By C. R. Henderson (auth.), Prof. Dr. Daniel Gianola, Dr. Keith Hammond (eds.)
Developments in facts and computing in addition to their program to genetic development of farm animals received momentum during the last two decades. this article stories and consolidates the statistical foundations of animal breeding. this article will end up precious as a reference resource to animal breeders, quantitative geneticists and statisticians operating in those components. it is going to additionally function a textual content in graduate classes in animal breeding method with prerequisite classes in linear versions, statistical inference and quantitative genetics.
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Additional resources for Advances in Statistical Methods for Genetic Improvement of Livestock
Qnll.. Qny); this shows that for large n, the dependence of II. on y is nil. Now, we want to find a relationship between the parameters of y[An and those of y. Consider first the identity where it is assumed without loss of generality that X has full-column rank p. 10) 21 where 1 is a vector of ones, and ,=(X'X)"lX'E(y). 12) It is assumed that prior knowledge about " 0;* and a;* is vague, so using the theory of non- informative priors (Zellner 1971; Box and Tiao 1973) it is reasonable to take: as prior density.
J Dairy Sci 14:209-220 Lush JL (1933) The bull index problem in the light of modern genetics. J Dairy Sci 16:501522 Lush JL (1948) The genetics of populations. Animal breeding graduate students, Iowa State Univ, Ames, Iowa Mimeo, p 381 Patterson HD, Thompson R (1971) Recovery ofinterblock information when block sizes are unequal. Biometrika 58:545-554 Pearson K (1903) Mathematical contributions to the theory of evolution. XI. On the influence of natural selection on the variability of organs. Phil Trans of the R Soc London A 200:1-66 Quaas RL, Pollak EJ (1980) Mixed model methodology for farm and ranch beef cattle testing programs.
The first summation in this expression is over the parental and F1 lines; the last two are over the backcross progeny to the two parental lines, respectively. There is a total of four parameters: the two parental means (~1 and ~3)' the F 1 mean ~~ and the common environmental variance (02). These are reduced to three parameters in the cases of additive genes [~=(~1+~3)/2], parent 1 dominant (~1 =~) or parent 3 dominant ~=~). 2 Polygenic Inheritance If the trait difference between the two parental lines is due to a large number of additive loci with equal effects, then, in the limit as the number of loci tends to infinity, the log likelihood is where ~loo=(~l+~)/2 and ~oo=(~3+~)/2.