Abstract：
Most genes are part of larger families of evolutionary-related genes. The history of gene families typically involves duplications and losses of genes as well as horizontal transfers into other organisms. The reconstruction of detailed gene family histories, i.e., the precise dating of evolutionary events relative to phylogenetic tree of the underlying species has remained a challenging topic despite their importance as a basis for detailed investigations into adaptation and functional evolution of individual members of the gene family. The identification of orthologs, moreover, is a particularly important subproblem of the more general setting considered here. In the last few years, an extensive body of mathematical results has appeared that tightly links orthology, a formal notion of best matches among genes, and horizontal gene transfer. The purpose of this chapter is to broadly outline some of the key mathematical insights and to discuss their implication for practical applications. In particular, we focus on tree-free methods, i.e., methods to infer orthology or horizontal gene transfer as well as gene trees, species trees, and reconciliations between them without using a priori knowledge of the underlying trees or statistical models for the inference of phylogenetic trees. Instead, the initial step aims to extract binary relations among genes.
摘要：
大多数基因是进化相关基因的较大家族的一部分。基因家族的历史通常涉及基因的复制和丢失以及向其他生物体的水平转移。详细的基因家族史的重建，即，进化事件相对于基础物种的系统发育树的精确年代仍然是一个具有挑战性的话题，尽管它们作为详细研究基因家族单个成员的适应和功能进化的基础很重要。直系同源物的鉴定，此外,是这里考虑的更一般设置的一个特别重要的子问题。在过去的几年里，大量的数学结果已经出现，它们紧密地联系在一起，基因间最佳匹配的正式概念，和水平基因转移。本章的目的是大致概述一些关键的数学见解，并讨论它们对实际应用的启示。特别是,我们专注于无树方法，即，推断正交或水平基因转移以及基因树的方法，树种,以及它们之间的协调，而无需使用基础树的先验知识或统计模型来推断系统发育树。相反，第一步旨在提取基因之间的二元关系。
