The Genetic Structure of Populations

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. Stochastic Models with Migration.- 2.1. Migration.- 2.2. Stochastic 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. Stochastic Matrices.- 5.1. The Eigenvalues of Stochastic Matrices.- 5.2. The Spectral Analysis of a Stochastic Matrix.- References.