Biology subjects

Reinsch, N.

Publications and source records attributed to Reinsch, N..

5 recordsLinked to original sources

bioRxiv2026

Improved Scalar Deregression of Estimated Breeding Values

Background In genomic studies of animals and plants, analyses are often split into two stages. In the first stage, the average phenotype of each genotyped candidate is calculated from its estimated breeding value (EBV). This average is adjusted for all other effects and is known as the deregressed breeding value. Scalar deregression removes the inherent shrinkage from the original EBVs candidate-by-candidate, rather than for a vector of EBVs. A previously published standard method is easy to apply but implicitly assumes no inbreeding. Results An improved method uses inbreeding coefficients of each candidate and its parents and the three-by-three prediction error covariance matrix of their EBVs. The candidate's effective number of observations can be derived as the root of a second-order polynomial, and the deregressed EBV is then obtained. Two mathematically equivalent polynomials differed in numerical stability. Applications to small examples demonstrated that the improved method produced deregressed EBVs unbiased by inbreeding, whereas the standard method underestimated their absolute magnitude. The same prediction error covariance matrix also allows filtering out uninformative candidates if their estimated Mendelian sampling term has zero reliability. Conclusions The improved method requires access to selected off-diagonal elements of the inverted coefficient matrix of the mixed model equations. The resulting deregressed EBVs and their appropriate weights are unbiased by inbreeding, thereby improving the baseline for the second stage of the analysis. Additionally, uninformative observations can be reliably filtered out. Studies involving traits with low heritability or sparsely recorded phenotypes are expected to benefit most.

genomics↗

bioRxiv2025

PyMSQ: a python package for fast Mendelian sampling (co)variance and haplotype-based similarity in genomic selection

BackgroundWhile genomic selection (GS) boosts rapid genetic gains by leveraging dense marker data for genomic estimated breeding values (GEBVs), prolonged application can reduce haplotype diversity and increase inbreeding. To address these risks, recent research has emphasized Mendelian sampling variance (MSV) and covariance (MSC), which capture within-family (co)variation not fully reflected in GEBVs. In parallel, theoretical advances have introduced a haplotype-based similarity measure that targets shared heterozygous segments, enabling more direct control over haplotype diversity--either standalone or in combination with conventional coancestry-based and genomic relationship matrices. ResultsWe present PyMSQ, an open-source Python package that implements two key developments: (1) a matrix-based approach for computing MSV and MSC in single-trait, multi-trait, and zygotic contexts, and (2) a haplotype-based similarity metric. By combining this matrix-based framework with optimized scientific libraries, PyMSQ achieves up to 332-fold faster computations than gamevar--a publicly available alternative--while preserving numerical accuracy. Using a Holstein-Friesian dataset, we demonstrate PyMSQs effectiveness in deriving MSV and MSC, as well as its novel similarity measure, which complements standard genomic relationship matrices by explicitly quantifying shared heterozygous segments rather than overall allele sharing, thereby providing additional insights for balancing immediate gains with long-term diversity. ConclusionBy facilitating the practical use of MSV, MSC, and a haplotype-based similarity metric, PyMSQ enables breeders and quantitative geneticists to adopt haplotype diversity constraints--whether as a standalone criterion or in synergy with optimal contribution selection. This framework opens new possibilities for preserving key haplotypic segments, ultimately supporting more sustainable genomic selection strategies. PyMSQ is freely available under an MIT License at https://github.com/aromemusa/PyMSQ.

genetics↗

bioRxiv2023

A similarity matrix for preserving haplotype diversity among parents in genomic selection

Mendelian sampling variability (MSV), determined by the heterozygosity and linkage phases of the parental haplotypes, quantifies the chance of producing offspring with high breeding values. Recent genomic selection criteria combine expected breeding values with MSV to maximize the chance of producing offspring with exceptional breeding values. These criteria, however, tend to select similar parents with high variability potential. Therefore, a measure of haplotype similarity is required to avoid this tendency and preserve diversity. Here, we derive this measure by pairing all potential gametes from two parents based on their segregating marker patterns. Subsequently, a similarity measure between two parents is defined as the absolute value of the covariance between the additive values of the paired gametes on a chromosome. A similarity matrix with absolute covariances as off-diagonal elements and MSVs as diagonal elements summarizes all pairwise similarities between parents. A parents similarity to itself equals its MSV. High similarity indicates that the parents share many heterozygous markers with large effects on a trait in the same linkage phase. The concept generalizes to multiple chromosomes, an aggregate genotype with multiple traits, and similarity between zygotes. We demonstrated the properties of the similarity matrix using empirical data. Through simulations, we showed that incorporating the matrix into genomic selection preserves up to 1630% more genetic variability and yields up to 7% more genetic gain relative to index selection in the long term. Although further research is needed, our results show that including similarity matrices preserves haplotype diversity and improves long-term genomic selection.

genetics↗

bioRxiv2021

Genomic characterization of world's longest selection experiment in mouse reveals the complexity of polygenic traits.

A unique set of mouse outbred lines has been generated through selective breeding in the longest selection experiment ever conducted on mice. Over the course of >140 generations, selection on the control line has given rise to two extremely fertile lines (>20 pups per litter each), two giant growth lines (one lean, one obese) and one long-distance running line. Genomic analysis revealed line-specific patterns of genetic variation among lines and high levels of homozygosity within lines as a result of long-term intensive selection, genetic drift and isolation. Detection of line-specific patterns of genetic differentiation and structural variation revealed multiple candidate genes behind the improvement of the selected traits. We conclude that the genomes of these lines are rich in beneficial alleles for the respective selected traits and represent an invaluable resource for unraveling the polygenic basis of fertility, obesity, muscle growth and endurance fitness.

genomics↗

bioRxiv2020

Generalized gametic relationships for flexible analyses of parent-of-origin effects

Genomic imprinting causes alleles to influence the phenotype in a parent-of-origin-specific manner. In attempts to determine the effects of imprinted loci, gametic relationship matrices have widely been used in pedigree-based parent-of-origin analyses of population data. One drawback of this is the size of these matrices because they represent each individual by two gametic effects. Significantly fewer equations are needed if a previously published reduced imprinting model is used that relates observations from progeny without its own offspring to the transmitting abilities of their parents. This can be accomplished using a numerator relationship matrix, with only a single row and column per parent and ancestors. However, the reduced model is not applicable when the parents have records. To better handle the curse of dimensionality, we propose a combination of average gametic effects (transmitting abilities) for individuals without their own records and single gametic effects for others. The generalized gametic relationship matrix is the covariance of this mixture of genetic effects that allows for a significant reduction in the number of equations in gametic models depending on the trait, depth of pedigree, and population structure. It can also render the reduced model much more flexible by including observations from parents. Rules for setting-up its inverse from a pedigree are derived and implemented on an open-source program. The application of the same principles to phased marker data leads to a genomic version of the generalized gametic relationships. The implementation of generalized gametic models to the ASReml package is illustrated through worked examples.

genetics↗