The Genetic Structure of Populations

by A. Jacquard, B. Charlesworth (Translator), D. Charlesworth (Translator)

Overview

It is part of the ideology of science that it is an international enterprise, carried out by a community that knows no barriers of nation or culture. But the reality is somewhat different. Despite the best intentions of scientists to form a single community, unseparated by differences of national and political viewpoint, they are, in fact, separated by language. Scientific literature in German is not generally assimilated by French workers, nor that appearing in French by those whose native language is English. The problem appears to have become more severe since the last war, because the ascendance of the United States as the preeminent economic power led, in a time of big and expensive science, to a pre­ dominance of American scientific production and a growing tendency (at least among English-speakers) to regard English as the international language of science. International congresses and journals of world circulation have come more and more to take English as their standard or official language. As a result, students and scientific workers in the English speaking world have become more linguistically parochial than ever before and have been cut off from a considerable scientific literature. Population genetics has been no exception to the rule. The elegant and extremely innovative theoreticaI work of Malecot, for example, is only now being properly assimilated by population biologists outside France. It was therefore with some sense of frustration that I read Prof.

Product Details

ISBN-13:	9783642884177
Publisher:	Springer Berlin Heidelberg
Publication date:	06/05/2012
Series:	Biomathematics , #5
Edition description:	1970
Pages:	572
Product dimensions:	6.10(w) x 9.25(h) x 0.05(d)

Table of Contents

The Individual.- The Population.- General Bibliography.- 1 Basic Facts and Concepts.- 1. The Foundations of Genetics.- 1. The Mendelian Theory of Inheritance.- 1.1. Mendel’s First Law. The Law of Segregation.- 1.2. Mendel’s Second Law. Independent Assortment.- 1.3. Restriction of Mendel’s Second Law. Linkage.- 1.4. Some Definitions.- 2. The Physical Basis of Mendelian Inheritance. The Chromosomes.- 2.1. The Behaviour of the Chromosomes. Mitosis and Meiosis.- 2.2. Consequences of Chromosome Behaviour for Hereditary Transmission of Characters.- 2.3. Linkage and Crossing Over.- 2.4. Human Chromosomes.- 2.5. The Sex Chromosomes.- 2.6. Chromosome Structure. DNA.- 2.7. Mutation.- 2.8. Individual Diversity.- 2. Basic Concepts and Notation. Genetic Structure of Populations and of Individuals.- 1. Probability.- 1.1. Definition of Probability.- 1.2. Principle of Addition of Probabilities.- 1.3. Principle of Multiplication of Probabilities.- 1.4. Bayes’ Theorem.- 1.5. Random Variables.- 1.6. The Expectation and Variance of a Random Variable.- 1.7. Examples of Random Variables.- 2. Genetic Structures.- 2.1. The Definition of Genic and Genotypic Structures.- 2.2. The Relation between Genic and Genotypic Structures.- 2.3. The Probability Structures of Populations.- 2.4. Probability Structures of Individuals.- 3. Sexual Reproduction.- 3.1. Genic Structures of Parents and Offspring.- 3.2. Genotypic Structure of Parents and Offspring.- 2 A Reference Model: Absence of Evolutionary Factors.- 3. The Hardy-Weinberg Equilibrium for one Locus.- 1. Populations.- 2. The Hardy-Weinberg Principle.- 2.1. Stability of the Genic Structure.- 2.2. Genotypic Structure.- 2.3. Panmixia and Perfect Panmixia.- 2.4. The Hardy-Weinberg Principle.- 3. The Classical Treatment of the Hardy-Weinberg Equilibrium.- 3.1. Establishment of the Equilibrium.- 3.2. Random Union of Gametes.- 3.3. Properties of the Hardy-Weinberg Equilibrium.- 4. The Equilibrium for Sex-Linked Genes.- 4.1. Passage from One Generation to the Next.- 4.2. The Equilibrium State.- 5. The Hardy-Weinberg Principle in Human Populations.- 5.1. Autosomal Loci with Two Alleles.- 5.2. Autosomal Loci with Three Alleles.- 5.3. Sex-Linked Genes.- 5.4. Y-Linked Genes.- 4. The Equilibrium for Two Loci.- 1. The Role of Individuals.- 2. Genic Structure.- 2.1. The Recurrence Relation for the Transition from One Generation to the Next.- 2.2. The Constancy of Gene Frequencies.- 2.3. The Approach to Equilibrium.- 3. Genotypic Structure.- 4. Two Loci, Each with Two Alleles.- 4.1. Gamete Frequencies.- 4.2. Fusion of Two Populations.- 4.3. Instantaneous Attainment of Equilibrium.- 5. The Detection and Measurement of Linkage.- 5.1. Detection of Linkage-Penrose’s Method.- 5.2. Estimation of Recombination Fractions-Morton’s Method.- 5.3. Smith’s “Bayesian” Method of Estimating Recombination Fractions.- 5.4. The Linkage Map of Man.- 5. The Inheritance of Quantitative Characters.- 1. The Mean.- 1.1. Definiton of Additive Effects and Dominance Deviations.- 1.2. Determination of the Additive Effects and Dominance Deviations.- 1.3. The Effect of a Small Change in Gene Frequency.- 1.4. The Case of a Single Locus with Two Alleles.- 1.5. Characters Controlled by Several Loci.- 1.6. An Example of a Character Controlled by Several Genes: Skin Colour.- 2. The Variance.- 2.1. Environmental Variance.- 2.2. Genotypic Variance.- 2.3. The Case of a Locus with Two Alleles.- 6. Genetic Relationships between Relatives.- 1. The Measure of Relatedness.- 1.1. Identity by Descent.- 1.2. The Definition of Coefficients of Identity.- 1.3. The Calculation of Coefficients of Identity.- 1.4. Sex-Linked Genes.- 2. The Genetic Structures of Related Individuals.- 2.1. The Relation between the Genic Structures of Related Individuals.- 2.2. The Relation between the Genotypic Structures of Related Individuals.- 2.3. The Relations between the Genic Structures of Inbred Individuals.- 2.4. Other Points.- 3. Resemblance between Relatives.- 3.1. The Determination of the Covariance between Relatives.- 3.2. Some Particular Relationships.- 3.3. The Case of a Locus with Two Alleles.- 3.4. The Interpretation of Observed Correlations between Relatives.- 7. Overlapping Generations.- 1. The Demographic Description of a Population.- 1.1. Demographic Parameters.- 1.2. The Future Demographic Structure of a Population.- 1.3. The Intrinsic Rate of Natural Increase.- 1.4. The Male Population.- 2. The Equilibrium Genetic Structure of a Population with Overlapping Generations.- 2.1. Genic and Genotypic Structures of Populations with Overlapping Generations.- 2.2. The Evolution of the Genetic Structure of a Population.- 2.3. The Evolution of the Genotypic Structure of a Population.- 2.4. Conclusions.- 3 The Causes of Evolutionary Changes in Populations.- 8. Finite Populations.- 1. Identity by Descent of Genes in Finite Populations.- 1.1. The Inbreeding Coefficient and Coefficient of Kinship of a Population.- 1.2. Increase of the Inbreeding Coefficient in a Finite Population.- 1.3. Constant Effective Population Size.- 1.4. Changing Effective Population Size.- 1.5. Relations between Relatives in a Finite Population.- 1.6. The Effect of Variance in Number of Offspring on the Effective Population Size.- 1.7. The Effect of the Prohibition of Incest on Effective Population Size.- 1.8. Effective Population Size in Populations with Overlapping Generations.- 2. Changes in the Genotypic Probability Structure.- 2.1. The Difference Equation for Genotypic Probability Structure.- 2.2. The Genotypic Probability Structure at Intermediate Stages.- 2.3. The Stages of Change in Genotypic Structure.- 2.4. Genetic Drift.- 2.5. The Disappearance of Heterozygotes.- 2.6. Sib-Mating.- 2.7. Summary.- 3. The Transmission of Genes from One Generation to the Next.- 3.1. The Probability Distribution of the Number of Genes Transmitted.- 3.2. Changes in Gene Frequencies.- 3.3. Genetic Drift.- 3.4. The Rate of Attainment of Homozygosity.- 4. Matings between Relatives in a Finite Population.- 4.1. Matings between Sibs.- 4.2. Matings between First Cousins.- 4.3. The Role of the Variance in Number of Offspring.- 5. Observations on Human Populations.- 5.1. The Frequency of Consanguineous Marriages.- 5.2. Consanguineous Marriages in France.- 5.3. Consanguineous Marriages in Several Catholic Countries.- 5.4. Consanguineous Marriages in some Non-Catholic Countries.- 5.5. Mating between Relatives in Populations with Overlapping Generations.- 6. Subdivision of a Population.- 6.1. Changes in Gene Frequencies and Coefficients of Kinship.- 6.2. Effect of Limited Sample Sizes.- 6.3. Sampling Variance of—.- 6.4. The Effect of Relationship between Groups.- 9. Deviations from Random Mating.- 1. Genotype Frequencies Among the Offspring of Consanguineous and Assortative Matings.- 1.1. An Example of Non-Independence between Mates.- 1.2. The Offspring of a Consanguineous Mating.- 1.3. The Biological Consequences of Consanguineous Mating.- 1.4. The Frequency of Consanguineous Marriages among the Parents of Children Affected with Genetic Disorders.- 2. Choice of Mates Based on Relatedness.- 2.1. Sib-Mating.- 2.2. Parent-Offspring Mating.- 2.3. Half-Sib Mating.- 2.4. Double First-Cousin Mating.- 2.5. First-Cousin Mating.- 2.6. Second-Cousin Mating.- 2.7. Number of Ancestors and the Approach Towards Homozygosity.- 2.8. Avoidance of or Preference for Certain Types of Marriage.- 3. Assortative Mating.- 3.1. Total Positive Assortative Mating Based on Genotype.- 3.2. Partial Positive Assortative Mating Based on Genotype.- 3.3. Total Positive Assortative Mating Based on Phenotype.- 3.4. Partial Positive Assortative Mating Based on Phenotype.- 3.5. Total Negative Assortative Mating Based on Genotype.- 3.6. Partial Negative Assortative Mating Based on Genotype.- 3.7. Total Negative Assortative Mating Based on Phenotype.- 3.8. Partial Negative Assortative Mating Based on Phenotype.- 4. The Offspring of Consanguineous Marriages.- 4.1. The American Medical Association Study of 1856.- 4.2. The Study in Morbihan and Loir-et-Cher of 1952. Definition of “Perinatal Mortality Rate”.- 4.3. The Study in the Vosges in 1968.- 4.4. The Study in Japan in 1958–60.- 4.5. Sex-Linked Genes.- 4.6. Conclusions.- Further Reading.- 10. Selection.- 1. Some Simple Models of Selection.- 1.1. Definition of Selective Values.- 1.2. Change in Gene Frequencies.- 1.3. Loci with Two Alleles.- 1.4. Constant Selective Values.- 1.5. Some Particular Cases.- 1.6. Variable Selective Values.- 1.7. Constant Selection for a Sex-Linked Gene.- 1.8. Selection in the Multi-Locus Case.- 2. The Consequences of Selection for the Mean Fitness of Populations.- 2.1. Constant Selective Values.- 2.2. Variable Selective Values.- 3. Selection in Populations with Overlapping Generations.- 3.1. Demographic Parameters and Selective Differences.- 3.2. Some Examples of Selection in Human Populations.- 4. The Study of Selection in Human Populations.- 4.1. Difficulties in Detecting Selective Effects.- 4.2. Direct Evidence for Selective Differences Associated with Human Polymorphisms.- 4.3. Indirect Evidence for Selection.- 4.4. The Index of the Opportunity for Selection.- Further Reading.- 11. Mutation.- 1. The Probability of Survival of a Mutant Gene.- 1.1. Elimination of a Neutral Allele.- 1.2. Survival of a Neutral Mutant Gene in a Finite Population.- 1.3. The Probability that an Advantageous New Mutant Gene will be Maintained in the Population.- 2. Recurrent Mutations.- 2.1. Change in Genic Structure due to Recurrent Mutation.- 2.2. The Case of a Locus with two Alleles.- 3. The Resultant Effect of Selection and Mutation at a Locus with Two Alleles.- 3.1. The Equilibrium between Mutation and Selection.- 3.2. Constant Selective Values.- 4. The Human Mutation Rate.- 5. The Spread of a Mutation: Congenital Dislocation of the Hip.- Further Reading.- 12. Migration.- 1. Deterministic Models with Migration.- 1.1. Changes in Genic Structure.- 1.2. Changes in Genotypic Structure.- 1.3. Applications to Actual Populations.- 1.4. Deterministic Models of Migration when Other Forces for Change are Acting.- 2. Shastic Models with Migration.- 2.1. Migration.- 2.2. Shastic Models of Migration with Other Evolutionary Forces also Acting.- 2.3. Migration and Mutation in a Spatially Continuous Population.- 3. Data on Migration in Human Populations.- 3.1. Models of the Migration Process.- 3.2. Comparison of the Genetic Models with the Models of Migration.- 4. Conclusions.- Further Reading.- 13. The Combined Effects of Different Evolutionary Forces.- 1. Wright’s Model.- 1.1. Change in Gene Frequency from One Generation to the Next.- 1.2. The Fundamental Equation.- 1.3. The Asymptotic Probability Distribution.- 1.4. Some Further Results on Selection and Mutation in Finite Populations.- 2. Simulation.- 2.1. The Principles of Monte Carlo Methods.- 2.2. The Use of Monte Carlo Methods.- 2.3. Simulation of the Genetic Structure of a Population.- 3. Maintenance of Polymorphisms. Genetic Load.- 3.1. The Equilibrium under Mutation and Selection.- 3.2. Maintenance of Variability by Neutral Mutation.- 3.3. Heterotic Equilibrium.- 3.4. The Genetic Load of a Locus.- 3.5. The Total Genetic Load.- 3.6. The Effect of Inbreeding on Selective Value.- 3.7. Conclusion: “Neo-Darwinian” Versus “Non-Darwinian” Evolution.- Further Reading.- 4 The Study of Human Population Structure.- 14. Genetic Distance. I. Basic Concepts and Methods.- 1. The Idea of Distance.- 1.1. The Definition of Distance.- 1.2. Distance between Objects Characterised by Measurements.- 1.3. Distance between Objects Characterised by Qualitative Attributes.- 2. Distance between Individuals of Known Ancestry.- 2.1. Inadequacy of the Coefficient of Kinship.- 2.2. Genotypic Distance between Relatives.- 2.3. Other Measures of Distance between Relatives.- 3. Distances between Populations.- 3.1. Distance between the Genetic Structures of Populations.- 3.2. Distance between Populations of Known Ancestry.- 3.3. Biometrical Estimation of the Relatedness of Two Populations.- 3.4. Conclusion.- Further Reading.- 15. Genetic Distance. II. The Representation of Sets of Objects.- 1. Principal Components Analysis.- 1.1. The First Principal Axis.- 1.2. The First Principal Surface.- 1.3. Generalisation.- 1.4. Normalisation of Measures.- 1.5. Interpretation of the Projections Obtained. Representation of Characters.- 2. Principal Components Analysis of Contingency Tables.- 2.1. The—2 Metric.- 2.2. The Projection of the Object-Points Onto the Principal Plane.- 2.3. The Principal Plane of the Character-Points.- 2.4. Interpretation of the Simultaneous Representation of Objects and Characters.- 3. Cluster Analysis.- 3.1. Information and Variance.- 3.2. Aggregation of Two Objects.- 3.3. Interpretation of the Decrease in Variance: The Diameter of a Class.- 3.4. Phylogenetic Trees.- 16. Some Studies of Human Populations.- 1. The Jicaque Indians of the Montaña de la Flor, Honduras.- 1.1. History of the Group.- 1.2. Inbreeding among the Jicaque Indians.- 1.3. Changes in the Genetic Composition of the Group.- 2. The Bedik of Eastern Senegal.- 2.1. History and Ecology.- 2.2. Marriages among the Bedik.- 2.3. Haematological Characters — Distances between Villages.- 2.4. Representation of the Structure of the Population.- 3. The Kel Kummer Tuareg of Mali.- 3.1. History, Ecology and Social Organisation.- 3.2. The Genealogy of the Kel Kummer People.- 3.3. Changes in the Genetic Make-up of the Population.- 3.4. Haematological Studies of the Kel Kummer Population.- 4. Classification of Populations Using the HL-A Systems.- 4.1. Data and Methods of Calculation.- 4.2. Results.- Conclusion.- Appendix A. Linear Difference Equations.- 1. Definitions.- 2. The Solution of Linear Difference Equations.- Appendix B. Some Definitions and Results in Matrix Algebra.- 1. Definitions.- 1.1. Types of Matrix.- 1.2. The Determinant of a Matrix.- 1.3. Matrix Addition and Multiplication.- 2. Diagonalisation of a Square Matrix.- 2.1. The Powers of a Matrix.- 2.2. The Eigenvalues of a Matrix.- 3. The Spectral Analysis of a Matrix.- 4. Real Symmetric Matrices.- 4.1. The Eigenvalues of a Real Symmetric Matrix are all Real.- 4.2. The Eigenvectors of a Real Symmetric Matrix Corresponding to Distinct Eigenvalues are Orthogonal.- 5. Shastic Matrices.- 5.1. The Eigenvalues of Shastic Matrices.- 5.2. The Spectral Analysis of a Shastic Matrix.- References.