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PBG 650 Advanced Plant Breeding and Quantitative Genetics (HW 4 from 2011 class) Analysis of Half-sib Families of Meadowfoam; 1 location, 2 replications, 214 families The data set is from a meadowfoam half-sib progeny trial. Data for the check entries were removed so that we could obtain estimates of genetic variances from the 214 families representing the parent population MF187. We will be analyzing the variable ‘thousand seed weight’ (TSW) which is measured in grams. For the purposes of this assignment, we will ignore the incomplete block structure of the original lattice design and just consider the two complete blocks (=Reps) as an RCBD. Use the annotated SAS output to respond to the questions on the right of the table. # 1 SAS PROGRAM PROC GLM data=ONE plots (unpack)=diagnostics; Title 'Fixed Effect Model using PROC GLM'; class Rep Entry; model TSW = Rep Entry; random rep entry; lsmeans Entry/stderr; RUN; QUESTIONS Use the output to calculate VP - VG - VX - VA - h2 MSF 0.5218469 0.26092345 r 2 VG VF MSF MSE / r 0.5218469 0.2249413 / 2 0.14845 VP MSE 0.224913 0.11247065 r 2 VA 4 * VF 4 *0.14845 0.5938 V VG 0.14845 h2 G 0.5689 VP VG VX 0.26092345 VX 1 # 2 SAS PROGRAM PROC VARCOMP METHOD = REML MAXITER = 100 data=ONE; Title 'PROC VARCOMP for a random model - REML estimation'; CLASS Rep Entry; MODEL TSW = Rep Entry; RUN; QUESTIONS PROC VARCOMP provides estimates of variance components when all effects in the model are random. Compare the REML estimates of variance components to your calculations in Part 1. Use the output to calculate - VA - h2 VA 4 * VF 4 * Var(Entry) 4 *0.14845 0.5938 h2 VG V(entry) 0.1485 0.5691 VP V(entry) V(Residual) 0.1485 0.2249 2 2 Use the output from the asymptotic covariance matrix to calculate a standard error for the estimate of VG. V( G2 ) 0.000758 3 PROC GLIMMIX data=one; Title 'GLIMMIX Procedure'; class Rep Entry; model TSW = /solution; Random Rep Entry/solution; /* I am not completely sure about this, but I think this will give us a likelihood ratio test for the variance among families*/ covtest general 0 1; run; se 0.000758 0.0275318 Compare the estimates of VG and its standard error to previous results. They are the same. The following calculation illustrates the meaning of BLUP and the relationship between the eblups and heritability for a balanced experiment using unrelated parents: Pick an eblup estimate for one of the entries from the solutions output for random effects. Calculate the difference between the observed mean for that entry (from the lsmeans in #1) and the grand mean of all entries. Is the magnitude of the observed deviation larger or smaller than the eblup? Calculate the ratio eblup/observed deviation. What does that tell you about the expected response to selection? 2 4 5 PROC MIXED data=one; Title 'Mixed Procedure - Full Model'; class Rep Entry; model TSW =; Random Rep Entry; run; PROC MIXED data=one; Title 'Mixed Procedure - Reduced Model'; class Rep; model TSW =; Random Rep; run; DATA prob; chiprob=0.5*(1-probchi(LR, 1)); PROC PRINT; RUN; QUIT; Entry 1 8.960-9.777=-0.817 Larger; eblup=-0.4649 Eblup/observed deviation = -0.4649/-0.817=0.5690h2 Use the values for -2 Res Log Likelihood from the output for the full and reduced models to calculate the Likelihood Ratio for the hypothesis that VG = 0. L r z LR 2ln 2 L r z L z L z LR=799.7-763.0=36.7 In class you will substitute your LR value in the chiprob equation shown on the left. The resulting probability value can be divided by two because we are really only considering a one-sided test for VG>0. What do your results indicate? chiprob=0.5*(1-probchi(36.7, 1))=6.88897E-10 The small probability value indicates that the estimated variance among entries is much greater than zero. 3