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Bulletin 191 of the Fisheries Research Board of Canada
by W. E. Ricker
Computation and Interpretation of Biological Statistics of Fish Populations, first published in 1975, is William Edwin Ricker’s third Bulletin that deals with the general field of biological statistics of fish populations. It is a compilation of the more important procedures used to estimate abundance, age composition, rate of growth, and mortality rates in fish populations, with working examples of all the computations.
Computation and Interpretation of Biological Statistics of Fish Populations is one of the most highly cited scientific references in the field of fisheries.
William Edwin (Bill) Ricker (1908 – 2001) is an important founder of fisheries science. He is best known for the Ricker model which can be used to predict the number of fish that will be present in a fishery. In fisheries, he researched issues centered on Canadian fisheries and how to manage them.
In 1950 Ricker became editor of the Journal of the Fisheries Research Board, and during his twelve year tenure developed this into perhaps the most influential fisheries science journal in the world.
Preface Chapter 1. Introduction The problems; Definitions, usages, and glossary; Symbols; Numerical representation of mortality; Recruitment, stock, and catch in numbers; Growth and yield in weight; Fishing effort and catch per unit of effort; Maximum sustainable yield; Sampling error Chapter 2. Estimation of Survival Rate and Mortality Rate from Age Composition Survival estimated from the abundance of successive age-groups; Simple catch curves; Non-uniform recruitment (Use of catch per unit effort for estimating survival); Recruitment to the fishery over several ages; Change in mortality rate with age; Change in mortality rate with time; Catch curves based on length frequencies; Catch curves for anadromous fishes; Stratified sampling for age composition; Effects of inaccurate age determinations on estimates of survival rate; Selectivity of fishing gear Chapter 3. Vital Statistics from Marking; Single Season Experiments General principles of population estimation by marking methods; Petersen method (single census); Effect of recruitment; Effects of marking and tagging; Loss of marks or tags; Non-random distribution of marks and of fishing effort; Unequal vulnerability of fish of different sizes; Incomplete checking of marks; Multiple censuses; Systematic errors in multiple censuses; Estimation of natural losses and additions to the stock; Schaefer method of stratified populations; Contributions of separate stocks to a common fishery Chapter 4. Population Statistics from Marking Experiments Extending Through Two or More Time Intervals, with Constant Survival Rate Marking done prior to the first fishing season; Marking done throughout the first fishing season with recoveries in at least two seasons; Systematic errors (Types A and B); Systematic Errors (Type C); Graphical methods of estimating effectiveness of fishing Chapter 5. Population Statistics from Marking Experiments Extending Through Two or More Time Intervals, with Variable Survival Rate Population and survival rate when marking is done at the start of fishing in two consecutive years—Ricker’s method; Survival rate when marking is done throughout the year; Population, survival, and recruitment from a triple-catch experiment—Bailey’s method; Population, survival, and recruitment from a 4-catch or longer experiment—Seber-Jolly method; Survival estimated from marking in one season, in conjunction with fishing effort data; Marking done throughout the year—Natural mortality varies with age; Rate of fishing during years of recruitment; Estimation of percentage of the younger age-groups present on the fishing grounds Chapter 6. Estimation of Survival and Rate of Fishing from the Relation of Fishing Success to Catch or Effort Principles of fishing-success methods; Population estimates from the relation of fishing success to catch already taken—Leslie’s method; Population estimates from the relation of fishing success to cumulative fishing effort—DeLury’s method; Systematic errors in fishing-success methods; Use of fishing-success methods with marked populations; Fishing-success methods when more than one kind of fishing effort is used, or when there are data for only a part of the effort Chapter 7. Estimation of Survival and Rate of Fishing from Catch and Fishing Effort in Successive Years Direct comparison of catch and fishing effort; Rate of exploitation estimated by equalization of fishing effort—Sette’s method; Rate of fishing and natural mortality from comparison of survival rates at two levels of fishing effort—Silliman’s method; Rate of fishing and natural mortality from catch and effort statistics, when effort varies continuously—Beverton and Holt’s method; Rates of fishing and natural mortality from catch and effort data—Paloheimo’s method; Rate of fishing from catch and effort data when natural mortality rate is known or postulated; Estimates of catchability made with incomplete information on catch and effort; Rate of fishing from catch and effort data, recruitment, and natural mortality rate—Allen’s method Chapter 8. Estimation of Stock and Mortality from Statistics of the Catch and Its Qualitative Composition Derzhavin’s biostatistical method of population analysis; Utilized stock and biostatistical rate of exploitation when age composition varies—Boiko’s method; Estimation of actual population from utilized population and recovery of marked fish—Fraser’s method; Combination of utilized stock estimates with the Beverton-Holt iterative procedure; Rates of natural and fishing mortality, given constant recruitment and natural mortality and two or more levels of stable catch—Tester-Gulland method; Sequential computation of rate of fishing and stock size (cohort analysis); Sequential computations when fishing precedes natural mortality; Population estimates by “change of composition” or “dichotomy” methods; Estimate of survival from differences between the sexes in age at maturity—Murphy’s method Chapter 9. Growth in Length and in Weight Estimation of age and rate of growth; Types of growth rates; Weight-length relationships; Effects of size-selective mortality; Computation of mean growth rates; Mathematical description of increase in length—the Brody-Bertalanffy procedure; Use of a Walford line for estimating growth of older fish; Walford lines and Brody-Bertalanffy equations from the growth of marked fish—Manzer and Taylor’s method; Increase in weight and age; Gompertz growth curve; Growth compensation; Estimation of survival rate from the average size of fish caught Chapter 10. Computation of Yield from a Given Recruitment General conditions; Estimation of equilibrium yield—method of Thompson and Bell; Estimation of equilibrium yield—Ricker’s method; Estimation of equilibrium yield—Baranov’s method; Estimation of equilibrium yield—method of Beverton and Holt; Estimation of equilibrium yield—Jones’ modification of the Beverton-Holt method; Approximations in Beverton-Holt yield computations; Changes in age structure and biomass resulting from fishing; Temporary effects of a change in the rate of fishing; Allen’s method of calculating best minimum size Chapter 11. Recruitment and Stock-recruitment Relationships Types of recruitment; Estimation of recruitment—biostatistical method; Estimation of recruitment—Allen’s method; Effects of environment upon recruitment; The relation between stock and recruitment; Ricker recruitment curves; Beverton-Holt recruitment curves; Other recruitment curves; Compensatory and density-independent mortality rates Chapter 12. Recruitment and the Fishery Relation of equilibrium yield to rate of fishing, for different recruitment curves (equilibrium situations); Interaction of a recruitment curve with a changing rate of fishing; Fisheries attacking mixtures of stocks having different recruitment potentials; Combinations of recruitment and yield-per-recruit analyses Chapter 13. Direct Estimation of the Relation of Equilibrium Yield to Size of Stock and Rate of Fishing General aspects of additions-and-removals methods; Parabolic surplus production curve and logistic growth curve—Graham’s method; Relation of equilibrium yield to fishing effort; Relation of surplus production to size of stock, using the yearly increase or decrease of stock—method of Schaefer (1954); Computation of a parabolic yield curve when catchability (q) is not known independently—method of Schaefer (1957); Generalized production model—method of Pella and Tomlinson; Relation of surplus production to stock size of the years that produced the current recruitment—Ricker’s method; Relation of catch per unit effort to the fishing effort of years immediately past—Gulland’s method Appendix I. Table of Exponential Functions and Derivatives Appendix II. Confidence Limits for Variables (x) Distributed in a Poisson Frequency Distribution, for Confidence Coefficients (= 1 - P) of 0.95 and 0.99 Appendix III. Characteristics and Relationships for Two Types of Recruitment Curve Appendix IV. Regression Lines References Index
by W. E. Ricker
Computation and Interpretation of Biological Statistics of Fish Populations, first published in 1975, is William Edwin Ricker’s third Bulletin that deals with the general field of biological statistics of fish populations. It is a compilation of the more important procedures used to estimate abundance, age composition, rate of growth, and mortality rates in fish populations, with working examples of all the computations.
Computation and Interpretation of Biological Statistics of Fish Populations is one of the most highly cited scientific references in the field of fisheries.
William Edwin (Bill) Ricker (1908 – 2001) is an important founder of fisheries science. He is best known for the Ricker model which can be used to predict the number of fish that will be present in a fishery. In fisheries, he researched issues centered on Canadian fisheries and how to manage them.
In 1950 Ricker became editor of the Journal of the Fisheries Research Board, and during his twelve year tenure developed this into perhaps the most influential fisheries science journal in the world.
Preface Chapter 1. Introduction The problems; Definitions, usages, and glossary; Symbols; Numerical representation of mortality; Recruitment, stock, and catch in numbers; Growth and yield in weight; Fishing effort and catch per unit of effort; Maximum sustainable yield; Sampling error Chapter 2. Estimation of Survival Rate and Mortality Rate from Age Composition Survival estimated from the abundance of successive age-groups; Simple catch curves; Non-uniform recruitment (Use of catch per unit effort for estimating survival); Recruitment to the fishery over several ages; Change in mortality rate with age; Change in mortality rate with time; Catch curves based on length frequencies; Catch curves for anadromous fishes; Stratified sampling for age composition; Effects of inaccurate age determinations on estimates of survival rate; Selectivity of fishing gear Chapter 3. Vital Statistics from Marking; Single Season Experiments General principles of population estimation by marking methods; Petersen method (single census); Effect of recruitment; Effects of marking and tagging; Loss of marks or tags; Non-random distribution of marks and of fishing effort; Unequal vulnerability of fish of different sizes; Incomplete checking of marks; Multiple censuses; Systematic errors in multiple censuses; Estimation of natural losses and additions to the stock; Schaefer method of stratified populations; Contributions of separate stocks to a common fishery Chapter 4. Population Statistics from Marking Experiments Extending Through Two or More Time Intervals, with Constant Survival Rate Marking done prior to the first fishing season; Marking done throughout the first fishing season with recoveries in at least two seasons; Systematic errors (Types A and B); Systematic Errors (Type C); Graphical methods of estimating effectiveness of fishing Chapter 5. Population Statistics from Marking Experiments Extending Through Two or More Time Intervals, with Variable Survival Rate Population and survival rate when marking is done at the start of fishing in two consecutive years—Ricker’s method; Survival rate when marking is done throughout the year; Population, survival, and recruitment from a triple-catch experiment—Bailey’s method; Population, survival, and recruitment from a 4-catch or longer experiment—Seber-Jolly method; Survival estimated from marking in one season, in conjunction with fishing effort data; Marking done throughout the year—Natural mortality varies with age; Rate of fishing during years of recruitment; Estimation of percentage of the younger age-groups present on the fishing grounds Chapter 6. Estimation of Survival and Rate of Fishing from the Relation of Fishing Success to Catch or Effort Principles of fishing-success methods; Population estimates from the relation of fishing success to catch already taken—Leslie’s method; Population estimates from the relation of fishing success to cumulative fishing effort—DeLury’s method; Systematic errors in fishing-success methods; Use of fishing-success methods with marked populations; Fishing-success methods when more than one kind of fishing effort is used, or when there are data for only a part of the effort Chapter 7. Estimation of Survival and Rate of Fishing from Catch and Fishing Effort in Successive Years Direct comparison of catch and fishing effort; Rate of exploitation estimated by equalization of fishing effort—Sette’s method; Rate of fishing and natural mortality from comparison of survival rates at two levels of fishing effort—Silliman’s method; Rate of fishing and natural mortality from catch and effort statistics, when effort varies continuously—Beverton and Holt’s method; Rates of fishing and natural mortality from catch and effort data—Paloheimo’s method; Rate of fishing from catch and effort data when natural mortality rate is known or postulated; Estimates of catchability made with incomplete information on catch and effort; Rate of fishing from catch and effort data, recruitment, and natural mortality rate—Allen’s method Chapter 8. Estimation of Stock and Mortality from Statistics of the Catch and Its Qualitative Composition Derzhavin’s biostatistical method of population analysis; Utilized stock and biostatistical rate of exploitation when age composition varies—Boiko’s method; Estimation of actual population from utilized population and recovery of marked fish—Fraser’s method; Combination of utilized stock estimates with the Beverton-Holt iterative procedure; Rates of natural and fishing mortality, given constant recruitment and natural mortality and two or more levels of stable catch—Tester-Gulland method; Sequential computation of rate of fishing and stock size (cohort analysis); Sequential computations when fishing precedes natural mortality; Population estimates by “change of composition” or “dichotomy” methods; Estimate of survival from differences between the sexes in age at maturity—Murphy’s method Chapter 9. Growth in Length and in Weight Estimation of age and rate of growth; Types of growth rates; Weight-length relationships; Effects of size-selective mortality; Computation of mean growth rates; Mathematical description of increase in length—the Brody-Bertalanffy procedure; Use of a Walford line for estimating growth of older fish; Walford lines and Brody-Bertalanffy equations from the growth of marked fish—Manzer and Taylor’s method; Increase in weight and age; Gompertz growth curve; Growth compensation; Estimation of survival rate from the average size of fish caught Chapter 10. Computation of Yield from a Given Recruitment General conditions; Estimation of equilibrium yield—method of Thompson and Bell; Estimation of equilibrium yield—Ricker’s method; Estimation of equilibrium yield—Baranov’s method; Estimation of equilibrium yield—method of Beverton and Holt; Estimation of equilibrium yield—Jones’ modification of the Beverton-Holt method; Approximations in Beverton-Holt yield computations; Changes in age structure and biomass resulting from fishing; Temporary effects of a change in the rate of fishing; Allen’s method of calculating best minimum size Chapter 11. Recruitment and Stock-recruitment Relationships Types of recruitment; Estimation of recruitment—biostatistical method; Estimation of recruitment—Allen’s method; Effects of environment upon recruitment; The relation between stock and recruitment; Ricker recruitment curves; Beverton-Holt recruitment curves; Other recruitment curves; Compensatory and density-independent mortality rates Chapter 12. Recruitment and the Fishery Relation of equilibrium yield to rate of fishing, for different recruitment curves (equilibrium situations); Interaction of a recruitment curve with a changing rate of fishing; Fisheries attacking mixtures of stocks having different recruitment potentials; Combinations of recruitment and yield-per-recruit analyses Chapter 13. Direct Estimation of the Relation of Equilibrium Yield to Size of Stock and Rate of Fishing General aspects of additions-and-removals methods; Parabolic surplus production curve and logistic growth curve—Graham’s method; Relation of equilibrium yield to fishing effort; Relation of surplus production to size of stock, using the yearly increase or decrease of stock—method of Schaefer (1954); Computation of a parabolic yield curve when catchability (q) is not known independently—method of Schaefer (1957); Generalized production model—method of Pella and Tomlinson; Relation of surplus production to stock size of the years that produced the current recruitment—Ricker’s method; Relation of catch per unit effort to the fishing effort of years immediately past—Gulland’s method Appendix I. Table of Exponential Functions and Derivatives Appendix II. Confidence Limits for Variables (x) Distributed in a Poisson Frequency Distribution, for Confidence Coefficients (= 1 - P) of 0.95 and 0.99 Appendix III. Characteristics and Relationships for Two Types of Recruitment Curve Appendix IV. Regression Lines References Index