Will models of genetic evaluation and genomic selection ‘converge’?

Fil: Cantet, Rodolfo Juan Carlos. Universidad de Buenos Aires. Facultad de Agronomia. Departamento de Producción Animal; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

Bayesian conjugate analysis using a generalized inverted Wishart distribution accounts for differential uncertainty among the genetic parameters - an application to the maternal animal model

Consider the estimation of genetic (co)variance components from a maternal animal model (MAM) using a conjugated Bayesian approach. Usually, more uncertainty is expected a priori on the value of the maternal additive variance than on the value of the direct additive variance. However, it is not possible to model such differential uncertainty when assuming an inverted Wishart (IW) distribution for the genetic covariance matrix. Instead, consider the use of a generalized inverted Wishart (GIW) distribution. The GIW is essentially an extension of the IW distribution with a larger set of distinct parameters. In this study, the GIW distribution in its full generality is introduced and theoretical results regarding its use as the prior distribution for the genetic covariance matrix of the MAM are derived. In particular, we prove that the conditional conjugacy property holds so that parameter estimation can be accomplished via the Gibbs sampler. A sampling algorithm is also sketched. Furthermore, we describe how to specify the hyperparameters to account for differential prior opinion on the (co)variance components. A recursive strategy to elicit these parameters is then presented and tested using field records and simulated data. The procedure returned accurate estimates and reduced standard errors when compared with non-informative prior settings while improving the convergence rates. In general, faster convergence was always observed when a stronger weight was placed on the prior distributions. However, analyses based on the IW distribution have also produced biased estimates when the prior means were set to over-dispersed values.Fil: Munilla, S.. Universidad de Buenos Aires. Facultad de Agronomía. Departamento de Producción Animal; ArgentinaFil: Cantet, Rodolfo Juan Carlos. Universidad de Buenos Aires. Facultad de Agronomía. Departamento de Producción Animal; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

Bayesian estimation in maternally ancestral animal models for weaning weight of beef cattle

The Bayesian approach was implemented for fitting several maternally ancestral models for weaning weight data of Angus calves. The goal was to evaluate to what extent genetic evaluation models with additive grand maternal effects (G), or with an ancestrally structured covariance matrix for maternal environmental effects (E), or with a sire × year interaction (ISY), or combinations thereof (GE, GSY, ESY, GESY), redistribute the additive variability and reduce the negative magnitude of the additive correlation between direct and maternal effects (rAoAm), when compared with the regular maternal animal model (I). All animals with records had known dams and maternal granddams. The sampling scheme induced low autocorrelations among all variables and tended to converge quickly. The signs of the estimates of rAoAm were consistently negative for all models fitted. The magnitudes of the estimates of rAoAm from models E, G, GE, ESY, and GESY were almost one-third of those from models I and ISY. Inclusion of the sire × year interaction had some effect in reducing the negative magnitude of rAoAm, but also reduced the size of the estimates of direct (ho 2) and maternal ( hm 2) heritabilities. In comparison, models E or G reduced the negative magnitude of rAoAm by 0.50 units and produced more favorable estimates of ho 2 and hm 2 than models I and ISY. The estimate of ho 2 from G was similar to the one from I; however, the estimated hm 2 was 0.04 units greater, whereas the estimate of rAoAm was much less negative (−0.21 vs. −0.71) than the respective estimates from I. The environmental correlation between the weaning weights of dams and their daughters (λ) was estimated to be −0.28 ± 0.03 in E and ESY, and −0.21 ± 0.03 in GE and GESY. Inclusion of the sire × year interaction effect by itself did not have much of an impact in the reduction of the estimated magnitude of rAoAm. Rank correlations among EBV for direct effects were larger than 0.94 and did not show any appreciable difference among models, whereas the rank correlation among maternal breeding values displayed differences in the ranking between I and the other models. Models E and ESY recovered the largest amount of total additive variability with maternal effects.Fil: Suárez, M. J.. Universidad de Buenos Aires. Facultad de Agronomia. Departamento de Producción Animal. Cátedra de Mejoramiento Genético Animal; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Cantet, Rodolfo Juan Carlos. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Agronomia. Departamento de Producción Animal. Cátedra de Mejoramiento Genético Animal; Argentin

Bayesian estimation of (co) variance components in Argentinian Brangus for carcass traits using the FCG algorithm

Se emplearon los datos de 2273 toritos y vaquillonas Brangus para estimar las heredabilidades (h2 ) y las correlaciones aditivas y ambientales de caracteres de calidad de carne medidos por ultrasonido. Los registros provenían del programa de evaluación genética de la Asociación Argentina de Brangus. Los caracteres medidos fueron el área del ojo del bife (AOB), el marmoreado (MB), la grasa dorsal (GD) y la grasa de cadera (GC). La edad media de los animales al momento de la medición fue 641 días en machos y 685 días en hembras. Los parámetros genéticos y ambientales fueron estimados mediante un algoritmo bayesiano conjugado. Los valores estimados de h2 fueron 0,22, 0,16, 0,12 y 0,21, para AOB, GD, CC y MB, respectivamente. En términos generales, las estimaciones de las correlaciones genéticas y ambientales se encontraron cercanas a la cifra media de la literatura. Si bien los valores estimados de h2 fueron inferiores al promedio de la investigación realizada en vacunos para carne, la variabilidad encontrada es suficiente como para que la respuesta a la selección por estos caracteres – empleando predicciones de los valores de cría calculadas con los parámetros estimados - sea moderadamente efectiva.Data on 2273 Brangus young bulls and heifers were used to estimate heritabilities (h2 ) and genetics and environmental correlations for ultrasound carcass measures. Records were from the genetic evaluation program of Asociación Argentina de Brangus. Traits measured were rib-eye area (AOB), marbling (MB), back-fat thickness (GD), and hip-fat thickness (GC). Average ages of measure were 641 days in males and 685 in females. The genetic and environmental dispersion parameters were estimated by a conjugate Bayesian algorithm (FCG). Estimates of h2 were 0,22, 0,16, 0,12, and 0,21, for AOB, GD, CC, and MB, respectively. In general, estimates of genetic and environmental correlations were close to the average published values. Even tough estimates of h2 were below the average of published estimates for beef cattle, the additive genetic variation found in the current study would lead to a moderate response to selection – using predictions of breeding value that are calculated with the estimate parameters.Fil: Cantet, Rodolfo Juan Carlos. Universidad de Buenos Aires. Facultad de Agronomia. Departamento de Producción Animal; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Birchmeier, A. N.. Universidad de Buenos Aires. Facultad de Agronomia. Departamento de Producción Animal; Argentin

Direct and Competition Additive Effects in Tree Breeding: Bayesian Estimation From an Individual Tree Mixed Model

An individual tree model with additive direct and competition effects is introduced to account for competitive effects in forest genetics evaluation. The mixed linear model includes fixed effects as well as direct and competition breeding values plus permanent environmental effects. Competition effects, either additive or environmental, are identified in the phenotype of a competitor tree by means of ‘intensity of competition’ elements (IC), which are non-zero elements of the incidence matrix of the additive competition effects. The ICs are inverse function of the distance and the number of competing individuals, either row-column wise or diagonally. The ICs allow standardization of the variance of competition effects in the phenotypic variance of any individual tree, so that the model accounts for unequal number of neighbors. Expressions are obtained for the bias in estimating additive variance using the covariance between half-sibs, when ignoring competition effects for row-plot designs and for single-tree plot designs. A data set of loblolly pines on growth at breast height is used to estimate the additive variances of direct and competition effects, the covariance between both effects, and the variance of permanent environmental effects using a Bayesian method via Gibbs sampling and Restricted Maximum Likelihood procedures (REML) via the Expectation-Maximization (EM) algorithm. No problem of convergence was detected with the model and ICs used when compared to what has been reported in the animal breeding literature for such models. Posterior means (standard error) of the estimated parameters were σˆ 2 Ad = 12.553 (1.447), σˆ 2 Ac = 1.259 (0.259), σˆ AdAc = –3.126 (0.492), σˆ 2 p = 1.186 (0.289), and σˆ 2 e = 5.819 (1.07). Leaving permanent environmental competition effects out of the model may bias the predictions of direct breeding values. Results suggest that selection for increasing direct growth while keeping a low level of competition is feasible.Fil: Cappa, Eduardo Pablo. Ministerio de Ciencia, Tecnología e Innovación Productiva. Agencia Nacional de Promoción Científica y Tecnológica. Fondo para la Investigación Científica y Tecnológica; Argentina. Universidad de Buenos Aires. Facultad de Agronomía. Departamento de Producción Animal; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Cantet, Rodolfo Juan Carlos. Universidad de Buenos Aires. Facultad de Agronomía. Departamento de Producción Animal; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

Full conjugate analysis of normal multiple traits with missing records using a generalized inverted Wishart distribution

A Markov chain Monte Carlo (MCMC) algorithm to sample an exchangeable covariance matrix, such as the one of the error terms (R0) in a multiple trait animal model with missing records under normal-inverted Wishart priors is presented. The algorithm (FCG) is based on a conjugate form of the inverted Wishart density that avoids sampling the missing error terms. Normal prior densities are assumed for the 'fixed' effects and breeding values, whereas the covariance matrices are assumed to follow inverted Wishart distributions. The inverted Wishart prior for the environmental covariance matrix is a product density of all patterns of missing data. The resulting MCMC scheme eliminates the correlation between the sampled missing residuals and the sampled R0, which in turn has the effect of decreasing the total amount of samples needed to reach convergence. The use of the FCG algorithm in a multiple trait data set with an extreme pattern of missing records produced a dramatic reduction in the size of the autocorrelations among samples for all lags from 1 to 50, and this increased the effective sample size from 2.5 to 7 times and reduced the number of samples needed to attain convergence, when compared with the 'data augmentation' algorithm

On parsimonious and equivalent animal models with (grand) maternal effects and missing (grand) dams

In breeds where a large fraction of animals with records on a maternally affected trait are from dams that have no records and unknown parents, the genetic evaluation of such trait may be hindered by misspecification of the genetic covariance matrix. The specified covariance structure for the additive direct and maternal effects in the regular maternal animal model (MAM) when dams have no records differs from the covariance between relatives with maternal effects. Two solutions are possible. One is to include in the vectors of breeding values for direct and maternal effects the dam or a "phantom" dam if the latter is unknown. As a consequence, the number of equations to be solved in the MAM may increase considerably. Alternatively, one may replace the maternal breeding value of the dam with 2/3 of the maternal breeding of the individual, and −1/3 of the maternal breeding value of the sire of the individual. As this "regression" of breeding values has been largely ignored, the goal of this paper is to present a parsimonious equivalent MAM using such regression. The approach is extended to a similar situation for models with grand maternal effects. Two small numerical examples are used to illustrate the proposed methods.Fil: Suárez, María José. Universidad de Buenos Aires. Facultad de Agronomía. Departamento de Producción Animal. Cátedra de Mejoramiento Genético Animal; ArgentinaFil: Birchmeier, Ana Nélida. Universidad de Buenos Aires. Facultad de Agronomía. Departamento de Producción Animal. Cátedra de Mejoramiento Genético Animal; ArgentinaFil: Cantet, Rodolfo Juan Carlos. Universidad de Buenos Aires. Facultad de Agronomía. Departamento de Producción Animal. Cátedra de Mejoramiento Genético Animal; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario; Argentin

Weighting familiar and individual information in animal models and BLUP: 1. Genetic group models, 2. Uncertain paternity models

El objetivo de este trabajo fue mostrar analíticamente como el modelo animal y BLUP "funcionan", ponderando de forma diferente la información familiar e individual. Para ello se consideraron dos situaciones clásicas de desconocimiento de la genealogía: el modelo con grupos genéticos y con paternidad incierta. La importancia relativa de la información individual y familiar se analizó para diversos valores de heredabiiidad y de consanguinidad.The goal of this research was to show analytically how thc animal model and BLUP "work", weighting differently individual and family information (by the data of parents and sibs). Two classic situations of unknown genealogy were considered: model with genetic groups and with uncertain paternity. The weights of individual and family information were analyzed for different values of heritability and of inbreeding.Fil: Vitezica, Zulma G.. Institut National de la Recherche Agronomique; Francia. Universidad de Buenos Aires. Facultad de Agronomía. Departamento de Producción Animal; ArgentinaFil: Cantet, Rodolfo Juan Carlos. Universidad de Buenos Aires. Facultad de Agronomía. Departamento de Producción Animal; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario; Argentin

Efecto de la varianza genética aditiva generacional sobre las componentes de la respuesta a la selección en una población con generaciones superpuestas

p.221-230El objetivo de esta investigación fue comparar la respuesta a la selección usando el Modelo Animal-BLUP con grupos genéticos, utilizando la variancia genética aditiva de cada generación (s²A(C), con aquel que utiliza la variancia aditiva en la población base (s²a), mediante simulación estocastica de una población animal con generaciones superpuestas. A diferencia de otros estudios, el modelo de generación de datos incluyó efectos fijos como el sexo (variable clasificatoria) y la edad del animal a la medición del carácter (covariable), con el objeto de asemejarse a los modelos de evaluación en poblaciones reales. Los resultados corresponden a 20 años de selección, tomando el promedio de 100 réplicas. La h² original en la población fue 0,4. La pérdida de información consistió en omitir al azar relaciones de parentesco, afín de incorporar los grupos al modelo de evaluación animal. El 25 por ciento de los animales poseían ambos padres desconocidos, 25 por ciento poseían la madre desconocida, 25 por ciento el padre y el 25 por ciento restante poseían ambos padres conocidos. En las condiciones simuladas no se observaron diferencias significativas (pmayor a 0,05), en las variables estudiadas: respuesta a la selección, variancia aditiva, exactitud, intensidad de selección, consanguinidad e intervalo generacional, para los casos de información completa e incompleta con la inclusión de grupos, según se consideró las s²a ó la s²a(g