Optimisation of contribution of candidate parents to maximise genetic gain and restricting inbreeding using semidefinite programming (Open Access publication)

An approach for optimising genetic contributions of candidates to control inbreeding in the offspring generation using semidefinite programming (SDP) was proposed. Formulations were done for maximising genetic gain while restricting inbreeding to a preset value and for minimising inbreeding without regard of gain. Adaptations to account for candidates with fixed contributions were also shown. Using small but traceable numerical examples, the SDP method was compared with an alternative based upon Lagrangian multipliers (RSRO). The SDP method always found the optimum solution that maximises genetic gain at any level of restriction imposed on inbreeding, unlike RSRO which failed to do so in several situations. For these situations, the expected gains from the solution obtained with RSRO were between 1.5–9% lower than those expected from the optimum solution found with SDP with assigned contributions varying widely. In conclusion SDP is a reliable and flexible method for solving contribution problems

Response to mass selection when an identified major gene is segregating

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On the Genetic Interpretation of Disease Data

Background: The understanding of host genetic variation in disease resistance increasingly requires the use of field data to obtain sufficient numbers of phenotypes. We introduce concepts necessary for a genetic interpretation of field disease data, for diseases caused by microparasites such as bacteria or viruses. Our focus is on variance component estimation and we introduce epidemiological concepts to quantitative genetics. Methodology/Principal Findings: We have derived simple deterministic formulae to predict the impacts of incomplete exposure to infection, or imperfect diagnostic test sensitivity and specificity on heritabilities for disease resistance. We show that these factors all reduce the estimable heritabilities. The impacts of incomplete exposure depend on disease prevalence but are relatively linear with the exposure probability. For prevalences less than 0.5, imperfect diagnostic test sensitivity results in a small underestimation of heritability, whereas imperfect specificity leads to a much greater underestimation, with the impact increasing as prevalence declines. These impacts are reversed for prevalences greater than 0.5. Incomplete data recording in which infected or diseased individuals are not observed, e.g. data recording for too short a period, has impacts analogous to imperfect sensitivity. Conclusions/Significance: These results help to explain the often low disease resistance heritabilities observed under field conditions. They also demonstrate that incomplete exposure to infection, or suboptimal diagnoses, are not fata

Comparative analyses of genetic trends and prospects for selection against hip and elbow dysplasia in 15 UK dog breeds

BACKGROUND: Hip dysplasia remains one of the most serious hereditary diseases occurring in dogs despite long-standing evaluation schemes designed to aid selection for healthy joints. Many researchers have recommended the use of estimated breeding values (EBV) to improve the rate of genetic progress from selection against hip and elbow dysplasia (another common developmental orthopaedic disorder), but few have empirically quantified the benefits of their use. This study aimed to both determine recent genetic trends in hip and elbow dysplasia, and evaluate the potential improvements in response to selection that publication of EBV for such diseases would provide, across a wide range of pure-bred dog breeds. RESULTS: The genetic trend with respect to hip and elbow condition due to phenotypic selection had improved in all breeds, except the Siberian Husky. However, derived selection intensities are extremely weak, equivalent to excluding less than a maximum of 18% of the highest risk animals from breeding. EBV for hip and elbow score were predicted to be on average between 1.16 and 1.34 times more accurate than selection on individual or both parental phenotypes. Additionally, compared to the proportion of juvenile animals with both parental phenotypes, the proportion with EBV of a greater accuracy than selection on such phenotypes increased by up to 3-fold for hip score and up to 13-fold for elbow score. CONCLUSIONS: EBV are shown to be both more accurate and abundant than phenotype, providing more reliable information on the genetic risk of disease for a greater proportion of the population. Because the accuracy of selection is directly related to genetic progress, use of EBV can be expected to benefit selection for the improvement of canine health and welfare. Public availability of EBV for hip score for the fifteen breeds included in this study will provide information on the genetic risk of disease in nearly a third of all dogs annually registered by the UK Kennel Club, with in excess of a quarter having an EBV for elbow score as well

The advantage of factorial mating under selection is uncovered by deterministically predicted rates of inbreeding

Rates of inbreeding (ΔF) in selected populations were predicted using the framework of long-term genetic contributions and validated against stochastic simulations. Deterministic predictions decomposed ΔF into four components due to: finite population size, directional selection, covariance of genetic contribution of mates, and deviation of variance of family size from that expected from a Poisson distribution. Factorial (FM) and hierarchical (HM) mating systems were compared under mass and sib-index selection. Prediction errors were in most cases for ΔF less than 10% and for rate of gain less than 5%. ΔF was higher with index than mass selection. ΔF was lower with FM than HM in all cases except random selection. FM reduced the variance of the average breeding value of the mates of an individual. This reduced the impact of the covariance of contributions of mates on ΔF. Thus, contributions of mates were less correlated with FM than HM, causing smaller deviations of converged contributions from the optimum contributions. With index selection, FM also caused a smaller variance of number of offspring selected from each parent. This reduced variance of family size reduced ΔF further. FM increases the flexibility in breeding schemes for achieving the optimum genetic contributions

Prediction of IBD based on population history for fine gene mapping

A novel multiple regression method (RM) is developed to predict identity-by-descent probabilities at a locus L (IBDL), among individuals without pedigree, given information on surrounding markers and population history. These IBDL probabilities are a function of the increase in linkage disequilibrium (LD) generated by drift in a homogeneous population over generations. Three parameters are sufficient to describe population history: effective population size (Ne), number of generations since foundation (T), and marker allele frequencies among founders (p). IBDL are used in a simulation study to map a quantitative trait locus (QTL) via variance component estimation. RM is compared to a coalescent method (CM) in terms of power and robustness of QTL detection. Differences between RM and CM are small but significant. For example, RM is more powerful than CM in dioecious populations, but not in monoecious populations. Moreover, RM is more robust than CM when marker phases are unknown or when there is complete LD among founders or Ne is wrong, and less robust when p is wrong. CM utilises all marker haplotype information, whereas RM utilises information contained in each individual marker and all possible marker pairs but not in higher order interactions. RM consists of a family of models encompassing four different population structures, and two ways of using marker information, which contrasts with the single model that must cater for all possible evolutionary scenarios in CM

Genomic selection and complex trait prediction using a fast EM algorithm applied to genome-wide markers

Background: The information provided by dense genome-wide markers using high throughput technology is of considerable potential in human disease studies and livestock breeding programs. Genome-wide association studies relate individual single nucleotide polymorphisms (SNP) from dense SNP panels to individual measurements of complex traits, with the underlying assumption being that any association is caused by linkage disequilibrium (LD) between SNP and quantitative trait loci (QTL) affecting the trait. Often SNP are in genomic regions of no trait variation. Whole genome Bayesian models are an effective way of incorporating important prior information into modelling. However a full Bayesian analysis is often not feasible due to the amount of data and the computational time involved. Results: This article proposes an expectation-maximization (EM) algorithm called emBayesB which allows only a proportion of SNP to be in LD with QTL and incorporates important prior information about the distribution of SNP effects. The posterior probability of being in LD with at least one QTL is calculated for each SNP along with estimates of the hyperparameters for the mixture prior. A simulated example of genomic selection from an international workshop is used to demonstrate the features of the EM algorithm. The accuracy of prediction is comparable to a full Bayesian analysis but the EM algorithm is considerably faster. The EM algorithm was accurate in locating QTL which explained more than 1% of the total genetic variation. A computational algorithm for very large SNP panels is described. Conclusions: emBayesB is a fast and accurate EM algorithm for implementing genomic selection and predicting complex traits by mapping QTL in genome-wide dense SNP marker data. Its accuracy is similar to Bayesian methods but it takes only a fraction of the time

Potential benefit from using an identified major gene in BLUP evaluation with truncation and optimal selection

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Behaviour of the additive finite locus model

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