Discipline of Mathematics, School of Natural Sciences, University of Tasmania, Private Bag 37, Sandy Bay, Tasmania, 7001, Australia.
Bull Math Biol. 2019 Feb;81(2):535-567. doi: 10.1007/s11538-018-0511-6. Epub 2018 Sep 27.
The calculation of evolutionary distance via models of genome rearrangement has an inherent combinatorial complexity. Various algorithms and estimators have been used to address this; however, many of these set quite specific conditions for the underlying model. A recently proposed technique, applying representation theory to calculate evolutionary distance between circular genomes as a maximum likelihood estimate, reduces the computational load by converting the combinatorial problem into a numerical one. We show that the technique may be applied to models with any choice of rearrangements and relative probabilities thereof; we then investigate the symmetry of circular genome rearrangement models in general. We discuss the practical implementation of the technique and, without introducing any bona fide numerical approximations, give the results of some initial calculations for genomes with up to 11 regions.
通过基因组重排模型计算进化距离具有内在的组合复杂性。已经使用了各种算法和估计器来解决这个问题；然而，其中许多方法对基础模型设定了相当具体的条件。最近提出的一种技术，应用表示论将圆形基因组之间的进化距离作为最大似然估计，通过将组合问题转换为数值问题来降低计算负载。我们表明，该技术可应用于任何选择的重排及其相对概率的模型；然后我们一般研究圆形基因组重排模型的对称性。我们讨论了该技术的实际实现，并在不引入任何真正的数值逼近的情况下，给出了最多有 11 个区域的基因组的一些初始计算结果。
