Abstract

BackgroundMost developments in quantitative genetics theory focus on the study of intra-breed/line concepts. With the availability of massive genomic information, it becomes necessary to revisit the theory for crossbred populations. We propose methods to construct genomic covariances with additive and non-additive (dominance) inheritance in the case of pure lines and crossbred populations.ResultsWe describe substitution effects and dominant deviations across two pure parental populations and the crossbred population. Gene effects are assumed to be independent of the origin of alleles and allelic frequencies can differ between parental populations. Based on these assumptions, the theoretical variance components (additive and dominant) are obtained as a function of marker effects and allelic frequencies. The additive genetic variance in the crossbred population includes the biological additive and dominant effects of a gene and a covariance term. Dominance variance in the crossbred population is proportional to the product of the heterozygosity coefficients of both parental populations. A genomic BLUP (best linear unbiased prediction) equivalent model is presented. We illustrate this approach by using pig data (two pure lines and their cross, including 8265 phenotyped and genotyped sows). For the total number of piglets born, the dominance variance in the crossbred population represented about 13 % of the total genetic variance. Dominance variation is only marginally important for litter size in the crossbred population.ConclusionsWe present a coherent marker-based model that includes purebred and crossbred data and additive and dominant actions. Using this model, it is possible to estimate breeding values, dominant deviations and variance components in a dataset that comprises data on purebred and crossbred individuals. These methods can be exploited to plan assortative mating in pig, maize or other species, in order to generate superior crossbred individuals in terms of performance.

Highlights

  • Most developments in quantitative genetics theory focus on the study of intra-breed/line concepts

  • In the absence of inbreeding, it is necessary to estimate nine genetic variance components for an F1 cross between breeds/lines (A and B): additive variance for breed A, dominance variance for breed A, additive variance for breed B, dominance variance for breed B, additive variance for the F1 population due to the effects of the alleles inherited from breed A, additive variance for the F1 population due to the effects of the alleles inherited from breed B, the dominance variance for the F1 population, additive covariance between a parent from breed A and an F1 offspring, and the additive covariance between a parent from breed B and an F1 offspring

  • Results show how important it is to estimate the variances for the F1 population and point out that withinline variances cannot be directly related to variances for the F1 population

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Summary

Introduction

Most developments in quantitative genetics theory focus on the study of intra-breed/line concepts. We propose methods to construct genomic covariances with additive and non-additive (dominance) inherit‐ ance in the case of pure lines and crossbred populations. In the case of dominant inheritance, the theory of pedigree-based genetic evaluation and estimation of genetic parameters for crossbred populations was proposed by Lo et al [2, 3]. In this model, each individual has two genetic values, one on the purebred scale and Vitezica et al Genet Sel Evol (2016) 48:6 one on the crossbred scale. The relevance of the crossbred model has been shown [4, 5], its use in applied breeding programs is limited, because pedigree relationships between purebred and crossbred individuals are often not known, and large datasets on crosses are needed [6]

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