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Index Selection for Direct and Maternal Genetic Components of Economic Traits
- Source :
- Biometrics. 26:477
- Publication Year :
- 1970
- Publisher :
- JSTOR, 1970.
-
Abstract
- The selection index criterion for aggregate genetic value defined as H = v* g*, where g* is a vector of additive genetic values of the several economically important traits and v* is a vector of relative economic values is, as is well known, I = (P-'G*v*)'x, where P is the phenotypic covariance matrix of the data vector, x, and G* is the genetic covariance matrix of the economically importatn traits. When each trait has a direct and a maternal additive genetic component the selection index criterion becomes I = (P-'A'Gv)' x, where G is the covariance matrix of the direct and maternal genetic components of all the traits, (twice the order of G*), v is the vector of economic values of the direct and maternal components of all the traits (twice the length of v*), and A is a particular matrix consisting of zeros and additive relationships of the animal being evaluated with its relatives having records and with the dams of those relatives. The correlated response for the kth component (direct or maternal) of thejth trait is Agi = Agjk = v'G'AP-1(A'G)j/0-1 times the standardized selection differential, where (A'G)i is the ith column of A'G.
- Subjects :
- Statistics and Probability
General Immunology and Microbiology
Covariance matrix
Component (thermodynamics)
Applied Mathematics
Value (computer science)
General Medicine
Genetic correlation
General Biochemistry, Genetics and Molecular Biology
Matrix (mathematics)
Statistics
Trait
General Agricultural and Biological Sciences
Selection (genetic algorithm)
Index selection
Mathematics
Subjects
Details
- ISSN :
- 0006341X
- Volume :
- 26
- Database :
- OpenAIRE
- Journal :
- Biometrics
- Accession number :
- edsair.doi...........73fd3219f4078e4d74dac1d06879ce40