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Mathematical Population Genetics 1 : Theoretical Introduction - Warren J. Ewens

Mathematical Population Genetics 1

Theoretical Introduction


Published: 9th January 2004
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Population genetics occupies a central role in a number of important biological and social undertakings. It is fundamental to our understanding of evolutionary processes, of plant and animal breeding programs, and of various diseases of particular importance to mankind.

This is the first of a planned two-volume work discussing the mathematical aspects of population genetics, with an emphasis on the evolutionary theory. This first volume draws heavily from the author's classic 1979 edition, which appeared originally in Springer's Biomathematics series. It has been revised and expanded to include recent topics which follow naturally from the treatment in the earlier edition, e.g., the theory of molecular population genetics.

This book will appeal to graduate students and researchers in mathematical biology and other mathematically-trained scientists looking to enter the field of population genetics.

From reviews of the 1979 edition:

"Here we have perhaps the most articulate of the many fine Australian population geneticists bringing us up to date on the mathematical aspects of his field." -B. S. Weir, William Neal Reynolds Professor of Statistics and Genetics, Director, Bioinformatics Research Center, North Carolina State University

"This book is an excellent source to learn the field for a mathematician or mathematically sophisticated reader." -SIAM Review

"An important reference to anyone interested in the mathematical aspects of population genetics, not only to those actually doing it, but to anyone trying to bridge the now substantial gap between theoretical and experimental population genetics." -The Quarterly Review of Biology

From the reviews of the second edition:

"It is the first of a planned two-volume sequence treating mathematical aspects of population genetics theory and its applications to evolution. ... The presentation is very clear and the author confers many of his deep insights to the reader. Therefore, this new edition has very good prospects to serve as the most important introductory text to this active field of research ... ." (R. Burger, Monatshefte fur Mathematik, Vol. 145 (1), 2005)

From the reviews of the second edition:

"This book is an extensively revised and expanded second edition ... . It presents the principles of mathematical population genetics with an emphasis on evolutionary theory. ... Ewens presentation bridges marvellously mathematics and biology. The author effectively copes with the problem that mathematicians want to see technical details, while biologists do not like formalism." (Martin Moehle, Zeitschrift fur Angewandte Mathematik und Mechanik, Vol. 85 (1), 2005)

From the reviews of the second edition:

"The book concentrates on the mathematical aspects of population genetics at the graduate or research level. ... an excellent summary of the most important results, and very welcome in view of a vast scattered literature. I particularly like the many interesting connections that are made ... . Another highlight is an extra chapter on Moran model ... . Ewens' account of mathematical population genetics is unique ... . I am very happy to see this second edition in print ... ." (Ellen Baake, Mathematical Biosciences, Vol. 197, 2005)

"This is an excellent book on population genetics and evolution placing the emphasis on mathematical and statistical aspects of the theory. ... the author successfully connects classical prospective theory with the current retrospective viewpoint of population genetics. ... this is an exciting and significant book which reflects the author's enthusiasm and experience in the field through many decades. It should be read by graduate students and researchers interested in mathematical aspects of population genetics ... ." (Gunther Karigl, Zentralblatt MATH, Vol. 1060, 2005)

"This book is in a series of texts specializing in interdisciplinary applied mathematics and is scheduled as the first volume of two devoted to population genetics by the same author; it is the second edition of the book first published in 1979. ... This book will be of most use to postgraduate researchers ... . the book under review admirably sets the scene by including a discussion of the broad theories of population dynamics." (Tony Crilly, The Mathematical Gazette, Vol. 89 (516), 2005)

Historical Background
Biometricians, Saltationists and Mendelians
The Hardy-Weinberg Law
The Correlation Between Relatives
The Deterministic Theory
Non-Random-Mating Populations
The Stochastic Theory
Evolved Genetic Phenomena
Overall Evolutionary Theories
Technicalities and Generalizations
Random Union of Gametes
Dioecious Populations
Multiple Alleles
Frequency-Dependent Selection
Fertility Selection
Continuous-Time Models
Non-Random-Mating Populations
The Fundamental Theorem of Natural Selection
Two Loci
Genetic Loads
Finite Markov Chains
Wright-Fisher Model: Two Alleles
The Cannings (Exchangeable) Model: Two Alleles
Moran Models: Two Alleles
K-Allele Wright-Fisher Models
Infinitely Many Alleles Models
The Wright-Fisher In.nitely Many Alleles Model
The Cannings In.nitely Many Alleles Model
The Moran In.nitely Many Alleles Model
The Effective Population Size
Frequency-Dependent Selection
Two Loci
Diffusion Theory
The Forward and Backward Kolmogorov Equations
Fixation Probabilities
Absorption Time Properties
The Stationary Distribution
Conditional Processes
Diffusion Theory
Multi-dimensional Processes
Time Reversibility
Expectations of Functions of Di.usion Variables
Applications of Diffusion Theory
No Selection or Mutation
Selection: Absorption Time Properties
One-Way Mutation
Two-Way Mutation
Diffusion Approximations and Boundary Conditions
Random Environments
Time-Reversal and Age Properties
Multi-Allele Diffusion Processes
Two Loci
Evolutionary Properties of Mean Fitness
Equilibrium Points
Special Models
Modifier Theory
Two-Locus Diffusion Processes
Associative Overdominance and Hitchhiking
The Evolutionary Advantage of Recombination
Many Loci
The Random Mating Case
Linkage Disequilibrium, Means and Variances
Recurrence Relations for Gametic Frequencies
Components of Variance
Particular Models
Non-Random Mating
Notation and Theory
Marginal Fitnesses and Average Effects
The Fundamental Theorem of Natural Selection
Optimality Principles
The Correlation Between Relatives
Further Considerations
What is Fitness?
Sex Ratio
Geographical Structure
Age Structure
Ecological Considerations
Molecular Population Genetics: Introduction
Technical Comments
In.nitely Many Alleles Models: Population Properties
The Wright-Fisher Model
The Moran Model
In.nitely Many Sites Models: Population Properties
The Wright-Fisher Model
The Moran Model
Sample Properties of In.nitely Many Alleles Models
The Wright-Fisher Model
The Moran Model
Sample Properties of In.nitely Many Sites Models
The Wright-Fisher Model
The Moran Model
Relation Between In.nitely Many Alleles and Infinitely Many Sites Models
Genetic Variation Within and Between Populations
Age-Ordered Alleles: Frequencies and Ages
Looking Backward in Time: The Coalescent
Competing Poisson and Geometric Processes
The Coalescent Process
The Coalescent and Its Relation to Evolutionary Genetic Models
Coalescent Calculations: Wright-Fisher Models
Coalescent Calculations: Exact Moran Model Results
General Comments
The Coalescent and Human Genetics
Looking Backward: Testing the Neutral Theory
Testing in the Infinitely Many Alleles Model
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780387201917
ISBN-10: 0387201912
Series: Interdisciplinary Applied Mathematics
Audience: Tertiary; University or College
Format: Hardcover
Language: English
Number Of Pages: 418
Published: 9th January 2004
Country of Publication: US
Dimensions (cm): 23.62 x 15.49  x 2.54
Weight (kg): 0.72
Edition Number: 2
Edition Type: Revised