L, Fish Population Dynamics in Tropical Waters: A Manual for Use with Programmable Calculators INTERNATIONAL CENTER FOR LIVING AQUATIC RESOURCES MANAGEMENT MANILA, PHILIPPINES Fish Population Dynamics in Tropical Waters: A Manual for Use with Programmable Calculators Published by the International Center for Living Aquatic Resources Management, MCC P.O. Box 1501, Makati, Metro Manila, Philippines Copyright 1984 by Daniel Pauly and the International Center for Living Aquatic Resources Management Printed in Manila, Philippines Pauly, D. 1984. Fish population dynamics in tropical waters: a manual for use with programmable calculators. ICLARM Studies and Reviews 8,325 p. International Center for Living Aquatic Resources Management, Manila, Philippines. ISSN 0115-4389 ISBN 971-1022-03-6cloth ISBN 971-1022-04-4paper ICLARM Contribution No. 143 Table of Contents Foreword ..................................................... xiii Acknowledgements .............................................. xiv Abstract ...................................................... 1. How to Use this Manual ...................................... 2 . Length-Weight Relationships ................................... Inhoduction ............................................. Parameter Estimation ...................................... 3. Meshselection ............................................. Introduction ............................................. Trawl Mesh Selection ...................................... Gillnet Selection .......................................... Using a Selection Curve to Adjust Catch Samples ................. 4 . FishGrowth ............................................... Introduction ............................................. Data Needed for Parameter Estimation ......................... Methods for Parameter Estimation ............................ The von Bertalanffy plot ................................. The Ford-Walford plot ................................... The Gulland and Holt plot ................................ TheMunroplot ......................................... Fitting seasonally oscillating length-growth data ................ Extended Gulland and Holt plot ............................ Growth: A Concluding Program .............................. 5. Total, Natural and Fishing Mortalities ............................ Introduction ............................................. Estimating Total Mortality .................................. Total mortality from the oldest animal in the catch ............. Total mortality from the mean size in the catch ................ Estimation of Z from cumulative plots ....................... Catch curves and lengthconverted catch curves ................ Further inferences from lengthconverted catch curves ........... Estimating Z from a pseudocatch curve ...................... Simultaneous Estimation of Z and K ........................... EstimationofZ/K .......................................... 70 1st case: the Beverton and Holt formula of 1956 ................ 70 2nd case: using the variance of the mean length ................. 70 3rd case: using a nomogram and the mean weight of fish inthecatch ..................................... 70 4th case: estimating Z/K from the shape of the length-frequency distribution ........................ 70 Methods for Splitting Z into M and F ........................... 71 PlotofZoneffort ........................................ 72 Analysis of tagging data .................................... 73 Method for Obtaining Independent Estimates of M ................ 74 Exploitation Rates and Potential Yields ......................... 76 6 . Estimation of Population Size .................................. 91 Introduction .............................................. 91 Population Size Through Tagging (Petersen Estimates) .............. 91 Standing Stock Estimation with the Swept-Area Method ............ 92 Population Size from Catch and Fishing Mortality ................. 93 Population Size as Estimated by Leslie's Method .................. 94 7. Estimation of Past Population Sizes Using Virtual Population Analysis and Cohort Analysis ...................................100 Introduction ..............................................100 Derivation of a LengthStructured VPA Model .................... 101 Discussion of the Length-Structured VPA Model .................. 103 Applications of Age-Structured VPA and Cohort Analysis ........... 105 Application of Length Cohort Analysis and Length-Structured VPA ... 105 8. Yield-Per-Recruit Assessment ................................... 114 Introduction ..............................................114 Estimation of Yield Per Recruit ............................... 115 Comparison of Various Equations for Yield-Per-Recruit Estimation .... 119 The Use of the Yield-Per-Recruit Model: A Warning ................ 120 An Alternative Use of Beverton and Holt's Yield Equation ........... 121 9 . Stock-Recruitment Relationships ................................129 Introduction ..............................................129 The Stock-Recruitment Relationship of Beverton and Holt .......... 129 Ricker's Stock-Recruitment Relationships ....................... 132 First form of Ricker's curve ................................ 132 Second form of Ricker's curve .............................. 134 10 . Surplus-Yield Models.......................................... 138 Introduction ..............................................138 The "Equilibrium" Problem ..................................141 Some Modifications of the Parabolic Model ...................... 143 Applying Surplus-Yield Models to Multispecies Stocks .............. 146 11 . The Intrinsic Rate of Population Increase .......................... 152 Introduction .............................................. 152 Maximum Sustainable Yields and r, ............................ 152 Stock-Recruitment Relationships and r, ........................ 155 Introduction .............................................. 161 Modelling Multispecies Systems................................ 163 Two-species systems ......................................163 N-species systems ........................................167 Method for Constructing Quantitative "Box Models" ............... 168 Managing Multispecies Fisheries ............................... 171 Appendix I. Testing Models and Their Results: An Introduction to Sensitivity Analysis and the Jackknife .......................177 Appendix I1. List of Programs and Program Listings ...................... 180 Appendix I11 . Use of Calculators Other Than HP 67/97 ................... 305 List of Symbols and Their Definitions................................. 309 References...................................................... 314 Program Card Holder vii List of Figures Factors responsible for stock size increase and decrease .................... 2 Geographic distribution of examples used in this book. .................... 4 Length-weight relationship for the threadfin bream (Nemiptem maginatus) from the South China Sea. ............................... 7 Selection curve of slipmouth (Leiognathus equulus) caught with 7.8-cmmeshnets ............................................. 11 Nomogram for estimation of selection factors of fishes from their bodyproportion .............................................. 11 Logarithm of catch ratios plotted on length for Tilapia esculenta caught with gillnets of two different mesh sizes. ......................... 15 Selection curves for Tilapia esculenta caught with gillnets of two different mesh sizes. ........................................... 15 Plot of natural logarithms of catch ratios against length and In length to show effect of logarithmic transformation of length. .................... 16 Selection curve of Tilapia galilaea caught with gillnets of two meshsizes. ................................................. 16 Difference between a gillnet sample and the same sample, adjusted for meshselection ............................................... 17 Relationship between the maximum body weight reached in different groups of fh and the power linking their weight to their metabolic rateorgillsurfacearea .......................................... 25 Growth curve of millet-seed butterflyfish (Chaetodon miliaris) off Oahu,Hawaii ................................................ 27 Relationship between the goodness of fit of a von Bertalanffy plot and the selected value of I,(,). ..................................... 30 Two Ford-Walford plots for Atlantic yellowfin (Thunnus albacares) based on the special and generalized VBGF ............................ 32 Differences between the special and generalized VBGF as applied to growth data for Atlantic yellowfin (Thunnus albacares) .................... 32 Estimation of growth parameters for the ocean surgeon fish (Acanthurus bahianus) off the Virgin Islands by means of a Gulland and Holt plot ........... 34 Scattergram of growth increment for ocean surgeon fish (~canthurus bahianus), as obtained from tagging data .............................. 35 Gulland and Holt plot and "forced" Gulland and Holt plot for the Queen parrot fish (Scam vetula) off the Virgin Islands. .................... 36 Graph showing how the coefficient of variation of the K-values obtained from a Munro plot depends on the selected value of Lt,).. ............ 36 4.10 Seasonally oscillating growth of the halfbeak (Hemirhamphus brasiliensis) off Florida. ......................................... 37 4.11