Between-breed variability of stillbirth and its relationship with sow and piglet characteristics.

Litter characteristics at birth were recorded in 4 genetic types of sows with differing maternal abilities. Eighty-two litters from F(1) Duroc x Large White sows, 651 litters from Large White sows, 63 litters from Meishan sows, and 173 litters from Laconie sows were considered. Statistical models included random effects of sow, litter, or both; fixed effects of sow genetic type, parity, birth assistance, and piglet sex, as well as gestation length, farrowing duration, piglet birth weight, and litter size as linear covariates. The quadratic components of the last 2 factors were also considered. For statistical analyses, GLM were first considered, assuming a binomial distribution of stillbirth. Hierarchical models were also fitted to the data to take into account correlations among piglets from the same litter. Model selection was performed based on deviance and deviance information criterion. Finally, standard and robust generalized estimating equations (GEE) procedures were applied to quantify the importance of each effect on a piglet's probability of stillbirth. The 5 most important factors involved were, in decreasing order (contribution of each effect to variance reduction): difference between piglet birth weight and the litter mean (2.36%), individual birth weight (2.25%), piglet sex (1.01%), farrowing duration (0.99%), and sow genetic type (0.94%). Probability of stillbirth was greater for lighter piglets, for male piglets, and for piglets from small or very large litters. Probability of stillbirth increased with sow parity number and with farrowing duration. Piglets born from Meishan sows had a lower risk of stillbirth (P < 0.0001) and were little affected by the sources of variation mentioned above compared with the 3 other sow genetic types. Standard and robust GEE approaches gave similar results despite some disequilibrium in the data set structure highlighted with the robust GEE approach.

Genetic diversity analysis using lowly polymorphic dominant markers: the example of AFLP in pigs.

DNA markers are commonly used for large-scale evaluation of genetic diversity in farm animals, as a component of the management of animal genetic resources. AFLP markers are useful for such studies as they can be generated relatively simply; however, challenges in analysis arise from their dominant scoring and the low level of polymorphism of some markers. This paper describes the results obtained with a set of AFLP markers in a study of 59 pig breeds. AFLP fingerprints were generated using four primer combinations (PC), yielding a total of 148 marker loci, and average harmonic mean of breed sample size was 37.3. The average proportion of monomorphic populations was 63% (range across loci: 3%-98%). The moment-based method of Hill and Weir (2004, Mol Ecol 13:895-908) was applied to estimate gene frequencies, gene diversity (F(ST)), and Reynolds genetic distances. A highly significant average F(ST) of 0.11 was estimated, together with highly significant PC effects on gene diversity. The variance of F(ST) across loci also significantly exceeded the variance expected under the hypothesis of AFLP neutrality, strongly suggesting the sensitivity of AFLP to selection or other forces. Moment estimates were compared to estimates derived from the square root estimation of gene frequency, as currently applied for dominant markers, and the biases incurred in the latter method were evaluated. The paper discusses the hypotheses underlying the moment estimations and various issues relating to the biallelic, dominant, and lowly polymorphic nature of this set of AFLP markers and to their use as compared to microsatellites for measuring genetic diversity.

Daily variations in skin surface properties using mixed model methodology.

In order to explore the variations over the course of a day in certain skin biophysical properties, a study was conducted on 8 female volunteers. An assessment of several skin biophysical properties was carried out on the face and the volar forearm every 4 h over a period of 48 h. The biophysical parameters were assessed on the face for sebum secretion, skin surface pH, skin colour, transepidermal water loss, capacitance and skin surface temperature. The same parameters were measured on the volar forearm (excepted for sebum secretion). A statistical analysis based on mixed effect models was conducted. Four models, with different covariance structures, were successively tested. The analysis allowed us to identify a structure that repeated itself over time in the same way over each 24-hour period for capacitance on the forearm and for sebum secretion, skin surface pH and skin colour (L* and a* parameters) on the face. Mixed effect methodology is a powerful tool to analyse longitudinal data involving correlations among repeated measurements made on the same subject.

A completion simulator for the two-sided truncated normal distribution.

This paper presents simulation formulae of two-sided truncated normal random variables using a completion distribution and its two corresponding conditionals generated via a Gibbs sampler. This procedure extends formulae given by Robert and Casella for the one-sided case.

EM-REML estimation of covariance parameters in Gaussian mixed models for longitudinal data analysis.

This paper presents procedures for implementing the EM algorithm to compute REML estimates of variance covariance components in Gaussian mixed models for longitudinal data analysis. The class of models considered includes random coefficient factors, stationary time processes and measurement errors. The EM algorithm allows separation of the computations pertaining to parameters involved in the random coefficient factors from those pertaining to the time processes and errors. The procedures are illustrated with Pothoff and Roy's data example on growth measurements taken on 11 girls and 16 boys at four ages. Several variants and extensions are discussed.

The PX-EM algorithm for fast stable fitting of Henderson's mixed model.

This paper presents procedures for implementing the PX-EM algorithm of Liu, Rubin and Wu to compute REML estimates of variance covariance components in Henderson's linear mixed models. The class of models considered encompasses several correlated random factors having the same vector length e.g., as in random regression models for longitudinal data analysis and in sire-maternal grandsire models for genetic evaluation. Numerical examples are presented to illustrate the procedures. Much better results in terms of convergence characteristics (number of iterations and time required for convergence) are obtained for PX-EM relative to the basic EM algorithm in the random regression.

Genetic diversity of eleven European pig breeds.

A set of eleven pig breeds originating from six European countries, and including a small sample of wild pigs, was chosen for this study of genetic diversity. Diversity was evaluated on the basis of 18 microsatellite markers typed over a total of 483 DNA samples collected. Average breed heterozygosity varied from 0.35 to 0.60. Genotypic frequencies generally agreed with Hardy-Weinberg expectations, apart from the German Landrace and Schwäbisch-Hällisches breeds, which showed significantly reduced heterozygosity. Breed differentiation was significant as shown by the high among-breed fixation index (overall F(ST)= 0.27), and confirmed by the clustering based on the genetic distances between individuals, which grouped essentially all individuals in 11 clusters corresponding to the 11 breeds. The genetic distances between breeds were first used to construct phylogenetic trees. The trees indicated that a genetic drift model might explain the divergence of the two German breeds, but no reliable phylogeny could be inferred among the remaining breeds. The same distances were also used to measure the global diversity of the set of breeds considered, and to evaluate the marginal loss of diversity attached to each breed. In that respect, the French Basque breed appeared to be the most "unique" in the set considered. This study, which remains to be extended to a larger set of European breeds, indicates that using genetic distances between breeds of farm animals in a classical taxonomic approach may not give clear resolution, but points to their usefulness in a prospective evaluation of diversity.

Individual multilocus genotypes using microsatellite polymorphisms to permit the analysis of the genetic variability within and between Italian beef cattle breeds.

We investigated the genetic variability within and between cattle breeds. The polymorphisms of 17 microsatellites were studied in 220 unrelated animals belonging to four Italian beef cattle breeds (Chianina, Marchigiana, Romagnola, and Piemontese). Variations of allelic frequencies were examined to characterize the breeds and their relationships. Wahlund coefficients, Polymorphism Information Content values, and Haldane exact test for Hardy-Weinberg proportions were calculated. The results show that the Hardy-Weinberg equilibrium is not always maintained. Moreover, in addition to the classical genetic distances, a new method, based on the consideration of a multilocus genotype of each animal, was set up to measure the genetic similarity between animals or within groups of animals. All the results showed that, whereas Chianina occupies an intermediate position and Piemontese is the most distinct of all four breeds, Marchigiana and Romagnola display the strongest similarity. The new method also provides evidence that average similarities are always higher within breeds than between breeds. By comparing pairwise the multilocus genotypes, it was also possible to discriminate the individuals with higher or lower genetic similarities so that each breed could be subdivided into two groups of animals in relation to their similarity to the average breed multilocus genotype. High similarities between breeds were detected, somewhat surprisingly, when the most homogeneous groups of each breed were compared. The microsatellite multilocus genotype is particularly efficient in evaluating the between- and within-breeds genetic similarities and for subgrouping genetically more homogeneous animals.

Genetic implications of a bivariate threshold model for litter size components.

A bivariate threshold model for ovulation rate and embryonic survival was developed and the genetic relationships in the observed scale among ovulation rate, embryonic survival, and litter size were derived. This model was applied to data of nulliparous Lacaune sheep. Heritabilities assumed were .30, .05, and .12 for ovulation rate, embryonic survival, and litter size, respectively. Three values for genetic correlation between ovulation rate and embryonic survival were considered: -.78, -.30, and 0. Three criteria to increase litter size were studied: a linear index combining ovulation rate and embryonic survival, ovulation rate, and litter size. The linear index used gave an increasing weight to embryonic survival with higher ovulation rates. A selection scheme was simulated to test predications of response for the different criteria. A nucleus of 10 sires and 300 dams was simulated. Females were selected according to their own performance (mean of three records) and males according to their dam's performance. Selection was continued for six discrete generations. Response with an index was better than direct selection only in the short term, whereas this superiority was not maintained in the last generations of selection. Indirect selection on ovulation rate was clearly inferior to both index and direct selection. In the situation analyzed here, litter size seems to be close to the optimum 'natural index' combining ovulation rate and embryonic survival.

Long-term effects of selection based on the animal model BLUP in a finite population.

Monte Carlo simulation was used to assess the long-term effects of truncation selection within small populations using indices (I=ωf+m) combining mid-parent [f=(a i+a d)/2] and Mendelian-sampling (m=a-f) evaluations provided by an animal model BLUP (a=f+m). Phenotypic values of panmictic populations were generated for 30 discrete generations. Assuming a purely additive polygenic model, heritability (h 2) values were 0.10, 0.25 or 0.50. Two population sizes were considered: five males and 25 females selected out of 50 candidates of each sex (small populations, S) and 50 males and 250 females selected out of 500 candidates in each sex (large populations, L). Selection was carried out on the index defined above with ω = 1 (animal model BLUP), ω=1/2, or ω=0 (selection on within-family deviations). Mass selection was also considered. Selection based on the animal model BLUP (ω=1) maximized the cumulative genetic gain in L populations. In S populations, selection using ω = 1/2 and mass selection were more efficient than selection under an animal model (+ 3 to + 7% and + 1 to + 4% respectively, depending on h (2)). Selection on within-family deviations always led to the lowest gains. In most cases, the variance of response to selection between replicates did not depend on the selection method. The within-replicate genetic variance and the average coefficient of inbreeding (F) were highly affected by selection with ω=1 or 1/2, especially in populations of size S. As expected, selection based on within-family deviations was less detrimental in that respect. The number of copies of founder neutral genes at a separate locus, and the probability vector of origin of the genes in reference to the founder animals, were also observed in addition to F values. The conclusion was that selection procedures placing less emphasis on family information might be interesting alternatives to selection based on animal model BLUP, especially for small populations with long-term selection objectives.

Prediction of selection response for threshold dichotomous traits.

This paper presents a formula to predict expected response to one generation of truncation selection for a dichotomous trait under polygenic additive inheritance. The derivation relies on the threshold liability concept and on the normality assumption of the joint distribution of additive genetic values and their predictors used as selection criteria. This formula accounts for asymmetry of response when both the prevalence of the trait and the selection rate differ from 1/2 via a bivariate normal integral term. The relationship with the classical formula R = iota rho sigma G is explained with a Taylor expansion about a zero value of the correlation factor. Properties are illustrated with an example of sire selection based on progeny test performance which shows a departure from usual predictions up to 15-20% at low (0.05) or high (0.95) selection rates. Univariate approximations and extensions to several paths of genetic change are also discussed.

Estimation of heterogeneous variances using empirical Bayes methods: theoretical considerations.

Procedures are described to estimate variances when heterogeneity of genetic and residual dispersion parameters exists for some criterion. Genetic and residual variances are considered to follow distributions with either known or unknown parameters. The estimates of variances obtained are weighted averages of the corresponding parameter and of a data-based statistic. Although the techniques presented are largely inspired by Bayesian ideas, the procedures can be given a frequentist interpretation, and the parameters of the prior distributions can be estimated from the data at hand. Techniques are described and illustrated for situations in which animals are related or unrelated across herds. We conjecture that the proposed estimators have smaller mean squared error than those obtained by grouping observations in some way and then applying REML within each group.

Genetic analysis of dystocia in dairy cattle.

Breeding values and genetic parameters for dystocia were estimated in Normande and Holstein breeds. Dystocia scores were related to an underlying continuous variable via a threshold model. The underlying linear model included the effects of calving season, sex of calf by parity of dam, sire of calf, grandsire of calf, dam within maternal grandsire and herd-year effects. Typical results were found for the environmental effects, with a strong influence of dam parity on dystocia, a strong influence of sex of calf, and a small effect of calving season. Herd-year variances were 32 and 40% of the residual variance in the Normande and Holstein breeds, respectively. Heritabilities for the Normande (Holstein) breed were .08 (.07) for direct effects and .11 (.07) for maternal effects. Correlations between sire and grandsire effects were .51 and .36 for the Normande and Holstein breeds, respectively. The corresponding correlations between direct and maternal effects were .15 and -.09. The results of this study show that a complete model for dystocia including the threshold concept and maternal effects can be applied for routine evaluation of dairy AI bulls. Maternal effects are important, and they should be considered in dystocia analysis, especially if nonrandom mating is present. Selection for reducing dystocia in calf and cow effects are not antagonistic.

Predicting cumulated response to directional selection in finite panmictic populations.

Accurate prediction of the cumulated genetic gain requires predicting genetic variance over time under the joint effects of selection and limited population size. An algorithm is proposed to quantify at each generation the effects of these factors on average coefficient of inbreeding, genetic variance, and genetic mean, under a purely additive polygenic model, with no mutation, and under the assumption of absence of inbreeding depression on viability affecting selection differentials. This algorithm is relevant to populations where mating is at random and generations do not overlap. It was tested via Monte Carlo simulation on a population of 3 males and 25 females mass selected out of 50 candidates of each sex, over 30 generations. For two values of the initial heritability of the selected trait, 0.5 and 0.9 (to represent high accuracy in index selection), predicted values of the genetic variance are in agreement with observed results up to the 12th and 19th generations, respectively. Beyond these generations, the variance is overestimated, due to an underestimation of the effect of selection on the rate of inbreeding. Finally, the algorithm provides predictions of the cumulated responses close to the observed values in both selected populations. It is concluded that, as regards the hypotheses of the study, the proposed algorithm is satisfactory, and could be used to optimize selection methods with respect to the cumulated genetic gain in the mid- or long-term. Possible extensions of the algorithm to more realistic situations are discussed.

Likelihood estimation of quantitative genetic parameters when selection occurs: models and problems.

Conceptual aspects of estimation of genetic components of variance and covariance under selection are discussed, with special attention to likelihood methods. Certain selection processes are described and alternative likelihoods that can be used for analysis are specified. There is a mathematical relationship between the likelihoods that permits comparing the relative amount of information contained in them. Theoretical arguments and evidence indicate that point inferences made from likelihood functions are not affected by some forms of selection.

Effect of mass selection on the within-family genetic variance in finite populations.

The adequacy of an expression for the withinfamily genetic variance under pure random drift in an additive infinitesimal model was tested via simulation in populations undergoing mass selection. Two hundred or one thousand unlinked loci with two alleles at initial frequencies of 1/2 were considered. The size of the population was 100 (50 males and 50 females). Full-sib matings were carried out for 15 generations with only one male and one female chosen as parents each generation, either randomly or on an individual phenotypic value. In the unselected population, results obtained from 200 replicates were in agreement with predictions. With mass selection, within-family genetic variance was overpredicted by theory from the 12th and 4th generations for the 1,000 and 200 loci cases, respectively. Taking into account the observed change in gene frequencies in the algorithm led to a much better agreement with observed values. Results for the distribution of gene frequencies and the withinlocus genetic covariance are presented. It is concluded that the expression for the within-family genetic variance derived for pure random drift holds well for mass selection within the limits of an additive infinitesimal model.

Genetic evaluation of traits distributed as Poisson-binomial with reference to reproductive characters.

A procedure of genetic evaluation of reproductive traits such as litter size and survival in a polytocous species under the assumption of polygenic inheritance is described. Conditional distributions of these traits are assumed to be Poisson and Bernoulli, respectively. Using the concept of generalized linear models, logarithmic (litter size) and probit (survival) functions are described as linear combinations of "nuisance" environmental effects and of transmitting abilities of sires or individual breeding values. The liability of survival is expressed conditionally to the logarithm of litter size. Inferences on location parameters are based on the mode of their joint posterior density assuming a prior multivariate normal distribution. A method of estimation of the dispersion parameters is also presented. The use of a "truncated" Poisson distribution is suggested to account for missing records on litter size.

Sire evaluation for multiple binary responses when information is missing on some traits.

A procedure of sire evaluation for multiple binary responses when information is missing for some traits is described. The genetic model assumes a conceptual underlying multivariate normal distribution rendered discrete by abrupt thresholds. Statistical inferences are made from a posterior distribution consisting of several conditionally independent likelihood functions and a multivariate normal prior distribution. Each likelihood function corresponds to a particular class of information available. Point estimators and predictors of fixed and random effects are the values that maximize the posterior distribution conditionally on heritabilities and genetic correlations. The procedure involves nonlinear maximization. An example involving joint selection for calving ease and skeletal development illustrates the principles. Application of the methodology as a potential means of removing bias due to selection for categorical traits is discussed.