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Fisheries, Population Dynamics, And Modelling | |

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The Formulation Of Fish Population Dynamics | |

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Equilibrium vs. Non-Equilibrium | |

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Characteristics Of Mathematical Models | |

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General Properties | |

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Limitations Due to the Modeller | |

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Limitations Due to Model Type | |

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The Structure of Mathematical Models | |

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Parameters and Variables | |

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Types Of Model Structure | |

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Deterministic/Stochastic | |

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Continuous vs. Discrete Models | |

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Descriptive/Explanatory | |

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Testing Explanatory Models | |

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Realism/Generality | |

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When is a Model a Theory? | |

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Simple Population Models | |

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Introduction | |

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Biological Population Dynamics | |

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The Dynamics of Mathematical Models | |

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Assumptions - Explicit and Implicit | |

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All Assumptions Should be Explicit | |

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Density - Independent Growth | |

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Exponential Growth | |

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Standard Transformations | |

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Why Consider Equilibrium Conditions? | |

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Density - Dependent Models | |

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An Upper Limit and Persistence | |

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The Logistic Model of Growth | |

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Discrete Logistic Model | |

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Stability Properties | |

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Dynamic Behaviour | |

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Responses To Fishing Pressure | |

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The Logistic Model In Fisheries | |

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Age-Structured Models | |

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Age-Structured and Exponential Growth Models | |

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Annual vs. Instantaneous Mortality Rates | |

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Selection of a Target Fishing Mortality | |

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Simple Yield-Per-Recruit | |

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Is there an Optimum Fishing Mortality Rate? | |

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What is the Optimum Age or Size at First Capture? | |

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From Empirical Table to Mathematical Model | |

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The Model Structure and Assumptions | |

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The Model Equations | |

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Yield-Per-Recruit Management Targets | |

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Uncertainties in Yield-Per-Recruit Analyses | |

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Types of Over-Fishing | |

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Model Parameter Estimation | |

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Models And Data | |

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Fitting Data to a Model | |

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Which Comes First, the Data or the Model? | |

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Quality of Fit vs. Parsimony vs. Reality | |

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Uncertainty | |

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Alternative Criteria of Goodness of Fit | |

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Least-Squared Residuals | |

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Introduction | |

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Selection of Residual Error Structure | |

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Non-Linear Estimation | |

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Parameter Estimation Techniques | |

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Graphical Searches for Optimal Parameter Values | |

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Parameter Correlation and Confounding Effects | |

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Automated Directed Searches | |

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Automated Heuristic Searches | |

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Likelihood | |

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Maximum Likelihood Criterion of Fit | |

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The Normal Distribution | |

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Probability Density | |

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Likelihood Definition | |

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Maximum Likelihood Criterion | |

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Likelihoods with the Normal Probability Distribution | |

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Equivalence with Least Squares | |

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Fitting a Curve Using Normal Likelihoods | |

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Likelihoods from the Log-Normal Distribution | |

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Fitting a Curve Using Log-Normal Likelihoods | |

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Likelihoods with the Binomial Distribution | |

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Multiple Observation | |

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Percentile Confidence Intervals Using Likelihoods | |

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Likelihood Profile Confidence Intervals | |

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Likelihoods from the Poisson Distribution | |

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Likelihoods from the Gamma Distribution | |

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Likelihoods from the Multinomial Distribution | |

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Bayes' Theorem | |

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Introduction | |

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Bayes' Theorem | |

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Prior Probabilities | |

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An Example of a Useful Informative Prior | |

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Non-Informative Priors | |

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Concluding Remarks | |

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Computer Intensive Methods | |

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Introduction | |

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Resampling | |

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Randomization Tests | |

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Jackknife Methods | |

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Bootstrapping Methods | |

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Monte Carlo Methods | |

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Relationships Between Methods | |

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Computer Programming | |

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Randomization Tests | |

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Introduction | |

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Hypothesis Testing | |

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Introduction | |

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Standard Significance Testing | |

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Significance Testing by Randomization Test | |

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Mechanics of Randomization Tests | |

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Selection of a Test Statistic | |

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Ideal Test Statistics | |

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Randomization Of Structured Data | |

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Introduction | |

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More Complex Examples | |

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Statistical Bootstrap Methods | |

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The Jackknife And Pseudo-Values | |

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Introduction | |

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Parameter Estimation and Bias | |

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Jackknife Bias Estimation | |

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The Bootstrap | |

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The Value of Bootstrapping | |

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Empirical vs. Theoretical Probability Distributions | |

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Bootstrap Statistics | |

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Bootstrap Standard Errors | |

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Bootstrap Replicates | |

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Parametric Confidence Intervals | |

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Bootstrap Estimate of Bias | |

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Bootstrap Confidence Intervals | |

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Percentile Confidence Intervals | |

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Bias-Corrected Percentile Confidence Intervals | |

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Other Bootstrap Confidence Intervals | |

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Balanced Bootstraps | |

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Concluding Remarks | |

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Monte Carlo Modelling | |

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Monte Carlo Models | |

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The Uses of Monte Carlo Modelling | |

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Types of Uncertainty | |

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Practical Requirements | |

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The Model Definition | |

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Random Numbers | |

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Non-Uniform Random Numbers | |

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Other Practical Considerations | |

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A Simple Population Model | |

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A Non-Equilibrium Catch-Curve | |

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Ordinary Catch-Curve Analysis | |

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The Influence of Sampling Error | |

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The Influence of Recruitment Variability | |

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Concluding Remarks | |

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Growth Of Individuals | |

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Growth In Size | |

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Uses of Growth Information | |

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The Data | |

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Historical Usage | |

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Von Bertalanffy Growth Model | |

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Growth in Length | |

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Growth in Weight | |

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Seasonal Growth | |

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Fitting the Curve to Tagging Data | |

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Extensions to Fabens Method | |

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Comparability of Growth Curves | |

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Alternatives To Von Bertalanffy | |

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A Generalized Model | |

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Model Selection | |

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Polynomial Equations | |

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Problems with the Von Bertalanffy Growth Function | |

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Growth in Size-Based Population Models | |

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Comparing Growth Curves | |

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Non-Linear Comparisons | |

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An Overall Test of Coincident Curves | |

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Likelihood Ratio Tests | |

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Kimura's Likelihood Ratio Test | |

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Less than Perfect Data | |

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A Randomization Version of the Likelihood Ratio Test | |

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Concluding Remarks | |

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Appendix 8.1 | |

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Appendix 8.2 | |

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Stock-Recruitment Relationships | |

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Recruitment And Fisheries | |

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Introduction | |

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Recruitment Over-Fishing | |

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The Existence of a Stock Recruitment Relationship | |

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Stock-Recruitment Biology | |

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Properties of "Good" Stock-Recruitment Relationships | |

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Data Requirements - Spawning Stock | |

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Data Requirements - Recruitment | |

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Beverton-Holt Recruitment Model | |

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The Equations | |

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Biological Assumptions/Implications | |

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Ricker Model | |

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The Equation | |

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Biological Assumptions/Implications | |

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Deriso's Generalized Model | |

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The Equations | |

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Residual Error Structure | |

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The Impact Of Measurement Errors | |

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Appearance over Reality | |

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Observation Errors Obscuring Relationships | |

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Environmental Influences | |

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Recruitment In Age-Structured Models | |

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Strategies for Including Stock-Recruitment Relationships | |

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Steepness | |

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Beverton-Holt Redefined | |

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Concluding Remarks | |

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Derivation of Beverton-Holt Equations | |

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Derivation of the Ricker Equations | |

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Deriving the Beverton-Holt Parameters | |

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Surplus-Production Models | |

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Introduction | |

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Stock Assessment Modelling Options | |

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Surplus-Production | |

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Equilibrium Methods | |

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Surplus-Production Models | |

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Russell's Formulation | |

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Alternative Fitting Methodology | |

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Observation Error Estimates | |

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Outline of Method | |

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In Theory and Practice | |

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Model Outputs | |

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Beyond Simple Models | |

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Introduction | |

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Changes in Catchability | |

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The Limits of Production Modelling | |

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Uncertainty Of Parameter Estimates | |

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Likelihood Profiles | |

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Bootstrap Confidence Intervals and Estimates of Bias | |

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Risk Assessment Projections | |

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Introduction | |

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Bootstrap Projections | |

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Projections with Set Catches | |

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Projections with Set Effort | |

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Practical Considerations | |

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Introduction | |

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Fitting the Models | |

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Conclusions | |

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Derivation of Equilibrium-Based Stock-Production | |

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The Closed Form of the Estimate of the Catchability Coefficient | |

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Constant q | |

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Additive Increment to Catchability | |

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Constant Proportional Increase-q[subscript inc] | |

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Simplification of the Maximum Likelihood Estimator | |

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Age-Structured Models | |

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Types Of Models | |

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Introduction | |

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Age-Structured Population Dynamics | |

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Fitting Age-Structured Models | |

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Cohort Analysis | |

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Introduction | |

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The Equations | |

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Pope's and MacCall's Approximate Solutions | |

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Newton's Method | |

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Terminal F Estimates | |

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Potential Problems with Cohort Analysis | |

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Concluding Remarks on Cohort Analysis | |

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Statistical Catch-At-Age | |

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Introduction | |

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The Equations | |

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Fitting to Catch-at-Age Data | |

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Fitting to Fully Selected Fishing Mortality | |

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Adding a Stock-Recruitment Relationship | |

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Other Auxiliary Data and Different Criteria of Fit | |

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Relative Weight to Different Contributions | |

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Characterization of Uncertainty | |

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Model Projections and Risk Assessment | |

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Concluding Remarks | |

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Weight-at-Age Data and Optimum Fit to Catch-at-Age Model | |

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The Use Of Excel In Fisheries | |

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Introduction | |

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Workbook Skills | |

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Tools/Options, Auditing, and Customization | |

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Data Entry | |

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Movement Around Worksheets | |

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Range Selection | |

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Formatting and Naming Cells and Ranges | |

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Formulae | |

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Functions | |

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=SUMPRODUCT() | |

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=FREQUENCY() | |

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=LINEST() | |

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=VLOOKUP() | |

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Other Functions | |

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Visual Basic For Applications | |

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Introduction | |

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An Example Macro | |

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Using the Solver inside a Macro | |

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Concluding Remarks | |

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Bibliography | |

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Subject Index | |