Statistical Background (BARTKOWIAK 1974, 1978)

The study of the interdependence of characters in the below case is based on the analysis of regression. From the (p-character)-set r characters with the maximum information about the remaining p-r characters were extracted. All possible (r-character)-subsets from the initial set are analysed. Then the calculation for the linear functions of the 2, 3, 4 as well as (5-element)-sets of representatives were made in turn. The set of parameters W=1,..., p was divided each time into the regression set of representatives R=i₁,..., i_r as well as the NR set of rejected variables. For each set of parameters R= i₁,...i_r the function

X_ir+k=a₀+a₁xi1+...+ a_rx_ir at k=1,..., p-r were calculated. The measure of goodness of approximation is RV=1-R² statistic, RV-residual variation, R²-coefficient of determination (the square of multiple correlation coefficient). The calculation of RV was made for all variables with i_r+k indices belonging to NR-set. RV=max is remembered as the maximum loss of information about one of the rejected characters. From all (r-character)- subsets of the W-set the smallest maximum residual variation was extracted. The calculation was made in the Institute of Informatics Wroclaw University on the Odra-1204 computer.

Results

The synthetical results are given in Table 1. Set I includes the characters each of which includes a great amount of information. The max R² value indicates the presence of a certain amount of information in the, Iast, rejected fifth character. For some populations, it is the eleventh character, for others, the eighteenth. For the Ok2 x C2 hybrid the eleventh character has a great information value (max R²=0.805) while for the spelta form, considerably smaller (max R²=0.161). For the forms C3 x OP4, Sp x S1, O1 x P, the character no. 18 has an intermediate information value (max R²=0.256-0.410). For all populations, we lose too much information while chosing the four representative characters. The max R² value at the choice for each population in succession 1,2,3 or 4 representative parameters also indicates the great losses of information and, therefore, the information importance of all five characters. For set no. II, the information value of the characters is, as a rule, exhausted with the three (01, Sp) or the four (N x C1, C3 x OP4, Ok2 x C2, Sp x S1. O1 x P) representatives. In the first case one may not measure the width and thickenss of kernel, its weight, volume or degree of filling. In the second case it is most frequently the weight and the empirical volume of caryopsis. These characters can be removed from the complex of parameters characterizing the kernel, but their measurements are important for the information about the specific gravity of caryopsis, its shape or filling. In set no. III, just as in no. I, we lose much information in disregarding some characters. With 5 representatives, the max R²=0.220-0.531. The characters which are most frequently rejected with this number of representatives, are the dimensions of crease and cavity as well as the coefficient of endosperm yield or the shape of caryopsis. As the anatomical observations showed (KOSINA unpubl.), the parameters of crease and cavity can be of essential importance for the evaluation of the use value of caryopsis. The mentioned information value also indicates this. The data in Table 1, also indicate the most informative characters in the three considered sets, in case of the necessity of use of 1, 2, 3 and other representatives, as well as the information value of rejected characters in individual cases.