Evolutionary Dynamics: Mathematics

by Hugo Berg

Overview

Written for researchers and postgraduate students with a background in physics or applied mathematics and a desire to apply their skills to problems in the life sciences, this beautifully illustrated and stimulating book develops an understanding of the gene-to-trait problem in the context of evolutionary dynamics, from the modern perspective of integrative biology. The gene-to-trait problem resides at the heart of a great many questions in biology. The author presents both elementary and advanced material in a way that brings out how this gene-to-trait problem is treated in the contexts of bioinformatics and evolutionary dynamics. Key ideas and techniques that underlie some of the most-used bioinformatics methods are discussed in an integrative context and a wide range of examples of mathematical models of living things is developed in an evolutionary framework.

Product Details

ISBN-13:	9780750310956
Publisher:	Iop Publishing Ltd
Publication date:	10/19/2015
Pages:	538
Product dimensions:	7.00(w) x 10.10(h) x 1.20(d)

Table of Contents

Preface xiii

Acknowledgements xviii

1 Introduction 1-1

1.1 Of snails and snakes 1-4

1.2 The three key elements 1-8

1.2.1 Heritability 1-8

1.2.2 Selective pressure 1-12

1.2.3 Variation 1-13

1.3 Stochasticity 1-15

1.4 Towards a mathematics of evolution 1-17

1.4.1 A top-down concept of fitness 1-18

1.4.2 Trait fitness 1-21

1.5 Organization of this book 1-24

Suggested courses 1-24

Bibliography 1-25

Further reading 1-25

2 Cell biology and molecular genetics 2-1

2.1 Cellular architecture and proliferation 2-1

2.1.1 Genetics and cell division 2-3

2.2 DNA, RNA and proteins 2-9

2.2.1 Transcription and translation 2-9

2.2.2 Coding DNA, non-coding DNA and genes 2-15

2.3 Metabolism 2-18

Further reading 2-22

Exercises 2-22

3 Phylogeny and development 3-1

3.1 Phylogenic trees 3-2

3.1.1 Tree theory 3-3

3.1.2 In-groups and out-groups 3-4

3.1.3 Classification 3-5

3.1.4 Rooted and unrooted trees 3-7

3.1.5 Constructing trees 3-8

3.1.6 The distance matrix 3-10

3.1.7 Constructing an unrooted tree 3-11

3.2 Development 3-14

3.2.1 Developmental pathways in differentiation 3-14

3.2.2 'Recapitulation of phylogeny' versus 'bottleneck' 3-14

3.2.3 Modification of modular development 3-17

3.2.4 Patterning and cell fate commitment 3-22

3.2.5 Genetic innovation in evolving development 3-28

Bibliography 3-32

Further reading 3-32

Exercises 3-32

4 Elementary evolutionary dynamics 4-1

4.1 Conceptual challenges and the standard assumption 4-2

4.2 Haploids 4-3

4.2.1 Two genomic variants 4-3

4.2.2 Multiple genomic variants 4-10

4.2.3 Bilinear frequency dependence 4-12

4.3 Diploids 4-19

4.3.1 Two gametotypes 4-19

4.3.2 Multiple gametotypes 4-25

4.4 Projection onto tightly linked clusters of loci 4-27

4.4.1 Decay of linkage 4-27

4.4.2 Averaged fitness: a closure problem 4-29

4.4.3 Dynamics of entire gametotypes 4-31

4.5 Drift and fixation 4-32

4.5.1 A simple model of genetic drift 4-33

4.5.2 Connected demes 4-37

4.5.3 A genetic model of latent neutral variation 4-40

Further reading 4-43

Exercises 4-43

5 Probability and measurement 5-1

5.1 Fundamental laws of probability 5-1

5.2 Random variables and their distributions 5-3

5.2.1 Sampling from a given distribution function 5-5

5.2.2 Mixed distributions 5-5

5.2.3 The survivor 5-6

5.3 Expectation and variance 5-7

5.4 Common distributions and their properties 5-11

5.4.1 The exponential and geometric distributions 5-11

5.4.2 Common discrete distributions 5-12

5.4.3 The normal distribution and its ilk 5-15

5.5 Measurement scales 5-19

Further reading 5-21

Exercises 5-21

6 Statistical inference and estimation 6-1

6.1 The essential ideas 6-1

6.1.1 Dinosaur eggs: which species? 6-1

6.1.2 The concept of likelihood 6-3

6.1.3 The P-value 6-4

6.1.4 Dinosaur eggs: are the mean clutch sizes different? 6-5

6.2 Justifying the likelihood ratio principle 6-8

6.2.1 The Neyman-Pearson lemma 6-9

6.2.2 The generalized likelihood ratio principle 6-10

6.3 Linking alleles to traits 6-11

6.3.1 Nominal traits 6-12

6.3.2 Ordinal traits 6-16

6.3.3 Quantitative traits 6-18

6.4 Microarrays: the stepping down procedure 6-27

6.5 Analysis of bivariate data 6-28

6.5.1 The correlation coefficient 6-29

6.5.2 A non-parametric test and a parametric test 6-30

6.5.3 Conditional statistics 6-31

Bibliography 6-32

Further reading 6-32

Exercises 6-32

7 Sequence, structure and function 7-1

7.1 Principles of dynamic prograniming 7-2

7.2 Sequence phylogenies 7-5

7.2.1 Maximum-likelihood assignment of ancestral states 7-6

7.2.2 Maximum-likelihood tree topology 7-7

7.3 Sequence alignment 7-8

7.3.1 Alignment patterns 7-9

7.3.2 Scoring: matches and penalties 7-10

7.3.3 The alignment cursor 7-12

7.4 Deep structure 7-14

7.4.1 Hidden Markov chains 7-16

7.4.2 Reconstruction of the state sequence 7-17

7.5 From sequence to function 7-18

7.5.1 Cylinder sets 7-19

7.5.2 Correlation functions 7-20

Bibliography 7-27

Further reading 7-27

Exercises 7-27

8 Analysis of quantitative trait loci 8-1

8.1 Recombinant distributions 8-2

8.1.1 Dynamics of inbreeding 8-2

8.1.2 One locus 8-6

8.1.3 Two loci 8-7

8.1.4 More than two loci 8-14

8.2 Genetic markers and mapping 8-15

8.2.1 The marker framework 8-17

8.2.2 Generalization of the likelihood function 8-18

8.2.3 Marker framework maps 8-20

8.2.4 Applications 8-25

8.2.5 Expression QTL 8-26

8.3 The number of quantitative trait loci 8-28

8.3.1 A statistical quandary 8-29

8.3.2 Justification of the normal distribution 8-29

Bibliography 8-31

Further reading 8-31

Exercises 8-31

9 Evolutionary dynamics of QTL 9-1

9.1 Heritability 9-1

9.1.1 Breeding success, breeding failure 9-2

9.1.2 The rate of evolution 9-6

9.2 Dynamics of the additive genetic component 9-10

9.2.1 The next-generation map 9-10

9.2.2 Transfer kernel models 9-13

9.2.3 Dynamics of fully linked traits 9-17

9.2.4 Dynamics of completely unlinked traits 9-20

9.3 The persistence of sex 9-21

9.3.1 Persistence of polymorphy 9-23

9.3.2 Asexual advantage 9-27

9.3.3 The origins of sex 9-37

Bibliography 9-39

Further reading 9-39

Exercises 9-40

10 Adaptive dynamics and speciation 10-1

10.1 Adaptive dynamics 10-2

10.1.1 Invasion fitness 10-2

10.1.2 Stabilizing selection 10-4

10.1.3 Disruptive selection and speciation 10-7

10.1.4 Protected polymorphisms 10-9

10.2 Fisher's law for adaptive dynamics 10-10

10.3 Adaptive radiations and mass extinctions 10-14

10.3.1 A simple stochastic model of adaptive radiation 10-15

10.3.2 The quasi-stationary distribution 10-16

10.3.3 Persistence and extinction 10-19

Bibliography 10-23

Further reading 10-23

Exercises 10-23

11 Traits as objects of selection 11-1

11.1 Regimenting traits 11-2

11.1.1 The trouble with traits 11-3

11.1.2 Trait probes 11-7

11.1.3 Fitness for regimented traits 11-12

11.1.4 Specifications of the trait mapping 11-13

11.2 Scope and limitations of the additive genetic model 11-16

11.2.1 Estimation of the additive coefficients 11-18

11.2.2 Higher-order interactions 11-20

11.2.3 The generalized additive genetic model 11-23

Bibliography 11-26

Further reading 11-26

Exercises 11-26

12 Fitness and optimality 12-1

12.1 Evolution of protandry in butterflies 12-4

12.1.1 Virgins governing reproductive success 12-8

12.2 Evolution of juvenility 12-13

12.3 Evolution of homeostasis 12-17

12.3.1 Control diagrams in engineering and in living systems 12-18

12.3.2 The objective functional 12-21

12.4 Fitness probes 12-25

12.4.1 Construction of the fitness probe 12-26

12.4.2 General application of the fitness probe 12-31

12.4.3 Fitness probes for regimented traits and genotypes 12-36

12.4.4 A variational principle 12-40

Bibliography 12-44

Further reading 12-44

Exercises 12-44

Appendices

A A Species, speciation and systematics A-1

B Dangerous ideas B-1

C Dynamics C-1

D Constrained optimization D-1

E Thermal physics E-1