Kirkpatrick M, Heckman N
Department of Zoology, University of Texas, Austin 78712.
J Math Biol. 1989;27(4):429-50. doi: 10.1007/BF00290638.
Infinite-dimensional characters are those in which the phenotype of an individual is described by a function, rather than by a finite set of measurements. Examples include growth trajectories, morphological shapes, and norms of reaction. Methods are presented here that allow individual phenotypes, population means, and patterns of variance and covariance to be quantified for infinite-dimensional characters. A quantitative-genetic model is developed, and the recursion equation for the evolution of the population mean phenotype of an infinite-dimensional character is derived. The infinite-dimensional method offers three advantages over conventional finite-dimensional methods when applied to this kind of trait: (1) it describes the trait at all points rather than at a finite number of landmarks, (2) it eliminates errors in predicting the evolutionary response to selection made by conventional methods because they neglect the effects of selection on some parts of the trait, and (3) it estimates parameters of interest more efficiently.
无限维性状是指个体的表型由一个函数描述，而非由一组有限的测量值描述。例子包括生长轨迹、形态形状和反应规范。本文介绍了一些方法，可用于量化无限维性状的个体表型、群体均值以及方差和协方差模式。建立了一个数量遗传模型，并推导了无限维性状群体平均表型进化的递归方程。当应用于这类性状时，无限维方法相对于传统的有限维方法具有三个优点：（1）它描述了性状在所有点的情况，而不是在有限数量的地标点；（2）它消除了传统方法在预测选择的进化反应时所产生的误差，因为传统方法忽略了选择对性状某些部分的影响；（3）它能更有效地估计感兴趣的参数。
