This book deals with a key area of population genetics: the ratio of the sexes in a population, or the allocation of resources to male versus female reproductive function. Samuel Karlin and Sabin Lessard establish the formal theoretical aspects of the evolution of sex ratio within the constraints of genetic mechanisms of sex determination. Their results generalize and unify existing work on the topic, strengthening previous conceptions in some cases and, in other instances, offering new directions of research.
There are two main approaches to understanding the causes and effects of sex ratio. One approach focuses on the optimization and adaptive functions of sex allocation, while the other emphasizes the consequences of genetic sex determination mechanisms. In discussing the utility of these two approaches, Professors Karlin and Lessard examine the principal sex-determining mechanisms and facts involved in sex ratio representations, the various genetic and environmental factors that contribute to adaptive sex expression, and the evolution of sex determining systems and controls. From a population genetic perspective, the authors derive evolutionary properties in support of the high incidence of 1:1 sex ratio in natural populations and investigate the conditions that can explain the occurrence of biased sex ratio.
Author(s): Samuel Karlin, Sabin Lessard
Series: Monographs in Population Biology, 22
Publisher: Princeton University Press
Year: 1986
Language: English
Pages: 332
Cover Page
Half-title Page
Title Page
Copyright Page
Contents
Preface
1. Problems, Background, and Summary
1.1 Introduction
1.2 Sex Determination Systems and Sex Ratios
1.3 Adaptation and Strategy in Sex Ratio Determination
1.4 When and Why Is Sex Ratio One-to-One?
1.5 The Evolution of Sex-Determining Mechanisms
1.6 Review of the Literature on Sex Ratio Theory
1.7 Summary of the Main Results of This Book
2. Concepts and Parametrizations for One-Locus Multiallele Sex-Determining Systems and Related Systems
Model I. An Autosomal, Multiallele Sex- Determination System Based on the Genotype of the Offspring
Model I'. Model of Sex Determination in Relation to Sex-Differentiated Genotype Viability Effects
Model II. Multiallelic Sex Ratio Determination Model under Maternal (or Paternal) Genotypic Control
Model II'. Unequal Costs in Producing Offspring of Different Sexes
Model II". Differential Viability with Replacement under Maternal Control
Model III. One-Locus Multiallele Viability Model of Maternal Inheritance
Model IV. Sex Ratio Evolution under Sex- Specific Spatial Fitness Variation
Model V. Haplodiploid Models (Mixed Parthenogenesis Expressing Arrhenotoky)
Model VI. Sex Allocation of Resources to Female and Male Functions Determined at an Autosomal Locus
Model VII. Sex Determination at an X-Linked Locus with Multiple Alleles
Model VIII. Sex-Biased Viabilities under Maternal Control at a Sex-Linked Locus
Model VII' . Maternally Inherited Viability Controlled at a Sex-Linked Locus
Model IX. Multiallele Viability Regime Active in Only One Sex
Appendix A. A General One-Locus Selection Model
3. Characterizations and Stability Properties of Equilibria in One-Locus Multiallele Sex Determination Models and Related Models
3.1 Existence Conditions for Even and Non-Even Sex-Ratio Equilibria in the Sex Determination Model I
3.2 A Characterization of Equilibrium Points in One-Locus Multiallele Viability Systems
3.3 Stability Nature of the Symmetric (Non-Even Sex Ratio) Equilibrium States for the Sex Determination Model I
3.4 Nature and Properties of Even Sex-Ratio Equilibria of the Sex Determination Model I
3.5 Stable Equilibrium Possibilities for Dichotomous and X-Linked Sex Determination
3.6 The Relative Occurrence of Symmetric (Non-One-to-One) versus Even Sex-Ratio Equilibria
3.7 Optimality Properties of Even Sex-Ratio Equilibria
3.8 Results for the Maternally Controlled Sex Ratio Determination Models II and VIII
3.9 Results for One-Locus Multiallele Models of Maternally Inherited Viability
3.10 Results for the Mixed Parthenogenesis (Haplodiploid) Model V
Appendix A. Some Preliminaries
Appendix B. Proofs of the Main Results for One- Locus Multiallele Viability Systems
Appendix C. Proofs of the Results of Chapter 3 for the Sex Determination Models and Related Models of Chapter 2
Appendix D. On the Number of Stable Equilibria that Can Coexist in One-Locus Multiallele Viability Models
4. Examples and Special Results for Two- and Three-Allele Sex Determination Models
4.1 A Complete Enumeration of the Stable Equilibrium States of Genotype Sex Determination Involving Two Alleles
4.2 Description of Three-Allele Sex Ratio Outcomes
4.3 Some Parameter Specifications for Three-Allele Sex Ratio Outcomes
4.4 A Sex Determination Form Determined by the State of Heterozygosity Versus Homozygosity
4.5 Three-Allele Dichotomous Genotypic Sex Determination
4.6 Convergence Properties for the Sex Determination Model Where All Homozygotes Determine Females and Heterozygotes Determine Males with Multiple Alleles
Appendix A. Analysis of the General Two-Allele Sex-Determination Model
Appendix B. Proof that the Equilibrium Structures in Figure 4.3 Cannot Occur
Appendix C. Conditions Validating the Equilibrium Configurations Described in Figure 4.1
Appendix D. Global Convergence Behavior for Some Three Allele Dichotomous Sex Determination Models
Appendix E. Global Convergence for the Sex Determination Model Where all Homozygotes Determine Females and Heterozygotes Determine Males
5. Some Multilocus Sex Determination Systems
5.1 Two-Locus Sex Dichotomization with Male Double Heterozygotes
5.2 A Two-Locus Multiplicative Sex Determination Model
5.3 Sex Determination at Several Loci: A General Symmetric Heterozygosity Regime
5.4 Polymorphism in Sex-Differentiated Multilocus Viability Selection Models
6. Effects of Inbreeding, Population Structure, and Meiotic Drive on Sex Ratio Outcomes
6.1 Random Mating Haploid Sex-Allocation Models
6.2 A Haploid Sex-Allocation Model with Partial Selling
6.3 Y-Drive of the Sex Ratio: Partial Sib-Mating
6.4 X~Drive in the Heterogametic Sex: Random Mating
6.5 A Two-Locus Segregation Distortion Modification Model
6.6 Optimal Sex Ratios in Structured Populations: Breeding Groups of Random Size
6.7 Optimal Sex Ratios in Structured Populations: Breeding Groups with a Constant Fraction of Outbreeding and Population Regulation within Groups
Appendix A. A Criterion for Stability-Instability at Fixation States that Involve an Eigenvalue 1
Appendix B. Recurrence Equations for Partial Sib- Mating Sex-Allocation Models in Haplo-diploid Populations
Appendix C. Recurrence Equations for Partial Sib- Mating Sex-Allocation Models in Diplo-diploid Populations
Appendix D. Pure Selfing Models in Diploid Populations
7. General Two-Sex Two-Allele Viability Models
7.1 Conditions for the Existence of Polymorphic Equilibria
7.2 A Classification of Equilibrium Configurations
7.3 General Maternal Fertility Schemes with Sex Differences
7.4 The Product Characterization of an ESS in General Two-Sex Models
7.5 Sex Ratio Patterns When Male versus Female Fitness Varies Spatially
7.6 Age-Specific Variations, Overlapping Generations, and Sex Reversal
Appendix A. Monotonicity Properties of the Bisexual Two-Allele Viability Model
Appendix B. The Equilibrium Structures of the Bisexual Model under Specific Viability Regimes
Appendix C. Analysis of the General Two-Sex Two-Allele Maternal Inheritance Model
8. Some Incompatibility Models
8.1 Self-Incompatibility Classes and Isoplethic Equilibria
8.2 A Case of Self-Sterility Alleles
8.3 A Model of Negative Assortative Mating
8.4 Incompatibility Genetic System Determined at Two Loci
9. Multifactorial Sex Determination (MSD) Models
9.1 Background
9.2 Formulation and Issues of Multifactorial Sex Determination Models
9.3 Multifactorial Sex Determination Models with Random Residual Influences
9.4 Limit Sex Ratios for Pure Blending Inheritance with Threshold Sex Determination Criterion
9.5 Sex Determination Probability Function Symmetrical with Respect to a Central Index Value
9.6 Multifactorial Sex Ratio Evolution under Mother Control and in the Case of Haplodiploid Systems
9.7 Mixed Major Gene and Multifactorial Sex Determination Model
9.8 Some General Qualitative Implications of MSD
Appendix A. Proof of Theorem 9.1
Appendix B. Proof of Theorem 9.2
10. Concluding Observations and Open Problems
References
Author Index
Subject Index
