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Augmented Designs Mike Popelka & Jason Morales

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What is an augmented design? A replicated check experiment augmented by unreplicated entries. Step 1: Start with a field subdivided into plots

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What is an augmented design? A replicated check experiment augmented by unreplicated entries. Step 2: Divide plots into blocks

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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

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What is an augmented design? A replicated check experiment augmented by unreplicated entries. Step 4: Fill in empty plots with unique entries (genotypes). C11 25 C110 3 6 11 C131 20 C1 21C136 4 C127 5 C115 1914 33 1826 30 C1 9 16C1 24 32C1 17 45 C1 342 23 8C112 7 C1 28 C1 2229 C1 13C1

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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.

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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.

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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)

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Modeling Spatial Effects Yield = µ + treatn + rep + block(rep) + treat*new + Ɛ Rep and block(rep) are random effects C7C93C105C8 2 C7 6 1C10C94 C10 Rep 1 Rep 2Rep 3 Block 1 Block 2 Block 3Block 4 Block 5 Block 6

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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; YieldRepBlockTreattreatn*new* 1119991 11C7 0 11C8 0 1229991 12C9 0 12C10 0 2339991 23C8 0 23C9 0 2449991 24C7 0 24C10 0 3559991 35C7 0 35C9 0 3669991 36C8 0 36C10 0

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Modeling Spatial Effects Model 2: See paper, Other Augmented Designs Grain weight = µ + W F + treatn + W R + treat*new – W F = Orthogonal polynomials treated as fixed – W R = Orthogonal polynomials treated as random

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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.

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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;

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Randomized block trials with spatial correlation Workshop in Mixed Models Umeå, August 27-28, 2015 Johannes Forkman, Field Research Unit, SLU.

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