According to 10 traits values and their phenotypic correlation matriand heritability matrix of a Crossing combination of weak winteringwheat, the canonical character values and canonical heritabilities of F_3families and canonical genetic distances among families were estimatedand cluster analysis was done to these results.

APPROACHES TO CANONICAL CORRELATIONS OF MULTIPLE QUANTITATIVE TRAITS——II. CANONICAL CHARACTER SELECTION FOR THE OFFSPRING POPULATIONS OF CROSSING COMBINATION OF WHEAT

The concepts of canonical character and its heritability are proposed after studying correlation between genotypic and phenotypic variates of multiple quantitative traits with multivariate statistical analysis.

But when all traits are re- corded for each animal with equal design matrices and one random classifi- cation in the linear model, all correlated traits can be transformed into un- correlated canonical traits through the canonical transformation technique. Then it involves estimation of variance components for each canonical trait and retransformation of variance components on the canonical scale.

By using decision-making analysis of path analysis,this paper built a path analysis model for the canonical traits and complete decision-making analysis.

But when all traits are re- corded for each animal with equal design matrices and one random classifi- cation in the linear model, all correlated traits can be transformed into un- correlated canonical traits through the canonical transformation technique. Then it involves estimation of variance components for each canonical trait and retransformation of variance components on the canonical scale.

Comprehensive canonical trait (CCT) is set up in studying tile canonical correlation of the multiple quantitative characters' phenotypic and genotypic vectors by restriction of breeding objectives using integrative and optimal methods. CCT is a linear combination of s CTs which have larger heritability. The combination has maximal heritability.

This paper studies the relation between the selective characters' phenotypic vector and objective's genotypic vector under the restriction of breeding objectives and it also sets up the model of comprehensive canonical trait pair by using integreted and optimized methods CCT is a linear combination of S CTPs which has larger indirect hereditary coefficient (IHC) and a maximal IHC under the restriction of breeding objectives. As an indirect selection index,compreherrisive canonical trait can satisfy the needs of multi-objective breeding faily good.

Observed 12 characters of foxtail millet cultivars were analyzed by correlative heritability,canonical charac- ter,cluster and discriminant analytical methods.

, the determination coefficient was 0.9448. Principal component and path analysis showed that soluble solids were typical character of nutrient quality in breeding material selection, which should be selected in the low generation of breeding, moreover the rest characters should be selected in high generation according to breeding aim.

These six universals and two general relations are examined by experiment and numerical calculation of two-layer flow based on the canonical character of the coefficients of tlie fKdV equations.

They are intimately related to the Lagrangian variables, on the one side, and have the canonical character, on the other.

Except for angularity, conformation traits did not show important substitution effects that could be explained by this canonical trait.

For the third canonical trait, the influence was low but positive on milk and protein yields and negative on fat yield.

The first canonical trait was highly linked to the yield traits and angularity.

The concepts of canonical character and its heritability are proposed after studying correlation between genotypic and phenotypic variates of multiple quantitative traits with multivariate statistical analysis. The first canonical character is the linear combination which has the largest heritability among all linear combinations of the measured traits. And the i'th combination which is named the i'th canonical character has the largest heritability among all combinations of the characters uncorr-elated with...

The concepts of canonical character and its heritability are proposed after studying correlation between genotypic and phenotypic variates of multiple quantitative traits with multivariate statistical analysis. The first canonical character is the linear combination which has the largest heritability among all linear combinations of the measured traits. And the i'th combination which is named the i'th canonical character has the largest heritability among all combinations of the characters uncorr-elated with the previous (i-1) canonical ones. It can make a sufficient utilization of the information in the test only to study a few canonical characters in practical situations. A method for estimating canonical character and its heritability is proposed, and its possible uses in genetics and breeding are discussed.

after studying canonical correlation between the genotypic random ve-ctor g (m dimensions) and the phenotypic random vector p (m dimensions)of multiple quantitative traits P_i=g_i+e_i, i=1, ..., m or p=g+eand solving the matrix epuation (G-λ~2P) b=0 or (H-λ~2R_P)β=0,where G is genotypic covariance matrix (or H=D_P~(-1)GD_P~(-1) is heritabili-ty matrix, where D_P is a diagonal matrix and its i'th diagonal elementis the phenotypic standard deviation of i'th metrical trait) and P is phe-notypic covariance matrix...

after studying canonical correlation between the genotypic random ve-ctor g (m dimensions) and the phenotypic random vector p (m dimensions)of multiple quantitative traits P_i=g_i+e_i, i=1, ..., m or p=g+eand solving the matrix epuation (G-λ~2P) b=0 or (H-λ~2R_P)β=0,where G is genotypic covariance matrix (or H=D_P~(-1)GD_P~(-1) is heritabili-ty matrix, where D_P is a diagonal matrix and its i'th diagonal elementis the phenotypic standard deviation of i'th metrical trait) and P is phe-notypic covariance matrix (or R_P=D_P~(-1)PD_P~(-1) is phenotypic correlation-al matrix) , then finding characteristic roots λ_i~2 (1≤i≤m) and its cha-racteristic vectors b_i (or β_i=D_Pb_i) , the concepts of canonical charac-ter P_i*=g_i*+e*_i, i=1, ..., s

According to 10 traits values and their phenotypic correlation matriand heritability matrix of a Crossing combination of weak winteringwheat, the canonical character values and canonical heritabilities of F_3families and canonical genetic distances among families were estimatedand cluster analysis was done to these results. From this, two selectionsfor the offspring populations were conducted. One was directional and independent level selection according to the breading aim for the canonicalcharacters with higher...

According to 10 traits values and their phenotypic correlation matriand heritability matrix of a Crossing combination of weak winteringwheat, the canonical character values and canonical heritabilities of F_3families and canonical genetic distances among families were estimatedand cluster analysis was done to these results. From this, two selectionsfor the offspring populations were conducted. One was directional and independent level selection according to the breading aim for the canonicalcharacters with higher heritability. Another was to keep the genetic di-vergence in the different population of families. It was shown by usingactual case analysis that the former selection was a comprehensive selec-tion with higher reliability and was easy to grasp, the latter could preventthe lose of genetic divergence in progeny which resulted from directionalselection too earl ,