Seed shape is an important agronomic trait with continuous variation among genotypes. Therefore, the quantitative evaluation of this variation is highly important. Among geometric morphometrics methods, elliptic Fourier analysis and semi-landmark analysis are often used for the quantification of biological shape variations. Elliptic Fourier analysis is an approximation method to treat contours as a waveform. Semi-landmark analysis is a method of superimposed points in which the differences of multiple contour positions are minimized. However, no detailed comparison of these methods has been undertaken. Moreover, these shape descriptors vary when the scale and direction of the contour and the starting point of the contour trace change. Thus, these methods should be compared with respect to the standardization of the scale and direction of the contour and the starting point of the contour trace. In the present study, we evaluated seed shape variations in a sorghum (Sorghum bicolor Moench) germplasm collection to analyze the association between shape variations and genome-wide single-nucleotide polymorphisms by genomic prediction (GP) and genome-wide association studies (GWAS). In our analysis, we used all possible combinations of three shape description methods and eight standardization procedures for the scale and direction of the contour as well as the starting point of the contour trace; these combinations were compared in terms of GP accuracy and the GWAS results. We compared the shape description methods (elliptic Fourier descriptors and the coordinates of superposed pseudo-landmark points) and found that principal component analysis of their quantitative descriptors yielded similar results. Different scaling and direction standardization procedures caused differences in the principal component scores, average shape, and the results of GP and GWAS.
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