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Os objetivos deste trabalho foram analisar ganhos genéticos teóricos de milho como resultado da seleção entre famílias de irmãos completos e de meios-irmãos, obtidas pelos Delineamentos I, de Irmãos Completos e de Meios-Irmãos, e a variabilidade genotípica e perda de genes com seleção a longo prazo. Os delineamentos foram avaliados por simulação, com base nos ganhos médios estimados após dez ciclos de seleção. O processo de simulação considerou sete sistemas gênicos com dez genes (com distintos graus de dominância), três classes de populações (com diferentes freqüências gênicas), sob três condições de ambiente (valores de herdabilidade), e quatro estratégias de seleção. Cada combinação foi repetida dez vezes, totalizando 25.200 simulações. Seleção entre famílias de irmãos completos é geralmente mais eficiente do que seleção com base em progênies de meios-irmãos. Empregar famílias de irmãos completos obtidas pelo Delineamento I é geralmente mais eficiente que usar progênies derivadas do Delineamento de Irmãos Completos. O Delineamento I, com 50 machos e 200 fêmeas (tamanho efetivo de 160), não determinou população melhorada com variabilidade genotípica mínima. Nas populações melhoradas com menor tamanho efetivo (160 e 400), a perda de genes favoráveis é restrita àqueles recessivos em baixa freqüência. The objectives of this work were to analyze theoretical genetic gains of maize due to recurrent selection among full-sib and half-sib families, obtained by Design I, Full-Sib Design and Half-Sib Design, and genotypic variability and gene loss with long term selection. The designs were evaluated by simulation, based on average estimated gains after ten selection cycles. The simulation process was based on seven gene systems with ten genes (with distinct degrees of dominance), three population classes (with different gene frequencies), under three environmental conditions (heritability values), and four selection strategies. Each combination was repeated ten times, amounting to 25, 200 simulations. Full-sib selection is generally more efficient than half-sib selection, mainly with favorable dominant genes. The use of full-sib families derived by Design I is generally more efficient than using progenies obtained by Full-Sib Design. Using Design I with 50 males and 200 females (effective size of 160) did not result in improved populations with minimum genotypic variability. In the populations with lower effective size (160 and 400) the loss of favorable genes was restricted to recessive genes with reduced frequencies.

Evaluation of identity differences among breeding populations and classifying is an important issue to consider before selecting germplasm. The study was conducted to analyse the differences within and among red clover (Trifolium pratense L.) half-sib families by morphological trait data and to evaluate the level of relationships among families. A half- sib progeny nursery was established in a field trial at location Osijek (lat 45o32'N, long 18o44'E, altitude 90 m). Material was comprised of 120 half-sib families from 20 phenotypically desirable parental plants of six breeding populations. A total of 40 progeny plants per each family were described according to UPOV DUS guidelines for red clover. Differences of descriptor states among families were found and a number of qualitative and quantitative morphological traits were scored and used to calculate matrix of dissimilarities among families. Families were classified by clustering procedure.

QTL detection experiments in livestock species commonly use the half-sib design. Each male is mated to a number of females, each female producing a limited number of progeny. Analysis consists of attempting to detect associations between phenotype and genotype measured on the progeny. When family sizes are limiting experimenters may wish to incorporate as much information as possible into a single analysis. However, combining information across sires is problematic because of incomplete linkage disequilibrium between the markers and the QTL in the population. This study describes formulæ for obtaining MLEs via the expectation maximization (EM) algorithm for use in a multiple-trait, multiple-family analysis. A model specifying a QTL with only two alleles, and a common within sire error variance is assumed. Compared to single-family analyses, power can be improved up to fourfold with multi-family analyses. The accuracy and precision of QTL location estimates are also substantially improved. With small family sizes, the multi-family, multi-trait analyses reduce substantially, but not totally remove, biases in QTL effect estimates. In situations where multiple QTL alleles are segregating the multi-family analysis will average out the effects of the different QTL alleles.

International audience; In this paper, we compare four different methods of dealing with the unknown linkage phase of sire markers which occurs in the detection of quantitative trait loci (QTL) in a half-sib family structure when no information is available on grand-parents. The methods are compared by considering a Gaussian approximation of the progeny likelihood instead of the mixture likelihood. In the first simulation study, the properties of the Gaussian model and of the mixture model were investigated, using the simplest method for sire gamete reconstruction. Both models lead to comparable results as regards the test power but the mean square error of sib QTL effect estimates was larger for the Gaussian likelihood than for the mixture likelihood, especially for maps with widely spaced markers. The second simulation study revealed that the simplest method for sire marker genotype estimation was as powerful as complicated methods and that the method including all the possible sire marker genotypes was never the most powerful.; Dans ce papier, nous comparons quatre méthodes, qui permettent de résoudre le problème relatif à la phase inconnue des mâles aux marqueurs dans des familles de demi-germains, lorsque aucune information sur les grands-parents n’est disponible. Ces méthodes sont comparées, en utilisant l’approximation gaussienne de la vraisemblance à l’intérieur de chaque descendance à la place de la vraisemblance du mélange de distribution. Dans la première étude par simulation, les propriétés respectives du modèle gaussien et du modèle de mélange sont étudiées pour la méthode la plus simple de reconstruction des gamètes des mâles. Les deux modèles conduisent à des tests comparables au regard de leur puissance mais l’erreur quadratique moyenne d’estimation de l’effet de substitution du QTL intra-famille est plus grande pour le modèle gaussien que pour le modèle de mélange, en particulier pour les cartes génétiques très peu denses. La deuxième étude par simulation montre que la plus simple méthode d’estimation du génotype des mâles aux marqueurs est aussi puissante que les méthodes plus sophistiquées et que la méthode qui consiste à prendre en compte dans la vraisemblance tous les génotypes possibles d’un mâle aux marqueurs n’est jamais la plus puissante.

This paper describes two kinds of alternative models for QTL detection in livestock: an heteroskedastic model, and models corresponding to several hypotheses concerning the distribution of the QTL substitution effect among the sires: a fixed and limited number of alleles or an infinite number of alleles. The power of different tests built with these hypotheses were computed under different situations. The genetic variance associated with the QTL was shown in some situations. The results showed small power differences between the different models, but important differences in the quality of the estimations. In addition, a model was built in a simplified situation to investigate the gain in using possible linkage disequilibrium., Ce papier décrit deux types de modèles alternatifs pour la détection de QTL dans les populations animales : un modèle hétéroscédastique d’une part, et des modèles correspondants à différentes hypothèses sur la distribution de l’effet de substitution du QTL pour chaque mâle : un nombre fixe et limité d’allèles ou au contraire un nombre infini d’allèles. Les puissances des différents tests construits avec ces hypothèses sont calculées dans différentes situations. L’estimation de la variance génétique liée au QTL est donnée dans certaines situations. Les résultats montrent de faibles différences de puissance entre les différents modèles, mais des différences importantes dans la qualité des estimations. De plus, on construit un modèle dans une situation simplifiée pour étudier le gain que l’on peut obtenir en utilisant un éventuel déséquilibre de liaison.

International audience; This paper describes two kinds of alternative models for QTL detection in livestock: an heteroskedastic model, and models corresponding to several hypotheses concerning the distribution of the QTL substitution effect among the sires: a fixed and limited number of alleles or an infinite number of alleles. The power of different tests built with these hypotheses were computed under different situations. The genetic variance associated with the QTL was shown in some situations. The results showed small power differences between the different models, but important differences in the quality of the estimations. In addition, a model was built in a simplified situation to investigate the gain in using possible linkage disequilibrium.; Ce papier décrit deux types de modèles alternatifs pour la détection de QTL dans les populations animales : un modèle hétéroscédastique d’une part, et des modèles correspondants à différentes hypothèses sur la distribution de l’effet de substitution du QTL pour chaque mâle : un nombre fixe et limité d’allèles ou au contraire un nombre infini d’allèles. Les puissances des différents tests construits avec ces hypothèses sont calculées dans différentes situations. L’estimation de la variance génétique liée au QTL est donnée dans certaines situations. Les résultats montrent de faibles différences de puissance entre les différents modèles, mais des différences importantes dans la qualité des estimations. De plus, on construit un modèle dans une situation simplifiée pour étudier le gain que l’on peut obtenir en utilisant un éventuel déséquilibre de liaison.

Estudou-se a obtencao de parametros geneticos para alguns caracteres de planta e espiga de milho (Zea mays L.) cv. Composto Dentado. O material e do segundo ciclo de selecao entre e dentro de familias de meios-irmaos. Avaliaram-se 400 progenies num delineamento de latice simples 10 x 10 com repeticao por local: Caruaru e S.Bento do Una, PE. Os experimentos nao receberam tratamentos fitossanitarios, e foram isolados das areas que receberam tratamentos com inseticidas, utilizando-se infestacoes naturais. Foram coletados os dados para: altura da planta (AP) e da espiga (AE), numero de espigas por planta (NE) e de espigas mal empalhadas (NEME), danos causados por H.zea (HZ) e S.frugiperda (SF), e producao de graos (PG). As estimativas de variancia genetica aditiva foram altas (P

In this paper, we compare four different methods of dealing with the unknown linkage phase of sire markers which occurs in the detection of quantitative trait loci (QTL) in a half-sib family structure when no information is available on grand-parents. The methods are compared by considering a Gaussian approximation of the progeny likelihood instead of the mixture likelihood. In the first simulation study, the properties of the Gaussian model and of the mixture model were investigated, using the simplest method for sire gamete reconstruction. Both models lead to comparable results as regards the test power but the mean square error of sib QTL effect estimates was larger for the Gaussian likelihood than for the mixture likelihood, especially for maps with widely spaced markers. The second simulation study revealed that the simplest method for sire marker genotype estimation was as powerful as complicated methods and that the method including all the possible sire marker genotypes was never the most powerful., Dans ce papier, nous comparons quatre méthodes, qui permettent de résoudre le problème relatif à la phase inconnue des mâles aux marqueurs dans des familles de demi-germains, lorsque aucune information sur les grands-parents n’est disponible. Ces méthodes sont comparées, en utilisant l’approximation gaussienne de la vraisemblance à l’intérieur de chaque descendance à la place de la vraisemblance du mélange de distribution. Dans la première étude par simulation, les propriétés respectives du modèle gaussien et du modèle de mélange sont étudiées pour la méthode la plus simple de reconstruction des gamètes des mâles. Les deux modèles conduisent à des tests comparables au regard de leur puissance mais l’erreur quadratique moyenne d’estimation de l’effet de substitution du QTL intra-famille est plus grande pour le modèle gaussien que pour le modèle de mélange, en particulier pour les cartes génétiques très peu denses. La deuxième étude par simulation montre que la plus simple méthode d’estimation du génotype des mâles aux marqueurs est aussi puissante que les méthodes plus sophistiquées et que la méthode qui consiste à prendre en compte dans la vraisemblance tous les génotypes possibles d’un mâle aux marqueurs n’est jamais la plus puissante.

Although linkage disequilibrium, epistasis and inbreeding are common phenomena in genetic systems that control quantitative traits, theory development and analysis are very complex, especially when they are considered together. The objective of this study is to offer additional quantitative genetics theory to define and analyze, in relation to non-inbred cross pollinating populations, components of genotypic variance, heritabilities and predicted gains, assuming linkage disequilibrium and absence of epistasis. The genotypic variance and its components, additive and due to dominance genetic variances, are invariant over the generations only in regard to completely linked genes and to those in equilibrium. When the population is structured in half-sib families, the additive variance in the parents' generation and the genotypic variance in the population can be estimated. When the population is structured in full-sib families, none of the components of genotypic variance can be estimated. The narrow sense heritability level at plant level can be estimated from the parent-offspring or mid parent-offspring regression. When there is dominance, the narrow sense heritability estimate in the in F2 is biased due to linkage disequilibrium when estimated by the Warner method, but not when estimated by means of the plant F2-family F3 regression. The bias is proportional to the number of pairs of linked genes, without independent assortment, and to the degree of dominance, and tends to be positive when genes in the coupling phase predominate or negative and of higher value when genes in the repulsion phase predominate. Linkage disequilibrium is also cause of bias in estimates of the narrow sense heritabilities at full-sib family mean and at plant within half-sib and full-sib families levels. Generally, the magnitude of the bias is proportional to the number of pairs of genes in disequilibrium and to the frequency of recombining gametes.