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E-grāmata: Introduction to Quantitative Ecology: Mathematical and Statistical Modelling for Beginners

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(Professor, School of Aquatic and Fisheries Sciences; Director, Center for Quantitative Sciences and Director, QERM Graduate Program, University of Washington, USA, School of Aquatic and Fisheries Sciences, University of Washington, USA)
  • Formāts: 304 pages
  • Izdošanas datums: 30-Sep-2021
  • Izdevniecība: Oxford University Press
  • Valoda: eng
  • ISBN-13: 9780192655448
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Introduction to Quantitative Ecology: Mathematical and Statistical Modelling for BeginnersPalielināt
  • Formāts: 304 pages
  • Izdošanas datums: 30-Sep-2021
  • Izdevniecība: Oxford University Press
  • Valoda: eng
  • ISBN-13: 9780192655448
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Environmental science (ecology, conservation, and resource management) is an increasingly quantitative field. A well-trained ecologist now needs to evaluate evidence generated from complex quantitative methods, and to apply these methods in their own research. Yet the existing books and
academic coursework are not adequately serving most of the potential audience - instead they cater to the specialists who wish to focus on either mathematical or statistical aspects, and overwhelmingly appeal to those who already have confidence in their quantitative skills. At the same time, many
texts lack an explicit emphasis on the epistemology of quantitative techniques. That is, how do we gain understanding about the real world from models that are so vastly simplified?

This accessible textbook introduces quantitative ecology in a manner that aims to confront these limitations and thereby appeal to a far wider audience. It presents material in an informal, approachable, and encouraging manner that welcomes readers with any degree of confidence and prior training.
It covers foundational topics in both mathematical and statistical ecology before describing how to implement these concepts to choose, use, and analyse models, providing guidance and worked examples in both spreadsheet format and R. The emphasis throughout is on the skilful interpretation of models
to answer questions about the natural world.

Introduction to Quantitative Ecology is suitable for advanced undergraduate students and incoming graduate students, seeking to strengthen their understanding of quantitative methods and to apply them successfully to real world ecology, conservation, and resource management scenarios.

Recenzijas

Essington... shows how to fit and interpret a simple dynamic model to data clearly and concisely, integrating the main tools of the book... in one elegant case study. * Joseph D. T. Savage and Christopher M. Moore, The Quarterly Review of Biology * Very accessibly written and clearly aimed at readers who might be predisposed to hate math but are open to a gentle presentation with plenty of real-world examples. * J. Wilson White, Transactions of the American Fisheries Society *

Acknowledgements v
About This Book vii
Part I Fundamentals of Dynamic Models
1 Why Do We Model?
3(22)
1.1 Myths of modeling
8(1)
1.2 Types of models
9(2)
1.2.1 Organizational scales
9(1)
1.2.2 Purpose
9(1)
1.2.3 Model endpoint
10(1)
1.2.4 Statistical or mathematical?
10(1)
1.3 Developing your model
11(14)
1.3.1 Steps in model development
11(5)
1.3.2 Advanced applications and topics
16(4)
1.3.3 The rest of the process
20(2)
1.3.4 Modeling is not a linear process
22(3)
2 Introduction to Population Models
25(22)
2.1 Introduction to population dynamics
25(1)
2.2 Fundamental structure of population models
26(1)
2.3 Density-independent models
27(4)
2.3.1 Continuous-time density-independent models
30(1)
2.4 Developing a density-dependent model
31(6)
2.4.1 The logistic model
32(2)
2.4.2 Advanced: Continuous logistic models
34(1)
2.4.3 Other density-dependent models
34(2)
2.4.4 Allee effects
36(1)
2.5 Dynamic behavior of density-dependent models
37(1)
2.6 Cobwebbing
38(9)
2.6.1 Interpreting cobweb diagrams
40(3)
2.6.2 Advanced: What governs dynamic behavior?
43(4)
3 Structured Population Models
47(14)
3.1 Types of population structure: Age versus stage structure
47(5)
3.1.1 An example of age structure
48(1)
3.1.2 An example of stage structure
48(1)
3.1.3 Transient and stable behaviors of structured models
49(1)
3.1.4 Advanced: Deriving recursive equations
50(1)
3.1.5 Advanced: Life-table analysis, reproductive outputs, and Euler's equation
51(1)
3.2 Modeling using matrix notation
52(2)
3.2.1 Why do we bother with matrix representation?
53(1)
3.3 Characteristics of structured models
54(1)
3.4 Elasticity analysis
55(2)
3.4.1 Advanced: How to calculate elasticities
56(1)
3.5 Advanced: Structured density-dependent models
57(4)
4 Competition and Predation Models
61(24)
4.1 Introduction
61(1)
4.1.1 Consider the following two ecological scenarios
61(1)
4.1.2 What does "stability" mean?
61(1)
4.2 Solving for equilibria
62(2)
4.2.1 Continuous-time model
63(1)
4.3 Isocline analysis
64(5)
4.3.1 Continuous-time model
67(1)
4.3.2 Key points
67(2)
4.4 Analytic stability analysis
69(11)
4.4.1 Motivation
69(1)
4.4.2 A brief aside on predator-prey models
69(3)
4.4.3 Background and framework
72(1)
4.4.4 Calculating stability
73(3)
4.4.5 Advanced: Why does the eigenvalue predict stability?
76(4)
4.5 Larger models
80(5)
5 Stochastic Population Models
85(20)
5.1 Introduction
85(2)
5.1.1 What causes stochasticity?
86(1)
5.2 Why consider stochasticity?
87(3)
5.2.1 Reason 1
87(1)
5.2.2 Reason 2
88(1)
5.2.3 So, why aren't all models stochastic?
88(1)
5.2.4 Advanced: Why does stochasticity lower population abundance?
88(1)
5.2.5 Why was the arithmetic mean incorrect?
89(1)
5.3 Density-independent predictions: An analytic result
90(3)
5.3.1 Projecting forward with unknown future stochasticity
91(2)
5.4 Eastern Pacific Southern Resident killer whales
93(1)
5.5 Estimating extinction risk
94(4)
5.5.1 Advanced: Autocorrelation
96(2)
5.6 Uncertainty in model parameters
98(1)
5.7 Density-dependent stochastic models
99(2)
5.7.1 Allee effects
100(1)
5.8 Structured stochastic models
101(4)
Part II Fitting Models to Data
6 Why Fit Models to Data?
105(4)
7 Random Variables and Probability
109(16)
7.1 Introduction
109(2)
7.1.1 What is a random variable?
109(2)
7.2 Binomial
111(2)
7.2.1 Key things about this distribution
111(1)
7.2.2 The probability mass function
111(1)
7.2.3 When would I use this?
111(1)
7.2.4 Properties of the function
112(1)
7.2.5 Example
112(1)
7.3 Poisson
113(2)
7.3.1 Key things about this distribution
113(1)
7.3.2 The probability function
113(1)
7.3.3 When would I use this?
114(1)
7.3.4 Properties of the function
114(1)
7.3.5 Example
114(1)
7.4 Negative binomial
115(2)
7.4.1 Key things about this function
115(1)
7.4.2 When would I use this?
115(1)
7.4.3 The probability function
115(1)
7.4.4 Properties of the function
116(1)
7.4.5 Example
116(1)
7.5 Normal
117(1)
7.5.1 Key things about this distribution
117(1)
7.5.2 When would I use this?
117(1)
7.5.3 The probability density function
117(1)
7.5.4 Properties of the function
118(1)
7.5.5 Example
118(1)
7.6 Log-normal
118(1)
7.6.1 Key things about this distribution
118(1)
7.6.2 When would I use this?
119(1)
7.6.3 The probability density function
119(1)
7.6.4 Properties of the function
119(1)
7.6.5 Example
119(1)
7.7 Advanced: Other distributions
119(6)
7.7.1 The gamma distribution
119(1)
7.7.2 The beta distribution
120(1)
7.7.3 Student's t-distribution
120(1)
7.7.4 The beta-binomial distribution
121(1)
7.7.5 Zero-inflated models
122(3)
8 Likelihood and Its Applications
125(24)
8.1 Introduction
125(3)
8.1.1 Was this a fair coin?
126(1)
8.1.2 Likelihood to the rescue
126(1)
8.1.3 Maximum likelihood estimation
126(1)
8.1.4 What likelihood is not
127(1)
8.2 Parameter estimation using likelihood
128(2)
8.3 Uncertainty in maximum likelihood parameter estimates
130(3)
8.3.1 Calculating confidence intervals using likelihoods
130(2)
8.3.2 To summarize
132(1)
8.3.3 Practice example 1
132(1)
8.4 Likelihood with multiple observations
133(2)
8.5 Advanced: Nuisance parameters
135(3)
8.5.1 What is a likelihood profile?
135(1)
8.5.2 Example
136(1)
8.5.3 The likelihood profile
137(1)
8.6 Estimating parameters that do not appear in probability functions
138(4)
8.6.1 Entanglements of Hector's dolphins
138(3)
8.6.2 Practice example 2
141(1)
8.7 Estimating parameters of dynamic models
142(3)
8.8 Final comments on maximum likelihood estimation
145(1)
8.9 Overdispersion and what to do about it
146(3)
9 Model Selection
149(16)
9.1 Framework
150(2)
9.2 An intuitive method: Cross validation
152(1)
9.3 The Akaike information criterion as a measure of model performance
153(4)
9.3.1 Take-home points
154(1)
9.3.2 Advanced: Theoretical underpinnings of information theory
154(2)
9.3.3 Alternatives to the AIC
156(1)
9.4 Interpreting AIC values
157(5)
9.4.1 Nested versus nonnested
157(2)
9.4.2 Fit to data
159(3)
9.5 Final thoughts
162(3)
9.5.1 Model selection practices to avoid
162(1)
9.5.2 True story
162(3)
10 Bayesian Statistics
165(18)
10.1 Introduction
165(2)
10.1.1 Are you a frequentist or a Bayesian?
165(1)
10.1.2 Wait, what are you talking about?
165(1)
10.1.3 So, how is this different from likelihood?
166(1)
10.2 What is Bayes' theorem, and how is it used in statistics and model selection?
167(2)
10.2.1 Doesn't the prior probability influence the posterior probability?
168(1)
10.3 Practice example: The prosecutor's fallacy
169(1)
10.4 The prior
170(2)
10.4.1 Example: Do people have extrasensory perception?
171(1)
10.4.2 Criticisms
171(1)
10.5 Bayesian parameter estimation
172(6)
10.5.1 How do we do that?
173(1)
10.5.2 Monte Carlo methods
174(2)
10.5.3 Laplace approximation
176(1)
10.5.4 Mechanics of using the prior
177(1)
10.6 Final thoughts on Bayesian approaches
178(5)
Part III Skills
11 Mathematics Refresher
183(4)
11.1 Logarithms
183(1)
11.1.1 Common operations with logarithms
183(1)
11.2 Derivatives and integrals
184(1)
11.3 Matrix operations
185(2)
11.3.1 Dimensions of matrices
185(1)
11.3.2 Adding two matrices
185(1)
11.3.3 Multiplying two matrices
185(2)
12 Modeling in Spreadsheets
187(12)
12.1 Practicum: A logistic population model in Excel
188(2)
12.1.1 Naming spreadsheet cells
189(1)
12.2 Useful spreadsheet functions
190(2)
12.2.1 Exercise
191(1)
12.3 Array formulas
192(1)
12.3.1 Exercise
192(1)
12.4 The data table
192(2)
12.4.1 Exercise
193(1)
12.5 Programming in Visual Basic
194(5)
12.5.1 Creating your own functions in Visual Basic
196(3)
13 Modeling in R
199(14)
13.1 The basics
200(7)
13.1.1 First, some orientation
200(1)
13.1.2 Writing and running R code
200(3)
13.1.3 Statistical functions
203(1)
13.1.4 Basic plotting
204(1)
13.1.5 Data input and output
205(1)
13.1.6 Looping
206(1)
13.1.7 Loops within loops
207(1)
13.2 Practicum: A logistic population model in R
207(2)
13.3 Creating your own functions
209(4)
14 Skills for Dynamic Models
213(38)
14.1 Skills for population models
213(10)
14.1.1 Implementing structured population models
213(8)
14.1.2 Cobwebbing
221(2)
14.2 Skills for multivariable models
223(6)
14.2.1 Calculating isoclines
223(3)
14.2.2 Calculating Jacobian matrices
226(3)
14.3 Monte Carlo methods
229(6)
14.3.1 Monte Carlo example: What is π?
229(2)
14.3.2 Monte Carlo simulation of population models
231(1)
14.3.3 Spreadsheet guidance
232(2)
14.3.4 R guidance
234(1)
14.4 Skills for stochastic models
235(8)
14.4.1 Stochastic models in spreadsheets
235(3)
14.4.2 Stochastic models in R
238(1)
14.4.3 Advanced: Adding autocorrelation
239(3)
14.4.4 Propagating uncertainty
242(1)
14.5 Numerical solutions to differential equations
243(8)
14.5.1 The Euler method
244(1)
14.5.2 The Adams-Bashford method
245(1)
14.5.3 Runge-Kutta methods
246(5)
15 Sensitivity Analysis
251(12)
15.1 Introduction
251(4)
15.1.1 Types of sensitivity analysis
251(1)
15.1.2 Steps in sensitivity analysis
252(1)
15.1.3 Example: Tree snakes
252(3)
15.2 Individual parameter perturbation
255(3)
15.2.1 Quantifying sensitivity
256(1)
15.2.2 Global sensitivity analysis
257(1)
15.3 The Monte Carlo method
258(4)
15.4 Structural uncertainty
262(1)
16 Skills for Fitting Models to Data
263(20)
16.1 Maximum likelihood estimation
263(10)
16.1.1 Maximum likelihood estimation: Direct method
264(3)
16.1.2 Maximum likelihood estimation: Numerical methods
267(6)
16.2 Estimating parameters that do not appear in probability functions
273(2)
16.3 Likelihood profiles
275(8)
16.3.1 Profiles in spreadsheets
276(1)
16.3.2 Profiles in R
277(6)
Part IV Putting It All Together and Next Steps
17 Putting It Together: Fitting a Dynamic Model
283(12)
17.1 Fitting the observation error model
284(4)
17.1.1 Observation error model in spreadsheets
285(1)
17.1.2 Observation error model in R
286(1)
17.1.3 Evaluating fits of the observation error models
287(1)
17.2 Fitting the process error model
288(3)
17.2.1 Process error model in spreadsheets
289(1)
17.2.2 Process error model in R
289(1)
17.2.3 Evaluating fits of the process error models
290(1)
17.3 Parameter estimates and model selection
291(1)
17.4 Can this population exhibit complex population dynamics?
292(3)
18 Next Steps
295(3)
18.1 Reality check
295(1)
18.2 Learn by doing
296(2)
18.2.1 True story
297(1)
Bibliography 298(5)
Index 303
Timothy E. Essington is a Professor at the School of Aquatic and Fishery Sciences, University of Washington, USA. He is also Director of the Center for Quantitative Sciences and of the University of Washington's QERM Graduate Program. His research chiefly focuses on food web interactions involving fish in marine, estuarine and freshwater habitats.
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