Using R for Modelling and Quantitative Methods in Fisheries

Cover
Half Title
Series Page
Title Page
Copyright Page
Contents
Preface
1. On Modelling
	1.1 Characteristics of Mathematical Models
		1.1.1 General
		1.1.2 Model Design or Selection
		1.1.3 Constraints Due to the Model Type
		1.1.4 Mathematical Models
		1.1.5 Parameters and Variables
	1.2 Mathematical Model Properties
		1.2.1 Deterministic vs Stochastic
		1.2.2 Continuous vs Discrete Models
		1.2.3 Descriptive vs Explanatory
		1.2.4 Testing Explanatory Models
		1.2.5 Realism vs Generality
		1.2.6 When Is a Model a Theory?
	1.3 Concluding Remarks
2. A Non-Introduction to R
	2.1 Introduction
	2.2 Programming in R
		2.2.1 Getting Started with R
		2.2.2 R Packages
		2.2.3 Getting Started with MQMF
		2.2.4 Examining Code within Functions
		2.2.5 Using Functions
		2.2.6 Random Number Generation
		2.2.7 Printing in R
		2.2.8 Plotting in R
		2.2.9 Dealing with Factors
		2.2.10 Inputting Data
	2.3 Writing Functions
		2.3.1 Simple Functions
		2.3.2 Function Input Values
		2.3.3 R Objects
		2.3.4 Scoping of Objects
		2.3.5 Function Inputs and Outputs
	2.4 Appendix: Less-Traveled Functions
	2.5 Appendix: Additional Learning Resources
3. Simple Population Models
	3.1 Introduction
		3.1.1 The Discrete Logistic Model
		3.1.2 Dynamic Behaviour
		3.1.3 Finding Boundaries between Behaviours
		3.1.4 Classical Bifurcation Diagram of Chaos
		3.1.5 The Effect of Fishing on Dynamics
		3.1.6 Determinism
	3.2 Age-Structured Modelling Concepts
		3.2.1 Survivorship in a Cohort
		3.2.2 Instantaneous vs Annual Mortality Rates
	3.3 Simple Yield per Recruit
		3.3.1 Selectivity in Yield-per-Recruit
		3.3.2 The Baranov Catch Equation
		3.3.3 Growth and Weight-at-Age
	3.4 Full Yield-per-Recruit
	3.5 Concluding Remarks
4. Model Parameter Estimation
	4.1 Introduction
		4.1.1 Optimization
	4.2 Criteria of Best Fit
	4.3 Model Fitting in R
		4.3.1 Model Requirements
		4.3.2 A Length-at-Age Example
		4.3.3 Alternative Models of Growth
	4.4 Sum of Squared Residual Deviations
		4.4.1 Assumptions of Least-Squares
		4.4.2 Numerical Solutions
		4.4.3 Passing Functions as Arguments to Other Functions
		4.4.4 Fitting the Models
		4.4.5 Objective Model Selection
		4.4.6 The Influence of Residual Error Choice on Model Fit
		4.4.7 Remarks on Initial Model Fitting
	4.5 Maximum Likelihood
		4.5.1 Introductory Examples
	4.6 Likelihoods from the Normal Distribution
		4.6.1 Equivalence with Sum-of-Squares
		4.6.2 Fitting a Model to Data Using Normal Likelihoods
	4.7 Log-Normal Likelihoods
		4.7.1 Simplification of Log-Normal Likelihoods
		4.7.2 Log-Normal Properties
		4.7.3 Fitting a Curve Using Log-Normal Likelihoods
		4.7.4 Fitting a Dynamic Model Using Log-Normal Errors
	4.8 Likelihoods from the Binomial Distribution
		4.8.1 An Example Using Binomial Likelihoods
		4.8.2 Open Bay Juvenile Fur Seal Population Size
		4.8.3 Using Multiple Independent Samples
		4.8.4 Analytical Approaches
	4.9 Other Distributions
	4.10 Likelihoods from the Multinomial Distribution
		4.10.1 Using the Multinomial Distribution
	4.11 Likelihoods from the Gamma Distribution
	4.12 Likelihoods from the Beta Distribution
	4.13 Bayes’ Theorem
		4.13.1 Introduction
		4.13.2 Bayesian Methods
		4.13.3 Prior Probabilities
	4.14 Concluding Remarks
5. Static Models
	5.1 Introduction
	5.2 Productivity Parameters
	5.3 Growth
		5.3.1 Seasonal Growth Curves
		5.3.2 Fabens Method with Tagging Data
		5.3.3 Fitting Models to Tagging Data
		5.3.4 A Closer Look at the Fabens Methods
		5.3.5 Implementation of Non-Constant Variances
	5.4 Objective Model Selection
		5.4.1 Akiake’s Information Criterion
		5.4.2 Likelihood Ratio Test
		5.4.3 Caveats on Likelihood Ratio Tests
	5.5 Remarks on Growth
	5.6 Maturity
		5.6.1 Introduction
		5.6.2 Alternative Maturity Ogives
		5.6.3 The Assumption of Symmetry
	5.7 Recruitment
		5.7.1 Introduction
		5.7.2 Properties of “Good” Stock Recruitment Relationships
		5.7.3 Recruitment Overfishing
		5.7.4 Beverton and Holt Recruitment
		5.7.5 Ricker Recruitment
		5.7.6 Deriso’s Generalized Model
		5.7.7 Re-Parameterized Beverton-Holt Equation
		5.7.8 Re-Parameterized Ricker Equation
	5.8 Selectivity
		5.8.1 Introduction
		5.8.2 Logistic Selection
		5.8.3 Dome-Shaped Selection
	5.9 Concluding Remarks for Static Models
	5.10 Appendix: Derivation of Fabens Transformation
	5.11 Appendix: Reparameterization of Beverton-Holt
6. On Uncertainty
	6.1 Introduction
		6.1.1 Types of Uncertainty
		6.1.2 The Example Model
	6.2 Bootstrapping
		6.2.1 Empirical Probability Density Distributions
	6.3 A Simple Bootstrap Example
	6.4 Bootstrapping Time-Series Data
		6.4.1 Parameter Correlation
	6.5 Asymptotic Errors
		6.5.1 Uncertainty about the Model Outputs
		6.5.2 Sampling from a Multivariate Normal Distribution
	6.6 Likelihood Profiles
		6.6.1 Likelihood Ratio-Based Confidence Intervals
		6.6.2 -ve Log-Likelihoods or Likelihoods
		6.6.3 Percentile Likelihood Profiles for Model Outputs
	6.7 Bayesian Posterior Distributions
		6.7.1 Generating the Markov Chain
		6.7.2 The Starting Point
		6.7.3 The Burn-In Period
		6.7.4 Convergence to the Stationary Distribution
		6.7.5 The Jumping Distribution
		6.7.6 Application of MCMC to the Example
		6.7.7 Markov Chain Monte Carlo
		6.7.8 A First Example of an MCMC
		6.7.9 Marginal Distributions
	6.8 The Use of Rcpp
		6.8.1 Addressing Vectors and Matrices
		6.8.2 Replacement for simpspm()
		6.8.3 Multiple Independent Chains
		6.8.4 Replicates Required to Avoid Serial Correlation
	6.9 Concluding Remarks
7. Surplus Production Models
	7.1 Introduction
		7.1.1 Data Needs
		7.1.2 The Need for Contrast
		7.1.3 When Are Catch-Rates Informative?
	7.2 Some Equations
		7.2.1 Production Functions
		7.2.2 The Schaefer Model
		7.2.3 Sum of Squared Residuals
		7.2.4 Estimating Management Statistics
		7.2.5 The Trouble with Equilibria
	7.3 Model Fitting
		7.3.1 A Possible Workflow for Stock Assessment
		7.3.2 Is the Analysis Robust?
		7.3.3 Using Different Data
	7.4 Uncertainty
		7.4.1 Likelihood Profiles
		7.4.2 Bootstrap Confidence Intervals
		7.4.3 Parameter Correlations
		7.4.4 Asymptotic Errors
		7.4.5 Sometimes Asymptotic Errors Work
		7.4.6 Bayesian Posteriors
	7.5 Management Advice
		7.5.1 Two Views of Risk
		7.5.2 Harvest Strategies
	7.6 Risk Assessment Projections
		7.6.1 Deterministic Projections
		7.6.2 Accounting for Uncertainty
		7.6.3 Using Asymptotic Errors
		7.6.4 Using Bootstrap Parameter Vectors
		7.6.5 Using Samples from a Bayesian Posterior
	7.7 Concluding Remarks
	7.8 Appendix: The Use of Rcpp to Replace simpspm
References
Index