As the consequence of complex interactions between different parts of an organ, shape can be used as a predictor of structural-functional relationships implicated in changing environments. Despite such importance, however, it is no surprise that little is known about the genetic detail involved in shape variation, because no approach is currently available for mapping quantitative trait loci (QTLs) that control shape. Here, we address this problem by developing a statistical model that integrates the principle of shape analysis into a mixture-model-based likelihood formulated for QTL mapping. One state-of-the-art approach for shape analysis is to identify and analyze the polar coordinates of anatomical landmarks on a shape measured in terms of radii from the centroid to the contour at regular intervals. A procrustes analysis is used to align shapes to filter out position, scale and rotation effects on shape variation. To the end, the accurate and quantitative representation of a shape is produced with aligned radius-centroid-contour (RCC) curves, that is, a function of radial angle at the centroid. The high dimensionality of the RCC data, crucial for a comprehensive description of the geometric feature of a shape, is reduced by principal component (PC) analysis, and the resulting PC axes are treated as phenotypic traits, allowing specific QTLs for global and local shape variability to be mapped, respectively. The usefulness and utilization of the new model for shape mapping in practice are validated by analyzing a mapping data collected from a natural population of poplar, Populus szechuanica var tibetica, and identifying several QTLs for leaf shape in this species. The model provides a powerful tool to compute which genes determine biological shape in plants, animals and humans.
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