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Biplots of Linear-Bilinear Models for Studying Crossover Genotype x Environment Interaction

^a Biometrics and Statistics Unit, International Maize and Wheat Improvement Center (CIMMYT), Lisboa 27, Apdo. Postal 6-641, 06600 Mexico D.F., Mexico
^b Dep. of Agronomy and Dep. of Statistics, Univ. of Kentucky, Lexington, KY 40546-0091
^c Dep. of Plant Agriculture, Univ. of Guelph, Guelph, ON, Canada N1G2W1

View larger version (32K): [in a new window]   Fig. 1. Trial 1 biplots of: (A) SREG2(U/U) = sites regression model on unscaled data and unconstrained solution; (B) SREG2(U/CSVD) = sites regression model on unscaled data and constrained SVD solution; (C) SREG2(S/U) = sites regression model on scaled data and unconstrained solution; (D) SREG2(S/CSVD) = sites regression model on scaled data and constrained SVD solution.

View larger version (31K): [in a new window]   Fig. 2. Trial 1 biplots of: (A) SREG2(U/CLS+1) = sites regression model on unscaled data and a constrained LS solution; (B) SREG2(S/CLS+1) = sites regression model on scaled data and constrained LS solution; (C) SREGM+1 (U) = Mandel's sites regression model on unscaled data and unconstrained solution; (D) SREGM+1(S) = Mandel's sites regression model on scaled data and unconstrained solution.

View larger version (31K): [in a new window]   Fig. 3. Trial 1 biplots of: (A) SHMM2(U/U) = shifted multiplicative model on unscaled data and unconstrained solution; (B) SHMM2U/CSVD) = shifted multiplicative model on unscaled data and a constrained SVD solution; (C) SHMM2(S/U) = shifted multiplicative model on scaled data and unconstrained solution; (D) SHMM2(U/CLS+1) = shifted multiplicative model on unscaled data and a constrained LS solution.

View larger version (10K): [in a new window]   Fig. 4. Dendrograms resulting from clustering 20 sites and nine cultivars of Trial 1 using empirical cell means as input data.

View larger version (9K): [in a new window]   Fig. 5. Dendrogram resulting from clustering 20 sites of Trial 1 using SREG shrinkage estimates of cell means as input data.

View larger version (29K): [in a new window]   Fig. 6. Trial 2 biplots of: (A) SREG2(U/U) = shifted multiplicative model on unscaled data and unconstrained solution; (B) SREG2(U/CLS+1) = shifted multiplicative model on unscaled data and a constrained SVD solution; (C) SHMM2(U/U) = shifted multiplicative model on unscaled data and unconstrained solution.