Scaling and shear transformations capture beak shape variation in Darwin's finches
Scaling and shear transformations capture beak shape variation in Darwin's finches
复制标题
DOI：
10.1073/pnas.0911575107
复制
发表时间：
2010-02-23
影响因子：
11.1
通讯作者：
Brenner, M. P.
中科院分区：
文献类型：
--
作者：
Campas, O.;Mallarino, R.;Brenner, M. P.
自然选择的进化导致了生物形态的显著多样性，长期以来一直吸引着科学家，并有助于建立物种之间的第一种关系。尽管形态学作为物种的表型的重要作用，但还没有一个正式的数学方案来量化形态表型并将其与基因型和潜在的发育遗传学相关联。在这里，我们证明了形态多样性的喙的达尔文的雀定量占的数学群的仿射变换。具体而言，我们表明，所有的喙形状的地雀（属Geospiza）相关的缩放变换（一个子群的仿射群），同样的关系适用于所有的喙形状的树，椰子，莺雀（三个不同的属）。这项分析表明，这些群体中的每一个的喙形状的不同之处仅在于它们的尺度，如长度和深度，这是由Bmp4和钙调蛋白遗传控制的。通过测量Bmp4在Geospiza属物种的喙原基中的表达，我们提供了喙形态和Bmp4表达水平之间的定量图。达尔文雀喙内的完整形态变异可以通过将尺度变换扩展到整个仿射群来解释，包括剪切变换。总之，我们的研究结果表明，数学理论的群体可以帮助解码形态的变化，并指出一个潜在的层次结构的形态多样性和潜在的发展过程。
Evolution by natural selection has resulted in a remarkable diversity of organism morphologies that has long fascinated scientists and served to establish the first relations among species. Despite the essential role of morphology as a phenotype of species, there is not yet a formal, mathematical scheme to quantify morphological phenotype and relate it to both the genotype and the underlying developmental genetics. Herein we demonstrate that the morphological diversity in the beaks of Darwin's Finches is quantitatively accounted for by the mathematical group of affine transformations. Specifically, we show that all beak shapes of Ground Finches (genus Geospiza) are related by scaling transformations (a subgroup of the affine group), and the same relationship holds true for all the beak shapes of Tree, Cocos, and Warbler Finches (three distinct genera). This analysis shows that the beak shapes within each of these groups differ only by their scales, such as length and depth, which are genetically controlled by Bmp4 and Calmodulin. By measuring Bmp4 expression in the beak primordia of the species in the genus Geospiza, we provide a quantitative map between beak morphology and the expression levels of Bmp4. The complete morphological variation within the beaks of Darwin's finches can be explained by extending the scaling transformations to the entire affine group, by including shear transformations. Altogether our results suggest that the mathematical theory of groups can help decode morphological variation, and points to a potentially hierarchical structure of morphological diversity and the underlying developmental processes.