NBSIR 74-522

First Interim Report on Salmon

Fisliery Modelling

Dr. Frederick C. Johnson

Applied Mathematics Division

Institute for Basic Standards

National Bureau of Standards

Washington, D. C. 20234

July 8, 1974

Progress Report

Prepared for Washington State Dept. of Fisheries

Oiympia, Washington 98504

NATIO.^>5AL BUREAU Oi- STANDARDS REPORT

r KZS Fr.OJ^CT NBS REPORT

2050571 July 8, 1974 74522

First Interim Report on

Salmon Fishery Modelling

by

Frederick C. Johnson

Applied Mathematics Division

U.S. DEPARTMENT OF COMMERCE

NATiO.XAL BUREAU OF STANDARDS

Preface

The salmon fishery modelling project is

a joint State-Federal program for the development of improved techniques for analyzing the

economic and biological effects of changes in

the Pacific Coast salmon fishe'ry regulatory

parameters. This interim report covers the

initial program design phase of the project.

This portion of the project was sponsored by

the Washington State Department of Fisheries

under Service Contract No. 549.
Table of Contents

Page

I. Introduction 1

II. The Fishery Model 3

11. 1 Input Requirements 5

11. 2 Calibration Process 10

11. 3 Regulatory Analysis 13

III. Project Status 15

References ' . 17
I. Introduction

r

The Pacific Coast salmon fisheries are a highly interconnected 'system composed of several types of fishing gear active

over large geographical areas. The fisheries harvest many

different stocks of salmon, and the biological characteristics

of these stocks can vary substantially even within a single

species. The large number of salmon stocks, their complex life

cycles and the dynamic nature of the fishery combine to present

a formidable challenge to successful salmon fisheries management.

Because of the overall complexity and importance of the fishery

management problem there has been an ongoing effort to develop

improved techniques for assessing the effects of fishery regulatory action on the economic and biological aspects of the

salmon fisheries. In a previous study [1] the development of

a management model of these fisheries was recommended in order

to provide regulatory agencies with a tool for systematically

analyzing the large amounts of data that are being obtained on

fisheries performance. This report covers the initial design

and implementation phases of such a model.

The purpose of the salmon fisheries management model is to

quantitatively analyze the effects of fishery regulatory changes

on the economic performance of the fisheries and on the abundance

and long term stability of the component stocks of the salmon
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i

resource. In this manner, the model can be used as a test bed

for the evaluation of alternative regulatory policies for the

salmon fisheries. Section II of this report outlines the components of the model, and the current status of the fishery

modelling project is given in Section III.
II. The Fishery Model

» The fishery model is a time oriented simulation model which

emulates the characteristic processes of the major components

of the salmon fishery system. The simulation begins with the

initial recruitment to the fisheries, continues through the

entire ocean life cycle of the salmon stocks and ends with the

final escapement by the oldest members of each stock. From

initial recruitment to final escapement the model simulates

the major biological processes (growth, natural mortality,

migration, maturation) of each stock and the stock-fishery

interactions. The effects of fishing are determined by the

population and location of the stocks, their length characteristics, the regulatory parameters of the different fisheries

and the historical performance of the fisheries as reflected

in catch statistics. The total catch, catch value and escapement is obtained for each stock, and this information forms the

basis of comparison between alternative fishery regulatory

policies.

The fishery model is termed a time oriented model because

the sequence of events in the model approximates as closely as

possible the actual event sequence. A variable time period is

used in the model as the basis of the sequential process. The

calendar year is divided into 32 time periods which vary from

a minimum length of one week to a maximum length of one month.

The time periods used in the model are identical to the reportin
periods established by the Department of Fisheries and Forestry

of Canada for documenting British Columbia catch statistics.

This system uses shorter reporting periods during the major

fishing seasons and longer periods throughout the rest of the

year. For the fishery model this has the advantage of providing a time period length that is inversely proportional to

fishery activity.

The prototype version of the fishery model is a steady state

deterministic model. It is a steady state model in the sense

that the fishery regulations and annual fishing effort are held

constant throughout the life of a stock. This emphasizes the

major long term effects of a stable fishery and eliminates

transitory effects caused by fluctuations in effort and regulatory changes. The model is a deterministic model because the

effects of random variations in fishing and in the biological

processes of the stocks are not considered. The emphasis of the

initial, prototype version of the model is to begin the analysis

of the major stock-fishery interactions in the simplest meaningful fashion. Subsequent versions of the model can be expanded

to consider transitory and random factors. In many cases, however, a parametric analysis of various combinations of fishing

effort and stock characteristics may well be more useful for

regulatory analysis for such purposes as the establishment of

confidence bounds.
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Spav.Tier-recruit relationships are not included in the' model

because of the great variability which exists in these relationships.' Instead, the model computes the total annual escapement

for each stock that results from a particular regulatory policy,

and it is left to the management agency to determine whether the

escapement is adequate. This approach is in keeping with the

management practice of establishing minimum escapement quotas

and adjusting the terminal fishery effort to achieve these goals.

Figure II. 1 gives a summary of the components of the fishery

model which consists of three principal tasks: input, calibration

and analysis, an outline of each of these tasks is given below.

II, 1 Input Requirements

The complexity of the salmon fishery system greatly impacts

the input requirements of the model in that large amounts of

data may be required in order to adequately describe the essential characteristics of the system. Consequently, the input

parameters for the model have been selected with a great deal

of care in order to minimize the costs of data preparation. A

prime consideration for the selection of the input parameters

was that the existing fishery performance data should not require

major reprocessing for use by the model. The input to the

fishery model consists of three major categories:
DATA irjPUT

PROCESS" 1

AREA DATA

STOCK DATA

CATCH DATA

CALIBRATION

BACK CALCULATE FOR INITIAL POPULATION

SIZE AT RECRUITMENT

COMPUTE MATURATION RATES

ALLOCATE FISHIfiG INDUCED MORTALITY

COMPUTE FISHING AND INDUCED

MORTALITY RATES

ANALYSIS

ENTER MODIFIED REGULATIONS

COMPUTE SCALE FACTORS FOR FISHING

RATES

PROCESS STOCKS AND ACCUMULATE

FISHERY PERFORMANCE STATISTICS

Figure IM. Fishery Model Task Sequence
7

o area data,

o stock data,

o catch data.

Fishery regulatory data are included in the area data category.

The basic geographical unit of the model is the area which

is used to specify the location of the various fisheries and the

migration patterns of the stocks. An area may refer either to

a section of the ocean or to a freshwater location. The areas

that are defined in the input data serve to partition the fresh

and salt water environment into management zones, each of which

may contain fisheries that are subject to different regulatory

parameters

.

The area data contain a description of the fisheries that

operate in each area. A fishery description consists of the

following items:

o fishery name,

o species fished,

o gear type,

o open season(s) , o minimum length(s)

,

o catch values.

o induced mortalities

A fishery season is defined by specifying the initial and

final time periods for the season and the minimum legal length
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r 1 of the catch during the season. A fishery is not restricted 1

to a single season by the model, and, therefore, the minimum

length regulation is not required to remain constant. Commercial catch values are specified by giving dollar/pound values

to weight ranges of the catch. Thus, a fish between eight and

twelve pounds may be valued at $1.00 per pound while a fish larger i

than twelve pounds may be valued at $1.25 per pound. For sport \ fisheries the catch values are in terms of dollar/fish rather

than dollar/pound, and the weight range feature also applies.

Induced mortality refers to hooking mortality and other

types of mortality that is caused by the act of fishing but

which does not generate any catch value. The initial version

of the fishery model considers the effects of "shaker" mortality ] caused by the catch and release of sublegal fish. Subsequent ; versions of the model will be expanded to include other types \ of induced mortality such as cross-species mortality caused by

incidental catch. Shaker mortality is specified as a fraction \ of the legal catch and applies only to sublegal fish. i

The primary unit for categorizing salmon in the model is the

s to ck . A salmon stock is any group of fish that is distinguished j for fishery management purposes. For hatchery produced fish a

stock would typically be identifed by a single tag code or by a

group of codes. l-Jhile a stock is considered to have uniform bioI logical characteristics, it may be divided into substocks which '
9

-

are similar in all respects except for migration patterns.

This enables the model to consider the situation in which portions of the stock are subjected to entirely different fishing

pressures because of differences in migration.

The stock data input describe the biological characteristics

of the fish. For each stock, this data consists of:

o growth rates,

o natural mortality rates,

o length frequency parameters,

o substock categories,

o migration patterns.

The growth of the stock is given by the initial mean length

at recruitment, the maximum mean length, and monthly growth

rates. These rates are both age and maturity specific. Thus,

the model allows fish growth to vary by time of year, by age

and by maturity. It is assumed that each stock has a normally

distributed length frequency function at initial recruitment,

and that, in the absence of fishing, the population will remain

normally distributed. The standard deviations of the initial

and final distributions are specified by the length frequency

parameters, and the standard deviation follows the same growth

law as length. Thus, again in the absence of fishing, the mean

length of the stock and the length frequency distribution can

be obtained at any point in time.
10

The natural mortality rates are percentage rates rather than

exponential rates. As with growth rates, the mortality rates are

distinguished by age and maturity, but annual mortality rates

rather than monthly rates are specified. The annual rates are

used to compute equal monthly mortality rates.

The substock categories identify the substocks and specify

the fraction of the total initial recruitment population of the

stock that each substock comprises. The migration patterns are

specified for each substock by giving the areas in which the

substock resides by age and maturity type (mature or immature)

.

The catch data forms the major portion of the model input.

For each stock the number of fish caught is given by age of

fish, time period of the catch, maturity, area, gear type and

fishery. In addition the average fish length and weight are

given. This data is obtained from historial catch statistics

and provides the basis for calibrating all parameters of the model.

II . 2 Calibration Process

The calibration section of the fishery model calculates all

the fishing rates, maturation rates and induced mortality rates

required for a fishery simulation. These rates are based on the

catch data and on the number of fish of a given age that are of

legal or sublegal size. The first step of the calibration process

is the computation of the number of fish of each stock that are
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r initially recruited to the fisheries. A partial estimate of

the initial recruitment number is obtained by back calculation

using the escapement data, catch data and natural mortality

rate data. At the same time that these partial estimates are

obtained, the induced fishing mortality data is used to compute

the total hooking mortality for each species. Since hooking

mortality is calculated by species and not by stock, the next

step is to allocate the hooking mortality to the stocks of each

species. This computation is based on the relative number of

sublegal fish of each stock that is in the area where the hooking

mortality occurred. The distribution of the stocks among the

various areas is governed by the migration data, and the number

of sublegal fish is determined by the growth rates and length

frequency curves

.

After hooking mortality has been allocated to each stock,

it is also back calculated, and the final estimate of the total

initial recruitment is obtained. Thus, this estimate takes into

account escapement, catch, natural mortality and fishing induced

mortality.

At the same time that the back calculations are performed

it is convenient to store the number of immature and maturing

fish that are alive at the beginning of each year. The ratio

of the number of maturing fish to the total number of fish gives

the maturation rate for each age, and this rate is computed

separately for males and females.
12

The next step of the calibration process is the computation

of fishing rates and induced mortality rates. These rates are

obtained by sweeping forward in time and computing the ratio of

catch to legal fish population and the ratio of induced mortality

to the sublegal fish population for each area and for each time

period. This set of computations is performed separately for

each substock. The initial number of recruits for each stock is

decomposed into substocks using the estimated population percentage of each substock. Since both the catch data and the induced

mortality data are categorized by stock rather than by substock,

catches and induced mortality must be allocated to each substock.

This process is identical to the allocation of hooking mortality

to the stocks of each species and uses both the migration data

and growth data. , . .

,

The rates obtained from the calibration process are dependent

upon the age of the fish and the area and time period of the

catch. Thus, if 1000 fish of age 3 enter a fishing area in the

first week of June, the fishing and induced mortality rates determine how many fish are caught, and how many are killed by

fishing induced riortality. The entire calibration process is

based on a modified version of the standard catch equation

which takes into account migration effects and induced mortality

effects

.

By far the greatest amount of computation in the fishery

model occurs in the calibration process, and it would be wasteful
13

to repeat the calibration for each analysis. Therefore, Che

calibrated fishing rates, induced mortality rates, stock characteristics and supporting data can be saved on magnetic tape

and used for subsequent analyses. This substantially reduces

the cost of a regulatory analysis, and simplifies the data

processing requirements of the program.

II. 3 Regulation Analysis

The calibration process calculates fishing rates which are

based upon stock characteristics and catch data, and the catch

data, in turn, reflect a particulary set of fishery regulations

in force when the data were obtained. Thus, an analysis of a

regulatory change requires the determination of the impact of

the new regulation on the fishing and induced mortality rates.

Generally, a regulatory change either increases or decreases

the catch rate as, for example, when a fishing season is lengthened or shortened or when fishing effort is controlled. However,

a change in the minimum length regulation of a fishery does not

change the fishing and induced mortality rates but alters the

split betvreen legal and sublegal populations instead.

The regulation analysis section of the fishing model first

accepts the new regulatory data as specified by the user. This

data may change the season length, the fishing effort, the minimum length requirement or impose a catch quota. Based upon the
- 14 -

new regulations, scale factors are computed for the fishing and

induced mortality rates. The scale factors alter these rates

to correspond to the fishing effort under the new regulations.

The next step of the regulatory analysis process is a forward

time sweep which begins with the initial recruitment of each

stock to the fisheries. The modified fishing and induced

mortality rates are used to compute new catch estimates and

hooking mortality estimates. The split between catch and hooking

mortality reflects any changes in minimum length regulations

since the model uses minimum length to divide the stock population into legal and sublegal components.

The for\>7ard sweep continues through the first year of each

stock until the escapement (if any) is computed. The fish

remaining at the end of the year are split into immature and

maturing groups for the next year, and the process is repeated

for these older fish. This sequence continues until all maturation has occurred and the processing of the stock catch and

escapement estimates is completed. Processing concludes with

the preparation of catch, catch value, escapement and induced

mortality summaries. A new set of regulations may be then

entered and the entire cycle repeated as often as required for

an analysis of various regulatory alternatives.

i
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» III. Project Status

A mathematical description of the major components of the

biological, economic, fishery and regulatory sectors of the

fishery model has been completed. The input requirements for

the model have been specified, and these requirements have been

approved by the Washington State Department of Fisheries.

A simplified prototype fisheries model is being implemented.

This model is designed to test the basic structure of the

modelling approach and will serve as the basis for the full

fishery model. Because of the complexity of the full fishery

model, it is more efficient to begin with a relatively small

submodel which can gradually evolve into the full operating

model. This approach simplifies both the construction and

validation of the model. In particular, the prototype model

can be used to pin-point trouble areas very early when corrections can be easily made. This is m.ost important since it is

most likely that the validation process will indicate a need

for modifications and adjustments. The prototype model has

been specifically designed to accommodate this possibility.

A complete set of test data for the, prototype model has

been prepared for a Willipa Bay Coho stock. This data set

consists of approximately 750 cards which contain about 4500

data items. The stock is divided into two substocks, a north
migrating substock and a south migrating substock. The area

data consists of ten ocean areas and one freshwater area, and

the ocean areas range from central British Columbia to the

California coast. Fishery regulatory data and catch performance data is given for the American and Canadian troll fisheries,

the Willipa Bay gill net fishery, the Juan de Fuca Strait gill

net fishery, and ocean and river sport fisheries. This data set

will provide the principal initial test data for the prototype

model. Additional data sets are in preparation which cover

both Coho and Chinook salmon stocks.
17 -

References

1, Johnson, F.C., "Fishery Modelling and Analysis". Report

No. D180-17515-1, The Boeing Company, June 1973.
NBS-lUA (REV. 7-73)

U.S. DEPT. OF COMM.

R!RI inf;[?APHI(~ DATA

SHEET

1. PUIU.ICA I ION OR KliPOR 1 NO.

NBSIR 74-522

2. Gov't Accession

Mr. IN O.

3. Recipient's Acce,s,<;ion No.

4.iT[TLE AND SUBTITLE

First Interim Report on Salmon Fishery Modelling

5. Publication Date July 8, 1974

6. Performing Organization Code

7. AUTHOR(S)

Dr. Frederick C. Johnson

8- Performing Organ. Report No. NBSm 74-522

9. PERFORMING ORGANIZA TION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Hroiect/ lasK/Work Unit No. 2050571

11. Contract/Grant No.

12. Sponsoring Organization Name and Complete Address (Street, City, State, ZIP)

Washington State Dept. of Fisheries

Ol3mpia, Washington 98504

13. Type of Report & Period

Covered

1973-1974

15,, SUPPLEMENTARY. NOTES ; ,

16. ABSTRACT (A 200-word or less factual summary ol most sigpilicartt information. If document includes a significant

bibliography or literature survey, mention it here.)

The salmon fishery modelling project is a joint State-Federal program for the

development of improved techniques for analyzing the economic and biological effects

of changes in the Pacific Coast salmon fishery regulatory parameters. This interim

report covers the initial program design phase of the project.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name: separated by semicolons)

Analysis of Biological processes; Economic Performance; Fisheries Management; Fisheries Regulation; Mathematical Models; Salmon Fisheries Model.

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