Introduction to Tropical Fish Stock Assessment - Part 1: Manual













Table of Contents


by

Per Sparre
Danish Institute for Fisheries Research
Charlottenlund, Denmark

and

Siebren C. Venema
Project Manager
FAO Fisheries Department

FAO FISHERIES TECHNICAL PAPER 306/1 Rev. 2

INTERNATIONAL YEAR OF THE OCEAN '98

DANIDA

Food and Agriculture Organization of the United Nations

FAO - FIAT PANIS

Rome, 1998

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

M-43
ISBN 92-5-103996-8

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© FAO 1998

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Table of Contents


PREPARATION OF THIS DOCUMENT

LIST OF SYMBOLS

1. INTRODUCTION

1.1 THE PRIMARY OBJECTIVE OF FISH STOCK ASSESSMENT
1.2 THE STOCK CONCEPT
1.3 MODELS

1.3.1 Analytical models
1.3.2 Holistic models

1.4 ASSESSMENT OF STOCKS IN TROPICAL WATERS
1.5 DEFINITIONS OF BODY LENGTH
1.6 AGE AND RECRUITMENT
1.7 THE UNDERLYING ASSUMPTION OF RANDOM SAMPLES
1.8 THE ORGANIZATION OF THE MANUAL
1.9 FURTHER READING

2. BIOSTATISTICS

2.1 MEAN VALUE AND VARIANCE
2.2 THE NORMAL DISTRIBUTION
2.3 CONFIDENCE LIMITS
2.4 ORDINARY LINEAR REGRESSION ANALYSIS
2.5 THE CORRELATION COEFFICIENT AND FUNCTIONAL REGRESSION
2.6 LINEAR TRANSFORMATIONS

3. ESTIMATION OF GROWTH PARAMETERS

3.1 THE VON BERTALANFFY GROWTH EQUATION

3.1.1 Variability and applicability of growth parameters
3.1.2 The weight-based von Bertalanffy growth equation

3.2 INPUT DATA FOR THE VON BERTALANFFY GROWTH EQUATION

3.2.1 Data from age readings and length measurements
3.2.2 Length composition data (without age compositions)
3.2.3 Data from commercial catches

3.3 METHODS FOR ESTIMATION OF GROWTH PARAMETERS FROM LENGTH-AT-AGE DATA

3.3.1 The Gulland and Holt plot
3.3.2 The Ford-Walford plot and Chapman's method
3.3.3 The von Bertalanffy plot
3.3.4 The least squares method

3.4 ESTIMATION OF AGE COMPOSITION FROM LENGTH-FREQUENCIES

3.4.1 Bhattacharya's method
3.4.2 Modal progression analysis
3.4.3 The probability paper and parabola methods

3.5 FITTING GROWTH CURVES BY MEANS OF COMPUTER PROGRAMS

3.5.1 ELEFAN I
3.5.2 The seasonalized von Bertalanffy growth equation
3.5.3 Maximum likelihood methods
3.5.4 Limitations of length-frequency analysis

4. ESTIMATION OF MORTALITY RATES

4.1 THE CONCEPT OF A COHORT AND SOME BASIC NOTATION
4.2 THE DYNAMICS OF A COHORT, THE EXPONENTIAL DECAY MODEL
4.3 ESTIMATION OF Z FROM CATCH PER UNIT OF EFFORT DATA AND THE CONCEPT OF THE CATCHABILITY COEFFICIENT

4.3.1 Heincke's method
4.3.2 Robson and Chapman's method

4.4 ESTIMATION OF Z FROM A LINEARIZED CATCH CURVE

4.4.1 The constant parameter system
4.4.2 The linearized catch curve equation
4.4.3 The linearized catch curve based on age composition data
4.4.4 The linearized catch curve based on age compositions with variable time intervals
4.4.5 The linearized catch curve based on length composition data
4.4.6 The cumulated catch curve based on length composition data. (The Jones and van Zalinge method)
4.4.7 Summary of the linearized catch curve methods

4.5 BEVERTON AND HOLT'S Z-EQUATIONS

4.5.1 Beverton and Holt's Z-equation based on length data
4.5.2 Beverton and Holt's Z-equation based on age data
4.5.3 Beverton and Holt's Z-equation based on length-at-first-capture
4.5.4 The Powell-Wetherall method

4.6 A PLOT OF Z ON EFFORT FOR SEPARATE ESTIMATES OF F AND M
4.7 NATURAL MORTALITY

4.7.1 Natural mortality and longevity
4.7.2 Pauly's empirical formula
4.7.3 Rikhter and Efanov's formula

5. VIRTUAL POPULATION METHODS

5.1 VIRTUAL POPULATION ANALYSIS (VPA)
5.2 AGE-BASED COHORT ANALYSIS (POPE'S COHORT ANALYSIS)
5.3 JONES' LENGTH-BASED COHORT ANALYSIS
5.4 THE SLICING TECHNIQUE

6. GEAR SELECTIVITY

6.1 ESTIMATION OF TRAWL NET SELECTION
6.2 ESTIMATION OF GILL NET SELECTION

6.2.1 Symmetrical selection curves
6.2.2 The product of two logistic curves

6.3 DISCUSSION OF SELECTION BY OTHER GEARS
6.4 OTHER ASPECTS OF GEAR SELECTIVITY

6.4.1 Knife-edge selection
6.4.2 Recruitment and selectivity
6.4.3 Selectivity as a function of age

6.5 ESTIMATION OF THE RESULTANT OGIVE FROM A CATCH CURVE
6.6 GEAR SELECTIVITY AND VPA METHODS

6.6.1 Gear selectivity and fishing mortality
6.6.2 Estimation of selection curves from cohort analysis

6.7 USING A SELECTION CURVE TO ADJUST LENGTH-FREQUENCY SAMPLES

7. SAMPLING

7.1 SIMPLE RANDOM SAMPLING
7.2 STRATIFIED RANDOM SAMPLING
7.3 PROPORTIONAL SAMPLING
7.4 SAMPLING COMMERCIAL CATCHES
7.5 ESTIMATION OF THE TOTAL CATCH IN WEIGHT OF A CERTAIN SPECIES
7.6 ESTIMATION OF THE LENGTH COMPOSITION OF A CERTAIN SPECIES IN THE TOTAL CATCH

8. PREDICTION MODELS

8.1 ASSUMPTIONS AND MODELS UNDERLYING THE YIELD PER RECRUIT MODEL OF BEVERTON AND HOLT
8.2 BEVERTON AND HOLT'S YIELD PER RECRUIT MODEL
8.3 BEVERTON AND HOLT'S BIOMASS PER RECRUIT MODEL
8.4 BEVERTON AND HOLT'S RELATIVE YIELD PER RECRUIT MODEL
8.5 YIELD PER RECRUIT FROM LENGTH DATA
8.6 AGE-BASED THOMPSON AND BELL MODEL
8.7 LENGTH-BASED THOMPSON AND BELL MODEL
8.8 PREDICTION OF THE EFFECTS OF CHANGES OF MESH SIZES USING THE THOMPSON AND BELL METHOD

9. ESTIMATION OF MAXIMUM SUSTAINABLE YIELD USING SURPLUS PRODUCTION MODELS

9.1 THE SCHAEFER AND FOX MODELS
9.2 GULLAND'S FORMULA
9.3 CADIMA'S FORMULA
9.4 MSY ESTIMATORS BASED ON THE SURPLUS PRODUCTION MODEL

9.4.1 Validation of estimates of MSY based on empirical formulas

9.5 MUNRO AND THOMPSON PLOT
9.6 STANDARDIZATION OF EFFORT
9.7 THE DERISO/SCHNUTE DELAY DIFFERENCE MODEL

10. MULTISPECIES/MULTIFLEET PROBLEMS

10.1 SURPLUS PRODUCTION MODELS APPLIED TO MULTISPECIES/MULTIFLEET SYSTEMS
10.2 BIOLOGICAL INTERACTION
10.3 ECONOMIC INTERACTION
10.4 TECHNICAL INTERACTION

10.4.1 A yield per recruit model for mixed fisheries
10.4.2 Assessment of mixed fisheries based on length-frequency data
10.4.3 Multifleet mixed fisheries

11. ASSESSMENT OF MIGRATORY STOCKS

11.1 THE CONCEPT AND STUDY OF MIGRATION
11.2 BIAS CAUSED BY MIGRATION
11.3 THE ANNUAL-RETURN MATCHED SAMPLES METHOD

11.3.1 Estimation of growth parameters by the annual-return matched samples method

11.4 THE GENERAL MATCHED SAMPLES METHOD
11.5 ASSESSMENT BASED ON TAGGING DATA
11.6 ESTIMATION OF THE GROWTH PARAMETERS OF A MIGRATORY STOCK: THE ATLANTIC MACKEREL

12. THE STOCK/RECRUITMENT RELATIONSHIP

12.1 CLASSICAL S/R CONSIDERATIONS
12.2 THE STABILITY OF RECRUITMENT
12.3 TOWARDS MODELLING RECRUITMENT

13. DEMERSAL TRAWL SURVEYS

13.1 THE BOTTOM TRAWL
13.2 PLANNING A DEMERSAL TRAWL SURVEY
13.3 DATA RECORDING
13.4 DECK SAMPLING AND CATCH RECORDING PROCEDURES
13.5 THE SWEPT AREA
13.6 BIOMASS ESTIMATION BY THE SWEPT AREA METHOD
13.7 PRECISION OF THE ESTIMATE OF BIOMASS
13.8 ESTIMATION OF MAXIMUM SUSTAINABLE YIELD

14. SUMMARY OF FISH STOCK ASSESSMENT

14.1 GENERAL ASPECTS OF FISH STOCK ASSESSMENT
14.2 REVIEW OF METHODS TO BE USED ACCORDING TO THE TYPE OF DATA AVAILABLE

15. MICROCOMPUTER PROGRAM PACKAGES

15.1 THE LFSA PACKAGE

15.1.1 Length-frequency (LF) programs
15.1.2 Age/length analysis: estimation of growth parameters from age/length data
15.1.3 Miscellaneous programs

15.2 THE COMPLEAT ELEFAN PACKAGE
15.3 THE FiSAT PACKAGE
15.4 OTHER FISH STOCK ASSESSMENT PROGRAMS PRODUCED BY FAO

15.4.1 The ANACO package
15.4.2 The ANALEN package
15.4.3 BEAM 1 and BEAM 2
15.4.4 BEAM 3
15.4.5 BEAM 4
15.4.6 The NAN-SIS package
15.4.7 CLIMPROD

16. REFERENCES

SUBJECT INDEX

APPENDIX TABLES

TABLE A1 - LIST OF IMPORTANT FORMULAS
TABLE A2 - METHODS BASED ON LINEAR TRANSFORMATIONS AND ORDINARY LINEAR REGRESSION ANALYSIS: y = a + b*x
TABLE A3 - IMPORTANT DATES EXPRESSED AS FRACTIONS OF A YEAR FROM 1 JANUARY
TABLE A4 - FRACTILES OF THE t-DISTRIBUTION (STUDENT'S DISTRIBUTION)