Overview

This volume covers those areas of theoretical population genetics that can be investigated rigorously by elementary mathematical methods. An attempt has been made to formulate the various models fairly generally and to state the biological assumptions quite explicitly. The choice and treatment of topics should enable the reader to understand and evaluate detailed analyses of many specific models and applications in the literature. The material suffices for a one-year course and is almost entirely self-contained. The little basic genetics needed for understanding it is presented in the text. Calculus and linear algebra are used freely. Previous exposure to elementary probability theory would be helpful. The major mathematical theme of the book is the dynamical analysis of recursion relations. Many exact and approximate techniques for investigating linear and nonlinear recursion relations in one dimension and in several dimensions are developed and applied. The problems are an essential part of this book. Although some of them ask the reader merely to supply details of derivations in the text, many illuminate, rigorize, or extend these derivations. Some of the results in the problems are useful and important. They vary in difficulty; the harder ones offer a challenge even to good students.

Full Product Details

Author:   Thomas Nagylaki
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Volume:   v. 21
Weight:   0.785kg
ISBN:  

9783540533443

ISBN 10:   3540533443
Pages:   381
Publication Date:   04 June 1992
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   Out of stock  
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Table of Contents

1. Introduction.- 2. Asexual Haploid Populations.- 2.1 Selection.- 2.2 Mutation and Selection.- 2.3 Migration and Selection.- 2.4 Continuous Model with Overlapping Generations.- 2.5 Random Drift.- 2.6 Problems.- 3. Panmictic Populations.- 3.1 The Hardy-Weinberg Law.- 3.2 X-Linkage.- 3.3 Two Loci.- 3.4 Population Subdivision.- 3.5 Genotypic Frequencies in a Finite Population.- 3.6 Problems.- 4. Selection at an Autosomal Locus.- 4.1 Formulation for Multiple Alleles.- 4.2 Dynamics with Two Alleles.- 4.3 Dynamics with Multiple Alleles.- 4.4 Two Alleles with Inbreeding.- 4.5 Variable Environments.- 4.6 Intra-Family Selection.- 4.7 Maternal Inheritance.- 4.8 Meiotic Drive.- 4.9 Mutation and Selection.- 4.10 Continuous Model with Overlapping Generations.- 4.11 Density and Frequency Dependence.- 4.12 Problems.- 5. Nonrandom Mating.- 5.1 Selfing with Selection.- 5.2 Assortative Mating with Multiple Alleles and Distinguishable Genotypes.- 5.3 Assortative Mating with Two Alleles and Complete Dominance.- 5.4 Random Mating with Differential Fertility.- 5.5 Self-Incompatibility Alleles.- 5.6 Pollen and Zygote Elimination.- 5.7 Problems.- 6. Migration and Selection.- 6.1 The Island Model.- 6.2 General Analysis.- 6.3 The Levene Model.- 6.4 Two Diallelic Niches.- 6.5 Problems.- 7. X-Linkage.- 7.1 Formulation for Multiallelic Selection and Mutation.- 7.2 Selection with Two Alleles.- 7.3 Mutation-Selection Balance.- 7.4 Weak Selection.- 7.5 Problems.- 8. Two Loci.- 8.1 General Formulation for Multiple Loci.- 8.2 Analysis for Two Multiallelic Loci.- 8.3 Two Diallelic Loci.- 8.4 Continuous Model with Overlapping Generations.- 8.5 Problems.- 9. Inbreeding and Random Drift.- 9.1 The Inbreeding Coefficient.- 9.2 Calculation of the Inbreeding Coefficient from Pedigrees.- 9.3 Identity Relations Between Relatives.- 9.4 Phenotypic Effects of Inbreeding.- 9.5 Regular Systems of Inbreeding.- 9.6 Panmixia in Finite Populations.- 9.7 Heterozygosity under Mutation and Random Drift.- 9.8 The Inbreeding Effective Population Number.- 9.9 The Model for Random Drift of Gene Frequencies.- 9.10 Random Drift of Gene Frequencies.- 9.11 Gene-Frequency Change due to Mutation and Random Drift.- 9.12 The Island Model.- 9.13 The Variance Effective Population Number.- 9.14 Problems.- 10. Quantitative Genetics.- 10.1 The Decomposition of the Variance with Panmixia.- 10.2 The Correlation Between Relatives with Panmixia.- 10.3 The Change in Variance due to Assortative Mating.- 10.4 The Correlation Between Relatives with Assortative Mating.- 10.5 Selection.- 10.6 Mutation-Selection Balance.- 10.7 Problems.- References.- Author Index.

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