So far in this course we have dealt entirely with the evolution of characters that are controlled by simple Mendelian inheritance at a single locus. There are notes on the course website about gametic disequilibrium and how allele frequencies change at two loci simultaneously, but we didn’t discuss them. In every example we’ve considered we’ve imagined that we could understand something about evolution by examining the evolution of a single gene. That’s the domain of classical population genetics. For the next few weeks we’re going to be exploring a field that’s actually older than classical population genetics, although the approach we’ll be taking to it involves the use of population genetic machinery. If you know a little about the history of evolutionary biology, you may know that after the rediscovery of Mendel’s work in 1900 there was a heated debate between the “biometricians” (e.g., Galton and Pearson) and the “Mendelians” (e.g., de Vries, Correns, Bateson, and Morgan). Biometricians asserted that the really important variation in evolution didn’t follow Mendelian rules. Height, weight, skin color, and similar traits seemed to

Human biochemical genetics

Recent advances in molecular genetic techniques will make dense marker maps available and genotyping many individuals for these markers feasible. Here we attempted to estimate the effects of ∼50,000 marker haplotypes simultaneously from a limited number of phenotypic records. A genome of 1000 cM was simulated with a marker spacing of 1 cM. The markers surrounding every 1-cM region were combined into marker haplotypes. Due to finite population size (Ne = 100), the marker haplotypes were in linkage disequilibrium with the QTL located between the markers. Using least squares, all haplotype effects could not be estimated simultaneously. When only the biggest effects were included, they were overestimated and the accuracy of predicting genetic values of the offspring of the recorded animals was only 0.32. Best linear unbiased prediction of haplotype effects assumed equal variances associated to each 1-cM chromosomal segment, which yielded an accuracy of 0.73, although this assumption was far from true. Bayesian methods that assumed a prior distribution of the variance associated with each chromosome segment increased this accuracy to 0.85, even when the prior was not correct. It was concluded that selection on genetic values predicted from markers could substantially increase the rate of genetic gain in animals and plants, especially if combined with reproductive techniques to shorten the generation interval.

https://www.genetics.org/content/genetics/157/4/1819.full.pdf

Prediction of Total Genetic Value Using Genome-Wide Dense Marker Maps

Genetics and analysis of quantitative traits

ASREML user guide release 3.0

Stable non-Gaussian random processes , by G. Samorodnitsky and M. S. Taqqu. Pp. 632. £49.50. 1994. ISBN 0-412-05171-0 (Chapman and Hall).

The success of genomic selection depends on the potential to predict genome-assisted breeding values (GEBVs) with high accuracy over several generations without additional phenotyping after estimating marker effects. Results from both simulations and practical applications have to be evaluated for this potential, which requires linkage disequilibrium (LD) between markers and QTL. This study shows that markers can capture genetic relationships among genotyped animals, thereby affecting accuracies of GEBVs. Strategies to validate the accuracy of GEBVs due to LD are given. Simulations were used to show that accuracies of GEBVs obtained by fixed regression–least squares (FR–LS), random regression–best linear unbiased prediction (RR–BLUP), and Bayes-B are nonzero even without LD. When LD was present, accuracies decrease rapidly in generations after estimation due to the decay of genetic relationships. However, there is a persistent accuracy due to LD, which can be estimated by modeling the decay of genetic relationships and the decay of LD. The impact of genetic relationships was greatest for RR–BLUP. The accuracy of GEBVs can result entirely from genetic relationships captured by markers, and to validate the potential of genomic selection, several generations have to be analyzed to estimate the accuracy due to LD. The method of choice was Bayes-B; FR–LS should be investigated further, whereas RR–BLUP cannot be recommended.

https://www.genetics.org/content/genetics/177/4/2389.full.pdf

The Impact of Genetic Relationship Information on Genome-Assisted Breeding Values

Two Bayesian methods, BayesCπ and BayesDπ, were developed for genomic prediction to address the drawback of BayesA and BayesB regarding the impact of prior hyperparameters and treat the prior probability π that a SNP has zero effect as unknown. The methods were compared in terms of inference of the number of QTL and accuracy of genomic estimated breeding values (GEBVs), using simulated scenarios and real data from North American Holstein bulls. Estimates of π from BayesCπ, in contrast to BayesDπ, were sensitive to the number of simulated QTL and training data size, and provide information about genetic architecture. Milk yield and fat yield have QTL with larger effects than protein yield and somatic cell score. The drawback of BayesA and BayesB did not impair the accuracy of GEBVs. Accuracies of alternative Bayesian methods were similar. BayesA was a good choice for GEBV with the real data. Computing time was shorter for BayesCπ than for BayesDπ, and longest for our implementation of BayesA. Collectively, accounting for computing effort, uncertainty as to the number of QTL (which affects the GEBV accuracy of alternative methods), and fundamental interest in the number of QTL underlying quantitative traits, we believe that BayesCπ has merit for routine applications.

https://link.springer.com/content/pdf/10.1186%2F1471-2105-12-186.pdf

Extension of the bayesian alphabet for genomic selection

Background
Genomic prediction of breeding values involves a so-called training analysis that predicts the influence of small genomic regions by regression of observed information on marker genotypes for a given population of individuals. Available observations may take the form of individual phenotypes, repeated observations, records on close family members such as progeny, estimated breeding values (EBV) or their deregressed counterparts from genetic evaluations. The literature indicates that researchers are inconsistent in their approach to using EBV or deregressed data, and as to using the appropriate methods for weighting some data sources to account for heterogeneous variance.

/pdf/deregressing-estimated-breeding-values-and-weighting-2et4boye9h.pdf

Deregressing estimated breeding values and weighting information for genomic regression analyses

Best linear unbiased prediction (BLUP) is applied to a mixed linear model with additive effects for alleles at a market quantitative trait locus (MQTL) and additive effects for alleles at the remaining quantitative trait loci (QTL). A recursive algorithm is developed to obtain the covariance matrix of the effects of MQTL alleles. A simple method is presented to obtain its inverse. This approach allows simultaneous evaluation of fixed effects, effects of MQTL alleles, and effects of alleles at the remaining QTLs, using known relationships and phenotypic and marker information. The approach is sufficiently general to accommodate individuals with partial or no marker information. Extension of the approach to BLUP with multiple markers is discussed.

/pdf/marker-assisted-selection-using-best-linear-unbiased-1l2uye1be6.pdf

Marker assisted selection using best linear unbiased prediction

The use of all available molecular markers in statistical models for prediction of quantitative traits has led to what could be termed a genomic-assisted selection paradigm in animal and plant breeding This article provides a critical review of some theoretical and statistical concepts in the context of genomic-assisted genetic evaluation of animals and crops First, relationships between the (Bayesian) variance of marker effects in some regression models and additive genetic variance are examined under standard assumptions Second, the connection between marker genotypes and resemblance between relatives is explored, and linkages between a marker-based model and the infinitesimal model are reviewed Third, issues associated with the use of Bayesian models for marker-assisted selection, with a focus on the role of the priors, are examined from a theoretical angle The sensitivity of a Bayesian specification that has been proposed (called “Bayes A”) with respect to priors is illustrated with a simulation Methods that can solve potential shortcomings of some of these Bayesian regression procedures are discussed briefly

/pdf/additive-genetic-variability-and-the-bayesian-alphabet-12x9y9tx2q.pdf

Rohan L. Fernando

Papers

The Impact of Genetic Relationship Information on Genome-Assisted Breeding Values

Extension of the bayesian alphabet for genomic selection

Deregressing estimated breeding values and weighting information for genomic regression analyses

Marker assisted selection using best linear unbiased prediction

Additive Genetic Variability and the Bayesian Alphabet