Bayesian comparison of test-day models under different assumptions of heterogeneity for the residual variance: the change point technique versus arbitrary intervals

Test‐day milk yields from Spanish Holstein cows were analysed with two random regression models based on Legendre polynomials under two different assumptions of heterogeneity of residual variance which aim to describe the variability of temporary measurement errors along days in milk with a reduced number of parameters, such as (i) the change point identification technique with two unknown change points and (ii) using 10 arbitrary intervals of residual variance. Both implementations were based on a previous study where the trajectory of the residual variance was estimated using 30 intervals. The change point technique has been previously implemented in the analysis of the heterogeneity of the residual variance in the Spanish population, yet no comparisons with other methods have been reported so far. This study aims to compare the change point technique identification versus the use of arbitrary intervals as two possible techniques to deal with the characterization of the residual variance in random regression test‐day models. The Bayes factor and the cross‐validation predictive densities were employed for the model assessment. The two model‐selecting tools revealed a strong consistency between them. Both specifications for the residual variance were close to each other. The 10 intervals modelling showed a slightly better performance probably because the change point function overestimates the residual variance values at the very early lactation.     

Combining genetic test information and correlated phenotypic records for breeding value estimation

The use of marker assisted selection in the beef cattle industry to date has involved using traditional EPD in tandem with molecular test information. In the current study, a multiple-trait simulation was carried out to create a beef cattle data set using genetic parameter estimates from the literature to identify the best procedure for combining both sources of information and to assess the added benefit of the procedure. To reach these objectives, the following simulation/ analysis steps were implemented: (1) varying percentages (100, 5, or 0) of available records for the trait of interest, (2) varying percentages (100, 50, 25, or 0) of animals with molecular information, (3) scenarios where the favorable (F) or the unfavorable (U) allele was more frequent, and (4) analysis of the response due to selection over 5 generations. The data sets included 3 correlated traits in which 2 of them, birth weight and postweaning gain, had complete recording and the availability of records for the third trait (marbling score) varied. It was further assumed that molecular information was available for the third trait for a causative gene that explained 10% of the genetic variation. Estimates of Pearson correlations between true and predicted breeding values for marbling score declined as the amount of information declined, and instances in which the molecular information was recorded were always closer to the true values than in the case in which the molecular information was absent. When the U allele was more frequent, rank correlation estimates were increased among top sires, low accuracy sires, and high accuracy sires by approximately 24.9, 12.1, and 4.7% with limited marbling score records and complete genotyping compared with limited marbling score records and no genotyping. Similar results were seen when the F allele was more frequent. When there was a complete absence of recording for the trait of interest, the same trends in correlations were observed and were lower than when the trait of interest was recorded. Jointly considering molecular and phenotypic information showed a greater long-term response compared with tandem selection, showing that discrimination of candidates for selection based solely on molecular information is not optimal.     

Genetic analysis of age at first service, return rate, litter size, and weaning-to-first service interval of gilts and sows

The aim of this study was to estimate genetic parameters of seven traits related to sow reproductive performance. Data on all Norwegian Landrace pigs (NL) born in nucleus herds and raised in nucleus or multiplying herds from 1990 to 2000 were extracted from the Norwegian national recording scheme. Reproductive traits investigated were age at first service (AFS), return rate in gilts (RRg), age at first farrowing (AFF), live-born piglets in the first litter (NBA1), interval from weaning to first service after first litter (WTS1), return rate after first litter (RR1), live-born piglets in the second litter (NBA2), and interval from weaning to first service after second litter (WTS2). After editing, the data set comprised 12,583 to 56,042 records, depending on the trait. A mixed linear and a joint linear threshold animal model were used to estimate (co)variance components. A full Bayesian approach via Gibbs sampling was adopted. The statistical model used for analysis included contemporary groups of herd-year (-season), purebred or crossbred litter, single or double insemination, mating type, parity in which the animal was born, a regression on lactation length, and an additive genetic effect. Neither the estimated heritabilities nor the genetic correlations differed much between the two approaches, but there was a tendency for higher genetic correlations using the joint linear threshold model approach. Average heritabilities were as follows: AFS = 0.31; RRg = 0.03; RR1 = 0.02; NBA1 = 0.12; NBA2 = 0.14; WTS1 = 0.08; and WTS2 = 0.03. The highest genetic correlations were estimated between NBA1 and NBA2 (r(g) = 0.95), RR1 and WTS1 (r(g) = 0.93), and between WTS1 and WTS2 (r(g) = 0.78). The estimated genetic correlation between NBA and WTS were close to zero. Selection for increased NBA will slightly increase AFS and reduce the probability of a return. Selection for decreased AFS will have a favorable effect on WTS intervals; however, selection for decreased AFS seems to have an unfavorable effect on return rate both on gilts and sows. Conversely, selection for decreased WTS intervals will reduce the probability of a return. Potential selection candidates to include in a multivariate fertility index are AFS, NBA, and WTS1. Due to the low heritability and low, but favorable, genetic correlations to NBA and WTS, RR is not recommended as a selection candidate.     

Different methods of selecting animals for genotyping to maximize the amount of genetic information known in the population

It is possible to predict genotypes of some individuals based on genotypes of relatives. Different methods of sampling individuals to be genotyped from populations were evaluated using simulation. Simulated pedigrees included 5,000 animals and were assigned genotypes based on assumed allelic frequencies for a SNP (favorable/unfavorable) of 0.3/0.7, 0.5/0.5, and 0.8/0.2. A field data pedigree (29,101 animals) and a research pedigree (8,688 animals) were used to test selected methods using simulated genotypes with allelic frequencies of 0.3/0.7 and 0.5/0.5. For the simulated pedigrees, known and unknown allelic frequencies were assumed. The methods used included random sampling, selection of males, and selection of both sexes based on the diagonal element of the inverse of the relationship matrix (A(-1)) and absorption of either the A or A(-1) matrix. For random sampling, scenarios included selection of 5 and 15% of the animals, and all other methods presented concentrated on the selection of 5% of the animals for genotyping. The methods were evaluated based on the percentage of alleles correctly assigned after peeling (AK(P)), the probability of assigning true alleles (AK(G)), and the average probability of correctly assigning the true genotype. As expected, random sampling was the least desirable method. The most desirable method in the simulated pedigrees was selecting both males and females based on their diagonal element of A(-1). Increases in AK(P) and AK(G) ranged from 26.58 to 29.11% and 2.76 to 6.08%, respectively, when males and females (equal to 5% of all animals) were selected based on their diagonal element of A(-1) compared with selecting 15% of the animals at random. In the case of a real beef cattle pedigree, selection of males only or males and females yielded similar results and both selection methods were superior to random selection.     

Analysis of Multiple Binary Responses Using a Threshold Model

Several discrete responses, such as health status, reproduction performance and meat quality, are routinely collected for several livestock species. These traits are often of binary or discrete nature. Genetic evaluation for these traits is frequently conducted using a single-trait threshold model, or they are considered continuous responses either in univariate or in multivariate context. Implementation of threshold models in the presence of several binary responses or a mixture of binary and continuous responses is far from simple. The complexity of such implementation is primarily due to the incomplete randomness of the residual (co)variance matrix. In the current study, a multiple binary trait simulation was carried out in order to implement and validate a new procedure for dealing with the consequences of the restrictions imposed to the residual variance using threshold models. Using three and eight binary responses, the proposed method was able to estimate all unknown parameters without any noticeable bias. In fact, for simulated residual correlations ranging from ?0.8 to 0.8, the resulting HPD 95% intervals included the true values in all cases. The proposed procedure involved limited additional computational cost and is straightforward to implement independent of the number of binary responses involved in the analysis. Monitoring of the convergence of the procedure must be conducted at the identifiable scale, and special care must be placed on the selection of the prior of the non-identifiable model. The latter could have serious consequences on the final results due to potential truncation of the parameter space.     

Comparison of methods for handling censored records in beef fertility data: simulation study

A simulation study was conducted to compare methods for handling censored records for days to calving in beef cattle data. Days to calving was defined as the time, in days, between when a bull is turned out in the pasture and the subsequent parturition. Simulated data were generated to have data structure and genetic relationships similar to an available field data set. Records were simulated for 33,176 daughters of 4,238 sires. Data were simulated using a mixed linear model that included the fixed effects of contemporary group and sex of calf, linear and quadratic covariates for age at mating, and random effects of animal and residual error. Two methods for handling censored records were evaluated, and two censoring rates of 12 and 20% were applied to assess the influence of higher censoring rates on inferences. Censored records were assigned penalty values on a within-contemporary group basis under the first method (DCPEN). Under the second method (DCSIM), censored records were drawn from their respective predictive distributions. A Bayesian approach via Gibbs sampling was used to estimate variance components and predict breeding values. Posterior means (PM) and standard deviations (SD) of additive genetic variance for DCPEN at 12 and 20% censoring were 23.2 (3.7) and 21.0 (3.6), respectively, whereas the same estimates for DCSIM at 12 and 20% censoring were 23.7(3.3) and 21.9 (3.4), respectively. In all cases, the true value of the genetic variance was within the high posterior density (HPD) interval (95%). The PM (SD) of residual variance for DCPEN at 12 and 20% censoring were 415.7 (4.7) and 440.0 (4.8) respectively, whereas the same estimates for DCSIM at 12 and 20% censoring were 371.0 (4.3) and 365.4 (4.4), respectively. The true value of the residual variance was within the HPD (95%) for DCSIM, but it was outside this interval for DCPEN at both censoring rates, indicating a systematic bias for this parameter. Bayes Factor and Deviance Information Criteria were used for model comparisons, and both criteria indicated the superiority of the DCSIM method. However, little difference was observed between the two methods for correlations between true breeding values and posterior means of animal effects for sires, indicating that no major reranking of sires would be expected. This finding suggests that either censored data handling technique can be successfully used in a genetic evaluation for days to calving.     

Simulation study of teat score in first-parity Gelbvieh cows: parameter estimation

Teat scores from 9,598 first-parity Gelbvieh cows were used to investigate the adequacy of grouping approaches to decrease score misclassifications or inconsistencies as well as to simplify the data collection process. The procedure was tested using simulated data and then validated using teat score records of Gelbvieh cattle. First-parity cows were considered to be 4 yr of age or younger at first calving, did not have multiple records within 280 d, and were at least 50% Gelbvieh. Producers scored cows within 24 h of parturition. Teat score, a subjective measure of teat size, ranged from 0 (very large) to 50 (very small). A linear mixed model that included herd-year, month of calving, and age at calving as systematic effects; regression on the percentage of Gelbvieh; and additive breeding values (BV) and residual as random effects was used to generate the data. Simulated data were analyzed using one of three scoring methods: all values (S50), 10 classes (S10), and five classes (S5). The 10 classes were formed by subdividing every five scores into a single class starting at score zero. Similarly, the five classes were formed by combining every 10 scores into one class. The average Pearson correlations, based on five replicates, between the true and estimated BV (systematic effects) were 0.36 (0.85), 0.35 (0.89), and 0.32 (0.87) using S50, S10, and S5, respectively. Average correlations between estimated BV (systematic effects) were 0.97 (0.95), 0.89 (0.92), and 0.92 (0.97) based on S50 and S10, S50 and S5, and S10 and S5, respectively. Field data were used to validate the simulation procedure. The field data were categorized into 10 classes (F10) and five classes (F5) as described for the simulated data. Pearson correlations between estimated BV (systematic effects) were 0.99 (0.93), 0.93 (0.88), and 0.93 (0.96), based on F50 with F10, F50 with F5, and F10 with F5, respectively. The extremely high correlations between predicted BV based on S50, S10, S5, F50, F10, with F5 suggest that a simplified score classification method could be adopted without compromising the expected genetic progress for the trait under consideration. Furthermore, the difference in corresponding Pearson correlations across the field and simulated data might suggest the presence of some inconsistencies or misclassifications of the actual scoring system.     

The diversity of rhizobia nodulating chickpea (Cicer arietinum) under water deficiency as a source of more efficient inoculants

Chickpea is an important pulse crop grown mainly in the arid and semi-arid regions. The effect of water deficiency on nodulation, biomass production, and competition for nodule occupancy was evaluated in three different soils with two chickpea cultivars, Amdoun I and Chetoui. Two watering regimes were considered; a control that was irrigated three times per week and a water-deficient treatment that was irrigated only one time a week. Results showed that water deficiency significantly decreased the nodule number and the shoot dry weight for both cultivars. Root-nodule bacteria were isolated and characterized by PCR-RFLP of 16S rDNA and nifD-K intergenic spacer. The results show that water deficiency affects the diversity of nodulating rhizobia. The nodulation by Mesorhizobium mediterraneum was reduced while inefficient nodulation by Ensifer meliloti was favoured. In both treatments, chickpea was preferentially nodulated by nifD-K type N6. Analysis for NaCl tolerance showed that most of rhizobia nodulating chickpea under water deficiency are NaCl tolerant. Inoculation with the selected salt-tolerant strain of M. mediterraneum LILM10 increased significantly nodule number and grain yield in the field.     

Front-face fluorescence spectroscopy as a rapid and nondestructive tool for differentiating various cereal products: a preliminary investigation

The potential of intrinsic fluorescence spectroscopy was investigated for differentiating between processed grains (flours, pasta, and semolinas) of different wheat cereal products. A total of 59 samples (e.g., 20 complete Kamut, semicomplete Kamut, and soft wheat flours, 28 pasta, and 11 semolinas manufactured from complete Kamut, semicomplete Kamut, and hard wheat flours) were analyzed by front-face fluorescence spectroscopy. Tryptophan fluorescence spectra were scanned between 305 and 400 nm on samples following excitation at 290 nm. The principal component analysis (PCA) performed on flour spectra clearly differentiated complete Kamut and semicomplete Kamut samples from those produced from complete and semicomplete soft wheat flours. The PCA performed on pasta spectra discriminated samples manufactured from complete Kamut and complete hard wheat flours from those made with semicomplete Kamut and semicomplete hard wheat flours. The best discrimination was obtained from tryptophan spectra recorded on semolinas since the four groups were well discriminated. Correct classification amounting to 61.9% was obtained for pasta spectra. A better classification was obtained for flour and semolina spectra since correct classification amounted to 86.7% and 87.9%, respectively. Front-face fluorescence spectroscopy has the potential to be a rapid, low-cost, and efficient method for the authentication of cereal products.