Monteiro Leandro R, Diniz-Filho José Alexandre F, dos Reis Sérgio F, Araújo Edilson D
Laboratório de Ciências Ambientais, Centro de Biociencias e Biotecnologia, Universidade Estadual do Norte Fluminense, Horto, Campos dos Goytacazes, Rio de Janeiro, Brasil.
Evolution. 2002 Mar;56(3):563-72. doi: 10.1554/0014-3820(2002)056[0563:GEOHIB]2.0.CO;2.
The recently developed geometric morphometrics methods represent an important contribution of statistics and geometry to the study of biological shapes. We propose simple protocols using shape distances that incorporate geometric techniques into linear quantitative genetic models that should provide insights into the contribution of genetics to shape variation in organisms. The geometric approaches use Procrustes distances in a curved shape space and distances in tangent spaces within and among families to estimate shape heritability. We illustrate the protocols with an example of wing shape variation in the honeybee, Apis mellifera. The heritability of overall shape variation was small, but some localized components depicting shape changes on distal wing regions showed medium to large heritabilities. The genetic variance-covariance matrix of the geometric shape variables was significantly correlated with the phenotypic shape variance-covariance matrix. A comparison of the results of geometric methods with the traditional multivariate analysis of interlandmark distances indicated that even with a larger dimensionality, the interlandmark distances were not as rich in shape information as the landmark coordinates. Quantitative genetics studies of shape should greatly benefit from the application of geometric methods.
最近发展起来的几何形态测量学方法代表了统计学和几何学对生物形态研究的重要贡献。我们提出了使用形状距离的简单方案，将几何技术纳入线性数量遗传模型，这应该能够深入了解遗传学对生物体形态变异的贡献。几何方法在弯曲形状空间中使用普氏距离，并在家族内部和家族之间的切空间中使用距离来估计形状遗传力。我们以蜜蜂（Apis mellifera）翅膀形状变异为例来说明这些方案。整体形状变异的遗传力较小，但一些描绘翅膀远端区域形状变化的局部成分显示出中等至较大的遗传力。几何形状变量的遗传方差协方差矩阵与表型形状方差协方差矩阵显著相关。将几何方法的结果与传统的地标间距离多变量分析进行比较表明，即使维度更大，地标间距离在形状信息方面也不如地标坐标丰富。形状的数量遗传学研究应能从几何方法的应用中大大受益。
