Maximum Likelihood Estimation of Variances: Solving Complicated Pedigree Problems - Prof. , Study notes of Botany and Agronomy

Download Maximum Likelihood Estimation of Variances: Solving Complicated Pedigree Problems - Prof. and more Study notes Botany and Agronomy in PDF only on Docsity! Chapter 13: Maximum Likelihood Estimation of Variances Consider the following three pedigrees (families), y1 y2 y3 y4 y5 y6 y7 The genetic relationships between relatives are different from family to family. For example, y and y are full-sibs; 1 2 y3 and y are half-sibs; 4 y5 and y6 are full-sibs but both are cousins of y7. The number of sibs per family is also different from family to family. The analysis of variances method cannot solve such a complicated problem. The problem, however, can be easily solved using the maximum likelihood method. 15-1 Linear models y a e y a y a y a y a y a y a 1 1 2 2 3 3 4 4 5 5 6 6 7 7 e e e e e e 1 2 3 4 5 6 7 = + + = + + = + + = + + = + + = + + = + + μ μ μ μ μ μ μ where μ - population mean (fixed effect) ai - additive genetic effect of individual i with a N Vi A~ ( , )0 distribution (note VA A= σ 2 ) ei - environmental error with a e N Vi ~ ( ,0 E ) distribution (note VE e= σ 2 ). The expectation, variance and covariance of the model are E y ii( ) , , ,= =μ for 1 7 Var y r r V V ii ii A e ii A E( ) , , ,= + = + =σ σ 2 2 1 7for Cov y y r r V V i ji j ij A e ij A E( , ) , , , ,= + = + =σ σ 2 20 0 1for 7 15-2