Reconciling gene trees with a species tree is a fundamental problem to understand the evolution of gene families. Many existing approaches reconcile each gene tree independently. However, it is well-known that the evolution of gene families is interconnected. In this paper, we extend a previous approach to reconcile a set of gene trees with a species tree based on segmental macro-evolutionary events, where segmental duplication events and losses are associated with cost δ and λ , respectively. We show that the problem is polynomial-time solvable when δ ≤ λ (via LCA-mapping), while if δ > λ the problem is NP-hard, even when λ = 0 and a single gene tree is given, solving a long standing open problem on the complexity of multi-gene reconciliation. On the positive side, we give a fixed-parameter algorithm for the problem, where the parameters are δ / λ and the number d of segmental duplications, of time complexity O ⌈ δ λ ⌉ d · n · δ λ . Finally, we demonstrate the usefulness of this algorithm on two previously studied real datasets: we first show that our method can be used to confirm or raise doubt on hypothetical segmental duplications on a set of 16 eukaryotes, then show how we can detect whole genome duplications in yeast genomes.

中文翻译：

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通过分段重复和丢失来协调多个基因树。

使基因树与物种树协调一致是了解基因家族进化的基本问题。许多现有方法独立地调和每个基因树。然而，众所周知，基因家族的进化是相互联系的。在本文中，我们扩展了先前的方法，以基于分段宏观进化事件的物种树和一组基因树进行协调，其中分段重复事件和损失分别与成本δ和λ相关。我们证明当δ≤λ（通过LCA映射）时，该问题是多项式时间可解的，而如果δ>λ，即使λ= 0且给出了单个基因树，问题也是NP-hard的，解决了长期存在的问题多基因和解的复杂性存在开放性问题。从积极的方面来说，我们给出了一个固定参数的算法来解决该问题，其中参数为δ/λ和分段重复次数d，时间复杂度为Oδδλd·n·δλ。最后，我们在先前研究过的两个真实数据集上证明了该算法的有效性：我们首先证明了我们的方法可用于确认或质疑一组16个真核生物上假设的节段重复，然后说明如何检测完整的基因组重复在酵母基因组中。