Department of Medical Genetics, University of Oslo, Oslo, Norway.
J Math Biol. 2020 Jul;81(1):185-207. doi: 10.1007/s00285-020-01505-x. Epub 2020 Jun 8.
We study an extension of the standard framework for pedigree analysis, in which we allow pedigree founders to be inbred. This solves a number of practical challenges in calculating coefficients of relatedness, including condensed identity coefficients. As a consequence we expand considerably the class of pedigrees for which such coefficients may be efficiently computed. An application of this is the modelling of background inbreeding as a continuous effect. We also use inbred founders to shed new light on constructibility of relatedness coefficients, i.e., the problem of finding a genealogy yielding a given set of coefficients. In particular, we show that any theoretically admissible coefficients for a pair of noninbred individuals can be produced by a finite pedigree with inbred founders. Coupled with our computational methods, implemented in the R package ribd, this allows for the first time computer analysis of general constructibility solutions, thus making them accessible for practical use.
我们研究了一种扩展的标准家系分析框架，其中允许家系创始人进行近亲繁殖。这解决了计算相关系数（包括凝聚的身份系数）时的一些实际挑战。因此，我们大大扩展了可以有效计算这些系数的家系类。这一应用是将背景近交作为连续效应进行建模。我们还使用近亲创始人来深入了解相关系数的可构造性问题，即找到产生给定系数集的家系的问题。具体来说，我们表明，对于非近亲个体对，任何理论上可接受的相关系数都可以通过具有近亲创始人的有限家系产生。结合我们在 R 包 ribd 中实现的计算方法，这使得首次能够对一般的可构造性解决方案进行计算机分析，从而使其可用于实际应用。
