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An animal model takes the basic univariate form: y i = u + a i + e i Where y is the phenotypic value of individual i, u is the population mean value, a is the breeding value of individual i, and e is a vector of residual errors (reviewed in Kruuk 2004).
The pseudo-record for survival time of animal i was [ 33]: (1) where δ i is the censoring code of individual i (δ i= 1 if animal i is uncensored; δ i = 0 if animal i is censored); a i is the estimated direct breeding value of individual i; and ω i is the associated weight of individual i.
The value u i is known as the breeding value of individual i.
where the regression coefficient b = Cov Σ X ija j; TBV i)/ var(Σ X ija j), TBV i is the true breeding value of individual i.
Consider that the true breeding value of individual i is a i = ∑ z i j α j where z i j is the allelic state at locus j and z i j ε { − 1, 0, 1 }, α j is the true allelic substitution effect at locus j.
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Genomic selection (GS) allows estimation of the breeding value of individuals, even for non-phenotyped animals.
Each method used phenotypes from the reference populations to estimate the breeding value of individuals in the test set.
To ensure that the heritability of the four traits remains constant, the residual variance is scaled relative to the variance of the breeding values of individuals in the base generation of the pedigree, which was given by a′ a/(n − 1), where a is a vector of breeding value of individuals in the base generation and n is the number of individuals in that generation.
All gains were estimated using predicted breeding values of individual traits (i.e. RNC or NC) using spatial analyses.
(Co variance components were estimated by average information restricted maximum likelihood (AIREML) and breeding values of individuals were predicted with Best Linear Unbiased Prediction (BLUP) methodology under multi-trait animal models.
Quantitative genetic methods enable more effective selection on single or multiple complex traits than selection on phenotypes because of the estimation of additive genetic variance in the population (the chief cause of resemblance of relatives and the only genetic component that can be estimated from observations on the population) and estimated breeding values of individuals.
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