Direct and maternal additive effects are not the main determinants of Iberian piglet perinatal mortality.

Data of 127,800 Iberian piglets were used to study genetic parameters of mortality at birth at the piglet level. These records proceed from three data sets: 4,987 litter of 2,156 sows of a dam line, 2,768 litter of 817 sows of a complete diallel cross between four Iberian strains and 7,153 litter of 2,113 sows of the Torbiscal composite line. Perinatal mortality was considered as a binary trait, and Bayesian threshold animal models were fitted to separately analyse the three data sets. The posterior means of direct heritability were 0.010, 0.004 and 0.003, and those of maternal heritability were 0.034, 0.011 and 0.014 for dam line, diallel cross and Torbiscal line, respectively. Important effects of litter size and parity order were inferred in the three data sets, of within-breed cross-breeding parameters in the diallel cross and of sex and sow handling in the Torbiscal line Therefore, the inclusion of perinatal mortality in the objective of selection is questionable in this breed and strategies for reducing piglet mortality successful in other breeds should be considered.

The coefficient of dominance is not (always) estimable with biallelic markers.

The genetic relationship among individuals at one locus is characterized by nine coefficients of identity. The coefficients of inbreeding, coancestry and dominance (or fraternity) are just linear functions of them. Here, it is shown how they can be estimated using biallelic and triallelic markers using the method of moments, and comparisons are made with other methods based on molecular coancestry or molecular covariance. It is concluded that in the general case of dominance and inbreeding with biallelic markers, only the coefficients of inbreeding and coancestry can be estimated, but neither the single coefficients of identity nor the coefficient of dominance can be estimated. More than two alleles are required for a full estimation as illustrated with the triallelic situation.

Selection strategies for dairy buffaloes: economic and genetic consequences.

Buffaloes are generally raised in Brazil without milk-recording programs, and thus without genetic evaluations of any of their traits. This study evaluated the economic impacts of three different selection strategies on buffalo populations and the evolution of genetic trends, genetic variances and inbreeding coefficients resulting from each of them. The selection strategies used were as follows: (i) random selection; (ii) phenotypic selection; and (iii) progeny testing (PT). As the numbers of herds enrolled in milk-recording programs increased, phenotypic selection and PT strategies increased both monetary benefits and genetic trends. The extra costs of implementing milk recording (MR) and PT procedures were exceeded by the income resulting from better buffalo performance. Progeny testing is known to result in beneficial genetic trends and the use of artificial insemination promoted better distributions of genetic material into herds that were not enrolled in milk-recording programs. Phenotypic selection and PT increased mean milk production--a key factor in profitability. Inbreeding levels remained stable with phenotypic selection, even as the numbers of MR herds increased. Increases in the numbers of sires that were evaluated reduced the mean inbreeding coefficient in PT. Increasing the number of herds enrolled in milk-recording programs resulted in increased numbers of sires needed for PT, but this did not increase the inbreeding coefficient. In summary, phenotypic selection and PT strategies appear to be economically viable for buffalo husbandry in south-eastern Brazil under current (2007-2008) economic conditions and should be encouraged.

Accuracy of genome-wide evaluation for disease resistance in aquaculture breeding programs.

Current aquaculture breeding programs aimed at improving resistance to diseases are based on challenge tests, where performance is recorded on sibs of candidates to selection, and on selection between families. Genome-wide evaluation (GWE) of breeding values offers new opportunities for using variation within families when dealing with such traits. However, up-to-date studies on GWE in aquaculture programs have only considered continuous traits. The objectives of this study were to extend GWE methodology, in particular the Bayes B method, to analyze dichotomous traits such as resistance to disease, and to quantify, through computer simulation, the accuracy of GWE for disease resistance in aquaculture sib-based programs, using the methodology developed. Two heritabilities (0.1 and 0.3) and 2 disease prevalences (0.1 and 0.5) were assumed in the simulations. We followed the threshold liability model, which assumes that there is an underlying variable (liability) with a continuous distribution and assumed a BayesB model for the liabilities. It was shown that the threshold liability model used fits very well with the BayesB model of GWE. The advantage of using the threshold model was clear when dealing with disease resistance dichotomous phenotypes, particularly under the conditions where linear models are less appropriate (low heritability and disease prevalence). In the testing set (where individuals are genotyped but not measured), the increase in accuracy for the simulated schemes when using the threshold model ranged from 4 (for heritability equal to 0.3 and prevalence equal to 0.5) to 16% (for heritability and prevalence equal to 0.1) when compared with the linear model.

Parameter estimation in selected populations with missing data.

This study proposes a procedure to estimate genetic parameters in populations where a selection process results in the loss of an unknown number of observations. The method was developed under the Bayesian inference scope following the missing data theory approach. Its implementation requires slight modifications to the Gibbs sampler algorithm. In order to show the efficiency of this option, a simulation study was conducted.

Partition of the genetic trend to validate multiple selection decisions.

In this note, a procedure to partition the genetic trend of a selected population is presented. Each part of the genetic gain accounts for the Mendelian sampling terms of different groups of animals, which can be sometimes assigned to different selection policies. The method is based on a simple transformation of the predicted breeding values. The procedure was illustrated with two simulated examples. In the first example, the genetic trend is partitioned into two pieces, one coming from the selection on sires and the other coming from the selection on dams. The second example shows how the impact of an artificial insemination center in the genetic gain of the whole population can be evaluated.

Sex ratio variation in Iberian pigs.

Within the area of sex allocation, one of the topics that has attracted a lot of attention is the sex ratio problem. Fisher (1930) proposed that equal numbers of males and females have been promoted by natural selection and it has an adaptive significance. But the empirical success of Fisher's theory remains doubtful because a sex ratio of 0.50 is also expected from the chromosomal mechanism of sex determination. Another way of approaching the subject is to consider that Fisher's argument relies on the underlying assumption that offspring inherit their parent's tendency in biased sex ratio and therefore that genetic variance for this trait exists. Here, we analyzed sex ratio data of 56,807 piglets coming from 550 boars and 1893 dams. In addition to classical analysis of heterogeneity we performed analyses fitting linear and threshold animal models in a Bayesian framework using Gibbs sampling techniques. The marginal posterior mean of heritability was 2.63 x 10(-4) under the sire linear model and 9.17 x 10(-4) under the sire threshold model. The probability of the hypothesis p(h(2) = 0) fitting the last model was 0.996. Also, we did not detect any trend in sex ratio related to maternal age. From an evolutionary point of view, the chromosomal sex determination acts as a constraint that precludes control of offspring sex ratio in vertebrates and it should be included in the general theory of sex allocation. From a practical view that means that the sex ratio in domestic species is hardly susceptible to modification by artificial selection.

Alternative implementations of Monte Carlo EM algorithms for likelihood inferences.

Two methods of computing Monte Carlo estimators of variance components using restricted maximum likelihood via the expectation-maximisation algorithm are reviewed. A third approach is suggested and the performance of the methods is compared using simulated data.

Bayes factors for detection of quantitative trait loci.

A fundamental issue in quantitative trait locus (QTL) mapping is to determine the plausibility of the presence of a QTL at a given genome location. Bayesian analysis offers an attractive way of testing alternative models (here, QTL vs. no-QTL) via the Bayes factor. There have been several numerical approaches to computing the Bayes factor, mostly based on Markov Chain Monte Carlo (MCMC), but these strategies are subject to numerical or stability problems. We propose a simple and stable approach to calculating the Bayes factor between nested models. The procedure is based on a reparameterization of a variance component model in terms of intra-class correlation. The Bayes factor can then be easily calculated from the output of a MCMC scheme by averaging conditional densities at the null intra-class correlation. We studied the performance of the method using simulation. We applied this approach to QTL analysis in an outbred population. We also compared it with the Likelihood Ratio Test and we analyzed its stability. Simulation results were very similar to the simulated parameters. The posterior probability of the QTL model increases as the QTL effect does. The location of the QTL was also correctly obtained. The use of meta-analysis is suggested from the properties of the Bayes factor.

Hypothesis testing for the genetic background of quantitative traits.

The testing of Bayesian point null hypotheses on variance component models have resulted in a tough assigmment for which no clear and generally accepted method exists. In this work we present what we believe is a succeeding approach to such a task. It is based on a simple reparameterization of the model in terms of the total variance and the proportion of the additive genetic variance with respect to it, as well as on the explicit inclusion on the prior probability of a discrete component at origin. The reparameterization was used to bypass an arbitrariness related to the impropriety of uninformative priors onto unbounded variables while the discrete component was necessary to overcome the zero probability assigned to sets of null measure by the usual continuous variable models. The method was tested against computer simulations with appealing results.

Bayesian analysis of Wood's lactation curve for Spanish dairy cows.

A Bayesian procedure is presented to analyze test day performances in the scope of Wood's lactation function: atb (exp (-ct)), where a, b, and c = parameters, and t = time-dependent variable. The procedure has been applied to 148,557 test day controls corresponding to records for 15,349 first lactations of Spanish dairy cows. The procedure uses all available information and reduces the presence of atypical lactations. Moreover, the posterior marginal distribution of (co)variance components, breeding values, and systematic effects for the underlying variables of Wood's function are provided. The posterior means of the heritabilities were 0.43, 0.17, 0.40, and 0.29 for the parameters a (initial milk yield), b (ascent to peak), c (descent from peak), and total milk yield, respectively. Selection for total milk yield implies a great effect on the initial milk yield (a) but only minor effects on ascent to peak (b) and descent from peak (c).

Using coupling with the Gibbs sampler to assess convergence in animal models.

The coupling method was investigated as a method to assess the convergence of the Gibbs sampler when drawing marginal inferences with an animal model. This method is based on the output of two Markov chains with different starting values but the same conditional deviates. The coupling method shows that the Gibbs sampler has an exponential convergence when the variance components are assumed to be known. All the variables in the model have the same rate of convergence, and it is closely related with the largest eigenvalue of a matrix derived from the coefficient matrix of the mixed model equations. Models including the variance components as unknowns showed a rate of convergence equal for all the variables, and this rate of convergence was approximately exponential. The coupling method provides an estimation of the convergence at the current iteration, and it does not require a post-Gibbs analysis as do the single chain-based methods. The coupling method is less computationally demanding than multiple chain methods, because only two chains are required to assess convergence.

Bayesian inference of variance components for litter size in Rasa Aragonesa sheep.

Variance components were estimated for litter size in Rasa Aragonesa sheep, a meat breed from northern Spain, to determine whether selective breeding for litter size is a reasonable strategy to improve reproductive performance. We assumed an animal mixed effect threshold model with a binary response variable. Marginal estimates of the genetic parameters were obtained in the underlying scale using Bayesian inference, implemented via the Gibbs sampling procedure and a data augmentation approach. Posterior marginal means of heritability and repeatability were .077 and .141, respectively. Moreover, the 95% highest marginal posterior density region of heritability ranged from .051 to .101. Therefore, we conclude that litter size is a trait that could be selected for in breeding programs. The effect of the loss of pedigree information, a common feature of sheep production, on the estimation of the genetic parameters was also studied using simulation. The results indicate that the lack of pedigree information has little effect on our estimates of heritability.

Model determination in a case of heterogeneity of variance using sampling techniques.

SUMMARY: A sampling determination procedure has been described in a case of heterogeneity of variance. The procedure makes use of the predictive distributions of each data given the rest of the data and the structure of the assumed model. The computation of these predictive distributions is carried out using a Gibbs Sampling procedure. The final criterion to compare between models is the Mean Square Error between the expectation of predictive distributions and real data. The procedure has been applied to a data set of weight at 210 days in the Spanish Pirenaica beef cattle breed. Three proposed models have been compared: (a) Single Trait Animal Model; (b) Heterogeneous Variance Animal Model; and (c) Multiple Trait Animal Model. After applying the procedure, the most adjusted model was the Heterogeneous Variance Animal Model. This result is probably due to a compromise between the complexity of the model and the amount of available information. The estimated heritabilities under the preferred model have been 0.489 ± 0.076 for males and 0.331 ± 0.082 for females. RESUMEN: Contraste de modelos en un caso de heterogeneidad de varianzas usando métodos de muestreo Se ha descrito un método de contraste de modelos mediante técnicas de muestreo en un caso de heterogeneidad de varianza entre sexos. El procedimiento utiliza las distribucviones predictivas de cada dato, dado el resto de datos y la estructura del modelo. El criterio para coparar modelos es el error cuadrático medio entre la esperanza de las distribuciones predictivas y los datos reales. El procedimiento se ha aplicado en datos de peso a los 210 días en la raza bovina Pirenaica. Se han propuesto tres posibles modelos: (a) Modelo Animal Unicaracter; (b) Modelo Animal con Varianzas Heterogéneas; (c) Modelo Animal Multicaracter. El modelo mejor ajustado fue el Modelo Animal con Varianzas Heterogéneas. Este resultado es probablemente debido a un compromiso entre la complejidad del modelo y la cantidad de datos disponibles. Las heredabilidades estimadas bajo el modelo preferido han sido 0,489 ± 0,076 en los machos y 0,331 ± 0,082 en las hembras.