甘蔗实生苗的数量性状相关及选种标准的数学模型研究

本文用25个甘蔗杂交组合的2500丛实生苗的数量性状茎径、茎数、株高和锤度,进行净相关分析、各性状分级频率统计、多项式回归分析及多项式方程求解分析,结果表明：（1）各对数量性状的总体单相关,除茎数与锤度单相关接近显著外,其余均达到极显著水平;各对数量性状的二级净相关,茎数与锤度达显著水平,其余的均达极显著水平;这四个数量性状的复相关系数也达到极显著水平.表现为甘蔗数量性状间是互相影响、互为矛盾,构成品质、产量性状间的矛盾与统一.（2）经标准化的茎数（x′2）、株高（x′3）和锤度（x′4）分别依茎径（x1）真值回归的三次多项式回归方程为,x′2=10.543-14.534x′1＋6.55x2^2-0.968x1^3; x′3=-0.573-1.654x1＋1.249x1^2-0.185x1^3;x′4=-2.926＋3.502x1-1.221x1^2＋0.116x1^3.根据这些方程的升降性,分别组成联立方程组,寻找出这四个数量性状的数学摸型入选标准的最适值分别约为：茎径2.4cm、茎数4条/丛、株高180cm、锤度20.0%.最后根据茎径的标准差,求得甘蔗实生苗数量性状的入选标准数学模型值.

Correlations Analysis Among a Few Quantitative Traits of Seedlings and the Mathematical Model of Slected Standard Values in Sugarcane

Partial correlation,relative frequency of traits degree,polynomial regression and analysis of polynomial regression equation for the quantity traits such as stalk diameter, number of millable,stalk length and brix,were studied in 2500 sugarcaneseeding of 25 hybrid crosses.The results as follow：（1） the quantity traits were interrelated to each other.The correlation of number of millable and the brix was close to remarkable,while the correlation between other single traits was all significant remarkable.The second-rate partial correlation of number of millable and the brix was remarkable,while others were all significant remarkable. The multiple-correlations of the four traits were significant remarkable too.It revealed that the quantity traits of sugarcaneinfluenced and restricted each other,made contradictory integration for yielding and quality.（2） The polynomial regression equation of standard number of millable（x＇2）, stalk length（x＇3） and brixx＇4 regressed with stalk diameter（x1）respectively were as follow：x＇2= 10.543-14.534x＇1＋6.55x2^2-0.968x1^3;x＇3=-0.573-1.654x1＋1.249x1^2-0.185x1^3;x＇4=-2.926＋ 3.502x1-1.221x1^2＋0.116x1^3.The equations were grouped according to their tendency and the standard optimum value of four traits were found by mathematical modelas follow：Stalk diameter was 2.4cm;number of millable was 4 each;length was 180cm and brix was 20.0%.The selected standard value of mathematical model was calculated according mean squares of stalk diameter at last.