A simple algorithm to estimate genetic variance in an animal threshold model using Bayesian inference

<p>Abstract</p> <p>Background</p> <p>In the genetic analysis of binary traits with one observation per animal, animal threshold models frequently give biased heritability estimates. In some cases, this problem can be circumvented by fitting sire- or sire-dam models. However, these models are not appropriate in cases where individual records exist on parents. Therefore, the aim of our study was to develop a new Gibbs sampling algorithm for a proper estimation of genetic (co)variance components within an animal threshold model framework.</p> <p>Methods</p> <p>In the proposed algorithm, individuals are classified as either "informative" or "non-informative" with respect to genetic (co)variance components. The "non-informative" individuals are characterized by their Mendelian sampling deviations (deviance from the mid-parent mean) being completely confounded with a single residual on the underlying liability scale. For threshold models, residual variance on the underlying scale is not identifiable. Hence, variance of fully confounded Mendelian sampling deviations cannot be identified either, but can be inferred from the between-family variation. In the new algorithm, breeding values are sampled as in a standard animal model using the full relationship matrix, but genetic (co)variance components are inferred from the sampled breeding values and relationships between "informative" individuals (usually parents) only. The latter is analogous to a sire-dam model (in cases with no individual records on the parents).</p> <p>Results</p> <p>When applied to simulated data sets, the standard animal threshold model failed to produce useful results since samples of genetic variance always drifted towards infinity, while the new algorithm produced proper parameter estimates essentially identical to the results from a sire-dam model (given the fact that no individual records exist for the parents). Furthermore, the new algorithm showed much faster Markov chain mixing properties for genetic parameters (similar to the sire-dam model).</p> <p>Conclusions</p> <p>The new algorithm to estimate genetic parameters via Gibbs sampling solves the bias problems typically occurring in animal threshold model analysis of binary traits with one observation per animal. Furthermore, the method considerably speeds up mixing properties of the Gibbs sampler with respect to genetic parameters, which would be an advantage of any linear or non-linear animal model.</p

On some invariant ideals, and on extension of differentiations to seminormalization

AbstractLet A be a noetherian integral domain, D=(1,D1,…,Di…) be a differentation of A, and B be a ring such that A⊂B⊂Ā. In the paper we mainly prove (whenever Ā is finite over A): (a) if α is the conductor of A in B, then A√α is D-invariant. (b) D extends to the seminormalization +A of A in Ā

Norwegian mastitis control programme

This paper describes the methods and results of the Norwegian Mastitis Control Program implemented in 1982. The program has formed an integral part of the Norwegian Cattle Health Services (NCHS) since 1995. The NCHS also have specific programs for milk fever, ketosis, reproduction and calf diseases. The goal of the program is to improve udder health by keeping the bulk milk somatic cell count (BMSCC) low, to reduce the use of antibiotics, to keep the cost of mastitis low at herd level and improve the consumers' attitude to milk products. In 1996, a decision was made to reduce the use of antibiotics in all animal production enterprises in Norway by 25% within five years. Relevant data has been collected through the Norwegian Cattle Herd Recording System (NCHRS); including health records since 1975 and somatic cell count (SCC) data since 1980. These data have been integrated within the NCHRS. Since 2000, mastitis laboratory data have also been included in the NCHRS. Data on clinical disease, SCC and mastitis bacteriology have been presented to farmers and advisors in monthly health periodicals since 1996, and on the internet since 2005. In 1996, Norwegian recommendations on the treatment of mastitis were implemented. Optimal milking protocols and milking machine function have been emphasised and less emphasis has been placed on dry cow therapy. A selective dry cow therapy program (SDCTP) was implemented in 2006, and is still being implemented in new areas. Research demonstrates that the rate of clinical mastitis could be reduced by 15% after implementing SDCTP. The results so far show a 60% reduction in the clinical treatment of mastitis between 1994 and 2007, a reduction in BMSCC from 250,000 cells/ml to 114,000 cells/ml, and a total reduction in the mastitis cost from 0.23 NOK to 0.13 NOK per litre of milk delivered to the processors, corresponding to a fall from 9.2% to 1.7% of the milk price, respectively. This reduction is attributed to changes in attitude and breeding, eradicating bovine virus diarrhoea virus (BVDV) and a better implementation of mastitis prevention programmes

Genome-wide pleiotropy and shared biological pathways for resistance to bovine pathogens

<div><p>Host genetic architecture is a major factor in resistance to pathogens and parasites. The collection and analysis of sufficient data on both disease resistance and host genetics has, however, been a major obstacle to dissection the genetics of resistance to single or multiple pathogens. A severe challenge in the estimation of heritabilities and genetic correlations from pedigree-based studies has been the confounding effects of the common environment shared among relatives which are difficult to model in pedigree analyses, especially for health traits with low incidence rates. To circumvent this problem we used genome-wide single-nucleotide polymorphism data and implemented the Genomic-Restricted Maximum Likelihood (G-REML) method to estimate the heritabilities and genetic correlations for resistance to 23 different infectious pathogens in calves and cows in populations undergoing natural pathogen challenge. Furthermore, we conducted gene-based analysis and generalized gene-set analysis to understand the biological background of resistance to infectious diseases. The results showed relatively higher heritabilities of resistance in calves than in cows and significant pleiotropy (both positive and negative) among some calf and cow resistance traits. We also found significant pleiotropy between resistance and performance in both calves and cows. Finally, we confirmed the role of the B-lymphocyte pathway as one of the most important biological pathways associated with resistance to all pathogens. These results both illustrate the potential power of these approaches to illuminate the genetics of pathogen resistance in cattle and provide foundational information for future genomic selection aimed at improving the overall production fitness of cattle.</p></div

Reproductive Performance, Udder Health, and Antibiotic Resistance in Mastitis Bacteria isolated from Norwegian Red cows in Conventional and Organic Farming

<p>Abstract</p> <p>Background</p> <p>The objectives of this study were to investigate whether there were differences between Norwegian Red cows in conventional and organic farming with respect to reproductive performance, udder health, and antibiotic resistance in udder pathogens.</p> <p>Methods</p> <p>Twenty-five conventional and 24 organic herds from south-east and middle Norway participated in the study. Herds were matched such that geographical location, herd size, and barn types were similar across the cohorts. All organic herds were certified as organic between 1997 and 2003. All herds were members of the Norwegian Dairy Herd Recording System. The herds were visited once during the study. The relationship between the outcomes and explanatory variables were assessed using mixed linear models.</p> <p>Results</p> <p>There were less > 2nd parity cows in conventional farming. The conventional cows had higher milk yields and received more concentrates than organic cows. Although after adjustment for milk yield and parity, somatic cell count was lower in organic cows than conventional cows. There was a higher proportion of quarters that were dried off at the herd visit in organic herds. No differences in the interval to first AI, interval to last AI or calving interval was revealed between organic and conventional cows. There was no difference between conventional and organic cows in quarter samples positive for mastitis bacteria from the herd visit. Milk yield and parity were associated with the likelihood of at least one quarter positive for mastitis bacteria. There was few <it>S. aureus </it>isolates resistance to penicillin in both management systems. Penicillin resistance against Coagulase negative staphylococci isolated from subclinically infected quarters was 48.5% in conventional herds and 46.5% in organic herds.</p> <p>Conclusion</p> <p>There were no large differences between reproductive performance and udder health between conventional and organic farming for Norwegian Red cows.</p

Searching for phenotypic causal networks involving complex traits: an application to European quail

<p>Abstract</p> <p>Background</p> <p>Structural equation models (SEM) are used to model multiple traits and the casual links among them. The number of different causal structures that can be used to fit a SEM is typically very large, even when only a few traits are studied. In recent applications of SEM in quantitative genetics mixed model settings, causal structures were pre-selected based on prior beliefs alone. Alternatively, there are algorithms that search for structures that are compatible with the joint distribution of the data. However, such a search cannot be performed directly on the joint distribution of the phenotypes since causal relationships are possibly masked by genetic covariances. In this context, the application of the Inductive Causation (IC) algorithm to the joint distribution of phenotypes conditional to unobservable genetic effects has been proposed.</p> <p>Methods</p> <p>Here, we applied this approach to five traits in European quail: birth weight (BW), weight at 35 days of age (W35), age at first egg (AFE), average egg weight from 77 to 110 days of age (AEW), and number of eggs laid in the same period (NE). We have focused the discussion on the challenges and difficulties resulting from applying this method to field data. Statistical decisions regarding partial correlations were based on different Highest Posterior Density (HPD) interval contents and models based on the selected causal structures were compared using the Deviance Information Criterion (DIC). In addition, we used temporal information to perform additional edge orienting, overriding the algorithm output when necessary.</p> <p>Results</p> <p>As a result, the final causal structure consisted of two separated substructures: BW→AEW and W35→AFE→NE, where an arrow represents a direct effect. Comparison between a SEM with the selected structure and a Multiple Trait Animal Model using DIC indicated that the SEM is more plausible.</p> <p>Conclusions</p> <p>Coupling prior knowledge with the output provided by the IC algorithm allowed further learning regarding phenotypic causal structures when compared to standard mixed effects SEM applications.</p

Modeling relationships between calving traits: a comparison between standard and recursive mixed models

<p>Abstract</p> <p>Background</p> <p>The use of structural equation models for the analysis of recursive and simultaneous relationships between phenotypes has become more popular recently. The aim of this paper is to illustrate how these models can be applied in animal breeding to achieve parameterizations of different levels of complexity and, more specifically, to model phenotypic recursion between three calving traits: gestation length (GL), calving difficulty (CD) and stillbirth (SB). All recursive models considered here postulate heterogeneous recursive relationships between GL and liabilities to CD and SB, and between liability to CD and liability to SB, depending on categories of GL phenotype.</p> <p>Methods</p> <p>Four models were compared in terms of goodness of fit and predictive ability: 1) standard mixed model (SMM), a model with unstructured (co)variance matrices; 2) recursive mixed model 1 (RMM1), assuming that residual correlations are due to the recursive relationships between phenotypes; 3) RMM2, assuming that correlations between residuals and contemporary groups are due to recursive relationships between phenotypes; and 4) RMM3, postulating that the correlations between genetic effects, contemporary groups and residuals are due to recursive relationships between phenotypes.</p> <p>Results</p> <p>For all the RMM considered, the estimates of the structural coefficients were similar. Results revealed a nonlinear relationship between GL and the liabilities both to CD and to SB, and a linear relationship between the liabilities to CD and SB.</p> <p>Differences in terms of goodness of fit and predictive ability of the models considered were negligible, suggesting that RMM3 is plausible.</p> <p>Conclusions</p> <p>The applications examined in this study suggest the plausibility of a nonlinear recursive effect from GL onto CD and SB. Also, the fact that the most restrictive model RMM3, which assumes that the only cause of correlation is phenotypic recursion, performs as well as the others indicates that the phenotypic recursion may be an important cause of the observed patterns of genetic and environmental correlations.</p

Genetic parameters for somatic cell score according to udder infection status in Valle del Belice dairy sheep and impact of imperfect diagnosis of infection

<p>Abstract</p> <p>Background</p> <p>Somatic cell score (SCS) has been promoted as a selection criterion to improve mastitis resistance. However, SCS from healthy and infected animals may be considered as separate traits. Moreover, imperfect sensitivity and specificity could influence animals' classification and impact on estimated variance components. This study was aimed at: (1) estimating the heritability of bacteria negative SCS, bacteria positive SCS, and infection status, (2) estimating phenotypic and genetic correlations between bacteria negative and bacteria positive SCS, and the genetic correlation between bacteria negative SCS and infection status, and (3) evaluating the impact of imperfect diagnosis of infection on variance component estimates.</p> <p>Methods</p> <p>Data on SCS and udder infection status for 1,120 ewes were collected from four Valle del Belice flocks. The pedigree file included 1,603 animals. The SCS dataset was split according to whether animals were infected or not at the time of sampling. A repeatability test-day animal model was used to estimate genetic parameters for SCS traits and the heritability of infection status. The genetic correlation between bacteria negative SCS and infection status was estimated using an MCMC threshold model, implemented by Gibbs Sampling.</p> <p>Results</p> <p>The heritability was 0.10 for bacteria negative SCS, 0.03 for bacteria positive SCS, and 0.09 for infection status, on the liability scale. The genetic correlation between bacteria negative and bacteria positive SCS was 0.62, suggesting that they may be genetically different traits. The genetic correlation between bacteria negative SCS and infection status was 0.51. We demonstrate that imperfect diagnosis of infection leads to underestimation of differences between bacteria negative and bacteria positive SCS, and we derive formulae to predict impacts on estimated genetic parameters.</p> <p>Conclusions</p> <p>The results suggest that bacteria negative and bacteria positive SCS are genetically different traits. A positive genetic correlation between bacteria negative SCS and liability to infection was found, suggesting that the approach of selecting animals for decreased SCS should help to reduce mastitis prevalence. However, the results show that imperfect diagnosis of infection has an impact on estimated genetic parameters, which may reduce the efficiency of selection strategies aiming at distinguishing between bacteria negative and bacteria positive SCS.</p

Evaluating alternate models to estimate genetic parameters of calving traits in United Kingdom Holstein-Friesian dairy cattle

<p>Abstract</p> <p>Background</p> <p>The focus in dairy cattle breeding is gradually shifting from production to functional traits and genetic parameters of calving traits are estimated more frequently. However, across countries, various statistical models are used to estimate these parameters. This study evaluates different models for calving ease and stillbirth in United Kingdom Holstein-Friesian cattle.</p> <p>Methods</p> <p>Data from first and later parity records were used. Genetic parameters for calving ease, stillbirth and gestation length were estimated using the restricted maximum likelihood method, considering different models i.e. sire (−maternal grandsire), animal, univariate and bivariate models. Gestation length was fitted as a correlated indicator trait and, for all three traits, genetic correlations between first and later parities were estimated. Potential bias in estimates was avoided by acknowledging a possible environmental direct-maternal covariance. The total heritable variance was estimated for each trait to discuss its theoretical importance and practical value. Prediction error variances and accuracies were calculated to compare the models.</p> <p>Results and discussion</p> <p>On average, direct and maternal heritabilities for calving traits were low, except for direct gestation length. Calving ease in first parity had a significant and negative direct-maternal genetic correlation. Gestation length was maternally correlated to stillbirth in first parity and directly correlated to calving ease in later parities. Multi-trait models had a slightly greater predictive ability than univariate models, especially for the lowly heritable traits. The computation time needed for sire (−maternal grandsire) models was much smaller than for animal models with only small differences in accuracy. The sire (−maternal grandsire) model was robust when additional genetic components were estimated, while the equivalent animal model had difficulties reaching convergence.</p> <p>Conclusions</p> <p>For the evaluation of calving traits, multi-trait models show a slight advantage over univariate models. Extended sire models (−maternal grandsire) are more practical and robust than animal models. Estimated genetic parameters for calving traits of UK Holstein cattle are consistent with literature. Calculating an aggregate estimated breeding value including direct and maternal values should encourage breeders to consider both direct and maternal effects in selection decisions.</p