Impact of environmental temperature on production traits in pigs.

There is an urgent need to identify the effects of temperature on production traits. This study aimed to determine the impact of pig production in three environments (T°Cgrowing-°Cfattening-°Cfinishing = T24-24-21, T19-19-19, and T23-17-15) on growth curve parameters, body weight gain (DBWG), feed intake (DFI), and feed efficiency during the growing, fattening and finishing stages, and on carcass yield of primal cuts (ham, shoulder, and loin) in 158 Duroc × Iberian pigs. Maturation rate was higher in T23-17-15 than in T19-19-19 (P < 0.001). Pigs in T23-17-15 reached a lower mature body weight (P < 0.05). During the growing stage, pigs in T23-17-15 had higher DFI than those in T24-24-21 and T19-19-19 (P < 0.05); during the fattening stage, DFI was lowest in T24-24-21 (P < 0.001). In the growing stage, pigs had highest DBWG in the warmest environments (T24-24-21 and T23-17-15) and lowest in the coldest environment (T19-19-19; P < 0.001). Feed efficiency was highest in warmer environments (P < 0.01). Temperature T24-24-21 favored loin yield, T19-19-19 favored ham yield, and T23-17-15 favored shoulder yield (P < 0.01). The results imply a favorable effect of temperature on feed efficiency, however, possible negative implications for animal health and welfare should be considered.

An evaluation of the methods to estimate effective population size from measures of linkage disequilibrium.

In 1971, John Sved derived an approximate relationship between linkage disequilibrium (LD) and effective population size for an ideal finite population. This seminal work was extended by Sved and Feldman (Theor Pop Biol 4, 129, 1973) and Weir and Hill (Genetics 95, 477, 1980) who derived additional equations with the same purpose. These equations yield useful estimates of effective population size, as they require a single sample in time. As these estimates of effective population size are now commonly used on a variety of genomic data, from arrays of single nucleotide polymorphisms to whole genome data, some authors have investigated their bias through simulation studies and proposed corrections for different mating systems. However, the cause of the bias remains elusive. Here, we show the problems of using LD as a statistical measure and, analogously, the problems in estimating effective population size from such measure. For that purpose, we compare three commonly used approaches with a transition probability-based method that we develop here. It provides an exact computation of LD. We show here that the bias in the estimates of LD and effective population size are partly due to low-frequency markers, tightly linked markers or to a small total number of crossovers per generation. These biases, however, do not decrease when increasing sample size or using unlinked markers. Our results show the issues of such measures of effective population based on LD and suggest which of the method here studied should be used in empirical studies as well as the optimal distance between markers for such estimates.

A Novel Statistical Model to Estimate Host Genetic Effects Affecting Disease Transmission.

There is increasing recognition that genetic diversity can affect the spread of diseases, potentially affecting plant and livestock disease control as well as the emergence of human disease outbreaks. Nevertheless, even though computational tools can guide the control of infectious diseases, few epidemiological models can simultaneously accommodate the inherent individual heterogeneity in multiple infectious disease traits influencing disease transmission, such as the frequently modeled propensity to become infected and infectivity, which describes the host ability to transmit the infection to susceptible individuals. Furthermore, current quantitative genetic models fail to fully capture the heritable variation in host infectivity, mainly because they cannot accommodate the nonlinear infection dynamics underlying epidemiological data. We present in this article a novel statistical model and an inference method to estimate genetic parameters associated with both host susceptibility and infectivity. Our methodology combines quantitative genetic models of social interactions with stochastic processes to model the random, nonlinear, and dynamic nature of infections and uses adaptive Bayesian computational techniques to estimate the model parameters. Results using simulated epidemic data show that our model can accurately estimate heritabilities and genetic risks not only of susceptibility but also of infectivity, therefore exploring a trait whose heritable variation is currently ignored in disease genetics and can greatly influence the spread of infectious diseases. Our proposed methodology offers potential impacts in areas such as livestock disease control through selective breeding and also in predicting and controlling the emergence of disease outbreaks in human populations.

A novel recursive algorithm for the calculation of the detailed identity coefficients.

BACKGROUND: A recursive algorithm to calculate the fifteen detailed coefficients of identity is introduced. Previous recursive procedures based on the generalized coefficients of kinship provided the detailed coefficients of identity under the assumption that the two individuals were not an ancestor of each other. FINDINGS: By using gametic relationships to include three, four or two pairs of gametes, we can obtain these coefficients for any pair of individuals. We have developed a novel linear transformation that allows for the calculation of pairwise detailed identity coefficients for any pedigree given the gametic relationships. We illustrate the procedure using the well-known pedigree of Julio and Mencha, which contains 20 Jicaque Indians of Honduras, to calculate their detailed coefficients. CONCLUSIONS: The proposed algorithm can be used to calculate the detailed identity coefficients of two or more individuals with any pedigree relationship.

Artificial selection with traditional or genomic relationships: consequences in coancestry and genetic diversity.

Estimated breeding values (EBVs) are traditionally obtained from pedigree information. However, EBVs from high-density genotypes can have higher accuracy than EBVs from pedigree information. At the same time, it has been shown that EBVs from genomic data lead to lower increases in inbreeding compared with traditional selection based on genealogies. Here we evaluate the performance with BLUP selection based on genealogical coancestry with three different genome-based coancestry estimates: (1) an estimate based on shared segments of homozygosity, (2) an approach based on SNP-by-SNP count corrected by allelic frequencies, and (3) the identity by state methodology. We evaluate the effect of different population sizes, different number of genomic markers, and several heritability values for a quantitative trait. The performance of the different measures of coancestry in BLUP is evaluated in the true breeding values after truncation selection and also in terms of coancestry and diversity maintained. Accordingly, cross-performances were also carried out, that is, how prediction based on genealogical records impacts the three other measures of coancestry and inbreeding, and viceversa. Our results show that the genetic gains are very similar for all four coancestries, but the genomic-based methods are superior to using genealogical coancestries in terms of maintaining diversity measured as observed heterozygosity. Furthermore, the measure of coancestry based on shared segments of the genome seems to provide slightly better results on some scenarios, and the increase in inbreeding and loss in diversity is only slightly larger than the other genomic selection methods in those scenarios. Our results shed light on genomic selection vs. traditional genealogical-based BLUP and make the case to manage the population variability using genomic information to preserve the future success of selection programmes.

Combining genomic and genealogical information in a reproducing kernel Hilbert spaces regression model for genome-enabled predictions in dairy cattle.

Genome-enhanced genotypic evaluations are becoming popular in several livestock species. For this purpose, the combination of the pedigree-based relationship matrix with a genomic similarities matrix between individuals is a common approach. However, the weight placed on each matrix has been so far established with ad hoc procedures, without formal estimation thereof. In addition, when using marker- and pedigree-based relationship matrices together, the resulting combined relationship matrix needs to be adjusted to the same scale in reference to the base population. This study proposes a semi-parametric Bayesian method for combining marker- and pedigree-based information on genome-enabled predictions. A kernel matrix from a reproducing kernel Hilbert spaces regression model was used to combine genomic and genealogical information in a semi-parametric scenario, avoiding inversion and adjustment complications. In addition, the weights on marker- versus pedigree-based information were inferred from a Bayesian model with Markov chain Monte Carlo. The proposed method was assessed involving a large number of SNPs and a large reference population. Five phenotypes, including production and type traits of dairy cattle were evaluated. The reliability of the genome-based predictions was assessed using the correlation, regression coefficient and mean squared error between the predicted and observed values. The results indicated that when a larger weight was given to the pedigree-based relationship matrix the correlation coefficient was lower than in situations where more weight was given to genomic information. Importantly, the posterior means of the inferred weight were near the maximum of 1. The behavior of the regression coefficient and the mean squared error was similar to the performance of the correlation, that is, more weight to the genomic information provided a regression coefficient closer to one and a smaller mean squared error. Our results also indicated a greater accuracy of genomic predictions when using a large reference population.

Variance and covariance of actual relationships between relatives at one locus.

The relationship between pairs of individuals is an important topic in many areas of population and quantitative genetics. It is usually measured as the proportion of the genome identical by descent shared by the pair and it can be inferred from pedigree information. But there is a variance in actual relationships as a consequence of mendelian sampling, whose general formula has not been developed. The goal of this work is to develop this general formula for the one-locus situation,. We provide simple expressions for the variances and covariances of all actual relationships in an arbitrary complex pedigree. The proposed method relies on the use of the nine identity coefficients and the generalized relationship coefficients; formulas have been checked by computer simulation. Finally two examples for a short pedigree of dogs and a long pedigree of sheep are given.

A note on the rationale for estimating genealogical coancestry from molecular markers.

BACKGROUND: Genetic relatedness or similarity between individuals is a key concept in population, quantitative and conservation genetics. When the pedigree of a population is available and assuming a founder population from which the genealogical records start, genetic relatedness between individuals can be estimated by the coancestry coefficient. If pedigree data is lacking or incomplete, estimation of the genetic similarity between individuals relies on molecular markers, using either molecular coancestry or molecular covariance. Some relationships between genealogical and molecular coancestries and covariances have already been described in the literature. METHODS: We show how the expected values of the empirical measures of similarity based on molecular marker data are functions of the genealogical coancestry. From these formulas, it is easy to derive estimators of genealogical coancestry from molecular data. We include variation of allelic frequencies in the estimators. RESULTS: The estimators are illustrated with simulated examples and with a real dataset from dairy cattle. In general, estimators are accurate and only slightly biased. From the real data set, estimators based on covariances are more compatible with genealogical coancestries than those based on molecular coancestries. A frequently used estimator based on the average of estimated coancestries produced inflated coancestries and numerical instability. The consequences of unknown gene frequencies in the founder population are briefly discussed, along with alternatives to overcome this limitation. CONCLUSIONS: Estimators of genealogical coancestry based on molecular data are easy to derive. Estimators based on molecular covariance are more accurate than those based on identity by state. A correction considering the random distribution of allelic frequencies improves accuracy of these estimators, especially for populations with very strong drift.

Bayes factor between Student t and Gaussian mixed models within an animal breeding context.

The implementation of Student t mixed models in animal breeding has been suggested as a useful statistical tool to effectively mute the impact of preferential treatment or other sources of outliers in field data. Nevertheless, these additional sources of variation are undeclared and we do not know whether a Student t mixed model is required or if a standard, and less parameterized, Gaussian mixed model would be sufficient to serve the intended purpose. Within this context, our aim was to develop the Bayes factor between two nested models that only differed in a bounded variable in order to easily compare a Student t and a Gaussian mixed model. It is important to highlight that the Student t density converges to a Gaussian process when degrees of freedom tend to infinity. The two models can then be viewed as nested models that differ in terms of degrees of freedom. The Bayes factor can be easily calculated from the output of a Markov chain Monte Carlo sampling of the complex model (Student t mixed model). The performance of this Bayes factor was tested under simulation and on a real dataset, using the deviation information criterion (DIC) as the standard reference criterion. The two statistical tools showed similar trends along the parameter space, although the Bayes factor appeared to be the more conservative. There was considerable evidence favoring the Student t mixed model for data sets simulated under Student t processes with limited degrees of freedom, and moderate advantages associated with using the Gaussian mixed model when working with datasets simulated with 50 or more degrees of freedom. For the analysis of real data (weight of Pietrain pigs at six months), both the Bayes factor and DIC slightly favored the Student t mixed model, with there being a reduced incidence of outlier individuals in this population.

Multibreed analysis by splitting the breeding values.

An equivalent model for multibreed variance covariance estimation is presented. It considers the additive case including or not the segregation variances. The model is based on splitting the additive genetic values in several independent parts depending on their genetic origin. For each part, it expresses the covariance between relatives as a partial numerator relationship matrix times the corresponding variance component. Estimation of fixed effects, random effects or variance components provided by the model are as simple as any model including several random factors. We present a small example describing the mixed model equations for genetic evaluations and two simulated examples to illustrate the Bayesian variance component estimation.