Exploring and visualising spaces of tree reconciliations

Tree reconciliation is the mathematical tool that is used to investigate the coevolution of organisms, such as hosts and parasites. A common approach to tree reconciliation involves specifying a model that assigns costs to certain events, such as cospeciation, and then tries to find a mapping between two specified phylogenetic trees which minimises the total cost of the implied events. For such models, it has been shown that there may be a huge number of optimal solutions, or at least solutions that are close to optimal. It is therefore of interest to be able to systematically compare and visualise whole collections of reconciliations between a specified pair of trees. In this paper, we consider various metrics on the set of all possible reconciliations between a pair of trees, some that have been defined before but also new metrics that we shall propose. We show that the diameter for the resulting spaces of reconciliations can in some cases be determined theoretically, information that...

树重组（Tree reconciliation）是用于研究宿主与寄生虫等生物协同演化的数学工具。树重组的常用研究范式为：先构建为特定演化事件（如共成种事件（cospeciation））分配成本的模型，随后在两棵给定的系统发育树（phylogenetic tree）间寻找映射关系，使得隐含事件的总成本最小化。已有研究表明，此类模型可能存在海量最优解，或至少存在大量近似最优解。因此，能够系统性地比对并可视化指定两棵树间的全部重组结果集合，具备重要研究价值。本文中，我们针对两棵树间所有可能的重组结果集合，探讨了多种度量指标——其中既有此前已被定义的指标，也包含我们本次提出的全新度量。我们证明，在部分场景下可通过理论推导确定重组结果空间的直径，相关信息可用于……