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Given the vector of effects, it is then possible to predict phenotypes and estimate genetic breeding values.
SELECTION in animal or plant breeding is usually based on estimates of genetic breeding values (GEBVs) obtained with semiparametric mixed models (SPMMs) (Meuwissen et al. 2001; Lee et al. 2008).
In GS, thousands of markers are modeled simultaneously and the marker effects are summed, in order to compute the genomic (GEBV) equivalent of estimated additive genetic (breeding) values (EBV).
We denote the standard deviation of a sample with s and that of a population with σ and the sample and population variance of the true genetic breeding values g with s g 2 and σ g 2, respectively.
Also, we use r g, g ^, s g, g ^, s g ^ 2 and s p 2 to denote the sample correlation between the true and the predicted genetic breeding values, the sample covariance between the true and the predicted breeding values, and the sample variance of the predicted breeding value and the phenotypic sample variance, respectively.
Further, we denote with r, r g ^, p, ρ and ρ g, p the sample correlation, the sample correlation between the BLUP of g and the observed "phenotypes" p, the population correlation and the population correlation between the true genetic breeding values g and the observed "phenotypes" p, respectively.
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This refinement of the genetic breeding value is one potential advantage of EBV over phenotype for providing predictions of risk in a breeding program to reduce hip dysplasia.
The focus in the animal and plant literature has been in prediction of phenotype or genetic breeding value, rather than in variable selection per se.
The use of genetic markers to predict the genetic merit (breeding values) of individuals is commonplace in modern farm animal breeding schemes.
In our case studies we considered models with additive genetic effects (breeding values u ), individual effects (environmental effects ε ), and several fixed effects.
The success of genomic selection in animal breeding hinges on the availability of a large reference population on which genomic-based predictions of additive genetic or breeding values are built.
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