Abstract Genetic improvement to obtain purple popcorn hybrids from native corn is in its initial phase. The development of hybrids not only gives you the possibility to complement valuable traits, but also, it is a means to take advantage of superior combinations that express heterosis. However, the first step is to evaluate a large number of lines. Therefore, this research seeks two objectives: (1) to analyze the mode of segregation of the value characters: expansion volume (VE), grain expansion (EG), black pericarp (PN) and grain yield (RG) and (2) select outstanding S1 lines for VE and PN. For this, 256 segregating lines were evaluated in three experiments, one in Huánuco at 1986 msnm and two in La Molina at 241 msnm. The tests were installed under the Simple Latice 16x16 design with two repetitions. It was determined that the continuous distribution mode with mostly additive alleles is the one that predominates in the expression of the VE, EG, PN and RG traits, however, in the VE, EG and RG characteristics, a certain dominance of genes was observed with low values and in PN, the presence of three modes was noted, which would possibly indicate the presence of genes with greater effects. Considering the distribution mode and the phenotypic values of the 256 S1 lines for the VE and PN value characters, a selection index was established that allowed the identification of 80 outstanding lines that represent a selection pressure of 31.25%.

Resumen La mejora genética para la obtención de híbridos de maíz morado reventón, a partir de maíces nativos, está en su fase inicial. El desarrollo de híbridos no solo te da la posibilidad de complementar caracteres de valor, sino también, es un medio para aprovechar combinaciones superiores que expresan heterosis. Sin embargo, el paso previo es evaluar un gran número de líneas. Por ello, esta investigación busca dos objetivos: (1) analizar el modo de segregación de los caracteres de valor: volumen de expansión (VE), expansión de granos (EG), pericarpio negro (PN) y rendimiento de grano (RG) y (2) seleccionar líneas S1 sobresalientes para VE y PN. Para ello, 256 líneas segregantes fueron evaluados en tres experimentos, uno en Huánuco a 1986 msnm y dos en La Molina a 241 msnm. Los ensayos se instalaron bajo el diseño de Látice Simple 16x16 con dos repeticiones. Se determinó que, el modo de distribución continua con alelos mayormente aditivos es la que predomina en la expresión de las características VE, EG, PN y RG, sin embargo, en los caracteres VE, EG y RG, se observó cierta dominancia de genes con valores bajos y en PN se notó la presencia de tres modas, los cuales indicarían posiblemente la presencia de genes de efectos mayores. Considerando el modo de distribución y los valores fenotípicos de las 256 líneas S1 para los caracteres de valor VE y PN, se estableció un índice de selección que permitió identificar a 80 líneas sobresalientes que representan una presión de selección de 31,25%.

ABSTRACT. This paper aimed to evaluate the effectiveness of subset selection of markers for genome-enabled prediction of genetic values using radial basis function neural networks (RBFNN). To this end, an F1 population derived from the hybridization of divergent parents with 500 individuals genotyped with 1000 SNP-type markers was simulated. Phenotypic traits were determined by adopting three different gene action models - additive, additive-dominant, and epistatic, representing two dominance situations: partial and complete with quantitative traits having a heritability (h2) of 30 and 60%; traits were controlled by 50 loci, considering two alleles per locus. Twelve different scenarios were represented in the simulation. The stepwise regression was used before the prediction methods. The reliability and the root mean square error were used for estimation using a fivefold cross-validation scheme. Overall, dimensionality reduction improved the reliability values for all scenarios, specifically with h2 =30 the reliability value from 0.03 to 0.59 using RBFNN and from 0.10 to 0.57 with RR-BLUP in the scenario with additive effects. In the additive dominant scenario, the reliability values changed from 0.12 to 0.59 using RBFNN and from 0.12 to 0.58 with RR-BLUP, and in the epistasis scenarios, the reliability values changed from 0.07 to 0.50 using RBFNN and from 0.06 to 0.47 with RR-BLUP. The results showed that the use of stepwise regression before the use of these techniques led to an improvement in the accuracy of prediction of the genetic value and, mainly, to a large reduction of the root mean square error in addition to facilitating processing and analysis time due to a reduction in dimensionality.

Resumen Introducción. Los estudios de heredabilidad sobre la tolerancia a la hipoxia en el algodón son muy escasos. Objetivo. El objetivo de este trabajo fue estudiar el patrón de heredabilidad del rendimiento del algodón en semilla, desmote y la longitud de la fibra en condiciones normales e hipoxia. Materiales y métodos. Se empleó un sistema de apareamiento dialélico de 8 x 8 en la generación F1 de algodón. El experimento se realizó durante los años 2011-2012 en el Cotton Research Institute, Multan, Pakistán. Resultados. El análisis de la varianza reveló una variación significativa (P<0.01) para todos los rasgos bajo condiciones sin estrés y de estrés por inundación. El valor del coeficiente de regresión b se desvió significativamente de cero, pero no de la unidad para todos los rasgos, lo que permitió un mayor análisis de los datos. El componente aditivo (D) fue significativo para todos los rasgos y tiene más valores que los valores de los componentes de dominancia H1 y H2, lo que indica claramente la preponderancia de los efectos genéticos aditivos. En condiciones normales y de hipoxia, las estimaciones de heredabilidad de sentido estrecho fueron mayores. Conclusión. El predominio de los efectos genéticos aditivos, la alta heredabilidad, junto con dominancia parcial bajo ambas condiciones, sugirieron que sera útil la selección de estos rasgos en un ambiente hipóxico en la generación temprana.

Abstract Introduction. The inheritance studies on hypoxia tolerance in cotton are very scanty. Objective. The objective of this work was to study the inheritance pattern of seed cotton yield, ginning out-turn, and fiber length under normal and hypoxia conditions. Materials and Methods. An 8×8 diallel mating system was employed in F1 generation of cotton. The experiment was conducted during the years 2011-2012 at Cotton Research Institute, Multan, Pakistan. Results. Analysis of variance revealed significant variation (P<0.01) for all the traits under both non-stress and flooding stress conditions. The value of regression coefficient b deviated significantly from zero but not from unity for all the traits which enabled further analysis of the data. The additive component (D) was significant for all the traits and this has more values than the values of dominance components H1 and H2, which clearly indicates the preponderance of additive genetic effects. Under normal and hypoxia conditions the estimates of narrow sense heritability were higher. Conclusion. Predominance of additive genetic effects, high heritability along with partial dominance under both conditions suggested that selection for these traits under hypoxic environment at early generation will be useful.

ResumoEm mamoeiro, informações sobre o controle genético de características relacionadas à produção e à qualidade de frutos ainda são escassas. Nesse sentido, no presente estudo, foram estimados os parâmetros genéticos durante a análise da herança de características relacionadas à produção e à qualidade de seus frutos, por meio de cruzamento dialélico completo (F1's, recíprocos e genitores). Quantificaram-se o número de frutos comerciais (NFC), o peso médio do fruto (PMF), a produtividade (PROD), a espessura (ESP) e firmeza do fruto (FIRM) e o teor de sólidos solúveis (TSS). Somente NFC, FIRM e TSS tiveram ausência de significância nos três testes de suficiência do modelo aditivo-dominante. A estimativa do grau médio de dominância indicou a existência de dominância parcial entre os alelos que atuam no controle genético das três características. Observou-se o predomínio de efeitos associados a componentes aditivos se comparados aos componentes associados aos efeitos de dominância para as três características. Para número de frutos comerciais (NFC) e firmeza do fruto (FIRM), alelos recessivos, predominante, mas não exclusivamente, atuam no sentido de aumentar a média dessa variável. Por outro lado, para teor de sólidos solúveis (TSS), são os alelos dominantes que, predominante, mas não exclusivamente, atuam no sentido de aumentar a média dessa variável.

AbstractIn papaya, information on the genetic control of traits related to the production and fruit quality are still scarce. In this sense, this study estimated genetic parameters and analyzed the inheritance of traits related to the production and quality of papaya fruit through complete diallel cross (F1's, reciprocal and parents). The number of commercial fruit, fruit weight, fruit yield, thickness of the pulp, firmness of the fruit and the soluble solids content were quantified. Number of commercial fruit, firmness of the fruit and the total soluble solids content had no significant effect in the three sufficiency tests of the additive-dominant model. The estimate of the average degree of dominance indicated partial dominance between alleles that act in the genetic control of the three traits. There was predominance of effects associated with additive components compared to the components associated with dominance effects for the three traits. For the number of marketable fruits and fruit firmness, predominant, but not exclusive recessive alleles, work to increase the mean value of this variable. In turn, for soluble solids content, predominant, but not exclusive dominant alleles, work to increase the mean value of this variable.

Objetivou-se estudar a variabilidade genética a curto prazo de características quantitativas simuladas a partir de modelos com ação gênica aditiva e não-aditiva em populações controle e de seleção fenotípica. As duas características, uma de baixa (h² = 0,10) e outra de alta (h² = 0,60) herdabilidade, foram controladas por 600 locos bialélicos. A partir de um genoma-padrão, foram obtidos seis modelos genéticos que incluíram: apenas efeitos aditivos dos genes; dominância completa e positiva para 25, 50, 75 e 100% dos locos; e sobredominância positiva para 50% dos locos. Nos modelos com desvio da dominância também foram incluídos os efeitos aditivos dos alelos para 100% dos locos. A variabilidade genética foi quantificada de geração a geração por meio de componentes de variância genética. Na ausência de seleção, as variâncias genotípica e genética aditiva mantiveram-se mais elevadas. Nos modelos com ação gênica não-aditiva, surgiu um componente de covariância entre os efeitos genéticos aditivos e de dominância de pequena magnitude e cuja correlação tendeu a ser positiva na população controle e negativa sob seleção. A variância de dominância aumentou com o acréscimo no número de locos com desvio da dominância ou no valor do desvio, o que implicou aumento das variâncias genotípica e genética aditiva entre os sucessivos modelos.

The aim of this work was to investigate the short-term behavior of the genetic variability of quantitative traits simulated from models with additive and non-additive gene action in control and phenotypic selection populations. Both traits, one with low (h² = 0.10) and the other with high (h² = 0.60) heritability, were controlled by 600 biallelic loci. From a standard genome, it was obtained six genetic models which included the following: only the additive gene effects; complete and positive dominance for 25, 50, 75 and 100% of the loci; and positive overdominance for 50% of the loci. In the models with dominance deviation, the additive allelic effects were also included for 100% of the loci. Genetic variability was quantified from generation to generation using the genetic variance components. In the absence of selection, genotypic and additive genetic variances were higher. In the models with non-additive gene action, a small magnitude covariance component raised between the additive and dominance genetic effects whose correlation tended to be positive on the control population and negative under selection. Dominance variance increased as the number of loci with dominance deviation or the value of the deviation increased, implying on the increase in genotypic and additive genetic variances among the successive models.

Statistical procedures for mapping quantitative trait loci (QTL) have been extensively studied because they are the essential for improving the accuracy of genetic analyses. The objective of the present study was to examine QTL using multivariate methods, considering the principie of simple interval mapping. A microsatellite marker data set from a F2 population was simulated. It was assumed that the QTL control binomial and normal traits. In the normal case, five QTL mapping models were evaluated that had the following residual covariance structures: variance components (VC), compound symmetry (CS), unstructured (UN), banded main diagonal (UNÍ) and heterogeneous toeplitz. Akaike's information criterion (AIC) was used to select the appropriate structure. In the binary case, the Generalized Estimating Equations (GEE) procedure was used. UN structure minimized the AIC valué on the interval that indicated a higher probability of the QTL. In the binomial case, a non-independent working correlation matrix (WCM) was fitted (p = 0.47). In both cases, the additive effect of QTL was significant (p < 0.01), but dominance effects were not (p > 0.05). Thus, QTL mapping using a multivariate approach may be a useful tool for breeding programs that aim to improve quantitative traits that have phenotypic valúes that change over time.

Los procedimientos usados en el mapeo de loci de característica cuantitativa (QTL) son continuamente estudiados ya que son fundamentales para mejorar la precisión del análisis genético. El presente estudio tuvo como objetivo examinar QTLs a través de métodos muí ti variados, considerando el principio de mapeo por intervalo simple. Se simuló un conjunto de datos de marcadores moleculares microsatélites provenientes de una población F2. Al mismo tiempo se consideró que los QTLs controlan características de distribución normal y binomial. En el caso normal se consideraron cinco modelos con las siguientes estructuras de covarianzas residuales: Componentes de varianza (VC), simetría compuesta (CS), no estructurada (UN), diagonal principal (Banded Main Diagonal; UNÍ) y toeplitz heterogénea (TOEPH). El criterio de información de Akaike (AIC) se usó para seleccionar la estructura apropiada. En el caso binomial se usó el procedimiento de ecuaciones generalizadas (GEE). La estructura tipo UN minimizó el valor de AIC dentro del intervalo de mayor probabilidad de presencia del QTL. En el caso binario, una matriz de correlación dependiente fue la más adecuada (p = 0,47). En ambos casos el efecto aditivo del QTL fue altamente significativo (p < 0,01) opuestamente al efecto de dominancia (p > 0,05). Según los resultados obtenidos, se concluyó que el mapeo de QTLs usando un enfoque multivariado es una herramienta útil para los programas genéticos que buscan mejorar características cuantitativas cuyos valores fenotípicos cambian en el tiempo.

Although epistasis is common in gene systems that determine quantitative traits, it is usually not possible to estimate the epistatic components of genotypic variance because experiments in breeding programs include only one type of progeny. As the study of this phenomenon is complex, there is a lack of theoretical knowledge on the contribution of the epistatic variances when predicting gains from selection and on the bias in estimating genetic parameters when fitting the additive-dominant model. The objective of this paper is to discuss these aspects. Regarding a non-inbred population, the genetic value due to dominance and the epistatic components of the genotypic value are not indicators of the number of favorable genes present in an individual. Thus, the efficiency of a selection process should be based on the narrow-sense heritability, a function only of additive variance. If there is no epistasis, generally it is satisfactory to assess the selection efficiency and to predict gain based on the broad-sense heritability. Regardless of the selection unit or type of epistasis, the bias in the estimate of the additive variance when assuming the additive-dominant model is considerable. This implies overestimation of the heritabilities at half sib family mean, plant within family and plant levels, and underestimation if the selection units are full sib progenies. The predicted gains will have a bias proportional to that of the heritability.

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.

Growth data of 4319 calves, obtained from a herd in New South Wales, Australia in 1989- 1997, were used to estimate additive and nonadditive, direct and maternal genetic effects in a multibreed population on crossbred and purebred Angus, Gelbvieh, Polled Hereford, Red Angus and Santa Gertrudis. Age-adjusted weights to 200 (W2), 400 (W4) and 600-day (W6), were analyzed using a multiple-trait animal model including the maternal genetic effect for W2. Direct breed, maternal additive genetic effects (Santa Gertrudis vs. any other breed) and direct dominance effect (individual calf breed heterozygocity) for all studied traits, were included in the model as fixed covariates. Medium direct heritability values are high enough to allow genetic progress in the population from selection of best animals for W2, W4 and W6 using an animal model. Different emphasis on each trait could allow changes in the growth curve from 200-600 days of age. Maternal heritability for W2 was close to zero, indicating a low interference with direct effect genetic progress in growth traits and a reduced value for selection for this effect. The growth potential in Gelbvieh and Angus calves was higher than those for other breeds, with Santa Gertrudis being the lowest. Santa Gertrudis was superior for maternal breed effect to the average of other breeds. The estimate for the dominance average effect was positive for W2 and W6 and negative for W4 and lower than the maximum difference between direct breed effects.

Registros de pesos de 4319 bovinos, obtenidos entre 1989 y 1997 en un hato en New South Wales, Australia, fueron usados para estimar los efectos genéticos aditivos y no aditivos, directos y maternos para caracteres de crecimiento en una población que involucra animales de raza pura y cruzados de Angus, Gelbvieh, Polled Hereford, Red Angus y Santa Gertrudis. Los pesos ajustados para edad a 200 (W2), 400 (W4) y 600 días (W6), fueron analizados usando un modelo animal multicarácter incluyendo el efecto genético materno para W2. Se incluyeron en el modelo como covariables fijas, los efectos genéticos directos de raza, aditivo materno (Santa Gertrudis vs. otras razas) y los efectos directos de dominancia (heterocigocidad individual del animal) para todos los caracteres estudiados. Los valores intermedios obtenidos para las heredabilidades directas para W2, W4 y W6, son suficientemente altos para obtener progreso genético en la población mediante la selección de los mejores animales usando un modelo animal. Diferentes énfasis para cada característica pueden permitir cambios en la curva de crecimiento de los 200-600 días de edad. La heredabilidad materna para W2 fue cercana a cero, indicando una baja interferencia con el progreso genético de los efectos directos de las características de crecimiento y un valor reducido para la selección de este efecto. El potencial de crecimiento en terneros Gelbvieh y Angus fue mayor que en las otras razas, el potencial de crecimiento de Santa Gertrudis fue el menor. Santa Gertrudis fue superior al promedio de las otras razas para los efectos maternos de raza. El estimado del efecto promedio de dominancia fue positivo para W2 y W6 y negativo para W4 y menor que la diferencia máxima entre los efectos directos de raza.

Caupi [Vigna unguiculata (L.) Walp.] é uma das leguminosas mais adaptadas às regiões quentes da África, Ásia e das Américas. No semi-árido do nordeste do Brasil é a principal cultura de subsistência, por ser uma excelente fonte de proteína de baixo custo para a população mais carente. O objetivo deste trabalho foi estimar parâmetros genéticos que podem explicar a herança do tamanho das sementes de caupi. Os genótipos parentais P1 e P2 e as gerações F1, F2, RC1 e RC2 do cruzamento TVx5058-09C X Manteiguinha, constituíram o material genético utilizado no estudo. As seis populações (P1, P2, F1, F2, RC1 e RC2) foram avaliadas num experimento em blocos casualizados com seis repetições, em Teresina - PI; o plantio foi realizado em março de 1998. Os parâmetros genéticos estimados foram variâncias fenotípica, genética total, genética aditiva e dos desvios de dominância e devido aos efeitos do ambiente, herdabilidades no sentido amplo e restrito, grau médio de dominância e número dos genes que controlam o caráter. O modelo aditivo - dominante ajustou-se aos dados do peso de 100 sementes, visto que a média e o efeito gênico aditivo foram os parâmetros genéticos mais importantes na determinação desse caráter. O número dos genes que controlam sua expressão é cinco. A ocorrência de alto valor para a herdabilidade no sentido restrito indicou que a seleção para o tamanho da semente pode ser realizada em gerações segregantes iniciais.

Cowpea [Vigna unguiculata (L.) Walp.] is one of the most widely adapted grain legumes in hot regions of Africa, Asia and the Americas. In the semiarid Northeast of Brazil, it is the main subsistence crop, an excellent protein source of low cost, for the poor population. The objective of this work was to estimate genetic parameters to understand the inheritance of seed sizes in cowpea. The parents P1 and P2 and the generations, F1, F2, BC1 and BC2 of the cross TVx5058-09C X Manteiguinha formed the genetic material for this study. These six generates (P1, P2, F1, F2, BC1 and BC) were evaluated in a completely randomized block-design with six replications, in Teresina - PI, Brazil, in 1998. The genetic parameters estimated were: phenotypic and total genetic variance, additive and dominance genetic components of variance and the variance attributed to the environment, heritability in the broad and narrow senses, average degree of dominance and the number of genes controlling the character. The additive - dominance model fitted the data for 100-seeds weight in as much as the midparental value and the additive effect were the more important genetic parameters for the determination of this character. The number of genes that control its expression is five. The occurrence of high values for narrow sense heritability indicates that the selection for seed size can be made in early generations.

Considerando um sistema poligênico de uma espécie diplóide, sem epistasia, e uma população em equilíbrio de Hardy-Weinberg, não-endogâmica, e em equilíbrio de ligação gênica, demonstra-se que: 1) a herdabilidade em sentido restrito em nível de família de meios-irmãos é igual ao quadrado do coeficiente de correlação entre a média fenotípica de família e o valor genético aditivo do pai comum; 2) a herdabilidade em sentido restrito em nível de família de irmãos completos é igual ao quadrado do coeficiente de correlação entre a média fenotípica de família e a média dos valores genéticos aditivos dos progenitores; 3) a herdabilidade em sentido restrito em nível de família Sn é exatamente igual ao quadrado do coeficiente de correlação entre a média fenotípica de família e o valor genético aditivo de seu progenitor, somente na ausência de dominância ou quando as freqüências alélicas são iguais; e 4) a herdabilidade em sentido amplo em nível de família de irmãos completos ou Sn pode ser usada para analisar a eficiência da seleção, pois, em geral, a média genotípica da progênie é um bom indicador da superioridade dos pais ou da planta Sn-1, em termos de freqüência dos genes favoráveis.

Based on a polygenic system of a diploid species, without epistasis, and a population in Hardy-Weinberg equilibrium, without inbreeding and under linkage equilibrium, it can be shown that: (1) the narrow sense heritability at half-sib family level is equal to the square of the correlation coefficient between family mean and the additive genetic value of its common parent; (2) the narrow sense heritability at full-sib family level is equal to the square of the correlation coefficient between family mean and the mean of the additive genetic values of its parents; (3) the narrow sense heritability at Sn family level is exactly equal to the square of the correlation coefficient between family mean and the additive genetic value of its parent only in absence of dominance or when allele frequencies are equal; and (4) the broad sense heritability at full-sib or Sn family level can be used to analyze selection efficiency, since the progeny genotypic mean is, in general, a good indicator of parents, or Sn-1 plant superiority with respect to the frequency of favorable genes.