Fig 1.
Histogram and estimated probability density function (red line) of grain weight in six cultivars.
Blue and green points represent the weight of inferior and superior grain derived from the center primary branch on each panicle. The parameter ‘p’ indicates (a) mean (0.175), (b) < 5% (0.081), (c) 25% (0.110), (d) 50% (0.155), (e) 75% (0.210), and (f) 95% (0.347) for all cultivars.
Fig 2.
Histogram of estimated grain weight distribution parameters.
(a) p, (b) a1, (c) b1, (d) a2, and (e) b2 in Eq 1 are shown.
Fig 3.
Relations among feature values of grain weight distribution and panicle traits in examined cultivars.
The diagonal panel shows histograms of each trait. Lower and upper triangle panels show the scatter plot and correlation coefficient between the two traits. Black and red asterisks show the significance at 1% and 0.1%, respectively, in correlation test. nGrain: average number of grains per panicle, HD: days from sowing to heading, p.23mg: probability of grains that were lighter than 23mg, p.90%: probability of grains that were lighter than 90% weight of the weight at 95% point of the grain weight distribution, SinkFillingRate: sink-filling rate using the weight at 95% point of the grain weight distribution in each cultivar as the sink capacity of one grain.
Fig 4.
Relation between the distinguishability of left-side and right-side gamma distributions of grain weight distribution and the distribution parameter p (a), the probability of grains that were lighter than 23 mg (b), the probability of grains that were lighter than 90% weight of the weight at the 95% point of the grain weight distribution (c), and the sink-filling rate using the weight at the 95% point of the grain weight distribution for each cultivar considering the sink capacity of one grain (d). Black points represent the probability around the boundary point ±0.1 mg in the grain weight distribution. Green points represent the ratio of the probability around the boundary point ±0.1 mg to the probability around the mode of the right-side gamma distribution ±0.1 mg.
Fig 5.
Examples of the observed probability density function (red line) of the grain weight compared with fitted (green) and predicted (blue) ones that result from genomic prediction for weight distribution parameters.
The predicted squared residual error of each distribution was (a-d) minimum, (e-h) mean, and (i-l) maximum in GBLUP (a, e, and i), PLS using 1 parameter-group (b, f, and j), PLS using 3 parameter-group (c, g, and k), and PLS using each-parameter group (d, h, and l).
Table 1.
PRESS and prediction accuracy (Q2) for the grain weight distribution in genomic prediction.
Table 2.
Accuracy (correlation coefficient between observed and fitted/predicted values) for the parameters of grain weight distribution in genomic prediction.
The predicted values of feature values of distribution and the conventional traits was calculated using the predicted distribution parameters. The accuracy in parentheses is that from the prediction conducted for the trait itself.
Fig 6.
Relation between predicted squared residual error in each cultivar and observed parameter of grain weight distribution, mu2.
The diagonal panel shows histograms of each variable. The lower and upper triangle panels show the scatter plot and correlation coefficient between two variables. ResidualError.GBLUP, ResidualError.PLS1g, ResidualError.PLS3g, and ResidualError.PLSet represent the predicted squared residual errors in GBLUP, PLS using 1 parameter-group, PLS using 3 parameter-groups, and PLS using each-parameter group, respectively.