将几何形态测量学改造为变换网格方法学
Reworking geometric morphometrics into a methodology of transformation grids
摘要：
今天的典型应用几何形态计量学的定量比较的生物体解剖学开始标准化样品的同源标记的点配置的位置，方向和规模，然后呈现随后的比较图形薄板样条适用于组平均值，主成分，回归预测，或典型的变量。尺度标准化的步骤最近受到批评，认为不合适，至少对生长研究来说是这样。本文主张对居中和旋转进行类似的重新思考，然后用不同的策略替换所得到的配置的薄板样条插值，该策略在每个地标处单独留下无法解释的残差，以简化对显示网格的整体解释，自1917年达西·汤普森的论述以来，“转换网格”一直被强调为真正的潜在主题。对于涉及梯度在大的几何尺度的比较分析，本文主张用我的两点注册的1986年（最初是弗朗西斯高尔顿的1907年）的版本取代所有的Procrustes公约。这两个点的选择与另一个非普罗克鲁特斯问题相互作用，即根据拟合的多项式趋势而不是插值薄板样条变形的坐标系网格线的可解释性。本文使用先前发表的颅骨数据进行了两个示例;结果是与这两个经典数据集的解释相关的新发现。最后的讨论表明，目前的工具包几何形态测量学，集中在Procrustes形状坐标和薄板样条，太局限，以适应许多进化和发育生物学的解释目的。
英文摘要：
Today's typical application of geometric morphometrics to a quantitative comparison of organismal anatomies begins by standardizing samples of homologously labelled point configurations for location, orientation, and scale, and then renders the ensuing comparisons graphically by thin-plate spline as applied to group averages, principal components, regression predictions, or canonical variates. The scale-standardization step has recently come under criticism as inappropriate, at least for growth studies. This essay argues for a similar rethinking of the centering and rotation, and then the replacement of the thin-plate spline interpolant of the resulting configurations by a different strategy that leaves unexplained residuals at every landmark individually in order to simplify the interpretation of the displayed grid as a whole, the "transformation grid" that has been highlighted as the true underlying topic ever since D'Arcy Thompson's exposition of 1917. For analyses of comparisons involving gradients at large geometric scale, this paper argues for replacement of all the Procrustes conventions by a version of my two-point registration of 1986 (originally Francis Galton's of 1907). The choice of the two points interacts with another non-Procrustes concern, interpretability of the grid lines of a coordinate system deformed according to a fitted polynomial trend rather than an interpolating thin-plate spline. The paper works two examples using previously published cranial data; there result new findings pertinent to the interpretation of both of these classic data sets. A concluding discussion suggests that the current toolkit of geometric morphometrics, centered on Procrustes shape coordinates and thin-plate splines, is too restricted to suit many of the interpretive purposes of evolutionary and developmental biology.
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