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Modelling and Quantitative Methods in Fisheries

ISBN-10: 1584881771
ISBN-13: 9781584881773
Edition: 2001
Authors: Malcolm Haddon
List price: $89.95
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Description: Quantitative methods and mathematical modelling are of critical importance to fishery science and management but, until now, there has been no book that offers the sharp focus, methodological detail, and practical examples needed by fishery  More...

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Book details

List price: $89.95
Copyright year: 2001
Publisher: CRC Press LLC
Publication date: 5/31/2001
Binding: Hardcover
Pages: 424
Size: 6.00" wide x 9.00" long x 1.00" tall
Weight: 1.298
Language: English

Quantitative methods and mathematical modelling are of critical importance to fishery science and management but, until now, there has been no book that offers the sharp focus, methodological detail, and practical examples needed by fishery scientists, managers, and ecologists. This book fills that void. Addressing a topic of much recent debate in fisheries and ecology, it describes and compares the use of Least Squares, Maximum Likelihood, and Bayesian quantitative methods. It contains numerous examples from both the classic and recent literature and includes dedicated Excel spreadsheets, and a web-site containing Excel workbooks, that permit readers to delve into every detail of the analyses.

Fisheries, Population Dynamics, And Modelling
The Formulation Of Fish Population Dynamics
Equilibrium vs. Non-Equilibrium
Characteristics Of Mathematical Models
General Properties
Limitations Due to the Modeller
Limitations Due to Model Type
The Structure of Mathematical Models
Parameters and Variables
Types Of Model Structure
Deterministic/Stochastic
Continuous vs. Discrete Models
Descriptive/Explanatory
Testing Explanatory Models
Realism/Generality
When is a Model a Theory?
Simple Population Models
Introduction
Biological Population Dynamics
The Dynamics of Mathematical Models
Assumptions - Explicit and Implicit
All Assumptions Should be Explicit
Density - Independent Growth
Exponential Growth
Standard Transformations
Why Consider Equilibrium Conditions?
Density - Dependent Models
An Upper Limit and Persistence
The Logistic Model of Growth
Discrete Logistic Model
Stability Properties
Dynamic Behaviour
Responses To Fishing Pressure
The Logistic Model In Fisheries
Age-Structured Models
Age-Structured and Exponential Growth Models
Annual vs. Instantaneous Mortality Rates
Selection of a Target Fishing Mortality
Simple Yield-Per-Recruit
Is there an Optimum Fishing Mortality Rate?
What is the Optimum Age or Size at First Capture?
From Empirical Table to Mathematical Model
The Model Structure and Assumptions
The Model Equations
Yield-Per-Recruit Management Targets
Uncertainties in Yield-Per-Recruit Analyses
Types of Over-Fishing
Model Parameter Estimation
Models And Data
Fitting Data to a Model
Which Comes First, the Data or the Model?
Quality of Fit vs. Parsimony vs. Reality
Uncertainty
Alternative Criteria of Goodness of Fit
Least-Squared Residuals
Introduction
Selection of Residual Error Structure
Non-Linear Estimation
Parameter Estimation Techniques
Graphical Searches for Optimal Parameter Values
Parameter Correlation and Confounding Effects
Automated Directed Searches
Automated Heuristic Searches
Likelihood
Maximum Likelihood Criterion of Fit
The Normal Distribution
Probability Density
Likelihood Definition
Maximum Likelihood Criterion
Likelihoods with the Normal Probability Distribution
Equivalence with Least Squares
Fitting a Curve Using Normal Likelihoods
Likelihoods from the Log-Normal Distribution
Fitting a Curve Using Log-Normal Likelihoods
Likelihoods with the Binomial Distribution
Multiple Observation
Percentile Confidence Intervals Using Likelihoods
Likelihood Profile Confidence Intervals
Likelihoods from the Poisson Distribution
Likelihoods from the Gamma Distribution
Likelihoods from the Multinomial Distribution
Bayes' Theorem
Introduction
Bayes' Theorem
Prior Probabilities
An Example of a Useful Informative Prior
Non-Informative Priors
Concluding Remarks
Computer Intensive Methods
Introduction
Resampling
Randomization Tests
Jackknife Methods
Bootstrapping Methods
Monte Carlo Methods
Relationships Between Methods
Computer Programming
Randomization Tests
Introduction
Hypothesis Testing
Introduction
Standard Significance Testing
Significance Testing by Randomization Test
Mechanics of Randomization Tests
Selection of a Test Statistic
Ideal Test Statistics
Randomization Of Structured Data
Introduction
More Complex Examples
Statistical Bootstrap Methods
The Jackknife And Pseudo-Values
Introduction
Parameter Estimation and Bias
Jackknife Bias Estimation
The Bootstrap
The Value of Bootstrapping
Empirical vs. Theoretical Probability Distributions
Bootstrap Statistics
Bootstrap Standard Errors
Bootstrap Replicates
Parametric Confidence Intervals
Bootstrap Estimate of Bias
Bootstrap Confidence Intervals
Percentile Confidence Intervals
Bias-Corrected Percentile Confidence Intervals
Other Bootstrap Confidence Intervals
Balanced Bootstraps
Concluding Remarks
Monte Carlo Modelling
Monte Carlo Models
The Uses of Monte Carlo Modelling
Types of Uncertainty
Practical Requirements
The Model Definition
Random Numbers
Non-Uniform Random Numbers
Other Practical Considerations
A Simple Population Model
A Non-Equilibrium Catch-Curve
Ordinary Catch-Curve Analysis
The Influence of Sampling Error
The Influence of Recruitment Variability
Concluding Remarks
Growth Of Individuals
Growth In Size
Uses of Growth Information
The Data
Historical Usage
Von Bertalanffy Growth Model
Growth in Length
Growth in Weight
Seasonal Growth
Fitting the Curve to Tagging Data
Extensions to Fabens Method
Comparability of Growth Curves
Alternatives To Von Bertalanffy
A Generalized Model
Model Selection
Polynomial Equations
Problems with the Von Bertalanffy Growth Function
Growth in Size-Based Population Models
Comparing Growth Curves
Non-Linear Comparisons
An Overall Test of Coincident Curves
Likelihood Ratio Tests
Kimura's Likelihood Ratio Test
Less than Perfect Data
A Randomization Version of the Likelihood Ratio Test
Concluding Remarks
Appendix 8.1
Appendix 8.2
Stock-Recruitment Relationships
Recruitment And Fisheries
Introduction
Recruitment Over-Fishing
The Existence of a Stock Recruitment Relationship
Stock-Recruitment Biology
Properties of "Good" Stock-Recruitment Relationships
Data Requirements - Spawning Stock
Data Requirements - Recruitment
Beverton-Holt Recruitment Model
The Equations
Biological Assumptions/Implications
Ricker Model
The Equation
Biological Assumptions/Implications
Deriso's Generalized Model
The Equations
Residual Error Structure
The Impact Of Measurement Errors
Appearance over Reality
Observation Errors Obscuring Relationships
Environmental Influences
Recruitment In Age-Structured Models
Strategies for Including Stock-Recruitment Relationships
Steepness
Beverton-Holt Redefined
Concluding Remarks
Derivation of Beverton-Holt Equations
Derivation of the Ricker Equations
Deriving the Beverton-Holt Parameters
Surplus-Production Models
Introduction
Stock Assessment Modelling Options
Surplus-Production
Equilibrium Methods
Surplus-Production Models
Russell's Formulation
Alternative Fitting Methodology
Observation Error Estimates
Outline of Method
In Theory and Practice
Model Outputs
Beyond Simple Models
Introduction
Changes in Catchability
The Limits of Production Modelling
Uncertainty Of Parameter Estimates
Likelihood Profiles
Bootstrap Confidence Intervals and Estimates of Bias
Risk Assessment Projections
Introduction
Bootstrap Projections
Projections with Set Catches
Projections with Set Effort
Practical Considerations
Introduction
Fitting the Models
Conclusions
Derivation of Equilibrium-Based Stock-Production
The Closed Form of the Estimate of the Catchability Coefficient
Constant q
Additive Increment to Catchability
Constant Proportional Increase-q[subscript inc]
Simplification of the Maximum Likelihood Estimator
Age-Structured Models
Types Of Models
Introduction
Age-Structured Population Dynamics
Fitting Age-Structured Models
Cohort Analysis
Introduction
The Equations
Pope's and MacCall's Approximate Solutions
Newton's Method
Terminal F Estimates
Potential Problems with Cohort Analysis
Concluding Remarks on Cohort Analysis
Statistical Catch-At-Age
Introduction
The Equations
Fitting to Catch-at-Age Data
Fitting to Fully Selected Fishing Mortality
Adding a Stock-Recruitment Relationship
Other Auxiliary Data and Different Criteria of Fit
Relative Weight to Different Contributions
Characterization of Uncertainty
Model Projections and Risk Assessment
Concluding Remarks
Weight-at-Age Data and Optimum Fit to Catch-at-Age Model
The Use Of Excel In Fisheries
Introduction
Workbook Skills
Tools/Options, Auditing, and Customization
Data Entry
Movement Around Worksheets
Range Selection
Formatting and Naming Cells and Ranges
Formulae
Functions
=SUMPRODUCT()
=FREQUENCY()
=LINEST()
=VLOOKUP()
Other Functions
Visual Basic For Applications
Introduction
An Example Macro
Using the Solver inside a Macro
Concluding Remarks
Bibliography
Subject Index

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