Factors affecting the accuracy of selection indexes for the genetic improvement of pigs

Vandepitte, W.

doi:10.31274/rtd-180813-2273

Cited by 2 publications

(3 citation statements)

References 25 publications

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“…., t ) is the index weight for the cross products between the phenotype of the traits i and j. Vandepitte (1972) minimized Φ, but in this section we shall maximize ρ H q I q . Suppose that μ = 0, since α and β are constants that do not affect ρ H q I q , we can write I q and H q as I q = b 0 y + y 0 By and H q = w 0 g + g 0 Ag.…”

Section: The Quadratic Indexmentioning

confidence: 99%

Linear Selection Indices in Modern Plant Breeding

Cerón-Rojas

Crossa

2018

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Section: The Quadratic Indexmentioning

confidence: 99%

Linear Selection Indices in Modern Plant Breeding

Cerón-Rojas

Crossa

2018

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“…In this context, it is easier to maximize ρ H q I q than to minimize Φ. Vandepitte (1972) minimized Φ, but in this section we shall maximize ρ H q I q .…”

Section: The Vector and The Matrix Of Coefficients Of The Quadratic Imentioning

confidence: 99%

“…Thus, under the assumption that y and g have multivariate normal distribution with mean 0 and covariance matrix P and G, respectively, E(I q ) = tr(BP) and E(H q ) = tr(AG) are the expectations of I q and H q , whereas Var(I q ) = b 0 Pb + 2tr[(BP) 2 ] and Var(H q ) = w 0 Gw + 2tr[(AG) 2 ] are the variances of I q and H q , respectively. The covariance between I q and H q is Cov (H q , I q ) = w 0 Gb + 2tr(BGAG) (Vandepitte 1972), where tr(∘) denotes the trace function of matrices.…”

Section: The Vector and The Matrix Of Coefficients Of The Quadratic Imentioning

confidence: 99%

The Linear Phenotypic Selection Index Theory

Cerón-Rojas

Crossa

2018

Linear Selection Indices in Modern Plant Breeding

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The main distinction in the linear phenotypic selection index (LPSI) theory is between the net genetic merit and the LPSI. The net genetic merit is a linear combination of the true unobservable breeding values of the traits weighted by their respective economic values, whereas the LPSI is a linear combination of several observable and optimally weighted phenotypic trait values. It is assumed that the net genetic merit and the LPSI have bivariate normal distribution; thus, the regression of the net genetic merit on the LPSI is linear. The aims of the LPSI theory are to predict the net genetic merit, maximize the selection response and the expected genetic gains per trait (or multi-trait selection response), and provide the breeder with an objective rule for evaluating and selecting parents for the next selection cycle based on several traits. The selection response is the mean of the progeny of the selected parents, whereas the expected genetic gain per trait, or multi-trait selection response, is the population means of each trait under selection of the progeny of the selected parents. The LPSI allows extra merit in one trait to offset slight defects in another; thus, with its use, individuals with very high merit in one trait are saved for breeding even when they are slightly inferior in other traits. This chapter describes the LPSI theory and practice. We illustrate the theoretical results of the LPSI using real and simulated data. We end this chapter with a brief description of the quadratic selection index and its relationship with the LPSI. EHT PHT GY1 GY2 Fig. 2.1 Distribution of 252 phenotypic means of two maize (Zea mays) F 2 population traits: plant height (PHT, cm; a) and ear height (EHT, cm; b), evaluated in one environment, and of 599phenotypic means of the grain yield (GY1 and GY2, ton ha À1 ; c and d respectively) of one double haploid wheat (Triticum aestivum L.) population evaluated in two environments 2 The Linear Phenotypic Selection Index Theory 1. The expectation of e is zero, E(e) ¼ 0.2. Across several environments, the expectation of y is equal to the expectation of g, i.e., E(g) ¼ μ g ¼ E(y) ¼ μ y . 3. The covariance between g and e is equal to 0.The g value can be partitioned into three additional components: additive genetic (a) effects (or intra-locus additive allelic interaction), dominant genetic (d) effects (or intra-locus dominance allelic interaction), and epistasis (ι) effects (or inter-loci allelic interaction) such that g ¼ a + d + ι. In this book, we have assumed that g ¼ a.According to Kempthorne and Nordskog (1959), the following four theoretical conditions are necessary to construct a valid LPSI:1. The phenotypic value (Eq. 2.1) shall be additively made up of two parts: a genotypic value (g) (defined as the average of the phenotypic values possible across a population of environments), and an environmental contribution (e). 2. The genotypic value g is composed entirely of the additive effects of genes and is thus the individual breeding value. 3. The genotypic economic value ...

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Factors affecting the accuracy of selection indexes for the genetic improvement of pigs

Cited by 2 publications

References 25 publications

Linear Selection Indices in Modern Plant Breeding

Linear Selection Indices in Modern Plant Breeding

The Linear Phenotypic Selection Index Theory

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