Fisheries, Population Dynamics, And Modelling p. 1 The Formulation Of Fish Population Dynamics p. 1 Equilibrium vs. Non-Equilibrium p.

Transcription

1 Fisheries, Population Dynamics, And Modelling p. 1 The Formulation Of Fish Population Dynamics p. 1 Equilibrium vs. Non-Equilibrium p. 4 Characteristics Of Mathematical Models p. 6 General Properties p. 6 Limitations Due to the Modeller p. 7 Limitations Due to Model Type p. 7 The Structure of Mathematical Models p. 8 Parameters and Variables p. 9 Types Of Model Structure p. 10 Deterministic/Stochastic p. 10 Continuous vs. Discrete Models p. 11 Descriptive/Explanatory p. 12 Testing Explanatory Models p. 13 Realism/Generality p. 16 When is a Model a Theory? p. 16 Simple Population Models p. 19 Introduction p. 19 Biological Population Dynamics p. 19 The Dynamics of Mathematical Models p. 19 Assumptions - Explicit and Implicit p. 20 All Assumptions Should be Explicit p. 20 Density - Independent Growth p. 21 Exponential Growth p. 21 Standard Transformations p. 23 Why Consider Equilibrium Conditions? p. 24 Density - Dependent Models p. 25 An Upper Limit and Persistence p. 25 The Logistic Model of Growth p. 26 Discrete Logistic Model p. 31 Stability Properties p. 31 Dynamic Behaviour p. 33 Responses To Fishing Pressure p. 37 The Logistic Model In Fisheries p. 39 Age-Structured Models p. 40 Age-Structured and Exponential Growth Models p. 40 Annual vs. Instantaneous Mortality Rates p. 41 Selection of a Target Fishing Mortality p. 44 Simple Yield-Per-Recruit p. 44 Is there an Optimum Fishing Mortality Rate? p. 44 What is the Optimum Age or Size at First Capture? p. 46

2 From Empirical Table to Mathematical Model p. 49 The Model Structure and Assumptions p. 50 The Model Equations p. 51 Yield-Per-Recruit Management Targets p. 55 Uncertainties in Yield-Per-Recruit Analyses p. 57 Types of Over-Fishing p. 57 Model Parameter Estimation p. 59 Models And Data p. 59 Fitting Data to a Model p. 59 Which Comes First, the Data or the Model? p. 60 Quality of Fit vs. Parsimony vs. Reality p. 61 Uncertainty p. 62 Alternative Criteria of Goodness of Fit p. 63 Least-Squared Residuals p. 64 Introduction p. 64 Selection of Residual Error Structure p. 68 Non-Linear Estimation p. 69 Parameter Estimation Techniques p. 69 Graphical Searches for Optimal Parameter Values p. 69 Parameter Correlation and Confounding Effects p. 73 Automated Directed Searches p. 74 Automated Heuristic Searches p. 75 Likelihood p. 76 Maximum Likelihood Criterion of Fit p. 76 The Normal Distribution p. 76 Probability Density p. 79 Likelihood Definition p. 83 Maximum Likelihood Criterion p. 86 Likelihoods with the Normal Probability Distribution p. 86 Equivalence with Least Squares p. 90 Fitting a Curve Using Normal Likelihoods p. 91 Likelihoods from the Log-Normal Distribution p. 92 Fitting a Curve Using Log-Normal Likelihoods p. 96 Likelihoods with the Binomial Distribution p. 98 Multiple Observation p. 103 Percentile Confidence Intervals Using Likelihoods p. 104 Likelihood Profile Confidence Intervals p. 104 Likelihoods from the Poisson Distribution p. 109 Likelihoods from the Gamma Distribution p. 113 Likelihoods from the Multinomial Distribution p. 116 Bayes' Theorem p. 120

3 Introduction p. 120 Bayes' Theorem p. 121 Prior Probabilities p. 122 An Example of a Useful Informative Prior p. 124 Non-Informative Priors p. 126 Concluding Remarks p. 127 Computer Intensive Methods p. 129 Introduction p. 129 Resampling p. 130 Randomization Tests p. 131 Jackknife Methods p. 132 Bootstrapping Methods p. 132 Monte Carlo Methods p. 133 Relationships Between Methods p. 134 Computer Programming p. 135 Randomization Tests p. 137 Introduction p. 137 Hypothesis Testing p. 137 Introduction p. 137 Standard Significance Testing p. 137 Significance Testing by Randomization Test p. 140 Mechanics of Randomization Tests p. 141 Selection of a Test Statistic p. 143 Ideal Test Statistics p. 144 Randomization Of Structured Data p. 149 Introduction p. 149 More Complex Examples p. 151 Statistical Bootstrap Methods p. 153 The Jackknife And Pseudo-Values p. 153 Introduction p. 153 Parameter Estimation and Bias p. 153 Jackknife Bias Estimation p. 158 The Bootstrap p. 159 The Value of Bootstrapping p. 159 Empirical vs. Theoretical Probability Distributions p. 160 Bootstrap Statistics p. 162 Bootstrap Standard Errors p. 164 Bootstrap Replicates p. 166 Parametric Confidence Intervals p. 167 Bootstrap Estimate of Bias p. 167 Bootstrap Confidence Intervals p. 170

4 Percentile Confidence Intervals p. 170 Bias-Corrected Percentile Confidence Intervals p. 171 Other Bootstrap Confidence Intervals p. 173 Balanced Bootstraps p. 173 Concluding Remarks p. 174 Monte Carlo Modelling p. 175 Monte Carlo Models p. 175 The Uses of Monte Carlo Modelling p. 175 Types of Uncertainty p. 175 Practical Requirements p. 177 The Model Definition p. 177 Random Numbers p. 177 Non-Uniform Random Numbers p. 178 Other Practical Considerations p. 180 A Simple Population Model p. 182 A Non-Equilibrium Catch-Curve p. 184 Ordinary Catch-Curve Analysis p. 184 The Influence of Sampling Error p. 186 The Influence of Recruitment Variability p. 190 Concluding Remarks p. 193 Growth Of Individuals p. 197 Growth In Size p. 197 Uses of Growth Information p. 197 The Data p. 198 Historical Usage p. 199 Von Bertalanffy Growth Model p. 200 Growth in Length p. 200 Growth in Weight p. 201 Seasonal Growth p. 202 Fitting the Curve to Tagging Data p. 207 Extensions to Fabens Method p. 208 Comparability of Growth Curves p. 212 Alternatives To Von Bertalanffy p. 213 A Generalized Model p. 213 Model Selection p. 215 Polynomial Equations p. 215 Problems with the Von Bertalanffy Growth Function p. 216 Growth in Size-Based Population Models p. 217 Comparing Growth Curves p. 223 Non-Linear Comparisons p. 223 An Overall Test of Coincident Curves p. 224

5 Likelihood Ratio Tests p. 227 Kimura's Likelihood Ratio Test p. 232 Less than Perfect Data p. 232 A Randomization Version of the Likelihood Ratio Test p. 236 Concluding Remarks p. 239 Appendix 8.1 p. 241 Appendix 8.2 p. 243 Stock-Recruitment Relationships p. 247 Recruitment And Fisheries p. 247 Introduction p. 247 Recruitment Over-Fishing p. 247 The Existence of a Stock Recruitment Relationship p. 248 Stock-Recruitment Biology p. 249 Properties of "Good" Stock-Recruitment Relationships p. 249 Data Requirements - Spawning Stock p. 250 Data Requirements - Recruitment p. 251 Beverton-Holt Recruitment Model p. 251 The Equations p. 251 Biological Assumptions/Implications p. 252 Ricker Model p. 255 The Equation p. 255 Biological Assumptions/Implications p. 255 Deriso's Generalized Model p. 257 The Equations p. 257 Residual Error Structure p. 259 The Impact Of Measurement Errors p. 262 Appearance over Reality p. 262 Observation Errors Obscuring Relationships p. 262 Environmental Influences p. 265 Recruitment In Age-Structured Models p. 267 Strategies for Including Stock-Recruitment Relationships p. 267 Steepness p. 268 Beverton-Holt Redefined p. 269 Concluding Remarks p. 273 Derivation of Beverton-Holt Equations p. 273 Derivation of the Ricker Equations p. 274 Deriving the Beverton-Holt Parameters p. 275 Surplus-Production Models p. 279 Introduction p. 279 Stock Assessment Modelling Options p. 279 Surplus-Production p. 280

6 Equilibrium Methods p. 282 Surplus-Production Models p. 288 Russell's Formulation p. 288 Alternative Fitting Methodology p. 290 Observation Error Estimates p. 292 Outline of Method p. 292 In Theory and Practice p. 293 Model Outputs p. 295 Beyond Simple Models p. 298 Introduction p. 298 Changes in Catchability p. 298 The Limits of Production Modelling p. 300 Uncertainty Of Parameter Estimates p. 301 Likelihood Profiles p. 301 Bootstrap Confidence Intervals and Estimates of Bias p. 304 Risk Assessment Projections p. 313 Introduction p. 313 Bootstrap Projections p. 313 Projections with Set Catches p. 314 Projections with Set Effort p. 315 Practical Considerations p. 315 Introduction p. 315 Fitting the Models p. 317 Conclusions p. 319 Derivation of Equilibrium-Based Stock-Production p. 320 The Closed Form of the Estimate of the Catchability Coefficient p. 321 Constant q p. 321 Additive Increment to Catchability p. 323 Constant Proportional Increase-q[subscript inc] p. 324 Simplification of the Maximum Likelihood Estimator p. 326 Age-Structured Models p. 329 Types Of Models p. 329 Introduction p. 329 Age-Structured Population Dynamics p. 332 Fitting Age-Structured Models p. 337 Cohort Analysis p. 339 Introduction p. 339 The Equations p. 341 Pope's and MacCall's Approximate Solutions p. 343 Newton's Method p. 344 Terminal F Estimates p. 347

7 Potential Problems with Cohort Analysis p. 351 Concluding Remarks on Cohort Analysis p. 352 Statistical Catch-At-Age p. 352 Introduction p. 352 The Equations p. 353 Fitting to Catch-at-Age Data p. 354 Fitting to Fully Selected Fishing Mortality p. 357 Adding a Stock-Recruitment Relationship p. 360 Other Auxiliary Data and Different Criteria of Fit p. 363 Relative Weight to Different Contributions p. 364 Characterization of Uncertainty p. 366 Model Projections and Risk Assessment p. 369 Concluding Remarks p. 370 Weight-at-Age Data and Optimum Fit to Catch-at-Age Model p. 372 The Use Of Excel In Fisheries p. 373 Introduction p. 373 Workbook Skills p. 373 Tools/Options, Auditing, and Customization p. 373 Data Entry p. 375 Movement Around Worksheets p. 376 Range Selection p. 377 Formatting and Naming Cells and Ranges p. 377 Formulae p. 378 Functions p. 378 =SUMPRODUCT() p. 379 =FREQUENCY() p. 380 =LINEST() p. 380 =VLOOKUP() p. 381 Other Functions p. 381 Visual Basic For Applications p. 381 Introduction p. 381 An Example Macro p. 382 Using the Solver inside a Macro p. 385 Concluding Remarks p. 386 Bibliography p. 387 Subject Index p. 403 Table of Contents provided by Blackwell's Book Services and R.R. Bowker. Used with permission.