A Bayesian Genomic Regression Model with Skew Normal Random Errors.

Genomic selection (GS) has become a tool for selecting candidates in plant and animal breeding programs. In the case of quantitative traits, it is common to assume that the distribution of the response variable can be approximated by a normal distribution. However, it is known that the selection process leads to skewed distributions. There is vast statistical literature on skewed distributions, but the skew normal distribution is of particular interest in this research. This distribution includes a third parameter that drives the skewness, so that it generalizes the normal distribution. We propose an extension of the Bayesian whole-genome regression to skew normal distribution data in the context of GS applications, where usually the number of predictors vastly exceeds the sample size. However, it can also be applied when the number of predictors is smaller than the sample size. We used a stochastic representation of a skew normal random variable, which allows the implementation of standard Markov Chain Monte Carlo (MCMC) techniques to efficiently fit the proposed model. The predictive ability and goodness of fit of the proposed model were evaluated using simulated and real data, and the results were compared to those obtained by the Bayesian Ridge Regression model. Results indicate that the proposed model has a better fit and is as good as the conventional Bayesian Ridge Regression model for prediction, based on the DIC criterion and cross-validation, respectively. A computing program coded in the R statistical package and C programming language to fit the proposed model is available as supplementary material.

Genomic models with genotype × environment interaction for predicting hybrid performance: an application in maize hybrids.

KEY MESSAGE: A new genomic model that incorporates genotype × environment interaction gave increased prediction accuracy of untested hybrid response for traits such as percent starch content, percent dry matter content and silage yield of maize hybrids. The prediction of hybrid performance (HP) is very important in agricultural breeding programs. In plant breeding, multi-environment trials play an important role in the selection of important traits, such as stability across environments, grain yield and pest resistance. Environmental conditions modulate gene expression causing genotype × environment interaction (G × E), such that the estimated genetic correlations of the performance of individual lines across environments summarize the joint action of genes and environmental conditions. This article proposes a genomic statistical model that incorporates G × E for general and specific combining ability for predicting the performance of hybrids in environments. The proposed model can also be applied to any other hybrid species with distinct parental pools. In this study, we evaluated the predictive ability of two HP prediction models using a cross-validation approach applied in extensive maize hybrid data, comprising 2724 hybrids derived from 507 dent lines and 24 flint lines, which were evaluated for three traits in 58 environments over 12 years; analyses were performed for each year. On average, genomic models that include the interaction of general and specific combining ability with environments have greater predictive ability than genomic models without interaction with environments (ranging from 12 to 22%, depending on the trait). We concluded that including G × E in the prediction of untested maize hybrids increases the accuracy of genomic models.

Rango de movimientos mandibulares en niños de seis años de edad con dentición mixta temprana / Range of mandibular movement in six-year old children with early mixed dentition

La medición y examen del rango de movimientos mandibulares están considerados dentro del diagnóstico clínico. El reporte de dichos rangos es extenso en adultos pero se ha escrito poco sobre el tema en cuanto a niños. El objetivo de este estudio fue determinar el rango de movimientos mandibulares en escolares de seis años de edad en México. Se recolectaron los datos de 52 niños de seis años de edad; el 52% correspondió al sexo femenino y el 48% al sexo masculino; con la prueba χ² de bondad de ajuste a la distribución uniforme o proporciones iguales, se analizó diferencias entre las categorías de: patrón de apertura, desviación de la línea media y desviación en apertura y cierre. Cabe señalar que para dicha prueba, en el patrón de apertura se excluyó la categoría con frecuencia cero. Debido al incumplimiento del supuesto de normalidad se utilizó la prueba de Wilcoxon para muestras dependientes en la comparación de la máxima apertura sin asistir y asistida, y con la prueba de t para muestras dependientes, se comparó la lateralidad derecha e izquierda. El patrón de apertura difirió significativamente (χ² = 60.9231, p < 0.0001, gL = 3): Recto 71.1%, desviación lateral derecha no corregida 0%, desviación «S¼ corregida derecha 13.5%; desviación lateral izquierda no corregida 1.9% y desviación «S¼ corregida izquierda 13.5%. El promedio de la máxima apertura no asistida fue de 35.00 mm en comparación con la máxima apertura asistida que fue de 39.11 mm (T = 0, p < 0.0001). Conclusión: El rango de movimientos mandibulares hallados en la población infantil mexicana de seis años de edad en dentición mixta primaria difiere de los encontrados en los niños de la misma edad en otras regiones. Este hecho es debido probablemente a que dichos rangos se ven influenciados por las características craneofaciales, peso, talla de cada población.

Measurement and examination of mandibular movements are procedures considered within any clinical diagnosis. Reports on these ranges are quite widespread for adult patients, but little has been written on the subject when dealing with children. The aim of the present study was to determine range of mandibular movements in six year old schoolchildren in Mexico. Data were collected on 52 six year old children. In this sample, 52% were female and 48% male. With the χ2 goodness of fit test to uniform distribution or equal proportions, differences between the following categories were examined: opening pattern, midline deviation and deviation in opening and closing. It should be noted that for the present test zero frequency category was excluded from the opening pattern. Due to the breach of normality assumption, Wilcoxon test was used for dependent samples in the comparison of unassisted and assisted maximum opening, t test for dependent samples was used to compare left and right laterality. Opening patterns differed significantly (χ2 = 60.9231, p < 0.0001, gL = 3) straight 71.1%. Uncorrected right lateral deviation 0%, right corrected «S¼ deviation 13.5%; uncorrected left lateral deviation 1.9%, and corrected left «S¼ deviation 13.5%. Average of non assisted maximum opening was 35.00 mm when compared to maximum assisted opening which was 39.11 mm (T = 0, p < 0.0001). Conclusion: Range of observed mandibular movements in Mexican six year old children with primary mixed dentition was different from same- age children in other regions. This was probably due to the fact that ranks were under the influence of craniofacial, weight, height and size characteristics of each different population.