286. Genomic selection for breeding values under identity disequilibrium

Cantet, Rodolfo Juan Carlos; Barajas, Belcy Karine Angarita; Forneris, Natalia Soledad; Munilla, S.

doi:10.3920/978-90-8686-940-4_286

Cited by 1 publication

(2 citation statements)

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“…Since 2(β 2 S + β 2 D ) ≥ 0 , Var(φ X ) ≤ Var φ * X , the equality of Var(φ X ) and Var φ * X holds only if β S = β D = 0 . This result was previously obtained by Cantet and Vitezica [29] for any predictor of BV that incorporates pedigree and genomic information. Pourahmadi [30] found that there is a negative relationship between the diagonal element of the inverse covariance matrix and prediction error variance of the random variable.…”

Section: Ancestral Regressionsupporting

confidence: 76%

“…When considering the transmission of DNA across generations in a lineage or a pedigree (see Additional file 1), Matsen and Evans [46] differentiated the genealogical or ancestry process from the differential recombination of the grandparental genomes when producing the parental gamete that produces their grand progeny. Accounting for recombination, the fraction of the additive variance that is explained by the regression of the BV of a progeny on the BV of parents and grandparents exceeds the genetic variance explained by the "parental regression" by β S (a SS − a DS ) + β D (a SD − a DD ) , such that the difference of variances for the RBV in the animal model with the one from the AR is non-negative, i.e., Var(φ * ) − Var(φ AR ) ≥ 0 , as proven in [29]. In general, identity disequilibrium can be expressed as the matrix difference ( − A) .…”

Section: Discussionmentioning

confidence: 91%

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Causal inference for the covariance between breeding values under identity disequilibrium

et al. 2022

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Background The covariance matrix of breeding values is at the heart of prediction methods. Prediction of breeding values can be formulated using either an “observed” or a theoretical covariance matrix, and a major argument for choosing one or the other is the reduction of the computational burden for inverting such a matrix. In this regard, covariance matrices that are derived from Markov causal models possess properties that deliver sparse inverses. Results By using causal Markov models, we express the breeding value of an individual as a linear regression on ancestral breeding values, plus a residual term, which we call residual breeding value (RBV). The latter is a noise term that accounts for the uncertainty in prediction due to lack of fit of the linear regression. A notable property of these models is the parental Markov condition, through which the multivariate distribution of breeding values is uniquely determined by the distribution of the mutually independent RBV. Animal breeders have long been relying on a causal Markov model, while using the additive relationship matrix as the covariance matrix structure of breeding values, which is calculated assuming gametic equilibrium. However, additional covariances among breeding values arise due to identity disequilibrium, which is defined as the difference between the covariance matrix under the multi-loci probability of identity-by-descent ($$\varvec{\Sigma}$$ Σ ) and its expectation under gametic phase equilibrium, i.e., A. The disequilibrium term $$\varvec{\Sigma}$$ Σ −A is considered in the model for predicting breeding values called the “ancestral regression” (AR), a causal Markov model. Here, we introduce the “ancestral regression to parents” (PAR) causal Markov model, which reduces the computational burden of the AR approach. By taking advantage of the conditional independence property of the PAR Markov model, we derive covariances between the breeding values of grandparents and grand-offspring and between parents and offspring. In addition, we obtain analytical expressions for the covariance between collateral relatives under the PAR model, as well as for the inbreeding coefficient. Conclusions We introduced the causal PAR Markov model that captures identity disequilibrium in the covariances among breeding values and produces a sparse inverse covariance matrix to build and solve a set of mixed model equations.

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Section: Ancestral Regressionsupporting

confidence: 76%

Section: Discussionmentioning

confidence: 91%