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Augmented Designs Mike Popelka & Jason Morales What is an augmented design? • A replicated check experiment augmented by unreplicated entries. • Step 1: Start with a field subdivided into plots What is an augmented design? • A replicated check experiment augmented by unreplicated entries. • Step 2: Divide plots into blocks What is an augmented design? • A replicated check experiment augmented by unreplicated entries. • Step 3: Randomly place checks in each block – We now have 6 replicates of a randomized complete block design (RCBD). C1 C1 C1 C1 C1 C1 C1 C1 C1 C1 C1 C1 C1 C1 C1 C1 C1 C1 What is an augmented design? • A replicated check experiment augmented by unreplicated entries. • Step 4: Fill in empty plots with unique entries (genotypes). C1 1 25 C1 10 3 6 11 C1 31 20 C1 21 C1 36 4 C1 27 5 C1 15 19 14 33 18 26 30 C1 C1 9 C1 16 C1 24 32 C1 17 45 C1 34 2 23 8 C1 12 7 C1 28 C1 22 29 C1 13 C1 Purpose of Augmented Designs • Why use an augmented design? – Cost effective – Limited seed quantities or resources – Increase efficiency of genetic gains • Goal is to predict the true value of the genotype by adjusting for spatial effects. • Spatial effects can include soil fertility, field gradients, physical soil properties, management practices, biological competition. BLUPs • Best linear unbiased predictors • Purpose is to estimate the random effects and provide an adjusted dependent variable. • In augmented designs, the random effects are usually related to spatial correction – Ex: yield = µ + entry(block) + check • Entry is nested within block and is treated as a random effect • Check is treated as a fixed effect and is used to model and then remove field effects. Modeling Spatial Effects • Model 1: See paper, PROC MIXED for Recovering Both Interblocking and Intervariety Information • Yield = µ + treatn + rep + block(rep) + treat*new + Ɛ • Treatn (fixed) = Individual checks, entries bulked into one treatment – i.e. check1, check2, check 3, all non-check entries • Treat*new (random) = New entries (individually) Modeling Spatial Effects • Yield = µ + treatn + rep + block(rep) + treat*new + Ɛ • Rep and block(rep) are random effects Block 1 Block 2 Block 3 Block 4 Block 5 Block 6 C7 C9 3 C10 5 C8 C8 2 C8 C7 C7 6 1 C10 C9 4 C9 C10 Rep 1 Rep 2 Rep 3 SAS Code data augbibd; infile ’augbibd.dat’; input yield rep block treat; if (treat > 6) then new = 0 else new = 1; if (new) then treatn = 999; else treatn = treat; proc mixed data = augbibd; class rep block treat treatn; model yield = treatn; random rep block(rep) treat*new / solution; lsmeans treatn; make ’solutionr’ out = sr noprint; run; proc sort data = sr; by descending est; proc print; run; Yield Rep 1 1 1 1 1 1 2 2 2 2 2 2 3 3 3 3 3 3 Block 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 Treat 1 C7 C8 2 C9 C10 3 C8 C9 4 C7 C10 5 C7 C9 6 C8 C10 treatn* 999 C7 C8 999 C9 C10 999 C8 C9 999 C7 C10 999 C7 C9 999 C8 C10 new* 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 Modeling Spatial Effects • Model 2: See paper, Other Augmented Designs • Grain weight = µ + WF + treatn + WR + treat*new Range (Row) – WF = Orthogonal polynomials treated as fixed – WR = Orthogonal polynomials treated as random 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 121 23 24 122 25 26 121 27 28 122 29 30 121 21 22 32 121 34 33 122 35 36 121 37 38 122 39 40 122 31 42 43 121 44 45 122 46 47 121 48 49 122 50 41 122 122 53 54 121 55 56 122 57 58 121 59 60 122 51 52 62 122 63 64 121 65 66 122 67 68 121 69 70 121 61 Row (Column) 6 7 72 73 122 74 75 121 76 77 122 78 79 121 80 71 121 121 83 84 122 85 86 121 87 88 122 89 90 121 81 82 8 9 10 11 12 92 121 93 94 122 95 96 121 97 98 122 99 100 122 91 102 103 121 104 105 122 106 107 121 108 109 122 110 101 122 122 113 114 121 115 116 122 117 118 121 119 120 122 111 112 2 122 3 4 121 5 6 122 7 8 121 9 10 121 1 12 13 122 14 15 121 16 17 122 18 19 121 20 11 121 Orthogonal Polynomials • Orthogonal polynomials are used to detect effects that fit the given polynomial structure. • Final estimates are corrected using the covariance of the plot with the effect of the orthogonal polynomial. • GLM select is used to identify which orthogonal polynomials are significant. SAS Code • • • • • • • • • • • • • data augmercl; infile ’augmercl.dat’; input site col row treat gw cl c2 c3 c4 rl r2 r3 r4; - These are the orthogonal polynomials if (treat > 120) then new =0 else new = 1; if (new) then treatn = 999; else treatn = treat; ll = rl*cl; lq = r1"c2; proc glm data = augmercl; class row col treat treatn; modegl w= rl r2 r3 r4 cl c2 c3 c4 ll lq treatn treat*new; random row col treat*new; run; • • • • • • • • proc iml; opnl5 = orpo1(1:15,4); opnl5[,1] = (1:15)’; op15 = opnl5; create opnl5 from opnl5[colname = {’ROW’ ’RI’ ’R2’ ’R3’ ’R4’}]; append from opnl5; close opnl5; • • • • • • • • • proc glm data = augmercl; class row col treat treatn; model gw = rl r2 r3 r4 cl c2 c3 c4 11 Iq treat; Ismeans treat / out = Ismeans noprint; run; proc sort data = Ismeans; by descending Ismean; proc print; run;