ST1*CATCHT
FMTzSTZRCATCHT
FPT=ST3RCATCHT
FMM:SM1'CATCHM
FPM:SM2'CATCHM
FAC=CATCHM'.25
TRT:PT1'FMT+PT2‘FPT
TRM:PM1*FMM+PM2*FPM+PFAC*FAC
THFzHFETRIPT'TFV
TDF:DF'TRIPM*MFV
TCT=C1RTHF

TCM:C2'TDF
AC1:TCT/CATCHT
AC2:TCM/CATCHM
PFTT=TRT-TCT
PFTM:TRM-TCM

TPFTT=PFTT

TPFTM:PFTM

EGGS:EGG*SS
NBORN:EGGS*AFP

SUMCT:0.

SUMCM=O.

SSUMT:O.

SSUMM:O.

I=O.

XLMDA:.3

VAR1:65.

VAR2:124255.

188

R1:O.

R2=0.

T=O.

SPECIFICATIONS OF SIMULATION RUN.
DT:.2

RLGTH=20.

NIPP:1./DT+.OOO1

NIT=RLGTH/DT+.0001

NIOL:NIT/NIPP

EXECUTION PHASE

DO 3 I1:1,NIT

T:T+DT

COMPUTE STATE VARIABLES.

D0 5 J=20,2,-1
FP(J)=FP(J)+DT*(SR(J-1)‘FP(J-1)-FP(J))
CONTINUE
FP(1)=FP(1)+DT'((1.-MR)'NBORN-FP(1))
MFP=FP(1)+FP(2)
AFP=FP(3)+FP(A)+FP(5)+FP(6)+FP(7)+FP(8)+FP(9)+FP(10)+FP(11)+
FP(12)+FP(13)+FP(1N)+FP(15)+FP(16)+FP(17)+FP(18)+FP(19)+FP(20)
TFP:MFP+AFP

NBORN:EGGS’AFP

DO 6 J:1,20

FB(J):FP(J)*W(J)/1000.

CONTINUE

MFB:FB(1)+FB(2)
AFB:FB(3)+FB(N)+FB(5)+FB(6)+FB(7)+FB(8)+FB(9)+FB(10)+FB(11)+
FB(12)+FB(13)+FB(1H)+FB(15)+FB(16)+FB(17)+FB(18)+FE(19)+FB(20)
TFB:MFB+AFB

TPFTT:TPFTT+DT’(TRT-TCT)
TPFTM:TPFTM+DT'(TRM-TCM)
IF(TFV.LT.850) ENTRYT=.05
IF(TFV.GE.850) ENTRYT:.02
IF(MFV.LT.180) ENTRYM:.05
IF(MFV.GE.180) ENTRYM:.0U
IF(PFTT.LT.O.) TFVE=TFV‘(-EXITT)
IF(PFTT.CT.O.) TFVE=TFVRENTRYT
IF(PFTT.EQ.0.) TFVE=0.

IF(PFTM.LT.0.) MFVE=MFV*(-EXITM)
IF(PFTM.GT.O.) MFVE:MFV'ENTRYM
IF(PFTM.EQ.0.) MFVE=0.
TFV:TFV+DT‘(ACTFV)

MFV:MFV+DT*(ACMFV)

EMP:TFV'3.+MFV'7.
SEAFC:SEAFC+DT'(FST+FMT)
EERG:EERG+DT'(CATCHM*(PE1’EM1+PE2'EM2))
CALL DELAY(TFVE,ACTFV,RT,DELT,DT,K)
CALL DELAY(MFVE,ACMFV,RM,DELM,DT,K)
COMPUTE RATE VARIABLES.

BAF=TFB/FBE

IF(T.GE.7.) TRIPM=9.

TTRIPT:TRIPT*TFV

TTRIPMzTRIPM'MFV

189

CALL EXACOR(XLMDA,VAR1,DT,I,R1)
CATCHT=(ALPHA1'(HF**BETA1)+R1)‘BAF‘TTRIPT/1000.
CALL EXACOR(XLMDA,VAR2,DT,I,R2)
CATCHM:(ALPHA2*(DF'*BETA2)+R2)‘BAF'TTRIPM/1000.
CATCH:CATCHT+CATCHM
CPUE1=CATCHT/(TFV'TRIPT)
CPUE2=CATCHM/(MFV'TRIPM’DF)

DO 7 J=1,20
CT(J):ACT(J)*CATCHT/FB(J)
CM(J):ACM(J)’CATCHM/FB(J)
CC(J)=ACM(J)'CCUB/FB(J)
FR(J)=CT(J)+CM(J)+CC(J)
DR(J):FR(J)+MR

SR(J):1.-DR(J)

CONTINUE

FST:ST1'CATCHT

FMT:ST2*CATCHT

FPT=ST3'CATCHT

FMM=SM1RCATCHM

FPM=SM2'CATCHM

FAC:CATCHM'.25
TRT:PT1*FMT+PT2'FPT
TRM:PM1'FMM+PM2*FPM+PFAC*FAC
AR1:TRT/CATCHT

AR2:TRM/CATCHM
THF:HF'TRIPT'TFV
TDF=DFPTRIPMRMFV

TCT=C1ETHF

TCM:C2'TDF
U1:((CATCHT'1000./(TTRIPT'BAF))-R1/1000.)'*((1/BETA1)-1)

U2=((CATCHM’1000./(TTRIPM’BAF))-R2/1000.)**((1/BETA2)-1)
MC1=(C1'1000./((ALPHA1*'(1./BETA1))*BETA1*BAF))*U1
M02=(C2'1000./((ALPHA2*’(1./BETA2))*BETA2*BAF))*U2

AC1=TCT/CATCHT
AC2=TCM/CATCHM

PFTT:TRT-TCT

PFTM:TRM-TCM

MONTE CARLO EXPERIMENT 2: WITHIN RUN ANALYSIS.
IF(M.GT.1) GOTO 3

SUMCT=SUMCT+CPUE1

SUMCM=SUMCM+CPUE2

TCATT(I1)=CATCHT

TCATM(I1):CATCHM

XMEANT=SUMCT/NIT

XMEANM:SUMCM/NIT

RV1(I1)=R1

RV2(I1):R2

CONTINUE

DO 8 11:1,100

S1=(ABS(TCATT(I1)-XMEANT))**2.
52=(ABS(TCATM(I1)—XMEANM)>**2.

SSUMT:SSUMT+S1

SSUMM=SSUMM+SZ

1

3

)4

1

0

0

12

5

6

7
1

0

0

O
3

80

—n|\O
3:0

190

CONTINUE

STORE RUN DATA FOR STATISTICS.
BIOM(M)=TFB

TBIOMzTBIOM+TFB

PROFTT(M):PFTT

TTPFTT=TTPFTT+PFTT

PROFTM(M)=PPTM

TTPFTMzTTPFTM+PFTM

SS1=SSUMT/(NIT-1)

SS2=SSUMM/(NIT-1)

STDT:SQRT(SS1)

STDM:SQRT(SS2)

CONTINUE

COMPUTE MEANS AND STANDARD DEVIATIONS.
XMPFTT:TTPFTT/NR

XMPFTMzTTPFTM/NR

XMEANB=TBIOM/NR

DO 11 M=1,NR
S3=(ABS(BIOM(M)-XMEANB))**2.
su=(ABS(PROFTT(M)-XMPFTT))**2.
Ss=(ABS(PROFTM(M)-XMPFTM))**2.
SUMB=SUMB+S3

SUMPT=SUMPT+SA

SUMPM=SUMPM+SS

CONTINUE

SS3=SUMB/(NR-1)

SSA=SUMPT/(NR-1)

SSS=SUMPM/(NR-1)

STDB=SQRT(SS3)

STDPT=SQRT(SSA)

STDPM:SQRT(SSS)

HRITE (*,30)

FORMAT ('0',15X,'N',15X,'CATCHT',12X,'CATCHM')
DO 12 I1:1,NIT

WRITE (*,u0) I1,TCATT(I1),TCATM(I1)
FORMAT (11x,16,ux,2F17.1)

CONTINUE

wRITE (*,50) XMEANT,XMEANM,STDT,STDM
FORMAT ('0','XMEANT:',F6.1,3X,'XMEANM=',F6.1,3X,
'STDT:',F6.1,3X,'STDM:',F6.1)

wRITE (* 60)

FORMAT (111,15X,1N*,11X,1RV11,11X,1RV2')
DO 13 I1=1,NIT

NRITE (*,70) I1,RV1(I1),RV2(I1)
FORMAT (11X,IO,NX,F1O.3,ux,F1O.3)
CONTINUE 8 )

o
NORRET((11',1flX,'RUN',1OX,'BIOMASS',10X,'PROFTT',
1OX,'PROFTM'%

DO 1n M=1 N

wRITE (*,96) M,BIOM(M),PROFTT(M),PROFTM(M)
FORMAT (12X,16,3F17.1)

CONTINUE

100
110
120

1010

191

HRITE (*,100) XMEANB,STDB
FORMAT('O',12x,vXMEANB=v,F8.1,1OX,1sTDB=v,FB,1)
wRITE (*,11O) XMPFTT,STDPT

FORMAT ('0',12X,'XMPFTT:',F12.1,6X,'STDPT:',F12.1)
NRITE (*,120) XMPFTM,STDPM

EggMAT ('0'.12X.'XMPFTM=',F12.1,6X,'STDPM=',F12.1)
SUBROUTINE EXACOR(XLMDA,VAR,DT,I,U)
IF(I.NE.O) GO TO 1

U=0.

B=XLMDA*'DT

A=(1.+B)/(1.-B)
R=UNIF(ISEED,JSEED)
XK=(A*12.*VAR)*'.5

XN=XK*(R-.5)

U=B*U-(1.-B)*XN

I:I+1

RETURN

END

SUBROUTINE DELAY(RINR,ROUTR,CROUTR,DEL,DT,K)
DIMENSION CROUTR(1)
DEL1=DEL/(FLOAT<K)*DT)

RIN:RINR

DO 3 I:1,K

ABC:CROUTR(I)
CROUTR(I)=ABC+(RIN-ABC)/DEL1
RIN:ABC

ROUTR:CROUTR(K)

RETURN

END

SUBROUTINE RANDOM(I,B)

INTEGER*2 ISEED,I

CHARACTER BYTE(2),B

EOUIVALENCE (ISEED,BYTE(1))
ISEED=I

ISEED:ISEED*2837+1

B=BYTE(2)

IF(ISEED.LT.O) ISEED:ISEED+32767+1
I=ISEED

RETURN

END

FUNCTION UNIF(ISEED,JSEED)
INTEGER*2 ISEED,JSEED,IEXPO
CHARACTER'1 B(N),RBYTE
EOUIVALENCE (X,B(1))

CALL RANDOM(ISEED,B(2))

CALL RANDOM(ISEED,B(3))

CALL RANDOM(ISEED,B(1))

IEXPO=63

IF (B(3).LT.128) GOTO 1030
IEXPO:66

CALL RANDOM(JSEED,RBYTE)
IEXPO:IEXPO-N

1020
1030

192

IF (RBYTE.EQ.0) GOTO 1010
IF (RBYTE.GT.127) GOTO 1030
IF (RBYTE.GT.63) GOTO 1020
IEXPO:IEXPO-1

IF (RBYTE.GT.31) GOTO 1030
IF (RBYTE.GT.15) GOTO 1020
IEXPO=IEXPO-1

IF (RBYTE.GT.7) GOTO 1030
IF (RBYTE.GT.3) GOTO 1020
IEXPO:IEXPO-1

IF (RBYTE.GT.1) GOTO 1030
B(3)=CHAR(ICHAR(B(3) )-128)
B(u):CHAR(IEXPO)

UNIF=X

RETURN

END

APPENDIX F

 

H

APPENDIX F
SIMULATION RESULTS

SIMULATION MODEL OF THE RED GROUPER FISHERY
YUCATAN CONTINENTAL SHELF

OOOOOOOOOOOOOOOO

OkomflmUTC'UJN-‘oomQONU'I-C’LMN—P
c o o I
00000

mad-Add—h—ld—DJ

193

CPUE1 CPUE2 CATCH BIOMASS
.0388 .2723 9496.0 137783.3
.0342 .2504 8761.9 138725.1
.0406 .2410 9181.1 140491.3
.0393 .2835 10474.5 140414.7
.0367 .2754 10378.0 137792.9
.0453 .2602 10955.4 135259.9
.0327 .3071 11681.8 130849.7
.0286 .2771 8201.7 127140.7
.0278 .2534 7843.5 127357.3
.0402 .2688 9435.0 126943.6
.0320 .2905 9548.6 124331.2
.0309 .1892 7268.2 122661.4
.0243 .2154 7527.9 121177.7
.0303 .2327 8644.7 119192.5
.0351 .2229 9007.3 116718.9
.0400 .2465 10269.9 111318.5
.0375 .1971 8914.0 106641.2
.0324 .1751 8004.2 103315.7
.0253 .1534 6780.5 100265.8
.0288 .1838 7874.6 97073.3
.0175 .1874 6681.5 95130.2

 

.a.a .q
AOOQNO‘U'I-B'WN-fi

.A-d—lA—J—lA-J
\omNOsU'Ia-wm

N
O

RANVAR1
-.004700

.001089
-.000080
-.001968

.007471
-.004312
-.007742
.008675
.004903
.003275
.003996
.011104
.003647
.002731
.010846
.009816
.004589
.003891
.002245
-.013307

194

RANVAR2

213885
344297
097101
066637
041350
572591
329322
054458
240089
558007

.595116
.253756
.000627
.061732
.380420
.151064
.374663
.613079
.085024
.025220

CATCHT
2492.6
2995.7
2959.1
2815.5
3540.8
2602.2
2315.7
225509
3283.5
2649.2
2606.6
2087.9
3113.1
3612.9
3454.1
3043.1
2404.9
2736.7
1646.1

CATCHM
6269.
6185.
7515.
7562.
7u1u.
9079.
5886.
5587.
6151.
6899.
4661.
5440.
5993.
5894.
6657.
5&59.
4961.
4375.
5137.
5035.

womaoaw=o~lzmmao~mmc=w

.3... ...,
“OOQNO‘U'l-cwm—b

Nd—b—b—J—A—A—bc—A
00054001sz

ACTV

435.5
36705
378.9
405.9
329.0
456.5
521.8
537.1
371.2
466.4
482.6
614.1
491.7
424.9
372.6
397.2
459.

588.6
516.9
849.9

195

ACMV

711.7
739.5
628.5
647.2
684.8
580.3
643.2
703.2
662.9
613.4
941.9
827.3
766.0
799.4
722.9
904.1

1018.0
1161.6

9690”
951.0

PFTT
353935.1
628973.3
587812.8
483195.6
879750.8
314828.9
128993.1

91198.6
677318.8
294317.0
247466.1
~76331.3
227579.8
475103.6
740282.3
622819.0
359311-5
-26605.9
165762.9

-448429.3

PFTM

1219844.0
1031229.0
2087216.0
1959010.0
1641802.0
2959136.0
1548366.0
1134592.0
1497032.0
2020550.0
-166185.5

429392.0
840775.0
629578.5

1220318.0

11657.5

-554636.5
-1117311.0
-324307.0
-225519.5

H

Add—bdd—hdc—l.‘
omflmmzwmdoomqmchN—P

N
O

TRT
1439469.0
1730020.0
1708880.0
1625928.0
2044837.0
150275u.o
1337298.0
1302805.0
1896225.0
1529903.o
1505283.0
1205737.0
1531129.0
1797793.o
2086425.0
1994761.0
1757401.0
1388828.0
1580434.0

950632.6

196

TCT
1085534.0
1101047.0
1121068.0
1142732.0
1165087.0
1187925.0
1208305.0
1211606.0
1218906.0
1235586.0
1257817.0
1282068.0
1303550.0
1322690.0
1346143.0
1371942.0
1398089.0
1415434.0
1414671.0
1399062.0

TRM
5681521.0
5605522.0
6810812.0
6853543.0
6719414.0
8228381.
5334260.
5063708.
5574795-
6252583.
4224641.
4930019.
5431535.
5341693.
6032974.
4948040.
4496020.
3965375.0
4656240.0
4563275.0

OOOOOOOOOOOO

TCM
4461677.0
4574294.0
4723596.0
4894533.0
5077613.0
5269246.0
3785893.0
3929117.0
4077763.0
4232033.0
4390826.0
4500627.0
4590760.0
4712114.0
4812656.0
4936383.0
5050656.0
5082686.0
4980547.0
4788794.0

 

_a_.|_.n_.s_.|_5_5_s_s_.n O—l
koooqoxmzwmdooooflmmzwm-a

N
O

EMP
3851.7
3920.8
4011.0
4111.4
4216.9
4326.1
4431.5
4498.8
4577.7
4681.2
4799.7
4902.7
4991.0
5086.6
5183.9
5296.3
5405.6
5460.0
5415.8
5299.3

197

SEAFC
1695.7
2547.9
3439.5
4254.6
5140.4
6004.1
6654.5
7413.6
8253.9
9292.8
10279.2
11108.4
11910.9
12834.2
13891.6
14936.1
15745.0
16563.4
17329.1
17884.1

EERG
4123091.
5947948-
8057350.

10701960.
13148600.
15906910.
18649940.
20352570.
22044580.
23896740.
25516060.
27206640.
28982030.
30655520.
32709450.
34495940.
36153630.
37653400.
39154090.
40541400.

OOOOOOOOOOOOOOOOOOOO

4...: ...}
AOQmNIOUT-DWN-P

_A...|_s_s_n_s_.s_s
\om‘lO‘m-t—‘WN

N
O

TFV
856.7
869.0
884.8
901.9
919.5
937.6
953.6
956.3
962.0
975.2
992.7

1011.9
1028.8
1043.9
1062.4
1082.8
1103.4
1117.1
1116.5
1104.2

198

MFV
183.
187.
193.
200.
208.
216.
224.
232.
241.
250.
260.
266.
272.
279.
285.
292.
299.
301.
295.
283.

mNNWONdeNm‘lOkNwmmN—b

TPFTT
1106799.0
1654808.0
2260911.0
2698563.0
3250440.0
3737149.0
3790598.0
4041518.0
4444828.0
5218456.0
5871494.0
6198512.0
6450166.0
5915323.0
7617293.0
8269621.0
8442161.0
8610855.0
8667441.0
8327390.0

TPFTM
3189056.
3986516.
5480608.
8371086.

10508450.
13365240.
15982290.
17082280.
18005590.
19243530.
19647140.
20116170.
20740370.
20961090.
22176270.
22505380.
22333470.
21620170.
20941910.
20083630.

OOOOOOOOOOOOOOOOOOOO

_JA—Ad—A-d—Jc—l—A—J h.)
xomxlmmcwm—sooooxzomcwmd

N
O

MC1
445.5
”3909
440.1
448.5
456.9
472.3
486.
148503
486.8
497.1
503.8
510.0
518.5
529.5
555.2
579.5
598.2
616.4
636.6
649.6

199

MR1
577.5
577.5
577.5
577.5
577.5
577.5
577.5
577.5
577.5
577.5
577.5
577.5
577.5
577.5
577.5
577.5
577.5
577.5
577.5
577.5

MR2
906.
906.
906.
906.
906.
906.
906.
906.
906.
906.
906.
906.
906.
906.
906.
906.
906.
906.
906.
906.

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58986310.0
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21860560.0
10617480.0
6235509.0
3683768.0
2201208.0
1199125.0
649983.1
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154861.7
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35596.7
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13608.9
9599.8
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4471.7
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200

BIOMASS
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17974.6
18082.9
13505.9
10965.2
8326.5
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3878.6
2393.8
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692.7
227.0
182.0
140.8
106.7
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18.8

 

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