Two lowland rice cultivars, Yamahoushi (panicle-weight type) and Kinki No. 33 (panicle-number type), were grown in three cropping seasons (early, normal and late plantings) at three levels of planting density (40, 20 and 10 hill/m
2) in 1968. Yamahoushi was square-planted and Kinki No. 33 was planted both in square and in low. Canopy structure was characterized by (1) total biomass of the aerial parts of plant and (2) vertical distribution of leaf blade determined by "the stratifying clip method" and was expressed as the percentage of leaf dry weight in each stratum to the total leaf dry weight. Sampling was done at four growth stages, that is, the active-tillering, young panicle formation, heading and maturing stage, respectively. The canopy profile (the space between the soil surface and the top of plants) was evenly divided into five strata and the stratifying clip method was applied to each stratum. The relationships between yield and total biomass and those between yield and vertical distribution of leaf blade were examined by principal component analysis. The first and second component axes obtained by the analysis (Table 1) were rotated to derive axes which are easier to understand and enable a more convenient comparison of the contributions of the strata (Table 2, Fig. 1). In general, the angle (degree) of rotation of axes on a plane, say θ is difined as θ=45°-ε/2, which maximizes f(θ) given by f(θ)=Σ^^p__(i=1) (α
iA
icsθ+α
iB
i sin θ)
2+Σ^^q__(j=1)(-β
jA
j sin θ+β
jB
j cos θ)
2. The formula for the parameter ε in the former equation is ε=tan
-1[Σ^^p__(i=1)(α
iA
i)
2+Σ^^q__(j=1)(β
jB
j)
2-Σ^^p__(i=1)(α
iB
i)
2-Σ^^q__(j=1)(β
jA
j)
2] ÷(2Σ^^p__(i=1)α
i2A
iB
i-2Σ^^q__(j=1)β
j2A
jB
j), where subscript i (=1, 2, ‥, p) designate the variables to be located on or approached to one of the rotated axes, subscript j. (=1, 2, ‥, q) showing the variables to be located on the other axis. Symbols A
i and B
i stand for the factor loadings of variable i for the first and second principal components, respectively, α
i being the weight which is determened according to agronomical importance. Symbols A
j, B
j and β
j are similarly defined for variable j. In the present experiment, the group of variable i consists of the two leaf strata, No. 2 and 4, and the group of j contains only one leaf stratum, No.3. The weights α
i and β
j were assumed to be unity for brevity. θ was calculated to be -8.62°. Using the factor scores in the two axes derived by the rotation (F
1 and F
2), the vertical distribution of leaf weight percentage (leaf stratified structure) and the relation between yield and these scores were investigated. The results are summarized as follows: 1. As F
1 score increased, the leaf weight percentage of the upper stratum increased, whereas that of the lower stratum decreased. As F
2 score increased, the leaf weight percentage of the middle stratum decreased. After rotation of the axes, the tendencies found in these factors were clearer than in the original principal components (Fig. 2). These two factors explained approximately 90% of total variation (Table 2). 2. Leaf weight percentage in the upper stratum became larger as plants grew. [the rest omitted]
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