Contents -- Preface -- Notations of the main parameters -- Main particularities of autopolyploids as compared with diploids -- CHAPTER 1. Some General aspects of autopolyploid genetics -- 1. Types and occurrence of polyploids -- 2. Meiosis in autopolyploids -- 2.1. The phenomenon of double reduction in autotetraploids -- 2.2. Double reduction in other autopolyploids -- 2.3. Gametic association of alleles -- 3. The production of unreduced gametes in diploids -- 4. Segregation for two loci -- 4.1. Segregation with bivalent formation -- 4.2. Segregation with multivalent formation -- 5. Mapping in autopolyploids -- CHAPTER 2. Large Random Mating Populations -- 1. Genetic constitution of a random mating population -- 1.1. Genetic constitution at a single locus -- 1.1.1. Gamete frequencies -- 1.1.2. Genotype frequencies -- 1.2. Genetic constitution of a population for two loci -- 1.2.1. The concept of linkage disequilibrium. Definition for diploids -- 1.2.2. Study of linkage disequilibrium in an autopolyploid random mating population -- 1.2.3. A generalisation: the concept of "link by descent" in a random mating population -- 2. Changes of gene frequency due to mutation and selection -- 2.1. Mutation and migration -- 2.2. Selection pressure -- 2.2.1. One-locus selection -- 2.2.2. Balance between mutation and selection -- CHAPTER 3. Kinship, inbreeding and small populations -- 1. Kinship coefficients and coefficients of inbreeding -- 1.1. The concept of identity by descent -- 1.2. Kinships between non-inbred relatives -- 1.2.1. Kinship coefficients for autotetraploids -- 1.2.2. Kinship coefficients for a 2v-ploidy level -- 1.2.3. Kinship coefficients in presence of gametic disequilibrium -- 1.3. Kinship between inbred relatives -- 1.4. Coefficients of inbreeding -- 1.5. Relationships between kinship and inbreeding -- 2. Inbreeding in large populations.

2.1. Genotype frequencies in an inbred population -- 2.1.1. Genotype frequencies in terms of coefficients of inbreeding -- 2.1.2. Genotype distribution in terms of coefficients of identity in state -- 2.2. Gamete and genotype frequencies with double reduction -- 2.2.1. Gamete frequencies -- 2.2.2. Genotype frequencies in an arbitrary generation -- 2.3. Random mating after inbreeding -- 2.4. Change in the coefficients of identity by descent with regular self-fertilization -- 2.4.1. Study from the generation matrix with chromosome segregation -- 2.4.2. The effect of double reduction -- 2.4.3. Direct study of the coefficient of inbreeding of order 1 (F) -- 2.4.4. Genome structure and juctions under inbreeding in autotetraploids -- 2.5. Inbreeding of a population with a rate S of self-fertilization -- 3. Finite and structured populations -- 3.1. Finite populations - the effects of genetic drift -- 3.1.1. Change of mean and variance in gene frequencies due to genetic drift -- 3.1.2. Inbreeding coefficient in a population of restricted size -- 3.2. Subdivided populations -- 3.2.1. The Wahlund effect -- 3.2.2. Wright's F-Statistics and their extension to autopolyploids -- 3.2.3. Equilibrium values of the Wright's F-coefficients in an island model of population structure -- 3.2.4. Estimation Wright's F-Statistics by ANOVA -- 4. Natural selection in inbreeding populations -- 4.1. Balance between mutation and selection in partially self-fertilizing populations -- 4.2. Inbreeding depression as a function of the selfing rate in autotetraploid populations -- CHAPTER 4. Genetic effects and quantitative genetics in random mating populations -- 1. Genetic effects in random mating populations -- 1.1. Definition of genotypic values and broad-sense heritability -- 1.1.1. Definition within a macro-environment.

1.1.2. Genotypic values and broad-sense heritability with several macro-environments -- 1.2. Model for genotypic value with multiallelism -- 1.2.1. Definition of genetic effects -- 1.2.2. Genetic effects and combining ability -- 1.3. Genetic effects with biallelism -- 1.3.1. Tetragenic interaction model (M4 model) -- 1.3.2. Trigenic interaction model (M3 or trigenic model) -- 1.3.3. Digenic interaction model (M2 or dig en ic model) -- 1.3.4. Additive model -- 1.3.5. Another writing of the models -- 1.3.6. A unified notation for biallelism -- 1.3.7. A biochemical basis of dominance -- 1.4. Extension of the model to several loci -- 1.4.1. The model at several loci in the absence of epistasis -- 1.4.2. Genetic effects in the presence of epistasis -- 1.4.3. An approximate estimate of additive variance -- 1.4.4. Definition and meaning of narrow-sense heritability -- 1.5. Comparison of genetic effects between diploids and autotetraploids -- 1.5.1. One-locus autotetraploids and one-locus diploids -- 1.5.2. Two-locus diploids and one-locus autotetraploids -- 1.6. Genetic effects and variance components in presence of GE interactions -- 1.7. Phenotypic and genetic correlations among traits -- 2. Covariance between relatives in panmictic populations -- 2.1. General formulation -- 2.1.1. Expression of covariance for autotetraploids -- 2.1.2. Expression of covariances for 2v-ploids -- 2.2. Relationships between kinship coefficients, genotypic or phenotypic correlations among relatives and narrow-sense heritability -- 2.3. Comparison between one-locus autotetraploids and two-locus diploids -- 3. Means and variances for non-equilibrium populations -- 3.1. Means and variances with panmictic disequilibrium -- 3.1.1. Population mean with panmictic disequilibrium -- 3.1.2. Covariances between relatives with panmictic disequilibrium.

3.2. Means and variances with linkage disequilibrium -- 3.2.1. Population mean with linkage disequilibrium -- 3.2.2. Covariances between relatives with linkage disequilibrium -- 4. Mating designs to estimate variance components of random mating populations -- 4.1. General considerations -- 4.2. One-way mating designs -- 4.3. Two-way mating designs -- 4.3.1. Principles of analysis -- 4.3.2. North Carolina design I or nested design -- 4.3.3. North Carolina design II or factorial design -- 4.3.4. Diallel mating design -- 4.3.5. Adding the cloned parents to the two-factor mating designs -- 4.4. Three and four-way mating designs -- 4.4.1. Example of a three-way mating designs: the mating design A (BxC) -- 4.4.2. Example of a four-way mating design: the mating design (B/A)(D/C) -- 4.5. Some elements to determine the accuracy of variance components estimates -- 5. QTL detection in autotetraploids -- 5.1. Principles of QTL detection -- 5.2. Marker-genotype means for different segregating populations -- 5.2.1. Recombinant Inbred Lines (RIL) or Quadrupled-Haploid Lines (QHL) -- 5.2.2. Backcross populations -- 5.2.3. F2 Populations -- 5.2.4. F1from the cross between two heterozygous plants -- 5.3. Studies with markers one by one -- 5.3.1. Analysis of variance -- 5.3.2. Test of epistasis and QTL x environment interactions -- 5.3.3. Factors influencing QTL detection -- 5.4. Maximum likelihood estimation and interval mapping -- 5.4.1. Principle of the maximum likelihood estimation -- 5.4.2. Maximum likelihood interval mapping -- 5.5. A regression approach of interval mapping -- 5.6. Composite interval mapping -- 5.7. A practical approach of QTL detection -- CHAPTER 5. Quantitative genetics of inbred populations -- 1. Means of inbred populations -- 1.1. General formulation of means -- 1.1.1. Inbred population deriving from a random mating population in equilibrium.

1.1.2. Inbred population deriving from apopulation inpanmictic disequilibrium -- 1.2. Comparison of autotetraploids with isogenic allotetraploids -- 1.3. Expected value of zygotic states of identity by descent in autotetraploids -- 1.4. Application to the study of inbreeding depression in self-fertilization -- 1.4.1. Change in the contribution of some parameters -- 1.4.2. Principal components of the mean under self-fertilization -- 1.5. Experimental results -- 1.5.1. Inbreeding effects under self-fertilization -- 1.5.2. Estimation of the value of the zygotic states of identity by descent -- 1.6. Mean of an induced tetraploid population -- 1.6.1. General formulation of the population mean -- 1.6.2. Origin of the doubling depression -- 1.6.3. Comparison of inbreeding depression in autotetraploids and isogenic allotetraploids -- 2. Covariances among inbred relatives -- 2.1. General formulation of the covariance -- 2.1.1. Covariances between inbred relatives with multiallelism and no restriction on genic interactions -- 2.1.2. Covariances between inbred relatives with biallelism and only digenic interactions -- 2.1.3. Effect of double reduction on covariances between relatives in a random mating population -- 2.1.4. Effect of panmictic and linkage disequilibria -- 2.2. The change in variance under self-fertilization -- 2.2.1. Change in the total genotypic variance -- 2.2.2. The redistribution of variance under self-fertilization -- 2.3. Estimation of variance components -- 2.4. Experimental results in lucerne -- 2.5. Reducing the number of parameters -- 2.6. Particular cases of inbreeding -- 2.6.1. The effect of chromosome doubling -- 2.6.2. Effect of FDR and SDR meiosis -- 2.6.3. Triploid endosperm -- 3. Effect of random mating after inbreeding -- 3.1. General formulation of the population mean.

3.2.1. Crossing after inbreeding from a random mating population.